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Questions in mathematics

📝 Answered - In the year 2000, there were 200,000 cell phone subscribers in a city in New York. The number of subscribers increased by 60 percent per year after 2000. Which equation can be used to model the number of subscribers, $y$, in the city $t$ years after 2000? A. $y=200,000(1+60)^t$ B. $y=200,000(1+0.6)^t$ C. $y=200,000(1-60)^t$ D. $y=200,000(1-0.6)^t$

📝 Answered - Select the best answer for the question. 14. Which of the following is a multiple of 5? A. 17 B. 48 C. 235 D. 532

📝 Answered - If events A and B are independent, what must be true? [tex]$P(A)=P(B)$[/tex] [tex]$P(A \mid B )=P(B)$[/tex] [tex]$P(A \mid B )=P(A)$[/tex] [tex]$P(A \mid B )=P(B \mid A )$[/tex]

📝 Answered - Which shows all the exact solutions of $2 \sec ^2 x-\tan ^4 x=-1$ ? Give your answer in radians. A. $\frac{\pi}{3}+k \pi$ and $\frac{2 \pi}{3}+k \pi$ B. $\frac{\pi}{3}+2 k \pi$ and $\frac{5 \pi}{3}+2 k \pi$ C. $\frac{\pi}{4}+2 k \pi, \frac{3 \pi}{4}+2 k \pi, \frac{5 \pi}{4}+2 k \pi$, and $\frac{7 \pi}{4}+2 k \pi$ D. $\frac{\pi}{3}+k \pi, \frac{2 \pi}{3}+k \pi, \frac{4 \pi}{3}+k \pi$, and $\frac{5 \pi}{3}+k \pi$

📝 Answered - Consider the system of linear equations below. [tex]\begin{array}{r} 4 x-9 y=9 \\ -x+3 y=6 \end{array}[/tex] Rewrite one of the two equations above in the form [tex]$a x+b y=c$[/tex], where [tex]$a, b$[/tex], and [tex]$c$[/tex] are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.

📝 Answered - A piecewise function [tex]f(x)[/tex] is defined as shown. [tex]f(x)=\left\{\begin{array}{ll} -\frac{5}{4} x+90, & 0 \leq x\ \textless \ 40 \\ -\frac{3}{8} x+75, & 40 \leq x \leq 200 \end{array}\right.[/tex] Which table could be used to graph a piece of the function? A. | x | y | | --- | --- | | 0 | 90 | | 16 | 85 | | 40 | 75 | B. | x | y | | --- | --- | | 0 | 90 | | 40 | 40 | | 200 | 0 | C. | x | y | | --- | --- | | 40 | 75 | | 120 | 30 | | 200 | 0 | D. | x | y | | --- | --- | | 40 | 60 | | 160 | 15 | | 200 | 0 |

📝 Answered - If [tex]$\log _{10} 8=0.9031$[/tex], find the value of [tex]$4 \log _{10} 16$[/tex].

📝 Answered - Which one of the following statements expresses a true proportion? a) [tex]$3: 4=9: 12$[/tex] b) [tex]$7: 9=8: 9$[/tex] c) [tex]$2: 1=1: 2$[/tex] d) [tex]$54: 9=6: 3$[/tex]

📝 Answered - Draw a model of $\sqrt{12}$ using perfect squares.

📝 Answered - If [tex]f(x)=4-x^2[/tex] and [tex]g(x)=6x[/tex], which expression is equivalent to [tex](g-f)(3)[/tex]? A. [tex]6-3-(4+3)^2[/tex] B. [tex]6-3-(4-3^2)[/tex] C. [tex]6(3)-4+3^2[/tex] D. [tex]6(3)-4-3^2[/tex]