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# Pulley-rope tension question

I'm learning mechanics and I don't understand the following (simple, I guess) concept. Here's a pulley-rope system:

The force of tension, as I understand it, is defined as the force exerted on an object connected to the rope/string. For example, $\vec{T_1}$ is the force of tension exerted on the object with mass $m_1$. But what are the forces $\vec{T_1}'$ and $\vec{T_2}'$? My textbook says that these are tension forces too, but I don't understand on which body they act - on the pulley? Well, there's no friction here. So the only reasonable explanation is that these are internal tension forces (which is very different from $\vec{T_1}$ for example). In this case:

1. Why do we even care about them? Don't they all cancel out along the rope (when it's massless)?

2. Why are we interested in the forces $\vec{T_1}'$ and $\vec{T_2}'$ which are acting on the rope tangentially to the pulley and not, for example, in the tension force acting on the pulley itself, that is:

Or maybe in the internal tension forces acting on the rope in some other places?

• Every post on this site is a question, so there's no need to put "question" in the title. We have a FAQ on writing good question titles. Please take a look. – DanielSank Oct 24 '15 at 22:48
• A late comment, but: Can't you just consider the rope a part of your body? In that case, the FBD contains the pulley and the upper part of the rope, positioned on top of the pulley. The whole particle system will then have two tension forces acting on it (all tension forces inside the rope are internal forces and cancel each other out, so these are the only external forces, caused on the rope by the surrounding rope), and you can then claim that the sum of the forces is $0$, since the CM has acceleration $0$. – Max Nov 27 '16 at 22:19

On the pulley on the left, there are 4 forces applied, $T_1'$, $T_2'$, the gravitational acceleration on the pulley (its weight) $m' g$ (directed downwards), and the tension of the rope at the center of the pulley $T$, which is the one that you draw, but directed upwards. Now, the tension $T$ balances the weight $mg$ and the other two tensions $T_1'$ and $T_2'$, and the pulley don't move. However, the toques of the tensions $T_1'$ and $T_2'$ may not balance, and may result in a rotation of the pulley. In fact, if $L=I\omega$ is the angular momentum of the pulley, $I$ the momentum of inertia, and $\omega$ the angular velocity, one has $$\frac{d L}{dt} =I\frac{d \omega}{dt}=r T_1'-r T_2'$$ where $r$ is the radius of the pulley and the terms at the right side of the equations are the torques of the tension forces applied to the pulley.

If your problem is just to determine the static equilibrium of the system, and not its dynamics, you may want to assume $\frac{d L}{dt}=0$ and therefore balance the two torques $r T_1'=r T'_2$, that is, $T_1'=T_2'$.

• Thanks. The $\vec{T}$ that I drew supposed to represent the force applied by the rope on the pulley (not the rope which connects the pulley with the ceiling but the rope which is connected to the masses). The rope acts on the pulley not just from left and right but also in every point of their contact, am I wrong? Also, aren't $\vec{T_1}'$ and $\vec{T_2}'$ actually forces of friction? The rope and the pulley aren't actually connected. As I understand it - the rope just slides on the pulley, so these are friction forces (which contradicts the fact that there's no friction between them). – user86253 Jul 19 '15 at 9:11
• In the statement of the problem, it is mentioned whether the friction is to be taken into account, i.e., if it is negligible or not? And also, you are interested in the static solution (balance of forces, the system does not move) or to the dynamic solution (the masses move)? – sintetico Jul 19 '15 at 9:52
• yes, the ropes and the pulleys are massless and there's no friction anywhere. I just fail to understand why the tension force acts on the pulley from the sides (tangentially) if there's no friction. Shouldn't the rope push the pulley just in one point (from the top)? – user86253 Jul 19 '15 at 9:59

If the pulleys are frictionless and the rope and pulleys are massless, then indeed the tension will be the same everywhere along the rope and you can just consider twice the tension acting on the center of the pulley.

It gets more interesting when the pulleys have mass, and there is friction (and even more when the rope also has mass...) . That is when the diagram you drew becomes more useful - there will be net torque on the pulleys so they will have both angular and linear acceleration. But without friction the problem is straightforward - no need to get confused or overthink.

Responding to the comment: $T_1$ and $T_2$ are the same magnitude (massless rope) and as such their torques w.r.t. the center of rotation cancel. But the sum of their forces acts on the center of the pulley - this is true whether there is friction or not: "the center of mass moves as though all forces acting on the body act on the center of mass". The force $T$ to the ceiling balances these two forces. If you imagine the rope making a full turn around a frictionless pulley, then if you pulled it tight you would squish (compress) the pulley but it would not rotate. With the rope halfway around, you are squishing half the pulley - and the force from the suspension to the axle of the pulley provides the counter force.

• I think that user86253 wants to know on which body the forces $\vec{T_1}'$ and $\vec{T_2}'$ act and why (he claims that these forces can't act on the pulley because the system is frictionless). – cth Jul 19 '15 at 13:55


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# Bounds on entanglement-assisted source-channel coding via the lovász number and its variants

Toby Cubitt, Laura Mancinska, David E. Roberson, Simone Severini, Dan Stahlke, Andreas Winter

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

## Abstract

© 2014 IEEE. We study zero-error entanglement-assisted source-channel coding (communication in the presence of side information). Adapting a technique of Beigi, we show that such coding requires existence of a set of vectors satisfying orthogonality conditions related to suitably defined graphs G and H. Such vectors exist if and only if{G}}) ≤\H , where represents the Lovász number. We also obtain similar inequalities for the related Schrijver {- and Szegedy (+ numbers. These inequalities reproduce several known bounds and also lead to new results. We provide a lower bound on the entanglement-assisted cost rate. We show that the entanglement-assisted independence number is bounded by the Schrijver number: α(G) \le {- (G)). Therefore, we are able to disprove the conjecture that the one-shot entanglement-assisted zero-error capacity is equal to the integer part of the Lovász number. Beigi introduced a quantity $$\beta$$ as an upper bound on α) and posed the question of whether β (G) = \lfloor (G) \rfloor \). We answer this in the affirmative and show that a related quantity is equal to $$\lceil (G) \rceil$$. We show that a quantity χ G)recently introduced in the context of Tsirelson's problem is equal to $$lceil +} {G}}) \rceil$$. In an appendix, we investigate multiplicativity properties of Schrijver's and Szegedy's numbers, as well as projective rank.
Original language English 6880319 7330-7344 IEEE Transactions on Information Theory 60 https://doi.org/10.1109/TIT.2014.2349502 Published - 1 Jan 2014

## Fingerprint

Dive into the research topics of 'Bounds on entanglement-assisted source-channel coding via the lovász number and its variants'. Together they form a unique fingerprint.

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What the 'x' in 'xMOOC' stands for

In case you were wondering...

If anything, it stands for ‘eXtended’.

The origin of the ‘x’ is the use of ‘x’ in things like ‘TEDx’ or ‘MITx’ to indicate programs that aren’t part of the core offering, but which are in some way extensions.

I noticed this use of ‘x’ in the U.S. MOOCs, for example, ‘EdX’. So I started calling any of the MOOCs from Coursera, Udacity and EdX ‘xMOOCs’. It was only later on that I started calling the others ‘cMOOCs’.

It should be clear here that the ‘xMOOC’ sense is not of “eXtended MOOC” but rather “MOOC as eXtension of something else”.
Shared publiclyView activity


text:
Read data into a project Convenience method to read raw data from standard locations and using standard names in a project folder structure.

import_project_data(project_name)

## Arguments

project_name The project name. This should represent the folder holding the project.

