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# Number Theory Quicke

• Jun 21st 2010, 02:37 PM
Chris11
Number Theory Quicke
This is a chalenge question. It has been approved by Mr.Fantastic

Let $Q(n)=\lfloor\frac{n}{\lfloor{n}^{1/2}\rfloor}\rfloor$, where n is a natural number. Find the natural numbers a for which Q(a)>Q(a+1)

Moderator edit: Approved Challenge question.
• Jun 21st 2010, 03:17 PM
undefined
Spoiler:

Let $k\in\mathbb{Z},k>0$ and consider the sets $S=\{k^2,k^2+1,\dots, (k+1)^2-2\}$ and $S'=\{k^2,k^2+1,\dots, (k+1)^2-1\}$. It is clear that $\forall a\in S':\lfloor\sqrt{a} \rfloor=k$. Therefore $\forall a\in S: Q(a)=\left\lfloor\frac{a}{\lfloor\sqrt{a}\rfloor}\ right\rfloor = \left\lfloor\frac{a}{k}\right\rfloor \le Q(a+1) = \left\lfloor\frac{a+1}{k}\right\rfloor$.

So the only candidates are of the form $a=k^2-1$ for some $k\in\mathbb{Z},k>1$. We know that $\lfloor\sqrt{a} \rfloor=k-1$ and $\lfloor\sqrt{a+1} \rfloor=k$. So we compare

$Q(a)=\left\lfloor\frac{a}{k-1}\right\rfloor=\left\lfloor\frac{k^2-1}{k-1}\right\rfloor=\left\lfloor k+1 \right\rfloor=k+1$

with

$Q(a+1)=\left\lfloor\frac{a+1}{k}\right\rfloor=\lef t\lfloor\frac{k^2}{k}\right\rfloor=k$

Therefore the complete solution set is $\{a|a=k^2-1, k\in\mathbb{Z},k>1\}$.
• Jun 21st 2010, 04:04 PM
Chris11
Good job!


