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Questions in mathematics

[Jawaban] Differentiate the following $y=\frac{1}{x}$

[Jawaban] Aryson is playing green beans. He has already picked $1\frac{1}{4}$ bushels and picks at a rate of $\frac{7}{8}$ of a bushel each hour. The equation $\frac{7}{8}h + 1\frac{1}{4} = 6$ can be used to represent $h$, the number of hours it will take him to pick 6 bushels. What is the value of h? A. $4\frac{8}{7}$ hours B. $5\frac{3}{7}$ hours C. $5\frac{17}{28}$ hours D. $5\frac{2}{7}$ hours

[Jawaban] Steve completed 9 homework problems in class. The function [tex]$p(m)$[/tex] relates the time (in minutes) Steve spent on his homework at home to the total number of problems he completed. The input is the number of minutes worked. The output is the number of problems completed. [tex]$p(m)=\frac{m}{6}+9$[/tex] Which equation represents the inverse function [tex]$m(p)$[/tex], which uses problems completed as the input and gives minutes worked as the output? A. [tex]$m(p)=54 p+6$[/tex] B. [tex]$m(p)=54 p-6$[/tex] C. [tex]$m(p)=6 p-54$[/tex] D. [tex]$m(p)=6 p+54$[/tex]

[Jawaban] Which equation shows the quadratic formula used correctly to solve $5 x^2+3 x-4=0$ for $x ?$ A. $x=\frac{-3 \pm \sqrt{(3)^2-4(5)(-4)}}{2(5)}$ B. $x=\frac{3 \pm \sqrt{(3)^2+4(5)(-4)}}{2(5)}$ C. $x=\frac{3 \pm \sqrt{(3)^2-4(5)(-4)}}{2(5)}$ D. $x=\frac{-3 \pm \sqrt{(3)^2+4(5)(-4)}}{2(5)}$

[Jawaban] What is the vertex of the graph of $f(x)=|x-13|+11$? A. $(-11,13)$ B. $(-13,11)$ C. $(11,13)$ D. $(13,11)$

[Jawaban] Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? Round the answer to the nearest thousandth. [tex] \begin{aligned} P(k \text { successes }) & = {}_n C_k p^k(1-p)^{n-k} \ { }_n C_k & =\frac{n!}{(n-k)!\cdot k!} \end{aligned} [/tex]

[Jawaban] Nina is 10 years younger than Deepak. Deepak is 3 times as old as Nina. Which system of equations can be used to find $d$, Deepak's age, and $n$, Nina's age? $\begin{array}{l} d=n+10 \\ d=3 n \end{array}$ $\begin{array}{l} d=n-10 \\ d=3 n \end{array}$ $\begin{array}{l} d=n+10 \\ n=3 d \end{array}$ $\begin{array}{l} d=n-10 \\ n=3 d \end{array}$

[Jawaban] The height of a window is 0.6 feet less than 2.5 times its width. If the height of the window is 4.9 feet, which equation can be used to determine $x$, the width of the window? A. $2.5 x+0.6=4.9$ B. $2.5 x-0.6=4.9$ C. $0.6 x+2.5=4.9$ D. $0.6 x-2.5=4.9

[Jawaban] Consider this system: $\begin{array}{l} 3 x+\frac{1}{2} y=3 \\ 6 x-y=2 \end{array}$ Which of the following operations would eliminate the $x$-terms if the two equations were added together afterward? A. Multiply the first equation by -6. B. Multiply the first equation by -2. C. Multiply the first equation by 2. D. Multiply the first equation by 6.

[Jawaban] A father is 7 times as old as his son. Three years ago, the father was 13 times as old as his son. What are their present ages?