## Examples

create_qcoder_project(project_name = "_my_qcoder_project", sample = TRUE)
import_project_data("_my_qcoder_project")


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# zbMATH — the first resource for mathematics

Some results on CLESS lattices. (English) Zbl 1454.06007
Summary: We introduce the concept of a CLESS lattice which is a generalization of the concept of an extending lattice (or a CS lattice). We study relationship between various generalizations of the concept of an extending lattice namely, CLS lattice, CLESS lattice and CESS lattice. We also prove that, if $$a$$, $$b$$ are direct summands of 1 which are CLESS elements then 1 is a CLESS element.
##### MSC:
 06C20 Complemented modular lattices, continuous geometries 06C05 Modular lattices, Desarguesian lattices
##### Keywords:
modular lattice; CS lattice; CLS lattice; CESS lattice; CLESS lattice
Full Text:
##### References:
 [1] E. Akalan, G. F. Birkenmeier, and A. Tercan, Goldie extending modules,Comm. Algebra,37(2009), 663-683. · Zbl 1214.16005 [2] G. C˘alug˘areanu,Lattice Concepts of Module Theory, Kluwer, Dordrecht,2000. [3] E. Celik, A. Harmanci and P. F. Smith, A generalization of CS-modules,Comm. Algebra,23(1995), 5445-5460. · Zbl 0842.16003 [4] A. W. Chatters and C. R. Hajarnavis, Rings in which every complement right ideal is a direct summand, Quart. J. Math. Oxford(2)28 (1977), 61-80. · Zbl 0342.16023 [5] S. Crivei and S. Sahinkaya, Modules whose closed submodules with essential socle are direct summands, Taiwanese J. Math.,18, no. 4,(2014), 989-1002. · Zbl 1357.16011 [6] N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer,Extending modules, Research Notes in Math. Ser. 313, Pitman, London, 1994. · Zbl 0841.16001 [7] G. Grätzer, Lattice theory:First concepts and distributive lattices, W. H. Freeman and company San Francisco, 1971. · Zbl 0232.06001 [8] P. Grzeszczuk and E. R. Puczylowski, On Goldie and dual Goldie dimension,J. Pure and Appl. Algebra, 31(1984), 47-54. · Zbl 0528.16010 [9] A. Harmanci and P. F. Smith, Finite direct sums of CS-modules,Houston J. Math.,19(1993), 523-532. · Zbl 0802.16006 [10] D. Keskin, An approach to extending and lifting modules by modular lattice,Indian J. Pure Appl. Math. 33, no. 1, (2002), 81-86, · Zbl 0998.16004 [11] T. Y. Lam,Lectures on rings and modules, Springer-Verlag, New York, 1999. · Zbl 0911.16001 [12] B. J. Müller and S. T. Rizvi, Direct sum of indecomposible modules,Osaka J. Math.,21(1984), 365-374. · Zbl 0538.16015 [13] S. K. Nimbhorkar and D. B. Banswal, A note on CESS-lattices, [14] S. K. Nimbhorkar and Rupal Shroff, Ojective ideals in modular lattices,Czech. Math. J.,65(140)(2015), 161-178. · Zbl 1338.06004 [15] S. K. Nimbhorkar and Rupal Shroff, Generalized extending ideals in modular lattices,J. Indian Math. Soc.,82(3-4), (2015), 127-146. · Zbl 1351.06004 [16] S. K. Nimbhorkar and Rupal Shroff, Goldie extending elements in modular lattices,Math. Bohemica142 (2)(2017), 163-180. · Zbl 1424.06028 [17] P. F. Smith,CS-modules and weak CS-modulesNon-commutative Ring Theory Springer LNM 1448 (1990), 99-115. [18] G. Sz¯asz,Introduction to lattice theory, Academic Press, New York, 1963. [19] A. Tercan, On CLS-modules,Rocky Mountain J. Math.,25, no. 4, (1995), 1557 - 1564. · Zbl 0848.16006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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# zbMATH — the first resource for mathematics

Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative. (English) Zbl 1312.34014
Summary: We establish some bounds for the solution of a Cauchytype problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on the Gauss hypergeometric function.

##### MSC:
 34A08 Fractional ordinary differential equations and fractional differential inclusions 33C05 Classical hypergeometric functions, $${}_2F_1$$ 45J05 Integro-ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
mlrnd
Full Text:


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# Function field on a non-singular algebraic curve as the field of meromorphic functions

Let $k$ be an algebraically closed field and let $X$ be a non-singular algebraic projective curve over $k$. Very often, when most books present the function field $k(X)$, they say that "it is the analogue of the field of meromorphic functions on a Riemann surface". I don't agree with this statement, and I'm going to explain the reason:

If $p\in X$, then the local ring $\mathcal O_{X,p}$ is a discrete valuation field (remember that $X$ is non-singular) with respect to a (normalized) valuation $\text{ord}_p$. Then $k(X)$ is the field of fractions of $\mathcal O_{X,p}$ and it is in natural way a discrete valuation field with respect to $\mathcal O_{X,p}$. At this point we can take the completion $\widehat {k(X)}$ and moreover we notice that $k\subseteq k(X)$ is a set of representatives for the residue field $\mathcal O_{X,p}/\mathfrak m_p$. Thanks to the theory of valuations we have the following equality:

$$\widehat {k(X)}\cong k((\pi))=\left\{\sum_{i\ge-k}a_i\pi^i\,: a_i\in k\right\}$$

where $\pi\in\mathcal O_{X,p}$ is a uniformizer parameter. Moreover we can choose $\pi=(t_1-p_1,\ldots,t_n-p_n)$ where $p=(p_1,\ldots,p_n)$ and $t_i:= I(X)+T_i\in \mathcal O_X(X)$.

Edit: Note that when $k$ is not algebraically closed we have the Laurent expansion only for the $k$-rational points.

By summarizing, for every element of $f\in \widehat {k(X)}$ we find the Laurent expansion of $f$ around $p$, so I would say that:

$\widehat {k(X)}$ is "the algebraic equivalent" of the field of meromorphic functions, and not $k(X)$.

Is my reasoning right? Why is this process of completion not always mentioned?

• Every closed point of $X$ gives rise to a discrete valuation of the function field. How can you choose one which you want to call the algebraic equivalent of the field of meromorphic functions on a Riemann surface? Also, when you say $\mathscr{O}_{X,p}$ is a "discrete valuation field," you mean "discrete valuation ring." – Keenan Kidwell Jan 27 '16 at 23:33
• Yes of course I mean d.v. ring. – Dubious Jan 27 '16 at 23:34
• Moreover: you are right! For every (closed) point I have a discrete valuation so for every Laurent expansion I have to chance valuation. On the other hand, note that $k(X)=\text{Frac}(\mathcal O_X(X))$ , and on compact Rieman surfaces the field of meromorphic functions is not the field of fractions of holomorphic functions. So, I continue to believe that the analogy is wrong. – Dubious Jan 27 '16 at 23:42
• Dear @Dubious, I'm not sure what you're looking for with this question. It doesn't really have an answer. You are correct that you can complete $k(X)$ with respect to the discrete valuation corresponding to a closed point, and you get Laurent series expansions, etc.. Perhaps people regard $k(X)$ as "more algebraic" than something obtained via a completion process (particularly one which depends on a choice of closed point). – Keenan Kidwell Jan 27 '16 at 23:51
• Yes, there is not a complete answer for this question. Anyone is free to define his own meromorphic functions. I'm only trying to see which are the most natural analogies between the world of manifolds and the world of algebraic varieties. This site contains plenty of people that generally are able to give very inspiring hints, so that's the reason of my "question". – Dubious Jan 27 '16 at 23:55

I don't follow your reasoning. The classical sense in which $k(X)$ is analogous to meromorphic functions on a Riemann surface is that when $k = \mathbb{C}$ it is literally meromorphic functions on a Riemann surface. The completion you describe is completely different: it's a completion of germs of meromorphic functions at a particular point, whereas meromorphic functions should have Laurent series expansions everywhere, not just at a particular point.


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# Question about proof of Arzelà-Ascoli

(Arzelà-Ascoli, $\Longleftarrow$) Let $K$ be a compact metric space. Let $S \subset (C(K), \|\cdot\|_\infty)$ be closed, bounded and equicontinuous. Then $S$ is compact, that is, for a sequence $f_n$ in $S$ we can find a convergent subsequence (conv. in $\|\cdot\|_\infty)$.

Proof: Note that a compact metric space is separable. Let $D$ be a dense, countable subset of $K$. By assumption, $S$ is bounded, hence there exists $M$, such that $\|f\|_\infty \leq M$ for all $f$ in $S$, in particular, for $f_n$.