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text: (41) Intersection points between circles - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP-41C Software Library (/forum-11.html) +--- Thread: (41) Intersection points between circles (/thread-15954.html) (41) Intersection points between circles - rawi - 11-25-2020 03:07 PM Hi, if somebody else already did a program to find the intersection points of two circles I could not find it. So here is mine: Program CIP Program to determine the intersection points of two circles. Circles are defined by coordinates of central point and radius. Output is coordinates of the intercept points of the two circles. If there is no solution message is given. If both solutions are the same there is only 1 solution. Use of registers: Circle 1: Coordinates of midpoint: x: 01, y: 02 Radius: 03 Circle 2: Coordinates of midpoint: x: 04, y: 05 Radius: 06 07: Distance between the two midpoints. 08: Angle between x-axis and line between midpoints 09: Angle at midpoint of first circle of the triangle formed by midpoints and first intersection of cycles 10: For computation Output: Coordinates of intersection points: Point 1: x: 11, y: 12; Point 2: x: 13, y: 14 Flags used: 01, 02 Example: Circle 1 has the central point x=13, y=4 and the radius 6.8 Circle 2 has the central point x=6, y=10 and the radius 4 Keystrokes: XEQ Alpha CIP Alpha -> CIRCLE1? 13 ENTER 4 ENTER 6.8 R/S -> CIRCLE2? 6 ENTER 10 ENTER 4 R/S -> 9.9987 (x-value of 1st intersection point) X<>Y 10.1018 (y-value of 1st intersection point) – R/S - -> 6.5109 (x-value of 2nd intersection point) X<>Y 6.0328 (y-value of 2nd intersection point) A revised version that is shorter and does not use Flag 02 is below. Thanks to Albert Chan who showed me ways to improve the program! Code: 01 LBL „CIP“ 02 CF 01 03 CF 02 04 “CIRCLE1?” 05 PROMPT        Input of midpoint and radius of circle 1 06 STO 03 07 RDN 08 STO 02 09 RDN 10 STO 01 11 “CIRCLE2?” 12 PROMPT        Input of midpoint and radius of circle 2 13 STO 06 13 RDN 15 STO 05 16 RCL 02 17 X>Y? 18 SF 02 19 - 20 X² 21 X<>Y 22 STO 04 23 RCL 01  24 X>Y? 25 SF 01 26 - 27 X² 28 + 29 SQRT 30 STO 07        Distance between midpoints 31 RCL 05 32 RCL 02 33 - 34 X<>Y 35 / 36 ASIN 37 ABS 38 STO 08        Angle between line between midpoints and x-axis 39 RCL 07 40 X² 41 RCL 03 42 X² 43 + 44 RCL 06 45 X² 46 - 47 2 48 / 49 RCL 07 50 / 51 RCL 03 52 / 53 ACOS 54 STO 09 55 + 56 COS 57 LASTX 58 SIN 59 RCL 03 60 * 61 FS? 02 62 CHS 63 RCL 02 64 + 65 STO 12 66 X<>Y 67 RCL 03 68 * 69 FS? 01 70 CHS 71 RCL 01  72 + 73 STO 11 74 STOP        X-register: x-coordinate, Y register: y-coordinate of first intersection point 75 RCL 08 76 RCL 09 77 - 78 COS 79 LASTX 80 SIN 81 RCL 03 82 * 83 FS? 02 84 CHS 85 RCL 02 86 + 87 STO 14 88 X<>Y 89 RCL 03 90 * 91 FS? 01 92 CHS 93 RCL 01 94 + 95 STO 13 96 GTO 02 97 LBL 01 98 “NO SOLUTION” 99 AON 100 STOP 101 AOFF 102 LBL 02 103 CF 01 104 CF 02 105 END RE: Intersection points between circles - Albert Chan - 11-25-2020 06:16 PM Hi, rawi We can get the 2 circles intersection points, without trig. functions. lua> I = require'complex'.I lua> p1, r1 = 13+4*I, 6.8 lua> p2, r2 = 6+10*I, 4.0 lua> d = (p2-p1):abs() lua> d -- center-to-center distance 9.219544457292887 |r1-r2| ≤ d ≤ |r1+r2|, thus 2 circles do intersect somewhere. My code, from Area of Triangle post Code: function area(a,b,c)                -- area of triangle: side a,b,c     if a > b then a, b = b, a end     if a > c then a, c = c, a end   -- a = shortest side, b-c guaranteed exact     b, c = b-c, b*c     b = (a+b)*(a-b)/4     return sqrt(b*(c-b)), b/c       -- area, sin(A/2)^2 end lua> h = area(r1,r2,d) * 2 / d -- height of triangle lua> d1 = sqrt((r1+h)*(r1-h)) -- base of triangle lua> d1, h 6.249766489755484      2.6796303520316775 If p1=(0,0), p2=(d,0), then intersected points at (d1, ±h) Note: we setup with r1 ≥ r2, to force d1 ≥ d/2 > 0, see post #4 -- Complex multiply and addition for rotatation and translation, to get intersection points: lua> v1 = (p2-p1) / d lua> p1 + v1*(d1+h*I) 6.51094321225877+6.032767080968563*I lua> p1 + v1*(d1-h*I) 9.99870384656476+10.101821154325554*I --- Update: we can remove r1 ≥ r2 requirement, by combine this post and post #4 It might also be faster, since real part of v2 does not use square root. Note: Lua math.sqrt(x) return -NaN if x < 0, is exactly what we wanted. With "bad" triangle, area = -NaN ⇒ v2 = -NaN-NaN*I ⇒ 2 circles do not intersect. lua> v2 = (1/2 + (r1+r2)*(r1-r2)/(2*d*d)) + 2*area(r1,r2,d) / (d*d) * I lua> p1 + (p2-p1)*v2 6.510943212258768+6.032767080968563*I lua> p1 + (p2-p1)*v2:conj() 9.99870384656476+10.101821154325554*I Intersection points might be closer to mid-point of p1, p2. We may use that as refercence. Code: function intersection(p1, r1, p2, r2)     local d = (p2-p1):abs()     local v2 = ((r1+r2)*(r1-r2) + 4*area(r1,r2,d)*I) / (d*d)     p1, p2 = (p1+p2)/2, (p2-p1)/2   -- mid-point as reference         return p1 + p2*v2, p1 + p2*v2:conj() end lua> intersection(p1, r1, p2, r2) 6.510943212258769+6.032767080968563*I      9.99870384656476+10.101821154325554*I RE: Intersection points between circles - rawi - 11-25-2020 06:48 PM Hi Albert, thank you very much. As a statistician up to now I had not to handle complex numbers. So - frankly spoken - I have some difficulties to understand your solution. But more and more I have the feeling that I should dig in complex numbers. There seem to be a lot of things that can be solved more elegant and easier than by solving it only with real numbers. RE: Intersection points between circles - Albert Chan - 11-26-2020 12:22 AM Another way is to solve for x, then get h (half chord length) XCAS> circle1 := x^2 + y^2 - r1^2 = 0 XCAS> circle2 := (x-d)^2 + y^2 - r2^2 = 0 XCAS> chord := simplify(circle1 - circle2); // equation for chord $$(2d)x + (r_2^2 - r_1^2 - d^2)=0\\⇒ x = \large{d\over2} + {r_1^2 - r_2^2 \over 2d}$$ XCAS> p1, r1 := 13 + 4*i, 6.8 XCAS> p2, r2 := 6 + 10*i, 4.0 XCAS> d := abs(p1-p2)                                 → √85 ≈ 9.21954445729 XCAS> d1 := d/2 + (r1+r2)*(r1-r2)/(2*d)      → 6.24976648976 XCAS> h := sqrt((r1+d1)*(r1-d1))                 → 2.67963035203 Rotate/translate d1±h*i, back to intersection coordinates. XCAS> v1 := (p2-p1)/d;   → (-7+6*i)/√85 = sign(p2-p1) XCAS> p1 + v1*(d1+h*i)   → 6.51094321226 + 6.03276708097*i XCAS> p1 + v1*(d1-h*i)   → 9.99870384656 + 10.1018211543*i RE: Intersection points between circles - Albert Chan - 11-30-2020 02:19 PM We can also get x directly, from Law of Cosine. Let R2 = angle corresponded to side r2 (the blue side) $$r_2^2 = d^2 + r_1^2 - 2\;d\;r_1 \cos(R_2) = d^2 + r_1^2 - 2\;d\;x \\ ⇒ x = \large{d\over2} + {r_1^2 - r_2^2 \over 2d}$$ Let Δ = area of the triangle, vertices = (0,0), (x,h), (d,0) $$Δ = \large{d\;h\over2}$$ $$⇒ h = \large{2Δ \over d}$$ RE: Intersection points between circles - rawi - 11-30-2020 05:19 PM Hi Albert, thank you very much for the interesting discussion. The solution that is used in my program indeed uses as well the Law of Cosine. The difference between your solution and mine is that I use directly the coordinates given. You first transfer it to an easier problem by setting one midpoint to (0;0) and the other to (d;0), but then you have it to transfer back. I am not yet sure which solution is easier. Unfortunately I do not know how to insert a image that is not on a website. So I try to describe it without a picture. Let (x1,y1) be the coordinates of the first midpoint (x2,y2) be the coordinates of the second midpoint r1 be the radius of the first circle r2 be the radius of the second circle First the distance between midpoints is computed (steps 16-30): z=((x1-x2)^2+(y1-y2)^2)^0.5 Then we compute the angle between line between midpoints and paralell to x-axis (steps31-38): alpha = arcsin((y2-y1)/z) The triangle made by the midpoints and the first intersection have the sides z, r1 and r2. Therefore we can compute the angle between line between midpoints and line from midpoint of first circle to first intersection point by using the Law of Cosine (steps 39-54): beta = arccos((z²+r1²-r2²)/(2*z*r1)) Now we must take into account, whether x2=x1 and analogue with y1 and y2. We set sg1 = 1 if x2>=x1 and sg1 = -1 if x2= y1 and sg2 = -1 if y2 < y1. This is done by using flag 01 and flag 02. Then we can compute the coordinates of the two intersection points (sx1, sy1) (steps 55-73) and (sx2, sy2) (steps 75-95): sx1 = x1 + r1*(cos(alpha+beta))*sg1 sy1 = y1 + r1*(sin(alpha+beta))*sg2 sx2 = x1 + r1*(cos(alpha-beta))*sg1 sy2 = y1 + r1*(sin(alpha-beta))*sg2 This is the solution given. I hope this makes it a little more transparent. Best Raimund RE: Intersection points between circles - SlideRule - 11-30-2020 08:51 PM perhaps Computer Numerical Control, pages 37 & 38 helps? BEST! SlideRule RE: Intersection points between circles - Albert Chan - 11-30-2020 09:03 PM (11-30-2020 05:19 PM)rawi Wrote:  Then we compute the angle between line between midpoints and paralell to x-axis (steps31-38): alpha = arcsin((y2-y1)/z) What we wanted is the angle between vector ((x1,y1) to (x2,y2)), and the x-axis. We should have: -pi ≤ alpha ≤ +pi Using arcsin, we have -pi/2 ≤ alpha ≤ pi/2. sg1/sg2 correction will not fix this. Correction should be:       alpha = arcsin((y2-y1)/z); if x2 < x1 then alpha = pi - alpha end Or, alpha = arccos((x2-x1)/z); if y2 < y1 then alpha = -alpha end Code: function intersection(p1, r1, p2, r2)     p2 = p2 - p1                    -- p2 relative to p1     local d, a = p2:abs(), p2:arg() -- polar form     local b = acos((d*d+(r1+r2)*(r1-r2)) / (2*d*r1))     return p1 + r1*((a+b)*I):exp(), p1 + r1*((a-b)*I):exp() end lua> I = require'complex'.I lua> p1, r1 = 13+4*I, 6.8 lua> p2, r2 = 6+10*I, 4.0 lua> lua> intersection(p1,r1, p2,r2) 6.510943212258769+6.032767080968563*I      9.998703846564759+10.101821154325552*I lua> intersection(p2,r2, p1,r1) 9.99870384656476+10.101821154325554*I      6.51094321225877+6.032767080968563*I Quote:The difference between your solution and mine is that I use directly the coordinates given. You first transfer it to an easier problem by setting one midpoint to (0;0) and the other to (d;0), but then you have it to transfer back. I am not yet sure which solution is easier. Your code do the polar form side, mine the rectangular side. Both ways are equivalent. circles intersections = p1 + r1 * exp((a±b)*I) = p1 + exp(a*I) * (r1*exp(±b*I)) exp(a*I) = (p2-p1) / d r1*exp(±b*I) = d1 ± h*I RE: Intersection points between circles - Albert Chan - 12-01-2020 12:17 AM (11-30-2020 05:19 PM)rawi Wrote:  alpha = arcsin((y2-y1)/z) ... We set sg1 = 1 if x2>=x1 and sg1 = -1 if x2= y1 and sg2 = -1 if y2 < y1. sx1 = x1 + r1*(cos(alpha+beta))*sg1 sy1 = y1 + r1*(sin(alpha+beta))*sg2 sx2 = x1 + r1*(cos(alpha-beta))*sg1 sy2 = y1 + r1*(sin(alpha-beta))*sg2 If x2 ≥ x1, we have the correct angle. No correction is needed. If x2 < x1, calculated alpha should really be pi - alpha cos((pi - alpha) ± beta) = cos(pi - (alpha ∓ beta)) = cos(alpha ∓ beta) * -1 sin((pi - alpha) ± beta) = sin(pi - (alpha ∓ beta)) = sin(alpha ∓ beta) → sy does not require correction. Code: function intersection(p1,r1, p2, r2)     p2 = p2 - p1        -- p2 relative to p1     local d = p2:abs()     local a = asin(p2:imag()/d)     local b = acos((d*d+(r1+r2)*(r1-r2)) / (2*d*r1))     local sg1 = p2:real()<0 and -1 or 1     return p1 + r1*(cos(a+b)*sg1 + sin(a+b)*I),            p1 + r1*(cos(a-b)*sg1 + sin(a-b)*I) end lua> I = require'complex'.I lua> p1, r1 = 13+4*I, 6.8 lua> p2, r2 = 6+10*I, 4.0 lua> lua> intersection(p1,r1,p2,r2) 9.99870384656476+10.101821154325554*I      6.510943212258768+6.032767080968563*I lua> intersection(p2,r2,p1,r1) 9.99870384656476+10.101821154325554*I      6.51094321225877+6.032767080968563*I RE: Intersection points between circles - rawi - 12-01-2020 09:25 AM Hi Albert, You wrote: Quote:We should have: -pi ≤ alpha ≤ +pi Using arcsin, we have -pi/2 ≤ alpha ≤ pi/2. sg1/sg2 correction will not fix this. Correction should be:       alpha = arcsin((y2-y1)/z); if x2 < x1 then alpha = pi - alpha end Or, alpha = arccos((x2-x1)/z); if y2 < y1 then alpha = -alpha end I forgot to mention that I take the absolute figure for computing alpha. I compute alpha = abs(arcsin((y2-y1)/z)) (see line 37 of program listing). So I limit it to the interval from 0 to pi/2. You wrote: Quote:sy does not require correction. The results tell me that the correction is needed. Take the following example: x1 = -1, y1= -3, r1 = 4; x2 = 6, y2 = 2, r2 = 5 If computed it with correction I get: sx1 = 1,3106; sy1=0.2651; sx2= 2,8380; sy2 = -1.8732 which is correct If I keep the circles, but use the former circle 2 as circle 1 and vice versa I get: sx1 = 2,8380; sy1= -1.8732; sx2 = 1.3106; sy2 = 0.2651 So the numbers of the intersection points are exchanged, but they still are correct. If I compute without correction of sy (I delete lines 83, 84, 61, 62 of the program) I get: For x1=-1, y1=-3, r1 = 4, x2 = 6, y2 = 2, r2 = 5 the same results as before. But if I change the number of circles, i.e. x1=6, y1=2, r1=5, x2=-1, y2=-3, r2=4 I get x1 = 2.8380, y1=5.8380, x2=1,3106, y2=3,7349 which is not correct for the y-coordinates. Perhaps by limiting alpha from 0 to pi/2 and doing the correction both for sx and sy I get correct results? I tested the program with numerous examples and it always delivered correct results. Best Raimund RE: Intersection points between circles - Albert Chan - 12-01-2020 11:59 AM (12-01-2020 09:25 AM)rawi Wrote:  I forgot to mention that I take the absolute figure for computing alpha. I compute alpha = abs(arcsin((y2-y1)/z)) (see line 37 of program listing). So I limit it to the interval from 0 to pi/2. ... If I compute without correction of sy (I delete lines 83, 84, 61, 62 of the program) I get: For x1=-1, y1=-3, r1 = 4, x2 = 6, y2 = 2, r2 = 5 the same results as before. But if I change the number of circles, i.e. x1=6, y1=2, r1=5, x2=-1, y2=-3, r2=4 I get x1 = 2.8380, y1=5.8380, x2=1,3106, y2=3,7349 which is not correct for the y-coordinates. Try it again, but remove the ABS applied to alpha. It is this extra ABS that made the program complicated, requiring sg2 correction to undo. Quote:Perhaps by limiting alpha from 0 to pi/2 and doing the correction both for sx and sy I get correct results? Yes, it does. Here is the proof that sg2 correction undo ABS. If y2-y1 ≥ 0, ABS does nothing to alpha, and we had already shown it work in previous post. If y2-y1 < 0, we have 2 possibilities: x2-x1 ≥ 0: calculated alpha should really be -alpha: cos(-alpha ± beta) = cos(alpha pi ∓ beta) * 1 sin(-alpha ± beta) = sin(alpha pi ∓ beta) * -1 x2-x1 < 0: calculated alpha should really be -(pi - alpha): cos(-(pi - alpha) ± beta) = cos(pi - (alpha ± beta)) = cos(alpha ± beta) * -1 sin(-(pi - alpha) ± beta) = -sin(pi - (alpha ± beta)) = sin(alpha ± beta) * -1 RE: Intersection points between circles - rawi - 12-01-2020 02:04 PM Hi Albert, I tried it and you are totally right. Thanks for pointing that out to me. Here is the improved method description: Let (x1, y1) be the coordinates of midpoint of circle 1 and (x2, y2) be the coordinates of midpoint of circle 2 and r1 resp. r2 be the radii. Let z be the distance between the midpoints: z=((x1-x2)²+(y1-y2)²)^0.5 The angle alpha between the line between the midpoints and the parallel to the x-axis through (x1, y1) using the sinus-function is: alpha = arcsin((y2-y1)/z) Beta can be computed by using the Law of Cosine: beta = arccos((z²+r1²-r2²)/(2*z*r1)) We must take into account, whether x2=x1. We set sg = 1 if x2>=x1 and sg1 = -1 if x2Y 19 STO 04 20 RCL 01  21 X>Y? 22 SF 01 23 - 24 X² 25 + 26 SQRT 27 STO 07        Distance between midpoints 28 RCL 05 29 RCL 02 30 - 31 X<>Y 32 / 33 ASIN 34 STO 08        Angle between line between midpoints and x-axis 35 RCL 07 36 X² 37 RCL 03 38 X² 39 + 40 RCL 06 41 X² 42 - 43 2 44 / 45 RCL 07 46 / 47 RCL 03 48 / 49 ACOS 55 STO 09 51 + 52 COS 53 LASTX 54 SIN 55 RCL 03 56 * 57 RCL 02 58 + 59 STO 12 60 X<>Y 61 RCL 03 62 * 63 FS? 01 64 CHS 65 RCL 01  66 + 67 STO 11 68 STOP        X-register: x-coordinate, Y register: y-coordinate of first intersection point 69 RCL 08 70 RCL 09 71 - 72 COS 73 LASTX 74 SIN 75 RCL 03 76 * 77 RCL 02 78 + 79 STO 14 80 X<>Y 81 RCL 03 82 * 83 FS? 01 84 CHS 85 RCL 01 86 + 87 STO 13 88 GTO 02 89 LBL 01 90 “NO SOLUTION” 91 AON 92 STOP 93 AOFF 94 LBL 02 95 CF 01 96 END` RE: Intersection points between circles - Albert Chan - 12-10-2020 01:34 PM (12-01-2020 02:04 PM)rawi Wrote:  sx1 = x1 + r1*(cos(alpha+beta))*sg sy1 = y1 + r1*(sin(alpha+beta)) sx2 = x1 + r1*(cos(alpha-beta))*sg sy2 = y1 + r1*(sin(alpha-beta)) To reduce errors, it may be better if we pick circle1 with the smaller radius, r1 ≤ r2. With circle1 having smaller radius, beta could be huge. (up to pi) We could use complement of beta instead: gamma = arcsin((z²+r1²-r2²)/(2*z*r1)) = pi/2 - beta With gamma, the coordinates are: sx1 = x1 + r1 * sin(gamma-alpha) * sg sy1 = y1 + r1 * cos(gamma-alpha) sx2 = x1 + r1 * sin(gamma+alpha) * sg sy2 = y1 − r1 * cos(gamma+alpha) Prove: If x ≥ 0, sg = 1 cos(alpha ± beta) = cos(beta ± alpha) = sin(gamma ∓ alpha) * 1 sin(alpha ± beta) = ±sin(beta ± alpha) = ±cos(gamma ∓ alpha) If x <0, sg = -1, alpha should really be pi - alpha cos(pi-alpha ∓ beta) = cos(alpha ± beta) * -1 sin(pi-alpha ∓ beta) = sin(alpha ± beta)


