MathDB

11

Part of 2015 AMC 10

Problems(2)

Area of Rectangle as a Function of Diagonal's Length

Source: 2015 AMC 12A #8/10A #11

2/4/2015
The ratio of the length to the width of a rectangle is 4:34:3. If the rectangle has diagonal of length dd, then the area may be expressed as kd2kd^2 for some constant kk. What is kk?
<spanclass=′latex−bold′>(A)</span>27<spanclass=′latex−bold′>(B)</span>37<spanclass=′latex−bold′>(C)</span>1225<spanclass=′latex−bold′>(D)</span>1625<spanclass=′latex−bold′>(E)</span>34<span class='latex-bold'>(A) </span>\dfrac27\qquad<span class='latex-bold'>(B) </span>\dfrac37\qquad<span class='latex-bold'>(C) </span>\dfrac{12}{25}\qquad<span class='latex-bold'>(D) </span>\dfrac{16}{25}\qquad<span class='latex-bold'>(E) </span>\dfrac34
geometryrectanglefunctionratioPythagorean TheoremAMC
Probability of Prime Numbers

Source: 2015 amc 10b #11

2/26/2015
Among the positive integers less than 100100, each of whose digits is a prime number, one is selected at random. What is the probablility that the selected number is prime? <spanclass=′latex−bold′>(A)</span>899<spanclass=′latex−bold′>(B)</span>25<spanclass=′latex−bold′>(C)</span>920<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>916<span class='latex-bold'>(A) </span> \dfrac{8}{99} \qquad<span class='latex-bold'>(B) </span> \dfrac{2}{5} \qquad<span class='latex-bold'>(C) </span> \dfrac{9}{20} \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{2} \qquad<span class='latex-bold'>(E) </span> \dfrac{9}{16}
probabilitynumber theoryprime numbersAMC