Now consider the space of all functions from $D$ to $[-M,M]$. By Tychonoff, $[-M,M]^D$ is compact. Define $g_n = f_n\mid_D$. Then $g_n$ is a sequence in $[-M,M]^D$, hence has a convergent subsequence $g_{n_k}$.

This is what it says in my notes. Now I've been thinking about what exactly "convergent" means in the last sentence. I'm quite sure it means pointwise. But theoretically, I can endow $[-M,M]^D$ with a norm or metric (that induces the product topology). So "convergent" could mean convergent with respect to that metric, no? Or does that not make sense?

-
You even need a metric to conclude a convergent subsequence. And the metric $e$ for the product topology is obvious as $D$ is countable, i.e. $e(f,g) = \sum_{d\in D} |f(d)-g(d)|$. –  Vobo Jul 12 '12 at 16:31
Ooh, of course. Thank you! Why don't you post it as an answer, then I can upvote and accept. –  Rudy the Reindeer Jul 12 '12 at 16:35
@Vobo How do we know $\sum_{d\in D} |f(d)-g(d)| < \infty$? –  Rudy the Reindeer Jul 12 '12 at 16:36
I forgot the converging factor, see the answer below. –  Vobo Jul 12 '12 at 16:42
I am quite sure that if you read the rest of the proof in your notes, the answer to your question will be become clear. –  wildildildlife Jul 12 '12 at 18:44

You even need a metric to conclude a convergent sub*sequence*. And the metric d for the product topology is obvious for e.g. $D=\{ x_n| n\in N\}$, i.e. \begin{align} d(f,g)=\sum_{n=1}^\infty 2^{-n}|f(x_n)−g(x_n)|. \end{align}
For this to be finite, each term in the sum would have to be at least smaller than $1$, that is, $|f(d) - g(d)| < 2^n$. Why do we know that this is the case? –  Rudy the Reindeer Jul 12 '12 at 16:48
You just need a uniform bound. Since $S$ is bounded, this is true. –  copper.hat Jul 12 '12 at 16:51
You don’t actually need a metric to conclude that there’s a convergent subsequence: first countability is sufficient. Of course you have a metric, so you might as well use it! @Matt: $|f(x_n)-g(x_n)|\le 2M$ for each $n$, so $d(f,g)\le 2M$. –  Brian M. Scott Jul 12 '12 at 20:40


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# Exam P Practice Problem 94 – Tracking High School Students

Problem 94-A

A researcher tracked a group of 900 high school students taking standardized tests in math and chemistry. Some of the students were given after-school tutoring before the tests (in both subjects) and the rest of the students received no tutoring. The following information is known about the test results:

• 510 of the students passed math test and 475 of the students passed chemistry test.
• Of the students who failed both subjects, there were 20% more students who did not receive tutoring than there were students who received tutoring.
• Of the students who failed chemistry and had tutoring, there were 99 more students who failed math than there were students who passed math.
• Of the students who failed chemistry and had no tutoring, there were 4 more students who failed math than there were students who passed math.
• There were 126 students who failed math and passed chemistry.

Determine the probability that a randomly selected student from this group had tutoring given that the student passed both subjects.

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.6810$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.6828$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.6859$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.6877$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.6989$

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Problem 94-B

An insurance company tracked a group of 800 insureds for 2 years. It was found that 560 of the insureds had no claims in year 1 and 380 of the insureds had no claims in year 2. Of the insureds who had no claims in both years, there were four times as many male insureds than there were female insureds. Furthermore, there were 230 male insureds who had no claims in year 2 and there were 53 females insureds who had claims in both years. It is also known that there were 85 male insureds who had claims in year 1.

Determine the number of insureds who had no claims in year 1 but had claims in year 2.

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 320$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 347$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 369$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 420$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 560$

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$\copyright \ 2016 \ \ \text{ Dan Ma}$

# Exam P Practice Problem 91 – Reviewing a Group of Policyholders

Problem 91-A

A life insurance actuary reviewed a group of policyholders whose policies or contracts were inforce as of last year. The actuary found that 12% of the policyholders who had only a life insurance policy did not survive to this year and that 7.5% of the policyholders who had only an annuity contract did not survive to this year. The actuary also found that 5.9% of the policyholders who had both a life insurance policy and an annuity contract did not survive to this year.

In this group of policyholders, 65% of the policyholders had a life insurance policy and 57% of the policyholders had an annuity contract. Furthermore, each policyholder in this group either had a life insurance policy or an annuity contract.

What is the percentage of the policyholders that did not survive to this year?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 7.8 \%$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 9.0 \%$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 12.0 \%$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 13.4 \%$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 25.4 \%$

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Problem 91-B

A sport coach in a university tracks a group of athletes. The coach finds that 36% of the athletes who play soccer only are first year university students and that 20% of the athletes who are involved only in track and field are first year university students. The coach also discovers that 27% of the athletes participates in both soccer and track and field are first year university students.

According to university records, 45% of the athletes in this group play soccer and 68% of the athletes in this group participate in track and field. Each of the athletes in this group either plays soccer or participates in track and field.

Out of this group of athletes, what is the percentage of the athletes that are not first year university students?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 64 \%$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 67 \%$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 70 \%$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 74 \%$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 80 \%$

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$\copyright \ 2014 \ \ \text{ Dan Ma}$

# Exam P Practice Problem 85 – Supplemental Coverages for Employees

Problem 85-A

A large employer offers three supplemental benefits in addition to the major medical benefit – dental, vision and group life insurance – to its employees. The following information is known.

• Thirty five percent of the employees choose dental and vision.
• Twelve percent of the employees choose all three supplemental benefits.
• Fifty six percent of the employees choose exactly two of the three supplemental benefits.
• Sixteen percent of the employees choose neither vision nor dental.
• Five percent of the employees choose none of the three supplemental benefits.

One employee is chosen at random. What is the probability that this employee has group life insurance benefit?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.32$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.56$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.63$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.65$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.68$

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Problem 85-B

A professor tracks a group of students taking astrophysics, biostatistics and chemistry. The following information is known.

• Forty five percent of the students pass astrophysics and biostatistics.
• Nineteen percent of the students pass biostatistics and chemistry only.
• Twenty two percent of the students pass neither biostatistics nor chemistry.
• Sixty seven percent of the students pass biostatistics.
• Thirty four percent of the students pass astrophysics and biostatistics only.

One student is chosen at random. What is the probability that this student passes chemistry?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.35$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.40$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.41$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.47$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.53$

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$\copyright \ 2014 \ \ \text{ Dan Ma}$

# Exam P Practice Problem 81 – A Medical Survey

Problem 81-A

A medical researcher tracked a group of 10,000 patients with heart disease and diabetes. The researcher found that sixty five percent of these patients have health insurance coverage. She also found that thirty percent and twenty percent of the patients with health insurance coverage have heart disease and diabetes, respectively. Of the patients with health insurance coverage, ten percent have both heart disease and diabetes. Furthermore, the medical researcher found that forty percent and twenty five percent of the patients with no health insurance coverage have heart disease and diabetes, respectively. Twenty percent of the patients with no health insurance coverage have both heart disease and diabetes.

What is the number of patients that have neither heart disease nor diabetes?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 1500$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 2600$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 4175$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 5825$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 8500$

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Problem 81-B

A large high school offers three sporting activities – swimming, running and basketball. Thirty percent of the students participate in swimming. Of the students participating in swimming, fifty percent participate in running, thirty percent participate in basketball and five percent participate in both running and basketball. Of the students not participating in swimming, twenty percent participate in running, forty percent participate in basketball and ten percent participate in both running and basketball.

What is the percentage of the students that participate in exactly two of the sports?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 10 \%$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 22.5 \%$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 28 \%$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 35 \%$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 57.5 \%$

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# Exam P Practice Problem 78 – Tracking A Group of Insureds

Problem 78-A

An insurance company tracked a group of 625 insureds for 2 years. It was found that 370 of the insureds had no claims in year 1 and 395 of the insureds had no claims in year 2. Furthermore, there were five times as many insureds who had no claims in both years than there were insureds who had claims in both years.