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Customize polygons and lines You can customize the appearance of line and polygon features on the map. Available with 3D Analyst license. Today, we are more committed than ever to producing products of preeminent technical merit and performance. - Basics We are going to create a simple Matlab function to add horizontal lines (and vertical ones) to any given Matlab-created plot. How to add or remove horizontal and vertical lines in MetaTarder 4 Horizontal lines in MetaTarder 4 Horizontal lines are mainly used to mark horizontal support and resistance areas on the chart, usually by connecting the price highs (resistance) or price lows (support). set number Adding line numbers only to certain files Edit. If the confirmation email ended up in your Spam/Bulk/Junk folder, please add the email address [email protected] to your Contacts list, so that future emails from us come to your Inbox. Brightness, Contrast, Horizontal Lines, Vertical Lines or Geometrical problems: The Screen is either too bright, too dim or has a black space on the top of the screen or on the bottom of the screen or has horizontal lines or vertical lines. – iago Jun 17 at 9:15. Add the following code right after the last paragraph in the document. After all, you don’t want to be the only business who shows up late to the first day of school. Vertical integration is a strategy where a company expands its business operations into different steps on the same production path, such as when a manufacturer owns its supplier and/or. The short answer is that there is a kind of Markdown support for tables in Markdown Extra - I'm surprised it hasn't been mentioned in this thread yet (according to CTRL-F search, at any rate), although we have had Github-flavoured Markdown mentioned. PowerPoint includes 48 patterns such patterns with names like plaid, weaves, shingle and zig zag. It imports the pipe %>% symbol from magrittr and verbalize all the functions, so basically you can add "layers" to a kable output in a way that is similar with ggplot2 and plotly. And the final effect can add to the perceived size and dimension of a room. Create a calculated field with the value of 1. They often dominate public architecture, from cathedrals to corporate headquarters. The vertical lines can only be added to a normal chart which has been created using the pivot table ; they cannot be added to a pivot chart. The following video shows 3 ways to manually move the labels. We will be doing a sample for each of these and then a combined one. Apply and extend previous understandings of numbers to the system of rational numbers. We examine three types: complementary, supplementary, and vertical angles. Vertical under the sea save the date magnets are a great way to announce your oceanside event, welcome your new bundle of joy, or invite guests to your birthday. Adding fractions with the same denominators, No simplifying (All answers already in lowest terms), All vertical problems. A CONTOUR LINE is a line representing an imaginary line on the ground along which all points are at the same elevation. 5th through 7th Grades. How can I add various horizontal lines to a plot? I have a plot and now I want to add several horizontal lines. Parallel Lines Cut By A Transversal Guided Notes 1. Basic Vector Operations Both a magnitude and a direction must be specified for a vector quantity, in contrast to a scalar quantity which can be quantified with just a number. Line( is affected by the window settings, although you can use a friendly window so there is no impact on the command. Shapes in Python How to make SVG shapes in python. R - Line Graphs - A line chart is a graph that connects a series of points by drawing line segments between them. Vertical Angles Two pairs of angles are formed by two intersecting lines. The h= and v= forms draw horizontal and vertical lines at the specified coordinates. This function takes the output of a kable() function and adds an header row on top of it. WASHINGTON: The military’s Future Vertical Lift initiative aims to replace a range of aging helicopters from all four services. Add a Vertical Line to a Column or Line Chart: Series Method. The y-intercept of a line is the y-coordinate of the point of intersection between the graph of the line and the y-intercept. If set to 1, horizontal marker lines are displayed behind the lines. It includes adding tasks that are on the same level of skill and responsibility. Vertical angles are congruent. If you prefer that data be displayed with additional formatting you can use the knitr::kable function, as in the. Made by @manski83 (on GitHub), based on work by @VorteXLP [email protected] Tweet. To access the parameter value in R code, use paramsparam_name , where param_name is the name of the parameter specified in the YAML header. Here's the set up for adding the Mean; you'd do a repeat of these steps to add the Median:. The coef form specifies the line by a vector containing the slope and intercept. VERTICAL LINES APPLY TO: all Mekko and Bar charts unless they have a linear axis. html div layout tutorial html and html5 tutorial How to draw a vertical line in html there is no tag for drawing vertical liine in html while horizontal line can easily be drawn with HR tag I am. It is not intended to replace any other R packages for making tables. Possible values are latex, html, markdown, pandoc, and rst; this will be automatically determined if the function is called within knitr; it can also be set in the global option knitr. Bugeyedreplyman is not responsible for anything anybody does with the information provided in all videos. Click here for K-12 lesson plans, family activities, virtual labs and more!. Once you've added your data, your line graph will automatically reflect its values. Need a belt for your washer or a new furnace filter? Dey Distributing has been serving as an appliance parts distributor since 1944. Addition: Single Digit, Vertical. If you have sublist items in a numbered list, use lowercase letters, and indent the sublist items to the text of the higher-level list items. In the order you click on it, you will see (1) the left indent, (2) the center indent, (3) the right ind. The setValignment method specifies the vertical position of the separator within the allocated layout space. Let’s take a closer look at each approach. You can add mutiple sets of footnote using differeny notation system. The mail icons are gone and has been replaced with a blue bar The subject is now in blue The sender name is being displayed larger than the rest The first line of a message in now being displayed. An asymptote is a line that the graph of a function approaches but never touches. Started by: Clearlydeb. Here’s a quick example of some pandoc-markdown -formatted text: first as the source you’d put into your file, then rendered as html. In fact, the extra. #carson-3-drawer-vertical-file-cabinet-by-ebern-designs #3-Drawer-Filing-Cabinets Clean lines and a rich black finish give this 3 drawer file cabinet a contemporary style that fits any ensemble. In this week's Tableau Tip Tuesday, I show you how I created a slope graph that includes vertical lines. These geoms add reference lines (sometimes called rules) to a plot, either horizontal, vertical, or diagonal (specified by slope and intercept). Strip lines, or strips, are horizontal or vertical ranges that shade the background of the chart in regular or custom intervals. Horizontal stripes make a room appear more spacious; vertical stripes make the ceiling appear higher. Add the date with current date to your data, for example: 2. I thought choosing "horizontal axis cuts on axis=0" in "format axis" options would do it but it seems to have no impact. Specifically. But how about vertical lines? Actually there are also a couple of tricks to insert vertical lines in your email messages easily. -16cc RD D-CUP DISH, SCAT 4340 FORGED 3. For more information, see Add or remove a secondary axis in a chart. To design your own, you can add the Custom CSS feature to your WordPress. In this Photoshop tutorial you will learn how to create the interlaced lines of a TV screen, this Hunger Games style effect is used on movie posters. In other words, the fact that the function's domain is restricted is reflected in the function's graph. It includes adding tasks that are on the same level of skill and responsibility. #norfolk-personalized-vertical-estate-4-line-wall-address-plaque-by-whitehall-products #Address-Plaques-Signs The Norfolk Personalized Vertical Estate 4-Line Wall Address Plaque will add the finishing touch to your home and instantly improve curb appeal. To add a trendline: Open Google Sheets. NIKE a Dow-30 component that engages in the design, development, marketing, and sale of athletic footwear, apparel, accessories, equipment, and services, has reported fiscal 2020 first-quarter (ended August 31st) financials that surpassed expectations on both the top and bottom lines. xlsx2() can be used to export data from R to an Excel workbook. BBQ GRILL ACCESSORIES The easiest way to up your grilling game is to start experimenting with BBQ accessories. Tip: By default, sliders are horizontal, but you can make them vertical if you'd like. See AC 90-107. One way draw such a line would be to calculate the values in cells in a worksheet, and plot these cells on the chart. 67 3-year protection plan from SquareTrade -1. The best way I found to add a vertical line to the left or right edge of a text box is to add an inner shadow with a size of "0" and a y-offset of "0" and an x-offset the width of the line you want. FULLY BALANCED SBC 421 ASSEMBLY WITH WISECO RACING FORGED PISTONS 4. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. As with the term "on-center," which is used for construction, the term "centerline" is an imaginary vertical line drawn through a key reference point (usually the drain pipe). Horizontal lines do not cross each other. -16cc RD D-CUP DISH, SCAT 4340 FORGED 3. The data is graphed in a simple bar format, and I'd just like an average line that stands out. Further adding to the intrigue, SixEight Research is named on documentation as being the importer of a 1957 Fiat Multipla 600 from the UK to the US in 2014 – a move that has led to rumours that. The Line( command is used to draw lines at any angle, as opposed to only drawing vertical or horizontal lines. Similarly, you can set the horizontal position of the separator line by applying the setHalignment method. The Line( command is used to draw lines at any angle, as opposed to only drawing vertical or horizontal lines. The above HTML code display two tables, one is 100 pixel width and another one is 100% width. tag to make the line display as multiple lines, like this:. These geoms add reference lines (sometimes called rules) to a plot, either horizontal, vertical, or diagonal (specified by slope and intercept). Horizontal lines do not cross each other. The first form specifies the line in intercept/slope form (alternatively a can be specified on its own and is taken to contain the slope and intercept in vector form). The goal of kableExtra is to help you build common complex tables and manipulate table styles. R news and tutorials contributed by (750) R bloggers. Create tables in LaTeX, HTML, Markdown and reStructuredText Description. Here, we detail a few of our favorite ways to get started on your own DIY vertical garden. To create a Vertical menu with sub-items: Enable Multiple menu levels in Artisteer > Vertical Menu tab -> Submenu -> Levels. Re: How to Add Horizontal Line to Scatter Plot?? A line on a scatter chart is defined by {X1,Y1} and {X2,Y2}. D2 Vertical Alignments and Profiles Chapter 1 - Page Number 11 * Alignments should be created to station South to North and West to East, for main line roads, and from the mainline out for side roads. xlsx2 achieves better performance compared to write. Special thanks to Sandra Daigle for an excellent rewrite of the PrintLines Class!!!!! New Release Ver 2. Spare yourself the prep, and clean up by dining out on the Jewish New Year. A vertical force causes a vertical acceleration - in this case, an acceleration of 9. The lines( ) function adds information to a graph. 875 STROKE CRANKSHAFT & 6. ) If we try to look at the class or mode of a data frame, it's not that informative:. (I'd do your red line with annotate as well, personally. My client wants vertical lines in the report. Right-click on the pill and choose Exact Date. The added ( + ) geom_line is the geometrical method that builds the line plot. Adding a vertical line in conditional formatting data bars at 100% Hello, I have a budgeting sheet where I'd like to show a vertical line against some progress bars at a value other than zero. You want to create a vertical line for the two TextViews, as shown below with callout 1: Open Component Tree to view your new barrier. The vertical displacement of a projectile t seconds before reaching the peak is the same as the vertical displacement of a projectile t seconds after reaching the peak. After you create a chart, you can add axis titles to the horizontal and vertical axes in charts that have axes. It can be done better. Add a Horizontal Line to a Column or Line Chart When you add a horizontal line to a chart that is not an XY Scatter chart type, it gets a bit more complicated. Issue Unable to add h orizontal and vertical lines to dashboards in order to separate views. To access the parameter value in R code, use params\$ param_name , where param_name is the name of the parameter specified in the YAML header. And you get a. The left one is created by Line Method. One example would be an elevator shaft within an interior transportation network. Identify line‐ symmetric figures and draw lines of symmetry. How to add vertical/average line to bar chart in Excel? When you use a bar chart to show the data, in some cases, you may want to add a vertical line into the bar chart to obviously show the average of the data as below screenshot shown. I want to draw a table with two \hline and two vertical line. These geoms add reference lines (sometimes called rules) to a plot, either horizontal, vertical, or diagonal (specified by slope and intercept). knitr::kable(data, caption = "Table with kable")  sub-option description citation_package The LaTeX package to process citations, natbib, biblatex or none X X X code_folding Let readers to toggle the display of R code, "none", "hide", or "show" X colortheme Beamer color theme to use X css CSS file to use to style document X X X. first class in the GCA-column-styles. Also, note that except for the vertical line x = 0, a vertical line does not go through the y-axis. In both cases X and Y will have the same value. g In this markup I am planning to insert a line in the second row so that it just appears as a separator between first and rest of the rows in the grid. