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Questions in mathematics

[Jawaban] A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function [tex]$m(x)$[/tex], where [tex]$x$[/tex] is the length of the radius of the circle in feet. The homeowner estimates that he will pay [tex]$\$1.50$[/tex] per square foot of mulch. This cost is represented by the function [tex]$g(m)$[/tex], where [tex]$m$[/tex] is the area requiring mulch. [tex]$\begin{array}{l} m(x)=8 x^2-2 \sqrt{2} x^2 \\ g(m)=1.50 m \end{array}$[/tex] Which expression represents the cost of the mulch based on the radius of the circle? A. [tex]$1.50\left(\pi x^2-2 \sqrt{2} x^2\right)$[/tex] B. [tex]$\pi(1.50 x)^2-2 \sqrt{2} x^2$[/tex] C. [tex]$1.50\left(\pi x^2-2 \sqrt{2} x^2\right)$[/tex] D. [tex]$1.50\left(\pi(1.50 x)^2-2 \sqrt{2}(1.50 x)^2\right)$[/tex]

[Jawaban] 3. [tex]\int(3x - 2)^6 dx[/tex] Ans: [tex](1/504)(3x - 2)^7 + C[/tex] 4. [tex]\int(x(x-4))/x dx[/tex] Ans: [tex](x^2 + 4x + 8)/x + C[/tex]

[Jawaban] Which equations represent circles that have a diameter of 12 units and a center that lies on the $y$-axis? Select two options. $x^2+(y-3)^2=36$ $x^2+(y-5)^2=6$ $(x-4)^2+y^2=36$ $(x+6)^2+y^2=144$ $x^2+(y+8)^2=36$

[Jawaban] Complete the table. \begin{tabular}{|c|c|} \hline$x$ & $y=5 x$ \\ \hline-3 & 1 \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{tabular}

[Jawaban] Giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. She draws 1 card out of the stack of cards, replaces it, and then draws another card. What is the probability that she will draw a king and then a jack, [tex]P( king, then jack )[/tex] ? [tex] \frac{1}{36} [/tex] [tex] \frac{1}{24} [/tex] [tex] \frac{1}{9} [/tex] [tex] \frac{1}{6} [/tex]

[Jawaban] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Jawaban] Solve the equation on the interval [tex]$0 \leq 0\ \textless \ 2 \pi$[/tex]. [tex]$(\tan \theta+1)(\cos \theta-1)=0$[/tex]

[Jawaban] A circle passes through points $A(1,2)$ and $B(3,4)$, and its center lies on the line $y=2 x-1$. What is the equation of this circle? Options: 1. $(x-2)^2+(y-3)^2=2$ 2. $(x-3)^2+(y-5)^2=10$ 3. $(x-1)^2+(y-1)^2=8$ 4. $(x-4)^2+(y-7)^2=26$ 5. $x^2+(y+1)^2=10

[Jawaban] According to a poll, $30 \%$ of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth. $\begin{aligned} P(k \text { successes }) & ={ }_n C_k p^k(1-p)^{n-k} \\ { }_n C_k & =\frac{n!}{(n-k)|\cdot k|} \end{aligned}$ A. 0.024 B. 0.031 C. 0.132 D. 0.309

[Jawaban] $\left[\begin{array}{lllllllll}43 & 45 & 50 & 47 & 51 & 58 & 52 & 47 & 0 \\ 61 & 50 & 45 & 55 & 57 & 41 & 46 & 49 & 31 \\ 59 & 44 & 53 & 57 & 49 & 40 & 48 & 52 & 51\end{array}\right]\\Using the class intervals of 43-44, 45-49 ... a) construct the frequency table b) draw a histogram for the distribution. c) draw a frequency polygon for it.