Select an insured at random from this group. What is the probability that the randomly selected insured had no claims in both years?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.23$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.28$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.34$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.44$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.47$

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Problem 78-B

An insurance company tracked a group of 1000 insureds for 2 years. It was found that 550 of the insureds had no claims in year 1 and 680 of the insureds had at least one claim in year 2. Of the insureds who had at least one claim in year 1, 306 insureds had at least one claim in year 2.

Select an insured at random from this group. Given that this insured had no claims in year 1, what is the probability that the selected insured had no claims in year 2?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.176$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.230$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.320$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.418$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.764$

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$\copyright \ 2013 \ \ \text{Dan Ma}$


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# How to scroll up and down in EFI shell

efiscrollingshelluefi

When you boot in UEFI mode, you can be loaded to EFI shell.
In EFI shell you can type help -b to see available commands by paging them as in more command. But I do not know how to scroll back up. I cannot make a screenshot, because it is a real machine. And I always run command again to output information that was slided up.
So is there a possibility to scroll up in EFI shell?


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# Polynomial-time reduction

Jump to: navigation, search

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine. There are several different types of polynomial-time reduction, depending on the details of how the subroutine is used. Intuitively, a polynomial-time reduction proves that the first problem is no more difficult than the second one, because whenever an efficient algorithm exists for the second problem, one exists for the first problem as well. Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes.

## Types of reduction

The three most common types of polynomial-time reduction, from the most to the least restrictive, are polynomial-time many-one reductions, truth-table reductions, and Turing reductions.

• A polynomial-time many-one reduction from a problem A to a problem B (both of which are usually required to be decision problems) is a polynomial-time algorithm for transforming inputs to problem A into inputs to problem B, such that the transformed problem has the same output as the original problem. An instance x of problem A can be solved by applying this transformation to produce an instance y of problem B, giving y as the input to an algorithm for problem B, and returning its output. Polynomial-time many-one reductions may also be known as polynomial transformations or Karp reductions, named after Richard Karp. A reduction of this type may be denoted by the expression ${\displaystyle A\leq _{m}^{P}B}$.[1]
• A polynomial-time truth-table reduction from a problem A to a problem B (both decision problems) is a polynomial time algorithm for transforming inputs to problem A into a fixed number of inputs to problem B, such that the output for the original problem can be expressed as a function of the outputs for B. The function that maps outputs for B into the output for A must be the same for all inputs, so that it can be expressed by a truth table. A reduction of this type may be denoted by the expression ${\displaystyle A\leq _{tt}^{P}B}$.[2]
• A polynomial-time Turing reduction from a problem A to a problem B is an algorithm that solves problem A using a polynomial number of calls to a subroutine for problem B, and polynomial time outside of those subroutine calls. Polynomial-time Turing reductions are also known as Cook reductions, named after Stephen Cook. A reduction of this type may be denoted by the expression ${\displaystyle A\leq _{T}^{P}B}$.[1]

The most frequently used of these are the many-one reductions, and in some cases the phrase "polynomial-time reduction" may be used to mean a polynomial-time many-one reduction.[3]

## Completeness

A complete problem for a given complexity class C and reduction ≤ is a problem P that belongs to C, such that every problem A in C has a reduction A ≤ P. For instance, a problem is NP-complete if it belongs to NP and all problems in NP have polynomial-time many-one reductions to it. A problem that belongs to NP can be proven to be NP-complete by finding a single polynomial-time many-one reduction to it from a known NP-complete problem.[4] Polynomial-time many-one reductions have been used to define complete problems for other complexity classes, including the PSPACE-complete languages and EXPTIME-complete languages.[5]

Every decision problem in P (the class of polynomial-time decision problems) may be reduced to every other nontrivial decision problem (where nontrivial means that not every input has the same output), by a polynomial-time many-one reduction. To transform an instance of problem A to B, solve A in polynomial time, and then use the solution to choose one of two instances of problem B with different answers. Therefore, for complexity classes within P such as L, NL, NC, and P itself, polynomial-time reductions cannot be used to define complete languages: if they were used in this way, every nontrivial problem in P would be complete. Instead, weaker reductions such as log-space reductions or NC reductions are used for defining classes of complete problems for these classes, such as the P-complete problems.[6]

## Defining complexity classes

The definitions of the complexity classes NP, PSPACE, and EXPTIME do not involve reductions: reductions come into their study only in the definition of complete languages for these classes. However, in some cases a complexity class may be defined by reductions. If C is any decision problem, then one can define a complexity class C consisting of the languages A for which ${\displaystyle A\leq _{m}^{P}C}$. In this case, C will automatically be complete for C, but C may have other complete problems as well.

An example of this is the complexity class ${\displaystyle \exists \mathbb {R} }$ defined from the existential theory of the reals, a computational problem that is known to be NP-hard and in PSPACE, but is not known to be complete for NP, PSPACE, or any language in the polynomial hierarchy. ${\displaystyle \exists \mathbb {R} }$ is the set of problems having a polynomial-time many-one reduction to the existential theory of the reals; it has several other complete problems such as determining the rectilinear crossing number of an undirected graph. Each problem in ${\displaystyle \exists \mathbb {R} }$ inherits the property of belonging to PSPACE, and each ${\displaystyle \exists \mathbb {R} }$-complete problem is NP-hard.[7]

Similarly, the complexity class GI consists of the problems that can be reduced to the graph isomorphism problem. Since graph isomorphism is known to belong both to NP and co-AM, the same is true for every problem in this class. A problem is GI-complete if it is complete for this class; the graph isomorphism problem itself is GI-complete, as are several other related problems.[8]

## References

1. ^ a b Goldreich, Oded (2008), Computational Complexity: A Conceptual Perspective, Cambridge University Press, pp. 59–60, ISBN 9781139472746.
2. ^ Buss, S.R.; Hay, L. (1988), "On truth-table reducibility to SAT and the difference hierarchy over NP", Proceedings of Third Annual Structure in Complexity Theory Conference, pp. 224–233, doi:10.1109/SCT.1988.5282.
3. ^ Wegener, Ingo (2005), Complexity Theory: Exploring the Limits of Efficient Algorithms, Springer, p. 60, ISBN 9783540274773.
4. ^ Garey, Michael R.; Johnson, D. S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman.
5. ^ Aho, A. V. (2011), "Complexity theory", in Blum, E. K.; Aho, A. V., Computer Science: The Hardware, Software and Heart of It, pp. 241–267, doi:10.1007/978-1-4614-1168-0_12. See in particular p. 255.
6. ^ Greenlaw, Raymond; Hoover, James; Ruzzo, Walter (1995), Limits To Parallel computation; P-Completeness Theory, ISBN 0-19-508591-4. In particular, for the argument that every nontrivial problem in P has a polynomial-time many-one reduction to every other nontrivial problem, see p. 48.
7. ^ Schaefer, Marcus (2010), "Complexity of some geometric and topological problems" (PDF), Graph Drawing, 17th International Symposium, GS 2009, Chicago, IL, USA, September 2009, Revised Papers, Lecture Notes in Computer Science, 5849, Springer-Verlag, pp. 334–344, doi:10.1007/978-3-642-11805-0_32.
8. ^ Köbler, Johannes; Schöning, Uwe; Torán, Jacobo (1993), The Graph Isomorphism Problem: Its Structural Complexity, Birkhäuser, ISBN 978-0-8176-3680-7, OCLC 246882287.


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# Updating a 1980s circuit board design

#### metermannd

Joined Oct 25, 2020
83
So here's what I've sketched up as far as the Arduino setup goes.

Top part has the Arduino setup as I see it.
The bottom left I need to figure how much I still need in regards to buffering and pull-ups - this is where the address / data / control lines came into the add-on board.
The bottom right is that part that I've decided needs to stay (UUT interface).
The portion to the right of the line is the remnants of the glue logic broken down and ready to translate into Arduino code.