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. echo -e "Hello my name \tis John Doe". – iago Jun 17 at 9:15. North Shore High running back Zachary Evans is planning to be in Baton. Sometimes you will need to add some points to an existing barplot. Spare yourself the prep, and clean up by dining out on the Jewish New Year. There was a nvspace{. By fostering employee success we advance the high quality education and research at UAlbany. If your lines are almost aligned with one other, it looks like a mistake that needs straightening. For example, if you train your telephone customer service representatives to handle store-level or walk-in customers, this is an example of job enlargement cross training. , same units) can be combined by basic vector operations. A vertical line can be drawn using the \vline command. Basically, draw or interpolate between the lines. LaTeX will position a parbox so its center lines up with the center of the text line. The parallel postulate is what sets Euclidean geometry apart from non-Euclidean geometry. D2 Vertical Alignments and Profiles Chapter 1 - Page Number 11 * Alignments should be created to station South to North and West to East, for main line roads, and from the mainline out for side roads. So a vertical line, well that just goes straight up and down. is a HUBzone certified supplier based out of Pocatello Idaho. Draw the graph of. It imports the pipe %>% symbol from magrittr and verbalize all the functions, so basically you can add “layers” to a kable output in a way that is similar with ggplot2 and plotly. The body is bent midsection at a 90-degree angle, and your legs are pressed up against a plate that faces downward. Their heights are determined by their respective minimum, preferred, and flexible heights according to the following model: The minimum heights of all the child layout elements are added together and the spacing between them is added as well. How can I modify these TeX code so that I can see both vertical lines at all rows? This code is generated from Excel2LaTeX add-in. By establishing content standards, stakeholders in an education system determine what students. Multiple rows can be added using the rows. The body is bent midsection at a 90-degree angle, and your legs are pressed up against a plate that faces downward. Agency media planners and buyers then translate data into insights for the creatives to use. You can add a vertical and/or horizontal line to emphasize a specific value in your chart. An R object, typically a matrix or data frame. We carry a great selection of indoor green and flowering plants, decorative containers and other items primarily related to interior plants. en English (en) Français (fr). 5" Wide Kable Lite Lamp, Satin Nickel - Wire System Track Lighting - Amazon. BEP Marine Products BEP engineers and manufactures a range of high quality electrical solutions designed for the harsh Marine and RV environments. FULLY BALANCED SBC 421 ASSEMBLY WITH WISECO RACING FORGED PISTONS 4. Manufacturer Warranty Detail We guarantee this product to be free from defects in. It allowed me to effectively present high-level timelines to executives who did not need to see, or want to see, all the minutia and complexity of my project. I have the following graph in excel, and I would like to add a single line at the level of the zero on the secondary axis. The spacing is set equal to the product of the pointsize, the vertical tic size, and 5#5vertical_spacing6#6. For this line, we used a 4px width. Now that we have points to connect, let’s draw smooth contour lines for each interval. Click anywhere on the chart you want to add axis labels to. Add to watchlist Unwatch Trackballs Vertical Mouse 1600 Max. I need to add this. When two lines intersect at a point, they form two pairs of angles that do not share a side. There are authorized user trade lines for sale at PersonalTradelines. Using SAS’s PROC GPLOT to plot data and lines PROC GPLOT creates “publication quality” color graphics which can easily be exported into documents, presentations, etc. Hi , I am not sure about the terminology in use. Line graph maker online. PowerPoint includes 48 patterns such patterns with names like plaid, weaves, shingle and zig zag. multiline or grid. by Charles Kyle Kenyon, Esq. For table. Because we’re always on the hunt for extra credit, we had to do more. In R, you add lines to a plot in a very similar way to adding points, except that you use the lines() function to achieve this. Skip to Navigation Skip to the Content of this Page Back to the Accessibility Menu. See this Help article for the steps to register an email address. Click the slide where you want the slider to appear. By using a SmartArt graphic, you can create a vertical bullet list and include it in your spreadsheet, e-mail message, presentation, or document. This is a technique commonly used to add a rule to legal pleadings. When a transversal intersects with two parallel lines eight angles are produced. Most creatives can’t derive insights from data on their own, so Heat leans on Deloitte consultants and strategists for vertical-specific knowledge. Today, we are more committed than ever to producing products of preeminent technical merit and performance. It does not allow row or cell spanning as well as putting multi-line text in a cell. Financing Available. Add Like And Or Is Not. Make sure that the sample Vertical Subitem works for you within the template previewed in Artisteer. startX - the horizontal coordinate of the start point of the line segment startY - the vertical coordinate of the start point of the line segment endX - the horizontal coordinate of the end point of the line segment endY - the vertical coordinate of the end point of the line segment; Method Detail. vertical and horizontal lines (Thanks to Dana for suggesting this addition to the page. Please follow these simple steps for this. xlsx2 achieves better performance compared to write. 7,151 Followers, 587 Following, 1,033 Posts - See Instagram photos and videos from just add honey tea company (@justaddhoney). Vertical blinds break far too easily. Need a belt for your washer or a new furnace filter? Dey Distributing has been serving as an appliance parts distributor since 1944. In three dimensions. A small group of boys walks down the street Throwing a ball in the air One says to another Hey I'll always be your brother I'll always be your friend Chorus Do you remember When we thought we were immortal And the games we played always had a happy end But in the game of life all the roses wither And time writes its lines upon your face Summer's here and three young men Drive through the town. I do not recommend this. Best Answer: add to the letters to spell TEN: add a top line to the first line for the " T " add 3 more horizontonal lines to the 2nd line for the " E " and 1 more diagonal line from the top of the 3rd line to the bottom of the 4th line for the " N ". However, the final piece, the vertical average line for that same metric, is missing. You can see patterns in your data by adding trendlines to charts in Google Sheets. com was featured on dumblittleman. frame really looks the way you think. Horizontal and Vertical Lines 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. The kable function in the knitr package To address the first question, we will use the dplyr package written by Hadley Wickham as below. -16cc RD D-CUP DISH, SCAT 4340 FORGED 3. The short answer is that there is a kind of Markdown support for tables in Markdown Extra - I'm surprised it hasn't been mentioned in this thread yet (according to CTRL-F search, at any rate), although we have had Github-flavoured Markdown mentioned. Information here may no longer be accurate, and links may no longer be available or reliable. I intended to add vertical lines between the 2nd and 3rd columns and between 5th and 6th columns. On the View tab, in the bottom left corner there is a checkmark by the word Gridlines. Is this currently. Is possible to add VERTICAL line in Bar (Horizontal) Chart? · Well, technically no and you should inform your client about the tool limitations. Re: How to Add Horizontal Line to Scatter Plot?? A line on a scatter chart is defined by {X1,Y1} and {X2,Y2}. Use the hline and vline File Exchange : [code]h = vline(42,'r','The Answer')[/code] Example:. ncl: Adding a polyline and shading above and below it: both color and b&w. Click to select an orb then click on empty tile to move selected orb to the new space. The article How to add horizontal lines to a Word 2016 document shows you two ways to add horizontal lines to a Word document. Note that you can not panel plots made with this function. abline() function adds a line to plot. Hundred Board Magic. After all, you don’t want to be the only business who shows up late to the first day of school. ∠2 and ∠8 are alternate exterior angles. To add a vertical line to your line or scatter chart, do the following:. All of the calendars are available in your choice of Acrobat (. The short answer is that there is a kind of Markdown support for tables in Markdown Extra - I'm surprised it hasn't been mentioned in this thread yet (according to CTRL-F search, at any rate), although we have had Github-flavoured Markdown mentioned. Butternut's trio of critically-acclaimed vertical antenna designs, including 2-band, 6-band, and 9-band models, provide excellent HF performance. ∠3 and ∠5 are alternate interior angles. HorizontalLines Default: 0. Hi , I am not sure about the terminology in use. Unfortunately, it’s a bit more complicated to delete a horizontal line in MS. It is diagonal (45 degrees). Today's blog post is brought to you by Cathy Harley a Program Manager on the Excel Chart team. And there we have it. A jQuery plug-in that adds scrolling vertical tickers to your site Just one line of javascript code is all you need to start a vTicker Items can be paused when the mouse hovers over an item. The numbers of professors from each of these groups is displayed in table r tabNumRankByDscpl`. Students use "magic" to navigate around the hundred board. DX Engineering now builds the best of Butternut's vertical antennas, plus add-on kits to bring added band coverage to your existing Butternut antenna. Arguments x. Add your comment. These geoms add reference lines (sometimes called rules) to a plot, either horizontal, vertical, or diagonal (specified by slope and intercept). < mat-divider [vertical]= "true" > link Lists with inset dividers. A horizontal line is any line normal to a vertical line. Examples of lines, circle, rectangle, and path. It is not intended to replace any other R packages for making tables. is a HUBzone certified supplier based out of Pocatello Idaho. There is also a nhspace{1in} after this. The lines( ) function adds information to a graph. XYZ always goes the extra mile to make sure your manual or CNC machine arrives on time and is delivered where you need it. april-rose. The following diagram shows parallel lines cut by a transversal. I want to add a simple horizontal line across a chart that represents the average of the lines of plotted data, in my case monthly grocery expenditures. For booktabs = TRUE: There are no vertical lines in the table, but you can add these lines via the vline argument. A VScrollBar control is a supporting control that is used to add vertical scrolling capability to a control that does not have built-in scrolling such as a container control. GitHub is home to over 36 million developers working together to host and review code, manage projects, and build software together. Vertical text is accomplished easily these days with CSS transforms:. april-rose. How do you add a nice vertical line to a column or line chart, to show a target value, or the series average? The method involves adding a new series, applying it to the secondary axes, and making the secondary axes disappear. No, wonder, then, that FVL is evolving, not into. Thus, you need to add an average line into this chart. You can add mutiple sets of footnote using differeny notation system. , a multiline cell — use the HTML. 3; 12; 4 years, 2 months ago. In this reference we will look at how to control text appearance using style sheets. I need to add this. In TQM control charts, it could be a line so-many standard deviations from the mean. After you create the line the way you want it to be, click the blue Save & Close button and it will be placed in your document. We will be doing a sample for each of these and then a combined one. References. Calculate the length of a line segment. 875 STROKE CRANKSHAFT & 6. Alternatively referred to as a vertical bar, the pipe is a computer keyboard key "|" is a verticalvertical line, sometimes depicted with a gap. These adorable magnets measure 2 inches wide by 3 1/2 inches long and can be personalized with up to 8 lines of custom text in any of our 19 magnet imprint colors and 32 magnet. We calculate the slope again, using the ratio of the vertical distance to the horizontal distance or. The R functions below can be used : geom_hline() for horizontal lines. You'll love our premium, high quality custom buttons and FAST ship today service. (I'd do your red line with annotate as well, personally. Add or remove a secondary axis in a chart in Office 2010. < mat-divider [vertical]= "true" > link Lists with inset dividers. If your lines are almost aligned with one other, it looks like a mistake that needs straightening. This add-on is more work than manually fixing inserted line breaks. This is indeed consistent with the fact that there is a vertical force acting upon a projectile but no horizontal force. I tried using line and rectangle in the pallete but that is not working (its taking lot of formatting effort and not achieving the desired result). You use the lm() function to estimate a linear regression model: fit. August 1, 2010 at 2:17 pm 3 comments. Adding a line to an existing graph requires a few more steps, therefore in many situations it would be much faster to create a new combo chart from scratch as explained above. Sum of vertical angles: Both pairs of vertical angles (four angles altogether) always sum to a full angle (360°). 1 requires the applicant to erect a minimum five-foot-high. In other words, the fact that the function's domain is restricted is reflected in the function's graph. A jQuery plug-in that adds scrolling vertical tickers to your site Just one line of javascript code is all you need to start a vTicker Items can be paused when the mouse hovers over an item. nvspace{ height} makes a vertical space. 3; 12; 4 years, 2 months ago. It will imports LaTeX package xcolor if enabled. To enable line numbers on startup, simply add the following to your vimrc. I click on the page and a line arrow appears. Connect to the server with the game client. Note that you can not panel plots made with this function. understands the appearance of any project is the one element that immediately reflects the quality and integrity of the building, as well as the construction team involved. Contour Lines. They're a good alternative to line charts when you have only a few data points in a series. This product offering covers the end suction, sump & sewage, split case, vertical multistage, vertical turbine and self-primer pumping products. by Charles Kyle Kenyon, Esq.


