Given a sentence in Tagalog language, translate the sentence to English language keeping the meaning of the original sentence intact.

Q: Tagalog sentence: a) Kung, Patunayan na may mga pagbabagong mula na para sa bawat permutasyon, May index iyon may karaniwang puntos.

A: a) If, prove that there are permutations from that for each permutation, there is an index that have common points.
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Q: Tagalog sentence: Ito ang inihayag ni Tesda Director-General Secretary Guiling Mamondiong sa ginanap na “Tapatan sa Tesda”sa New Town Plaza Hotel noong Oktubre 24, 2016. Aniya, bahagi ito ng may isang milyong scholarship grants na itinalaga para sa buong bansa. Ang scholarship grant ay bukas para sa lahat.

A: Congresswoman Vini Nola Ortega congratulates an ABONO Partylist scholar of Hilot Wellness Massage NCII during their Commencement Exercises last August 24, 2017 at the Diego Silang Hall, Provincial Capitol, City of San Fernando, La Union.
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Q: Tagalog sentence: ... sa panahon ng Ikalawang World War siya-aral ng hangin-pagsalakay bombahan pattern upang matukoy ang mga lokasyon ng German paglulunsad silos.

A:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
... during the Second World War she studied air-raid bombing patterns to determine the locations of German launching silos.
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