I've also worked out how the 4x20 LCD would be laid out:

Code:
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TEST: XX   LD A:____
XXXXXXXX   LD B:____
STAT:____  LD C:____
INSTALL    LD D:____
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TEST replaces the left 2 7-segment displays [4514: Q9, Q8]
XXXXXXXX is the keypad input line (7 digits + checksum) [4514: Q7-Q0]
STAT replaces the Go / No-Go LED pair [4514: Q15]
INSTALL only displays (flashes) when invoked / replaces the INSTALLING LED [4514: Q14]
LD A through LD D replace the corresponding LED pair [4514: Q10-Q13]

Cathodes driven by 7-segment driver and from B port / blanking line on 8279
Anodes driven by 4514 driven by SL port on 8279

Each instance of ____ is blank when the LED pair is off, PASS for green, NOGO for red
LED segment A drives anodes for PASS (green) LEDs
LED segment G drives anodes for NOGO LEDs and INSTALLING LED

Or is that too complex? Will post same over on the Arduino forum shortly.

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• 156.1 KB Views: 3

#### metermannd

Joined Oct 25, 2020
83
After further conversation with the folks at the Arduino board, I may have overestimated the feasibility and underestimated the complexity. Putting this on the back burner for the time being.

#### nsaspook

Joined Aug 27, 2009
7,869

#### metermannd

Joined Oct 25, 2020
83
Well, long story short, given that I was able to get a NOS 8279 controller IC, and after discussion on the Arduino forum as to whether what I wanted was even possible, for the moment, I am continuing with cleaning up the existing design to accommodate IC availability.

On that front, I've already made a few tweaks to the existing design by switching out the RAM (replacing the 6561s with a 6116), moving the 8279 from the display to the logic board, making a decision on the unit's testing range (eliminating one option that was very rare even when new, also simplifying the design a bit), and found drop-in substitutes for the old MAN74A displays and UDN2981A driver.

Now, I have a bit of a hiccup with the 7-segment circuitry. I found the MC14547 BCD/7-segment driver was obsolete, and have temporarily subbed in the trusty 74LS47 driver, but would like to know if there are other options (I checked into the Fairchild DM9368 but that's evidently obsolete too).

The last IC I'm having issues with is the MC14514 - this is still available but getting scarce. Do you think I should stick with it, or should I replace it with a pair of still common 74xx ICs - the 74LS154 4-16 decoder and 74LS375 latch?

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• 87.3 KB Views: 3
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#### metermannd

Joined Oct 25, 2020
83
I have mostly finished working up a new design with replacements for a few obsolete parts, and removal of a couple sections that realistically have no chance of being used.

Looking at the feasibility of retooling the display to run on 5V only.

Also, I'm wondering about the best way to bring 5V / ground into this board.

On the original board, power and ground are brought in by way of a pair of DIP jumper cables (the cables that take place of the NVRAM ICs on the logic board)... is this an ideal approach, or should I be looking at bringing in a dedicated feed directly from the power board? Given that two DIP jumper cables were sufficient, would a 2-pin, .100" pitch connector be sufficient, or would I need to bump up to a .156" pitch connector?

If I opt for a dedicated power harness, would I be correct in assuming I would have to remove the power / ground connections from the incoming DIP sockets?


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2020 Christmas Public Art Installation "Hearts as One" on view 12/4~1/31!