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# 0.1 Appendix a: solution sheets

 Page 1 / 1

## Hypothesis testing with one sample

Class Time: __________________________
Name: _____________________________________

1. H 0 : _______
2. H a : _______
3. In words, CLEARLY state what your random variable $\overline{X}$ or ${P}^{\prime }$ represents.
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value? In one or two complete sentences, explain what the p -value means for this problem.
7. Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the p -value.
8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences .
1. Alpha: _______
2. Decision: _______
3. Reason for decision: _______
4. Conclusion: _______
9. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

## Hypothesis testing with two samples

Class Time: __________________________
Name: _____________________________________

1. H 0 : _______
2. H a : _______
3. In words, clearly state what your random variable ${\overline{X}}_{1}-{\overline{X}}_{2}$ , ${{P}^{\prime }}_{1}-{{P}^{\prime }}_{2}$ or ${\overline{X}}_{d}$ represents.
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value? In one to two complete sentences, explain what the p-value means for this problem.
7. Use the previous information to sketch a picture of this situation. CLEARLY label and scale the horizontal axis and shade the region(s) corresponding to the p -value.
8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences .
1. Alpha: _______
2. Decision: _______
3. Reason for decision: _______
4. Conclusion: _______
9. In complete sentences, explain how you determined which distribution to use.

## The chi-square distribution

Class Time: __________________________
Name: ____________________________________

1. H 0 : _______
2. H a : _______
3. What are the degrees of freedom?
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value? In one to two complete sentences, explain what the p -value means for this problem.
7. Use the previous information to sketch a picture of this situation. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p -value.
8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences.
1. Alpha: _______
2. Decision: _______
3. Reason for decision: _______
4. Conclusion: _______

## F distribution and one-way anova

Class Time: __________________________
Name: ____________________________________

1. H 0 : _______
2. H a : _______
3. df ( n ) = ______ df ( d ) = _______
4. State the distribution to use for the test.
5. What is the test statistic?
6. What is the p -value?
7. Use the previous information to sketch a picture of this situation. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p -value.
8. Indicate the correct decision (“reject” or “do not reject” the null hypothesis) and write appropriate conclusions, using complete sentences .
1. Alpha: _______
2. Decision: _______
3. Reason for decision: _______
4. Conclusion: _______

Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
Got questions? Join the online conversation and get instant answers!


text:
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# Worked example: arc length

AP.CALC:
CHA‑6 (EU)
,
CHA‑6.A (LO)
,
CHA‑6.A.1 (EK)

## Video transcript

- [Voiceover] So, right over here, we have the graph of the function y is equal to x to the 3/2 power. And what I wanna do is find the arc length of this curve, from when x equals zero to when x is equal to-- and I'm gonna pick a strange number here, and I picked this strange number 'cause it makes the numbers work out very well-- to x is equal to 32/9. 32/9 is, let's see... That's three and 5/9, so it's gonna be right around... So that's three and 1/2, so it's gonna be a little bit past three and 1/2, so it's gonna be right over there. So we wanna find this arc length right over here, this thing that I have depicted in yellow. So it's from zero to 32/9. And I encourage you to pause the video and try this out on your own. So I'm assuming you've had a go at it. And if at any point while I'm working through it, you feel inspired, always feel free to pause the video and continue working with it. So let's just apply the arc length formula that we got kind of a conceptual proof for in the previous video. So we know that the arc length... Let me write this. The arc length is going to be equal to the definite integral from zero to 32/9 of the square root... Actually, let me just write it in general terms first, so that you can kinda see the formula and then how we apply it. So, it's the square root of one plus f-prime of x squared d x. And in this case, it's going to be the definite integral from zero to 32/9 of the square root of one plus... Now, what's the derivative? If f of x is x to the 3/2, then f-prime of x is going to be 3/2 x to the 1/2. And we picked this particular function because it simplifies quite well when we put it under the radical, and it's fairly straightforward to find the anti-derivative. So we've done a lot of engineering of this problem to make the numbers work out well, but let's just go through it. So this is f-prime of x; f-prime of x squared is going to be this quantity squared. It's going to be 9/4 x to the 1/2 squared is x. So, one plus 9/4 x d x. And so, now, we just have a definite integral that we know how to solve this type of thing. And you might be able to even do this in your head, essentially, do the u-substitution: say I have one plus 9/4 x. Its derivative is 9/4. I can kind of engineer that if I want, but instead, I'm just going to do straight up u-substitution. So, if I say u is equal to one plus 9/4 x, then we know... Let's see. D u d x is going to be equal to 9/4. Or, we could say d u is equal to 9/4 d x. Or, we could say d x... Let me scroll down a little bit. We could say d x is equal to... I'm just gonna multiply both sides times 4/9. Let's go to 4/9 d u. And then we just have to change the bounds of integration. When x is equal to zero, then u is going to be equal to... 9/4 times zero is just zero, so u is going to be equal to one. And when x is equal to 32/9-- and this is why that number was picked-- what's u going to be equal to? 32/9 times 9/4 is gonna be 32/4, which is going to be eight plus one. So that worked out very nicely; imagine that. So there we have it. So, this is going to be equal to the definite integral... Actually, let me make it clear that this is what is equal to this. The definite integral from u is equal to one, to u is equal to 9-- I'm gonna make it very explicit that I'm dealing with u now-- of the square root of u. And instead of d x, we have d x is 4/9 d u. Let me do it this way: the square root... Whoops, that's not the right color. Square root of u; instead of d x, we have times 4/9 d u. And I'm just gonna take the 4/9 and stick it out here. And we know how to apply the fundamental, or, I guess, the second fundamental theorem of calculus here, to evaluate this definite integral. This is going to be 4/9 times the anti-derivative of the square root of u, which is the same thing as u to the 1/2. It's going to be u to the 3/2, and then we divide by 3/2, which is the same thing as multiplying by 2/3. We're going to evaluate that at u equals nine and u is equal to one. And so, we're in the home stretch here. This is going to be equal to 4/9 times 2/3 times 9 to the 3/2 minus 2/3 times one to the 3/2. So, 9 to the 3/2, that is... Let's see: the square root of nine is three, to the third power is 27. And this, of course, is one. So we are left with 2/3 of... Actually, let's just factor out the 2/3, that makes it easier. This is going to be equal to 2/3 times 4/9 is equal to 8/27. I've just factored out the 2/3. And then we're gonna have 27 minus one inside, I guess you could say the brackets now. So 27 minus one is just going to be 26. Times 26. And we could obviously simplify this more if we want. Eight times 26 is... So, actually, let's just figure that out, just for fun. So, eight times 26 is going to be 160 plus eight times six is 48, so it's 208 over 27. And we are done.
AP® is a registered trademark of the College Board, which has not reviewed this resource.


text: Consider a convex 50-sided polygon $$P$$. A simple quadrilateral with all its vertices among those of $$P$$ is called good if it shares at least $$2$$ sides in common with $$P$$. Find the number of good quadrilaterals.


text:
# Real Analysis Limit Proof

1. May 14, 2013

### Bennigan88

I am trying to prove that $$\lim\left[\sqrt{n^2+n}-n\right]=\frac{1}{2}$$
Where $n \in \mathbb{N}$ and $\lim$ is the limit of a sequence as $n\to\infty$.