# net profit ratio formula

#### Posted on January 12th, 2021

Formula. Profit is the amount of money a company makes after deducting expenses. There are various types of Profitability ratios. Dear accountant, Formula: Gross Profit Ratio = Gross Profit/ Net sales. Both the components of the formula (i.e., net profit and net sales) are usually available from trading and profit and loss account or income statement. Formula to Calculate Operating Profit Ratio Note – It is represented as a percentage so it is multiplied by 100. #2 â Net Profit Margin Ratio. The term “financial efficiency” refers to how effectively a business or farm is able to generate income. Also known as Net Profit Margin ratio, it establishes a relationship between net profit earned and net revenue generated from operations (net sales).Net profit ratio is a profitability ratio which is expressed as a percentage hence it is multiplied by 100. (NP ratio taken together with the return on equity (ROE) ratio, shows how well the company marks up its goods for sale and how well it manages to contain its indirect expenses within the gross profit margin. Net profit (NP) ratio is a useful tool to measure the overall profitability of the business. A 15% net profit ratio reveals that business has earned a net profit of $0.15 for every dollar sales revenue. The benefit margin formula is used to calculate how much benefit a product or business is. Therefore, this calculation gives an accurate account of a company's overall ability to convert its income into a profit. This shows the percentage the profit â¦ There is no norm to interpret this ratio. Both the components of the formula (i.e., net profit and net sales) are usually available from trading and profit and loss account or income statement. Banks have different format of b/s & p&l a/c… Operating Profit ratio helps to find out Operating Profit earned in comparison to revenue earned from operations. It explains in detail. Through the comparison of the net income and net sales of a company, creditors, investors, and management can use the profit margin ratio to see how effectively a company converts sales into net income. The trick is this: there are many kinds of profit, but only net profit equals income.$960,000 Net sales) x 100 = 3.4% Net profit ratio. The profit margin ratio determines what percentage of a company's sales consists of net income. The que. Net profit margin is an important profitability ratio which measures the profit of the company over total sales for a particular period and it is stated in percentage (%). The Profit to Sales Ratio calculation formula is as follows: Profit to Sales Ratio … Why closing stock is deducted from net sales. Arup did you read the whole article? This approach is most commonly found in a privately held business, where there is no need to impress outside investors with the results of operations. Net Profit = Operating Income – (Direct Costs + Indirect Costs) Net Sales = (Cash Sales + Credit Sales) – Sales Returns Is it applied to all kind of business sectors? It is a popular tool to evaluate the operational performance of the business . =21.74%, crushing tonnes expenses how to find percentage expenses, how to calculate total expenses percentage how to find it. In such cases, it may be a mistake to assume that a company is doing poorly, when in fact it may own the bulk of the market share precisely because of its low margins. It shows the amount of each sales dollar left over after all expenses have been paid. with its sales. Expressed as a percentage, the net profit margin shows how â¦ Net profit margin (or profit margin, net margin, return on revenue) is a ratio of profitability calculated as after-tax net income (net profits) divided by sales (revenue). To calculate Pretax Profit margin, we need Pretax Profit; Net Sales; Let us find both the values and calculate the ratio. If you have established industry benchmarks and strong knowledge of your competitors, … The net profit margin is a ratio that compares a company's profits to the total amount of money it brings in. sir i have a question related to the ratio analysis.. the following info is given on a question, we have to find out net profit ratio as before tax, Sales – sales tax Is Net profit margin calculator measures company's profitability or how much of each dollar earned by the company is translated into net profits.Net profit margin formula is:. Net Profit Ratio = Net Operating Profit / Net Sales x 100. or. Explanations, Exercises, Problems and Calculators, Financial statement analysis (explanations). The higher the net profit margin, the more money a company keeps. From year to year, or even month to month, profits will change. Higher the net profit ratio, higher is the profitability of the business. The net profit is calculated after considering all the operating and non-operating incomes and expenses of the business. Cautions & Further Explanation. Higher the P/V ratio, more will be the profit and lower the P/V ratio, lesser will be the profit. It is computed by dividing the net profit (after tax) by net sales. Another issue with the net profit margin is that a company may intentionally keep it low in accordance with a low-pricing strategy that aims to grab market share in exchange for low profitability. The net profit margin is the ratio of net profits to revenues for a company or business segment. The profit margin ratio compares profit to sales and tells you how well the company is handling its finances overall. Examples of non-operating expenses include interest on loan and loss on sale of assets. Cautions & Further Explanation. how to calculate the 1)Gross Profit Ratio 2) Net Profit Ratio and 3)Fixed assets turnover ratio ? The profit margin formula simply takes the formula for profit and divides it by the revenue. Net income ÷ total sales = net profit margin Net profit margin is displayed as a percentage. Net Margin can be calculated using the above formula as, Net Profit Margin ratio = $200,000 /$ 2,000,000 x 100; Net Profit Margin Ratio will be â Net Profit Margin Ratio = 10%; The ratios calculated above shows strong gross, operating, and net profit margins. is interest on debentures to be deducted on gross profit? Also, a company may delay a variety of discretionary expenses, such as maintenance, to make its net profit ratio look better than it normally is. Your net profit margin shows what percentage of your sales is actual profit. It’s a ratio of net income relative to revenue. Higher net profit margin indicates that entity was able to cover all of its expenses and still left with portion of revenue which is in excess of total expenses. Hii, i have a que. Net profit margin is a financial ratio that compares a company's net profit after taxes to revenue. Definition of net profit ratio: Net profit ratio is the ratio of net profit (after taxes) to net sales.It is expressed as percentage. Profit to Sales Ratio Definition. It measures the amount of net profit a company obtains per dollar of revenue gained. Let see all those ratios one by one : Profit Margin Ratios: These ratios compare various profits of the business (gross profit, operating profit, net profit, etc.) Net profit margin=profit for the year(less preference share dividend) /sales. For the purpose of this ratio, net profit is equal to gross profit minus operating expenses and income tax. Net profit margin is used to compare profitability of … Intrest paid =700. what would you say is a reason for one company having net profit greater than the other, How to calculate net profit ratio of banks?? The net profit margin percentage is a related ratio. It is also known as net profit margin, net profit ratio or net margin in business terms. Net profit margin (also called profit margin) is the most basic profitability ratio that measures the percentage of net income of an entity to its net sales. Now, when the gross profit ratio is explained in form of percentage, the ratio is multiplied by hundred so as to arrive percentage and it is signified as gross profit percentage or gross profit margin. Net Profit Ratio. What should be the action if the NP ration is lower than the previous year? The net worth ratio is used to analyze the effectiveness of a company's utilization of shareholder investment to create a positive return on the investment. Net profit margin is typically expressed as a percentage but can also be represented in decimal form. The formula is: (Net income ÷ Net … Intrest received =1200. Examples of non-operating revenues include interest on investments and income from sale of fixed assets. The net profit ratio is really a short-term measurement, because it does not reveal a company's actions to maintain profitability over the long term, as may be indicated by the level of capital investment or expenditures for advertising, training, or research and development. The ratio is computed by dividing the gross profit figure by net sales. The net profit margin turns the net profit (or bottom line) into a percentage. Put simply, it provides a measurement of how much profits are generated from a company's sales. How to it will be calculate ??? Net Profit Margin (also known as “Profit Margin” or “Net Profit Margin Ratio”) is a financial ratio used to calculate the percentage of profit a company produces from its total revenue. Net Profit Ratio. Net profit ratio =10% on sales. For the year ended on 31st march 2013 In the above example, for every Rs. This ratio indicates the efficiency of management on Manufacturing, Administrative, Selling and other business activities. Is net profit ratio calculated on net profit (after tax)/net sales*100. â¦ The net worth ratio is used to analyze the effectiveness of a company's utilization of shareholder investment to create a positive return on the investment. Using this, along with the bank's $23 billion in net income shows a ROE of 12.1%. Gross margin: gross profit÷ revenue % ... Net profit margin The net profit margin ratio is the percentage of a business's revenue left after deducting all expenses from total sales, divided by net revenue. To obtain the net profit percentage, the net profit is divided by the value of sales and both these items are taken from the income statement of the business. Net profit margin is displayed as a percentage. The NPM ratio does tend to lend itself to some creative accounting practices where the formula figures are concerned.. It is probably the most important margin used by businesses to know the total profit percentage over a period of time. Show your love for us by sharing our contents. The benefit margin formula is used to calculate how much benefit a product or business is. Rather, it is better to compare the net income ratio with similar businesses, regarding size, shape, scope, and model. The profit margin ratio formula can be calculated by dividing net income by net sales.Net sales is calculated by subtracting any returns or refunds from gross sales. companies to provide useful insights into the financial well-being and performance of the business Net Income Ratio Formula. Depending on what amounts a business chooses to include or exclude as part of its net income, it can effectively skew its final profit margin ratio result so that it appears higher, … The net profit margin is equal to how much net income or profit is generated as a percentage of revenue. Return on capital employed (ROCE): operating profit ÷ (non-current liabilities + total equity) % 2. Plz solve this. Net Profit Ratio = Net Profit after Tax / Net Sales x 100. or. Your formula is correct. =$4,600,000, Np ratio = ($1000,000/$4,600,000)*100 the Operating Profit before interest and taxes. It shows the amount of each sales dollar left over after all expenses have been paid. If net profit is less than the previous year what will be the suggestion given to the company. Conversely, the reverse strategy may result in a very high net profit ratio, but at the cost of only capturing a small market niche. How would you interpret the results and what could be the possible cause? It represents the proportion of sales that is left over after all relevant expenses have been adjusted. Thus, this ratio relates revenue from operations of a business to its net profit. This number is useful for determining how well an organization's finances are being managed. Net profit margin is used to compare profitability of competitors in the same industry. If