From the definition of a limit, I know that I need to show that $$\exists{N}:n>N\Rightarrow\left|\sqrt{n^2+n}-n-\frac{1}{2}\right| < \epsilon$$

Through algebraic manipulation I was able to arrive at
$$\left| \sqrt{n^2+n} - n - \frac{1}{2} \right| = \left| \frac{n-\sqrt{n^2+n}}{n+ \sqrt{n^2+n}} \right|$$

Which now means that I must show that
$$\exists N : n>N \Rightarrow \left| \frac{n-\sqrt{n^2+n}}{n+ \sqrt{n^2+n}} \right| < 2\epsilon$$

The problem here is I'm not sure how this makes the proof any easier. It seems like now I must start with the assumption that this part is less than $2\cdot\epsilon$ but I don't see how to isolate n in this inequality. Any nudge in the right direction (no spoilers, please!) would be greatly appreciated.

Last edited: May 14, 2013
2. May 14, 2013

### Mandelbroth

...Limit of what? You need to define what your limit is doing.

3. May 14, 2013

### Bennigan88

Fixed.

4. May 14, 2013

### LCKurtz

I would try dividing numerator and denominator of the left side by $\sqrt{n^2+n}$ and see if that helps. Maybe you can get all the $n$'s under the square root.

 Apparently you solved it while I was typing.

5. May 14, 2013

### Bennigan88

Nope, still haven't solved this one. Came very close, filled up my hand-held whiteboard with stuff, but it fell apart at the last minute because of one little error at the beginning. I'm still working on it now.

6. May 14, 2013

### Bennigan88

I think I have $\left| \sqrt{n^2+n} - n - \frac{1}{2} \right| < 2\epsilon \Rightarrow \left( \sqrt{n+1} - \sqrt{n} \right)^2 < 2\epsilon$ but now I'm not sure where to go from here, or if this is even a useful place to be at. I get a nagging feeling that I am missing something very simple and elegant at the beginning of this problem. I have spent HOURS on this today...starting to get pretty demoralized. Not sure how hard this is "supposed" to be.

7. May 14, 2013

### Dick

I would divide numerator and denominator by n. The denominator will be greater than 1, so don't worry about it. Just try and make the numerator small.

8. May 14, 2013

### Bennigan88

Okay, I think what you're saying is this: $\left| \frac{n - \sqrt{n^2+n}}{\sqrt{n^2+n}+n} \right| = \left| \frac{1- \sqrt{1+\frac{1}{n}}}{\sqrt{1+\frac{1}{n}}+1} \right|$. The problem for me here is that I don't see how to get an inequality of the form $n > f(\epsilon)$. Keep in mind I am not using the limit theorems in this problem, this is an epsilon proof, also each algebraic step must be logically reversible, i.e. each implication must be bidirectional.

9. May 14, 2013

### Dick

Just concentrate on the numerator. How large does n have to be to make $\sqrt{1+\frac{1}{n}}-1 \lt \epsilon$?

10. May 14, 2013

### Bennigan88

Alright I have
$$\sqrt{1+\frac{1}{n}} - 1 < \epsilon$$
$$\Rightarrow \sqrt{1+\frac{1}{n}} < \epsilon + 1$$
$$\Rightarrow 1 + \frac{1}{n} < \left( \epsilon + 1 \right) ^2$$
$$\Rightarrow \frac{1}{n} < \left(\epsilon + 1 \right)^2 - 1$$
$$\Rightarrow n > \frac{1}{\left(\epsilon + 1 \right)^2 - 1}$$

I don't understand why I can forget about the denominator.

Edit: Oh! If something is less than epsilon, then something smaller than that is also less than epsilon! Is that the idea?

Last edited: May 14, 2013
11. May 14, 2013

### Dick

The denominator is greater than 2. If the numerator is less than ε, so is the fraction. $a < \epsilon \Rightarrow \frac{a}{b} < \epsilon$ if b>2.

12. May 14, 2013

### Dick

Of course!

13. May 14, 2013

### Bennigan88

Ok I think I'm with you. I was getting mixed up over the reversibility thing, but what your saying makes perfect sense to me now. Thank you! I will try to knock out the actual proof now.

14. May 14, 2013

### Bennigan88

It's solid! Thank you so much!

15. May 24, 2013

### deluks917

An alternate idea. Let an = $\sqrt{n^2 + n}$ and bn = $\frac{1}{2} +n$ Then bn2 - an2 = (bn - an)(bn + an) = 1/4.

As limn->∞(bn + an) = ∞ as we must have limn->∞(bn - an) = 0.


text:
# Deriving two properties of clocks

This two properties are given in my module as formulas for clock related problems:

$(1)$ If both the hands start moving together from the same position, both the hands will coincide after $65\frac5{11}$ minutes.

$(2)$ Interchangeable positions of minute hand and hour hand occur when the original interval between the two hands is $\frac{60}{13}$ minute spaces or a multiple of this.

Could somebody help me to derive this two formulas?

-

We assume that the clock hands rotate at constant speed. That mathematical model does not describe all clocks well. In some clocks, the minute hand stays at say $17$ for almost $1$ minute, then moves very rapidly to $18$, with an irritating click.

1. For the first problem, it is clear that it will take a little more than an hour, say an hour plus $x$ minutes, where $x$ is well under $60$.

In $12$ hours the hour hand travels $360$ degrees. So it travels $30$ degrees per hour, and therefore $1/2$ degree per minute. In an hour and $x$ minutes the hour hand will have advanced by $30+x/2$ degrees.

In an hour the minute hand travels $360$ degrees, so it travels at $6$ degrees per minute. In an hour and $x$ minutes it will have travelled $360+6x$ degrees. So the minute hand will have advanced by $6x$ minutes. We therefore obtain the equation $$30+\frac{x}{2}=6x.$$ Solve for $x$.

2. We sketch the interchangeability argument. Take some clock time $x$, where $x$ is measured in minutes from $12$:$00$. So for example $1$:$00$ o'clock is called $60$.

At time $x$, the hour hand is $x/2$ degrees clockwise from straight up. The minute hand is at $6x-360m$ degrees clockwise from straight up, for some integer $m$ chosen to make $6x-360m$ less than $360$ degrees.

Take another time $y$ minutes after straight up. Then the hour hand is at $y/2$ degrees from straight up, and the minute hand is at $6y-360n$ for some integer $n$.

Suppose that the hour and minute hands are identical in appearance. For us to be confused between $x$ and $y$, we must have $x\ne y$ and $$\frac{x}{2}=6y-360 n \qquad \text{and} \qquad \frac{y}{2}=6x-360m.$$ We can use these equations to find all times $x\ne y$ such that times $x$ and $y$ are confused when the hands are identical, plus, of course, all times when the hands coincide.

But that's not what we want, since we were asked about $x-y$. Use the two equations to solve for this. We get $13(x-y)=720(m-n)$. Note that we have measured the "times" $x$ and $y$ in minutes after straight up, since that's what we used in part $1$. Convert to minute spaces.

-

Start by finding a formula for the position of the hour hand at time $t$, and a formula for the position of the minute hand at time $t$. Do this by noting that the hour hand moves $2\pi$ radians in 12 hours, the minute hand, in 1 hour.

-

for 1) the hour hand has an angular velocity of $360$ deg$/60$ min$=6$ deg/min, while the hour hand has an angular velocity of $(360/12)$deg$/60$ min$=1/2$ deg/min. so if they star off equal and go, to meet up we need $6t=1/2t$ to be a multiple of 360 deg, or $5.5t$ divisible by 360. this happens at $t=0,65\text{ and } 5/11$, etc.

-


text:
# “Tensor product” $\otimes$ of monoids

Referring to the top answer in this post: http://mathoverflow.net/questions/19004/is-the-category-commutative-monoids-cartesian-closed

Would it be reasonable to explain what is a tensor product in this context? I only have an introductory level of experience with category theory and have never come across a tensor product (in any sort of context) until reading this. If this is not something that can be explained in concise way, reference to book I can begin learning from to gain the background I should have for understanding would be appreciated.

-
–  Martin Brandenburg Jul 13 '13 at 8:57
The basic notion here is that of a monoidal category, which is a category $C$ together with a functor $\otimes : C \times C \to C$, the monoidal operation, together with some extra data satisfying some extra properties. Any category with finite products is a monoidal category with $\otimes$ the product functor; these are the cartesian monoidal categories.
But there are many important examples which are not cartesian monoidal, the prototypical one being the category $\text{Vect}$ of vector spaces. $\text{Vect}$ can be made into a monoidal category where the monoidal operation is the tensor product of vector spaces, and this is why sometimes monoidal operations are called tensor products. If you aren't familiar with the tensor product of vector spaces, I strongly recommend becoming comfortable with that special case before trying to understand monoidal categories in general.


text:
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 256 MB 0 0 0 0.000%

## 문제

There is a beautiful fairy tale: Once upon a time in a far away land by the edge of the world, there existed a "Candy Kingdom". This nation is filled with skyscrapers; meanwhile, the little trails, flowers, and grass are all made out of candy. What's more magical is that the sky is filled with rainbow colored candy clouds floating about. Very often, heavy candy rain will pour onto the ground. The red colors are strawberry candy, the yellow colors are lemon, the green colors are mint, the black colors are chocolate, and so on. The children of Candy Kingdom will frequently hold open pouches of all sizes to catch the candy pieces that fall from the sky, bringing them home for their friends to enjoy.

Having a very big sweet tooth, little Z longs to be able to visit this fairy tale kingdom. As the old saying goes, what you think about in the day, you will dream about during the night. So one night, little Z dreamed that he has arrived in Candy Kingdom. He discovered that at any given moment, all of the clouds in the sky will have different colors. These different colored clouds continuously drop candies of corresponding colors. What's even more interesting is that all of the clouds are in constant back and forth motion. There's no harm in imagining that there are borders to the sky, which is why the clouds just happen to be moving back and forth between the two borders of the sky. During each unit of time, a cloud moves one unit of distance either to the left or to the right. When a cloud hits the left border of the sky, it will change its direction and start moving to the right; when a cloud completely moves past the right border of the sky, it will change its direction and start moving to the left.

We may as well think of the sky as a Cartesian coordinate plane, where clouds are represented by line segments (which may degenerate to points):

In the figure above, we set the left border of the sky to be 0 and the right border to be len. The figure contains a total of 5 clouds. The cloud labeled 1 is just changing its direction to move rightwards. The cloud labeled 2 is just changing its direction to move leftwards. The vertical coordinates of the clouds may be ignored, for the clouds will never affect each other during their movement process.

Little Z noticed that new clouds will continuously form in the sky (during some time, at some starting position, moving in some direction), and some clouds after moving for a certain time will disappear from the sky. While clouds are in motion, candy will continuously fall from them. Little Z decided to bring many bags to catch the falling candy. Bags have unlimited capacities, but the size of their openings are limited. For example at time T, little Z carries a bag which has an opening spanning the horizontal range [LR]. If [LR] contains a position x where candy falls, then the bag will be able to catch the candy. In extreme cases, the range of the bag's opening can be a point such as [0, 0] or [1, 1], but the bag will still be able to catch candy at the corresponding positions. It is generally known that the amount of candy one can catch is rather larger, so little Z would like to know for each time (the moment he pulls out a bag) how many different colors of candy can his bag catch? The falling times of the candy are negligible.

## 입력

The first line contains two positive integers n and len, representing the total number of events and the sky's "boundary", respectively.

For the following n lines, each line describes one event. All events happen in the input order. The first number of each line k (k = 1, 2, or 3) specifies the type of event that happens. There are three types of events: InsertQuery, and Delete. Their formats are as follows:

Event Type Input Format Explanation
Insert
(A new cloud appears in the sky)
1 Ti Ci Li Ri Di At time Ti, a new cloud of color Ci spanning the range [LiRi] will appear in the sky. The initial direction of the cloud may be leftwards (Di = −1) or rightwards (Di = 1). These parameters will satisfy 0 ≤ Li ≤ Ri ≤ len, and Di ∈ {−1, 1}.
The data guarantees that at any given moment, the sky will not contain two clouds that are the same color.
Query
(Determine how many different colors of candy a bag can catch)
2 Ti Li Ri At time Ti, little Z uses a bag with an opening that spans the range [LiRi] to catch candy. He would like to know how many different colors of them he can catch. The parameters will satisfy 0 ≤ Li ≤ Ri ≤ len.
Delete
(A cloud disappears from the sky)
3 Ti Ci At time Ti, the cloud colored Ci will disappear from the sky. The data guarantees that the sky will contain a cloud with color Ci at that time.

## 제한

n ≤ 200000, len ≤ 1000

All of the data will satisfy 0 ≤ Ti ≤ 2000000000 and 1 ≤ Ci ≤ 1000000.

The data guarantees that { Ti } forms a non-decreasing sequence T1 ≤ T2 ≤ … ≤ Tn−1 ≤ Tn.

For all of the Insert events, let Pi = Ri − Li, representing the length of each cloud. Then, Pi ≤ len.

## 예제 입력 1

10 10
1 0 10 1 3 -1
2 1 0 0
2 11 0 10
2 11 0 9
1 11 13 4 7 1
2 13 9 9
2 13 10 10
3 100 13
3 1999999999 10
1 2000000000 10 0 1 1

## 예제 출력 1

1
1
0
2
1

## 힌트

For each Query event, output one line containing one integer – the number of different colors of candy that can be caught by the corresponding bag.


text:
# FeenoX documentation index

FeenoX documentation is released under the terms of the GNU Free Documentation License v1.3, or any later version.

# 1 FeenoX manual and description

As per the GNU Coding Standards, “a manual should serve both as tutorial and reference.” Due to the formatting restrictions, the Texinfo version contains only the description and not the full reference.

The sources are in the doc directory of the Git repository. They are in Pandoc-flavored Markdown.

## 1.1 Design

The FeenoX project starts as an offer to an imaginary “request for quotations” that defines software requirements specifications for an open source computational tool. Then a fictitious “offer” to the above tender is given in a software design specifications document that explains the design decisions and features included in FeenoX.

## 1.3 UNIX manpage

See UNIX manpage converted to HTML. It should be accessible with man feenox after (global) installation and its sources are available in the Git repository.

# 2 Hands on

Go directly to the point and see how to solve problems with FeenoX. Everything (except the case files) is included in the Git repository.

## 2.1 Quick examples

Annotated examples can be found in the examples directory. These are simple and quick (but varied) cases. They are based on the August 2021 presentation:

Make sure you also browse the tests directory of the Git repository and the Software Design specifications document.

## 2.2 Tutorials

Step-by-step instructions and explanations to solve increasingly-complex problems are given in the tutorials directory.

TO BE DONE

## 2.3 Case files

Detailed solutions of benchmarks, V&V cases and/or problems with industrial interest. These cases include parametric studies for mesh convergence, comparisons with analytical or other programs, efficiency measurements, etc. Since these cases involve other tools, figures, data files, etc. they have a separate repository.

TO BE DONE

# 3 Background and generalities

## 3.1 Software requirements specifications

The FeenoX project starts as an offer to an imaginary “request for quotations” that defines software requirements specifications for a computational tool.

## 3.2 Software design specifications

The “quotation” to the above tender is given in a software design specifications document that explains the design decisions and features included in FeenoX.

## 3.3 History

See the FeenoX history.

# 4 Programming and contributing

## 4.3 Contributing guidelines

Any contribution is welcome, especially new types of PDEs and new formulations of existing PDEs. For elliptic operators feel free to use the Laplace equation as a template.


text:
Home > Standard Error > R Lm Output Standard Error

# R Lm Output Standard Error

## Contents

Also, the standard error $\sigma_{\beta_i}$ . In our example, the actual distance required to stop can deviate from the true regression line by approximately 15.3795867 feet, on average. r regression lm standard-error share|improve this question edited Oct 7 at 22:08 Zheyuan Li 18.7k52351 asked Jun 19 '12 at 10:40 Fabian Stolz 46051326 add a comment| 3 Answers 3 active Is the R-squared high enough to achieve this level of precision? http://caribtechsxm.com/standard-error/python-standard-error-output.php

Adjusted R-Squared normalizes Multiple R-Squared by taking into account how many samples you have and how many variables you're using. #Adjusted R-Squared n=length(y) k=length(model$coefficients)-1 #Subtract one to ignore intercept SSE=sum(model$residuals**2) SSyy=sum((y-mean(y))**2) In our example, we can see that the distribution of the residuals do not appear to be strongly symmetrical. Further, as I detailed here, R-squared is relevant mainly when you need precise predictions. share|improve this answer edited Sep 17 '13 at 19:58 answered Dec 4 '10 at 12:59 Gavin Simpson 17.2k34982 4 @Gavin (+1) Great response with nice illustrations! –chl♦ Dec 4 '10

## R Lm Residual Standard Error

Due to the presence of this error term, we are not capable of perfectly predicting our response variable (dist) from the predictor (speed) one. share|improve this answer answered Jun 19 '12 at 12:40 smillig 1,84332033 add a comment| up vote 8 down vote #some data x<-c(1,2,3,4) y<-c(2.1,3.9,6.3,7.8) #fitting a linear model fit<-lm(y~x) #look at the Coefficient - Pr(>|t|) The Pr(>|t|) acronym found in the model output relates to the probability of observing any value equal or larger than |t|.

• HTH, Marc Schwartz Henrique Dallazuanna wrote: > Try: > > summary(lm.D9)[["coefficients"]][,2] > > On Fri, Apr 25, 2008 at 10:55 AM, Uli Kleinwechter < > ulikleinwechter at yahoo.com.mx> wrote: > >>
• I thought about mentioning that equivalence too.
• When assessing how well the model fit the data, you should look for a symmetrical distribution across these points on the mean value zero (0).
• Error t value Pr(>|t|) (Intercept) 0.8278 1.7063 0.485 0.64058 x1 0.5299 0.1104 4.802 0.00135 ** x2 0.6443 0.4017 1.604 0.14744 --- Signif.
• The p-value is the probability of achieving a value of $t$ as larger or larger if the null hypothesis were true.
• Get a weekly summary of the latest blog posts.
• A side note: In multiple regression settings, the $$R^2$$ will always increase as more variables are included in the model.
• In the simple case of a single, continuous predictor (as per your example), $F = t_{\mathrm{Petal.Width}}^2$, which is why the p-values are the same.
• It will have a certain $R^2$.
• One thing you might clarifiy, with regard to calculating t values: sqrt(diag(vcov(mod))) produces the SE of the estimates.

This can artificially inflate the R-squared value. I know how to store the estimates but I don't know how to store their standard errors... the number of parameters in the model. Interpreting Linear Regression Output In R When it comes to distance to stop, there are cars that can stop in 2 feet and cars that need 120 feet to come to a stop.

The $t$ statistics are the estimates ($\hat{\beta_i}$) divided by their standard errors ($\hat{\sigma_i}$), e.g. $t_i = \frac{\hat{\beta_i}}{\hat{\sigma_i}}$. R Lm Extract Residual Standard Error Disregard my previous comment. –nico Dec 4 '10 at 14:34 6 Minor quibble: You cannot say anything about normality or non-normality based on those 5 quantiles alone. I hope someone can clarify that. How to explain leaving a job for a huge ethical/moral issue to a potential employer - without REALLY explaining it What is the practical duration of Prestidigitation?

once could use the five number summary to see if residuals were deviating from normal –Gavin Simpson Dec 4 '10 at 13:39 @Gavin Simpson: you're right, I misread the How To Extract Standard Error In R This quick guide will help the analyst who is starting with linear regression in R to understand what the model output looks like. This represents the probability of achieving a $t$ value greater than the absolute values of the observed $t$s. Now, we'll create a linear regression model using R's lm() function and we'll get the summary output using the summary() function.

## R Lm Extract Residual Standard Error

So you can use all the standard list operations. Misuse of parentheses for multiplication more hot questions question feed lang-r about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life R Lm Residual Standard Error However, S must be <= 2.5 to produce a sufficiently narrow 95% prediction interval. R Standard Error Lm F-Statistic F-statistic is a good indicator of whether there is a relationship between our predictor and the response variables.

At a glance, we can see that our model needs to be more precise. this page The Mean Sq column contains the two variances and $3.7945 / 0.1656 = 22.91$. The assumption in ordinary least squares is that the residuals are individually described by a Gaussian (normal) distribution with mean 0 and standard deviation $\sigma$. How to slow down sessions? Residual Standard Error Interpretation

It is multiplied by 2, because of course $t$ can be large in the negative direction too. One way we could start to improve is by transforming our response variable (try running a new model with the response variable log-transformed mod2 = lm(formula = log(dist) ~ speed.c, data You can now replicate the summary statistics produced by R's summary function on linear regression (lm) models! get redirected here I would really appreciate your thoughts and insights.

but I am interested in the standard errors... Residual Standard Error Formula Related 0How to calculate p value from ANOVA function for LMM results?1Multiple objective allocation function1How to do contrasts with weighted observations in R's linear model function lm()2How do I obtain the Mini-slump R2 = 0.98 DF SS F value Model 14 42070.4 20.8s Error 4 203.5 Total 20 42937.8 Name: Jim Frost • Thursday, July 3, 2014 Hi Nicholas, It appears like

## Minitab Inc.

However, you can’t use R-squared to assess the precision, which ultimately leaves it unhelpful. A long overdue riddle If the square root of two is irrational, why can it be created by dividing two numbers? Not the answer you're looking for? Extract Standard Error From Glm In R F-statistic: 22.91 on 1 and 148 DF, p-value: 4.073e-06 F and p for the whole model, not only for single $\beta_i$s as previous.

With those sections out of the way, we'll focus on the bottom of the summary output. How to make sure that my operating system is not affected by CVE-2016-5195? The model is probably overfit, which would produce an R-square that is too high. http://caribtechsxm.com/standard-error/r2-standard-error.php In our example, we’ve previously determined that for every 1 mph increase in the speed of a car, the required distance to stop goes up by 3.9324088 feet.

Customize ??? We could also consider bringing in new variables, new transformation of variables and then subsequent variable selection, and comparing between different models. Try our newsletter Sign up for our newsletter and get our top new questions delivered to your inbox (see an example). asked 4 years ago viewed 32120 times active 17 days ago Blog Stack Overflow Podcast #92 - The Guerilla Guide to Interviewing Related 2Getting standard errors from regressions using rpy27R calculate

For example: #some data (taken from Roland's example) x = c(1,2,3,4) y = c(2.1,3.9,6.3,7.8) #fitting a linear model fit = lm(y~x) m = summary(fit) The m object or list has a Getting Started: Build a Model Before we can examine a model summary, we need to build a model.  To follow along with this example, create these three variables. #Anscombe's Quartet Q1 The fitted line plot shown above is from my post where I use BMI to predict body fat percentage. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Estimates $\hat{\beta_i}$ , computed by least squares regression.