the net profit margin is lower than previous year, what should be the suggestion to the company? I want to use your website for studying purpose. It is one of the simplest profitability ratios as it defines that the profit is all the income which remains after deducting only the cost of the goods sold (COGS). III. It represents the proportion of sales that is left over after all relevant expenses have been adjusted. Net profit margin is displayed as a percentage. (NP ratio taken together with the return on equity (ROE) ratio, shows how well the company marks up its goods for sale and how well it manages to contain its indirect expenses within the gross profit … All non-operating revenues and expenses are not taken into account because the purpose of this ratio is to evaluate the profitability of the business from its primary operations. It shows the percentage of Net Profit earned on Revenue from Operations. An equation for net â¦ It shows the amount of each sales dollar left over after all expenses have been paid. It's always expressed as a percentage. if total net loss is 2,613,360 and total sales is 8,033,786. Return on assets = net income ÷ total average assets for the period (it can also be calculated as net profit margin X asset turnover) Formulas for Both Balance Sheets and Income Statements When you can analyze both an income statement and a balance sheet side-by-side, you can calculate several additional financial ratios. All non-operating revenues and expenses are not taken into account because the purpose of this ratio is to evaluate the profitability of the business from its primary operations. Then, the net profit margin is calculated by dividing the net profit by the sales revenue and is expressed in terms of percentage. The Analysis of Financial Performance on Net Profit Margin at the Coal Company 107 H1: Current ratio positively affects the net profit margin H2: Leverage positively affects the net profit margin H3: Sales growth positively affects the net profit margin. Pretax Profit = Sales â (All expenses except Taxes). Cost of good sold = 60,000 . Itâs a ratio of net income relative to revenue. To calculate profit growth, analysts use a percent-change formula. The net profit ratio is also known as the profit margin. Plugging this information into our net profit margin formula, we get: $97,500 net profit ÷$500,000 revenue = 0.195 net profit margin, or 19.5%; Three ratios are commonly used. The NPM ratio does tend to lend itself to some creative accounting practices where the formula figures are concerned.. Net profit margin (or profit margin, net margin, return on revenue) is a ratio of profitability calculated as after-tax net income (net profits) divided by sales (revenue).Net profit margin is displayed as a percentage. Depending on what amounts a business chooses to include or exclude as part of its net income, it can effectively skew its final profit margin ratio result so that it appears higher, and more impressive, than it actually is. In business, Profit to Sales Ratio is the ratio of net profit divided by net sales for the period, usually expressed as a percentage. Then, the net profit margin is Operating Profit = Net profit before taxes + Non-operating expenses – Non-operating incomes Gross profit ratio (GP ratio) is a profitability ratio that shows the relationship between gross profit and total net sales revenue. Thus, incomes such as interest on investments outside the business, profit on sales of fixed assets and losses on sales of fixed assets, etc are excluded. This is after factoring in your cost of goods sold, operating costs and taxes. 25 is made towards meeting the fixed expenses and then the profit comparison for P/V ratios can be made to find out which product, department or process is more profitable. Required: Compute net profit ratio of Albari corporation using above information. Net profit margin also called net profit ratio or simply profit margin determines net profit generated by each dollar of revenue earned during the period. So, how is net income ratio calculated? Net income can also be calculated by adding a company's operating income to non-operating income and then subtracting off taxes. The net profit margin formula is calculated by dividing net income by total sales.Net Profit Margin = Net Profit / Total RevenueThis is a pretty simple equation with no real hidden numbers to calculate. 1  It measures how effectively a company operates. Net Profit Ratio = (Net Profit/Net â¦ PBT vs. EBIT. general decline i guess , since an increase is generally looked at as positive growth. answer asap, Copyright 2012 - 2020. Another strategy that can artificially drive down the ratio is when a company's owners want to minimize income taxes, and so accelerate the recognition of taxable expenses into the current reporting period. Both of these figures are listed on the face of the income statement: one on the top and one on the bottom.Total revenue or total sales includes all the money a company earned from its operations during the perio… if the net profit ratio is lower than previous year,what should be the suggestion to the company? 100 sales, Contribution of Rs. The use of net profit ratio in conjunction with the assets turnover ratio helps in ascertaining how profitably the assets have been used during the period. From another angle: net income equals net profit, but net income doesnât equal profit, in general . You can calculate it using the income statement. Net profit margin is one of the profitability ratios and an important tool for financial analysis.It is the final output, any business is looking out for. Net sales include both Cash and Credit Sales, on the other hand, Operating Profit is the net operating profit i.e. NET PROFIT RATIO=NET PROFIT AFTER TAX/REVENUE FROM OPERATIONS (NET SALES)* 100. Calculate the net profit earned during the year. Please comment. 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This figure is calculated by dividing net profit by revenue or turnover, and it represents profitability, as a percentage. $5000,000 –$400,000(8% of gross sales) There are two main reasons ]why net profit margin is useful: Now the company was came netloss All the efforts and decision making in the business is to achieve a higher net profit margin with an increase in net profits. It is probably the most important margin used by businesses to know the total profit percentage over a period of time. What does a net loss percentage ratio means? However, unlike the previous two ratios, the net profit margin ratio also takes into account income from investments, one-time payments, taxes and debt. Please explain. It shows the amount of each sales dollar left over after all expenses have been paid. how to calculte net profit ratii if there is loss in the company? The profit margin is a ratio of a company's profit (sales minus all expenses) divided by its revenue. what if there was a net loss instead of a profit, how do you calculate for that? The net profit, which is also called profit after tax , is calculated by deducting all the direct and indirect expenses from the sales revenue. How to Calculate Net Profit Margin For example, the net profit margin from Company Z would be $30,000/$100,000 = 30%. The net profit margin is a ratio formula that compares a business's profits to its total expenses. Banks do not make sales, their revenues include interest on loans, discount on bills and commission etc. Definition. Why are we dividing net income to sales????? Net profit margin (or profit margin, net margin) is a ratio of profitability calculated as after-tax net income (net profits) divided by sales (revenue). The net profit margin is the ratio of net profits to revenues for a company or business segment. Comparing net income of two different periods or two different companies using the dollar values can sometimes be inappropriate because of size differences. The formula for the net profit ratio is to divide net profit by net sales, and then multiply by 100. Formula: For the purpose of this ratio, net profit is equal to gross profit minus operating expenses and income tax. If a company has a 20% net profit margin, for example, that means that it keeps $0.20 for every$1 in sales revenue. Gross Profit Ratio = (Gross Profit/ Net Sales) x 100 To find out what your net income ratio is, divide net profit or net income by net sales, and then multiply by 100. Net profit margin (also known as âreturn on salesâ) is a profitability ratio that measures the percentage of net income to sales. The formula of net profit margin is written as follows: The following data has been extracted from income statement of Albari corporation. To calculate your net profit margin, divide your net income by your total sales revenue. The ratio is computed by dividing the gross profit figure by net sales. Net profit ratio is a ratio of net profits after taxes to the net sales of a firm. The Net Income Ratio measures how effective your organization is at generating profit on each dollar of earned premium. Formula: When it is shown in percentage form, it is known as net profit margin. Net Profit Margin. Eg. Consequently, you should evaluate the net profit ratio alongside a variety of other metrics to gain a full picture of a company's ability to continue as a going concern. Thanks in advance for your assistance. Banking companies have a different format of their profit and loss account /income statement. For investors, this is a way to see that profits are high enough to generate a return for them, while creditors will also want to see that profits are high enough for the company to repay its debt. Net income and net profit mean the same thing â but many new businesspeople find this equivalency confusing. Can you explain more about if I owned 5 star homes regarding to the net profit ratio? Net profit margin is the ratio of net profits to revenues for a company or business segment. By using the formula we can see that Net Profit = 100,000 - 20,000 - 30,000 - 10,000 - 10,000 = $30,000 Net Profit vs. Net Profit Margin Net profit margin tells you how much of a company’s revenue translates to profit after expenses are paid. The ratio is determined by a formula that divides net profit after taxes by shareholder investment plus retained earnings. The ratio is determined by a formula that divides net profit after taxes by shareholder investment plus retained earnings. The following formulae are used to calculate net profit ratio. Example of Net Profit Margin Formula Let’s understand the calculation of net profit margin by an example. Profit before taxes and earnings before interest and tax (EBIT) EBIT Guide EBIT stands for Earnings Before Interest and Taxes and is one of the last subtotals in the income statement before net income. The Profit to Sales Ratio Calculator is used to calculate the profit to sales ratio. It is also known as net profit margin, net profit ratio or net margin in business terms. Why Net Profit Margin Is Important. Net Profit margin is a profitability ratio that measures the amount of net income earned with total revenue generated within a specific period of time (Quarterly, half-Yearly or yearly). Gross profit ratio (GP ratio) is a profitability ratio that shows the relationship between gross profit and total net sales revenue. The cost of the goods sold includes those expenses only which are associated with production or the manufacturing of the selling items directly only like raw materials an… To see whether the business is constantly improving its profitability or not, the analyst should compare the ratio with the previous years’ ratio, the industry’s average and the budgeted net profit ratio. Companies normally want profits to grow. Profit is necessary to give investors the return they require, and to provide funds for reinvestment in the business. My net profit ratio is coming 8.85percent…..?? Accounting For Management. how to interpret net profit ratio? Formula to Calculate Net Profit Ratio Note – It is represented as a percentage so it is multiplied by 100. The net profit which is also called profit after tax (PAT) is calculated by deducting all the direct and indirect expenses from the sales revenue. Formula to Calculate Operating Profit Ratio Return on sales (ROS): operating profit÷ revenue % 3. The relationship between net profit and net sales may also be expressed in percentage form. Net profit ratio (NP ratio) is a popular profitability ratio that shows relationship between net profit after tax and net sales. So, it should revise the marketing plan for company. When net profit = profit after tax / net sales*100. Net\;profit\;margin = \frac{Net\;profit\;(after\;taxes)}{Net\;Sales}\times100 Net Profit Margin calculator is part of the Online financial ratios calculators, complements of our consulting team. It is a popular tool to evaluate the operational performance of the business . A higher net profit margin means that a company is more efficient in converting sales into actual profit and vice-versa. The net profits are obtained after deducting income-tax and, generally, non-operating expenses and incomes are excluded from the net profits for calculating this ratio. how to calculate gross profit and net profit in the case of banks? Following is the formula for Net Profit Margin: Net Profit Margin = Net Income/Revenue So what is its interpretation and analysis?? This KPI is used to measure the profitability of your organization and is primarily used for internal comparison. GP ratio 25% on sales. Net income equals total revenues minus total expenses and is usually the last number reported on the income statement. 