Where's the 0xBEEF? model=lm(y~x1+x2) summary(model) This is the output you should receive. > summary(model) Call: lm(formula = y ~ x1 + x2) Residuals: Min 1Q Median 3Q Max -1.69194 -0.61053 -0.08073 0.60553 1.61689 Coefficients: Residual Standard Error Residual Standard Error is measure of the quality of a linear regression fit. t value: Estimate divided by Std.

S provides important information that R-squared does not. Our global network of representatives serves more than 40 countries around the world. More than 90% of Fortune 100 companies use Minitab Statistical Software, our flagship product, and more students worldwide have used Minitab to learn statistics than any other package. They are computed as (using tstats from above): > 2 * pt(abs(tstats), df = df.residual(mod), lower.tail = FALSE) (Intercept) Petal.Width 1.835999e-98 4.073229e-06 So we compute the upper tail probability of achieving

The Standard Error can be used to compute an estimate of the expected difference in case we ran the model again and again. Why is Pascal's Triangle called a Triangle? Note that the model we ran above was just an example to illustrate how a linear model output looks like in R and how we can start to interpret its components. All you can say based on that summary is whether the estimated residuals are approximately symmetric around zero.


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# Keynote equation: is it possible to predefine LaTeX macros?

Is it possible to add to the LaTeX preamble for the Keynote equation tool? For example, the default setting is that \vec{x} generates an arrow over the letter x, but I would like this to produce a bold x.


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# Convert MCD to Lumens

## This calculator is useful for calculating the luminous flux for LEDs where the angle is known.

### Inputs

Millicandelas (mcd)
Degrees

Lumens (lm)

### Overview

Luminous flux (in lumens) is a measure of the total amount of light an LED puts out, while luminous intensity (in candelas) is a measure of how bright the beam in a particular direction is. This calculator gives the luminous flux emitted by an LED given its intensity and beam angle. LED datasheets often include the luminous intensity, so you might need to check them out. You will find this calculator useful if you want to compare the light output of LEDs with different beam angles.

### Equations

$$\Phi_{V} = I_{V} * \Omega$$

Where:

$$\Phi_{V}$$ = luminous flux in Lumens (lm)

$$I_{V}$$ = luminous intensity in Candela (cd)

$$\Omega$$ = solid angle of the beam in Steradian (sr)

Note that the calculator asks for a beam angle and not the solid angle. The formula used to convert beam angle to solid angle is:

$$\Omega = 2\pi(1-cos(\theta*\frac{\pi}{360}))$$

Where:

$$\theta$$ = beam angle in degrees

### Applications

It's a good practice to know the light intensity of the LED you will be using, especially if the LED is going to be used to illuminate a room. However, light intensity does not exactly tell how bright an LED is since it doesn't radiate light in all directions. Luminous flux is a better measurement because it considers the viewing angle.

Note that manufacturers often list the most favorable luminous intensity value for their particular component. In truth, there is no standard for measuring luminous intensity and so suppliers tend to give only the maximum value. This means that this calculator might provide results that are different from what is actually measured since it only takes the average luminous intensity across a given beam angle.


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# Exercise 3.10Z: Amplitude and Angle Modulation in Comparison

Characteristic curves illustrating the noise behavior for  $\rm AM$  and  $\rm WM$

Consider the transmission of a cosine signal with amplitude modulation   $\rm (AM)$  and angle modulation $\rm (WM)$. The following boundary conditions apply::

• Message frequency  $f_{\rm N} = 10 \ \rm kHz$,
• Transmission power  $P_{\rm S} = 100 \ \rm kW$,
• Channel transmission factor  $20 · \lg α_{\rm K} = -120 \ \rm dB$,
• noise power density  $N_0 = 10^{–16} \ \rm W/Hz$.

These system parameters are conveniently combined to form the performance parameter: $$\xi = \frac{\alpha_{\rm K}^2 \cdot P_{\rm S}}{N_0 \cdot B_{\rm NF}}$$ The graph shows the resulting sink-to-noise ratio  $10 · \lg ρ_v$  as a function of the logarithmized performance parameter   $ξ$.

Hints:

• The following relationships hold:
$$\rho_{v } = \left\{ \begin{array}{c} \xi \\ {\eta^2}/2 \cdot\xi \\ 3{\eta^2}/2 \cdot\xi \\ \end{array} \right.\quad \begin{array}{*{10}c} {\rm{for}} \\ {\rm{for}} \\ {\rm{for}} \\ \end{array}\begin{array}{*{20}l} {\rm DSB/SSB-AM \hspace{0.15cm}without \hspace{0.15cm}carrier} \hspace{0.05cm}, \\ {\rm PM \hspace{0.15cm}with \hspace{0.15cm}modulation\hspace{0.15cm}depth \hspace{0.15cm} \eta } \hspace{0.05cm}, \\ {\rm FM \hspace{0.15cm}with \hspace{0.15cm}modulation\hspace{0.15cm}depth \hspace{0.15cm} \eta }\hspace{0.05cm}. \\ \end{array}$$
• The bandwidths  $B_{\rm K}$  for angle modulation shall be selected according to the "Carson rule" to guarantee a distortion factor of  $K < 1\%$ :
$$B_{\rm K} = 2 \cdot f_{\rm N} \cdot (\eta +2) \hspace{0.05cm}.$$

### Questions

1

Calculate the logarithmized power parameter  $ξ$.

 $10 · \lg \ ξ \ = \$ $\ \rm dB$

2

What is the sink-to-noise ratio for the AM system?

 $10 · \lg ρ_v \ = \$ $\ \rm dB$

3

What special kind of AM might be present here?

 It could be a DSB-AM. It could be a SSB-AM. It could be an AM without a carrier. It could be an AM with an added carrier.

4

In the case of the DSB-AM, what is the required channel bandwidth  $B_{\rm K}$?

 $B_{\rm K} \ = \$ $\ \rm kHz$

5

What is the sink-to-noise ratio for the WM system?

 $10 · \lg ρ_v \ = \$ $\ \rm dB$

6

What is the minimum bandwidth required for the given PM system if  $K < 1\%$  is to apply?

 $B_{\rm K} \ = \$ $\ \rm kHz$

7

For $K < 1\%$ , die erforderliche Bandbreite, what is the required bandwidth if the WM system implements frequency modulation??

 $B_{\rm K} \ = \$ $\ \rm kHz$

8

All other parameters being equal, what is the minimum transmit power  $P_{\rm S}$  required for the WM system to be no worse than the AM system?

 $P_{\rm S,\hspace{0.05cm}min} \ = \$ $\ \rm W$

### Solution

#### Solution

(1)  From  $20 · \lg α_{\rm K} = -120 \ \rm dB$  we get  $α_{\rm K} = 10^{–6}$.  Thus, with   $B_{\rm NF} = f_{\rm N}$, one obtains:

$$\xi = \frac{\alpha_{\rm K}^2 \cdot P_{\rm S}}{N_0 \cdot B_{\rm NF}}= \frac{10^{-12} \cdot 10^{5}\;{\rm W}}{10^{-16}\;{\rm W/Hz} \cdot 10^{4}\;{\rm Hz}}= 10^5 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}10 \cdot {\rm lg} \hspace{0.15cm}\xi \hspace{0.15cm}\underline {= 50\,{\rm dB}}\hspace{0.05cm}.$$

(2)  From the graph, it can be seen that   $ρ_v = ξ$  holds for the AM system. Thus, the sinking signal-to-noise ratio is:

$$10 \cdot {\rm lg} \hspace{0.15cm}\rho_{v }\hspace{0.15cm}\underline {= 50\,{\rm dB}}\hspace{0.05cm}.$$

(3)  The first three answers are correct:

• It is a DSB-AM or a SSB-AM without a carrier.
• DSB–AM and SSB–AM with a carrier can be ruled out.  In these instances, it would always be the case that   $ρ_v < \xi$ .

(4)  For DSB–AM,  $B_{\rm K} ≥ 2 · f_{\rm N}\hspace{0.15cm}\underline { = 20 \ \rm kHz}$  must hold.

(5) From the given graph, it can be seen that from about  $20 \ \rm dB$  onwards:

$$10 \cdot {\rm lg} \hspace{0.15cm}\rho_{v }= 10 \cdot {\rm lg} \hspace{0.15cm}\xi + 10\,{\rm dB}. \hspace{0.3cm}{\rm Mit}\hspace{0.15cm}10 \cdot {\rm lg} \hspace{0.15cm}\xi = 50\,{\rm dB}\hspace{0.05cm}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}10 \cdot {\rm lg} \hspace{0.15cm}\rho_{v }\hspace{0.15cm}\underline {= 60\,{\rm dB}}.$$

(6)  In the case of phase modulation:

$$\rho_{v }= \frac{\eta^2}{2} \cdot \xi \hspace{0.3cm}\Rightarrow \hspace{0.3cm} \eta^2 = \frac{2 \cdot \rho_{v }}{\xi} = 20\hspace{0.3cm}\Rightarrow \hspace{0.3cm} \eta \approx 4.47 \hspace{0.05cm}.$$
• Thus, the channel bandwidth needed for 𝐾<1% must be:
$$B_{\rm K} \ge 2 \cdot f_{\rm N} \cdot (\eta +2) = 20\,{\rm kHz}\cdot 6.47 \hspace{0.15cm}\underline { \approx 130\,{\rm kHz}}\hspace{0.05cm}.$$

(7) Here, a smaller modulation index is sufficient, and thus a smaller bandwidth:

$${3}/{2}\cdot \eta^2 = 10\hspace{0.3cm}\Rightarrow \hspace{0.3cm} \eta \approx 2.58 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}B_{\rm K} = 20\,{\rm kHz}\cdot 4.58 \hspace{0.15cm}\underline {\approx 91.6\,{\rm kHz}}\hspace{0.05cm}.$$

(8)  In the graph, one can see the so-called FM threshold effect.

• For  $10 · \lg \hspace{0.08cm} ξ = 15 \ \rm dB$  one obtains exactly the same sink SNR for the WM system as for the AM system.
• Thus, the transmit power can be   $35 \ \rm dB$  less than s  $100 \ \rm kW$:
$$10 \cdot {\rm lg} \hspace{0.15cm}\frac{P_{\rm S,\hspace{0.05cm}min}}{100\,{\rm kW}}= -35\,{\rm dB} \hspace{0.3cm}\Rightarrow \hspace{0.3cm} \frac{P_{\rm S,\hspace{0.05cm}min}}{100\,{\rm kW}}\approx 0.0003\hspace{0.3cm}\Rightarrow \hspace{0.3cm}P_{\rm S,\hspace{0.05cm}min} \hspace{0.15cm}\underline {\approx 30\,{\rm W}}\hspace{0.05cm}.$$