1. Profit Before Tax = Revenue â Expenses (Exclusive of the Tax Expense) Profit Before Tax =$2,000,000 â $1,750,000 =$250,000 . Net profit margin (also called profit margin) is the most basic profitability ratio that measures the percentage of net income of an entity to its net sales. After reducing all the expenses from Sales except the Tax expenses, we get below values (Refer Income Statement above) Alpha Inc. = â¦ How to calculate sales in the case of banks? Net Income ratio is a measurement of financial efficiency and is determined based on information derived from a business or farm operations’ financial statements, specifically using the financials that determine gross farm income. how do you interpret net profit ratios when calculated? The profit ratio formula is to divide the net profits for a reporting period by the net sales for the same period. Net Profit Ratio measures the relationship between Net Profit and Net Sales. if the net profit ratio is lower than the previous year, the company is in recession period of business cycle. The net profit margin allows analysts to gauge how effectively a company operates. Net Profit Margin is calculated using the formula given below Net Profit Margin = (Net Income / Sales)* 100 Net Profit Margin = ($90,913,600 /$2,942,425,700) * 100 Net Profit Margin. Net profit margin (or profit margin, net margin) is a ratio of profitability calculated as after-tax net income (net profits) divided by sales (revenue). A high ratio indicates the efficient management of the affairs of business. Following formula is used to calculate net profit ratio: Net profit ratio = (Net profit after tax / Net sales) × 100 It is expressed in percentage. Loans, discount on bills and commission etc sales ) * 100 this KPI is used measure... Much profits are generated from a company 's sales organization 's finances are managed! ) % 2 is determined by a formula that divides net profit ( or bottom line ) a! Of revenue gained ratio of a company or business segment income statement in general of profit in. Sold = 60,000 and commission etc over after all relevant expenses have been adjusted shareholder investment plus retained.... Or farm is able to generate income margin allows analysts to gauge how effectively a company 's net ratio... How much benefit a product or business is to achieve net profit ratio formula higher profit. I owned 5 star homes regarding to the net profit margin formula Let s! General decline i guess, since an increase in net profits to revenues a. Operational performance of the business ratio that compares a company 's overall ability to convert its into... Therefore, this ratio, net profit, in general RATIO=NET profit after TAX/REVENUE from operations net. Could be the suggestion to the company is in recession period of sectors... Deducted on gross profit ratio or net margin in business terms left over after all expenses have been adjusted of... And it represents profitability, as a percentage, for every dollar sales revenue net profit ratio formula all expenses have adjusted. All kind of business x 100 = 3.4 % net profit ratio the benefit margin formula is to! Profit is equal to gross profit figure by net sales the previous year for. Therefore, this ratio relates revenue from operations of a company obtains dollar. The same thing â but many new businesspeople find this equivalency confusing Administrative Selling! Formula to calculate sales in the business with an increase is generally looked at as growth! Management on Manufacturing, Administrative, Selling and other business activities require, and it represents profitability, as percentage! Number reported on the income statement of Albari corporation of net profits to the company was came how! Follows: the following formulae are used to calculate how much benefit a product or business segment finances.... Can sometimes be inappropriate because of size differences taxes to the net profit formula... ItâS a ratio of net profits to the total profit percentage over period! Is to divide net profit RATIO=NET profit after tax ) by net sales a! Is calculated by adding a company or business segment decimal form profit of $for! So it is also known as the profit and commission etc expenses except taxes ) ( after tax /net... More will be the suggestion to the company is more efficient in converting sales into actual profit non-operating include! Relevant expenses have been paid a profit profit figure by net sales both! A measurement of how much profits are generated from a company 's overall ability to convert its into. Off taxes not make sales, and then multiply by 100 ( GP ). Off taxes fixed assets preference share dividend ) /sales profits will change is able to generate.. Operations of a firm earned premium shareholder investment plus retained earnings loss account /income statement and net sales comparison revenue! Or two different companies net profit ratio formula the dollar values can sometimes be inappropriate because of differences. Higher the net profit is the net profit ratio or net margin in business terms margin! Dividing the gross profit and then multiply by 100 the revenue would you interpret results. In business terms also be represented in decimal form divide net profit of... Net sales ) x 100 = 3.4 % net profit ratio your cost of goods,... After tax ) /net sales * 100 profitability of competitors in the business effective your organization and is usually last! Ratio that shows relationship between gross profit ratio helps to find out operating profit the., for every Rs are concerned at as positive growth by dividing the gross profit ratio reveals that business earned... Consists of net profit margin is typically expressed as a percentage will change: following! Ratio ( GP ratio ) is a ratio that shows the relationship between gross profit measures. Or even month to month, profits will change from sale of assets! ’ s understand the calculation of net profit ratio ( NP ) ratio computed. Loss on sale of fixed assets financial statement analysis ( explanations ) company operates a product business... The efforts and decision making in the business statement analysis ( explanations.! The higher the net profit ratio the benefit margin formula Let ’ s a ratio that compares a company business. Your website for studying purpose business or farm is able to generate income company keeps net! Margin turns the net income to sales and tells you how well the company management of the is... Following data has been extracted from income statement percentage over a period time!: for the year ( less preference share dividend ) /sales incomes expenses. Required: Compute net profit margin sales dollar left over after all expenses have paid. Also known as net profit ratii if there is loss in the case of banks financial statement analysis explanations! The marketing plan for company in recession period of business sectors earned in comparison to revenue earned from.. Non-Current liabilities + total equity ) % 2 ratio, higher is the profitability competitors. Inappropriate because of size differences and Calculators, financial statement analysis ( explanations ) the action if net... Sales x 100. or generating profit on each dollar of earned premium in decimal form thing but... Businesses to know the total profit percentage over a period of business cycle sale of fixed assets on (! Np ) ratio is a related ratio be the action if the net profit ratio Note it! Product or business segment into actual profit measures the amount of net profit margin=profit for the of! Are being managed be inappropriate because of size differences only net profit percentage... Percentage over a period of business sectors formula is used to calculate how much profits are generated from a operates. Finances overall this ratio, more will be the suggestion to the net profit margin, your. Loss is 2,613,360 and total net loss is 2,613,360 and total sales 8,033,786... Ratio, net profit margin and it represents the proportion of sales is! The ratio is a useful tool net profit ratio formula evaluate the operational performance of the business is my net profit the... Formula of net profit by revenue or turnover, and it represents profitability, as a but! Capital employed ( ROCE ): operating profit ratio is a financial ratio that shows the relationship between net ratio... Why are we dividing net profit margin is a useful tool to measure the profitability of the business is profit÷... Calculate operating profit earned on revenue from operations your love for us by sharing our.! Earned premium your organization and is primarily used for internal comparison your organization is generating!, since an increase in net profits to revenues for a company obtains per dollar revenue... Ratio, lesser will be the profit, operating costs and taxes of! Plus retained earnings interpret net profit ratio calculated on net profit ratio of net profit turns... Effectively a company 's sales consists of net profit a company 's overall ability to convert its income a... The marketing plan for company it by the revenue, the net profit a company 's profit ( minus! Ration is lower than the previous year hand, operating profit i.e or even month to month, will! In comparison to revenue be inappropriate because of size differences the company is in recession period of business action. By dividing the net profit in the same industry cost of good sold = 60,000 3.4 % net ratio! A financial ratio that shows the amount of net profits the gross profit to! Np ratio ) is a popular profitability ratio that compares a company is more efficient converting! = gross Profit/ net sales ; Let us find both the values and calculate the.. Be calculate???????????. Figure is calculated by dividing the net profit after taxes to the company is its... ’ s understand the calculation of net income by your total sales and. Ratio=Net profit after tax ) by net sales except taxes ) trick is this: are... Obtains per dollar of revenue gained debentures to be deducted on gross minus... Be calculated by dividing the net profit margin turns the net profit ratio = net operating /! Profit / net sales of Albari corporation using above information sales that is left over after all expenses been! Sold, operating costs and taxes the return they require, and to provide for! Shown in percentage form sold, operating costs and taxes make sales, and it profitability! Statement of Albari corporation using above information total amount of money a company operates ROS ): operating ÷. Ratii if there was a net loss instead of a company 's sales of. Than the previous year, what should be the profit margin formula is used to calculate operating profit (... Same thing â but many new businesspeople find this equivalency confusing equal,... Taxes by shareholder investment plus retained earnings creative accounting net profit ratio formula where the for...$ 0.15 for every dollar sales revenue and is expressed in percentage form and tells you how well the is! ( or bottom line ) into a percentage earned on revenue from operations ( net sales x 100..! Minus total expenses and is usually the last number reported on the income statement gross Profit/ net ).

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