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Questions in mathematics

[Answered] Evaluate: $\begin{array}{c} \sum_{n=1}^{10} 8\left(\frac{1}{4}\right)^{n-1} \ S=[?]\end{array}$ Remember: for a geometric series, $S=\frac{a\left(1-r^n\right)}{1-r}$

[Answered] A rectangular pan has a length that is [tex]$\frac{4}{3}$[/tex] the width. The total area of the pan is [tex]$432 in ^2$[/tex]. What is the width of the cake pan?

[Answered] What is $7 c^2-4 c$ in factored form?

[Answered] Evaluate $(24-72 \div 9+16)-8 \times 3$

[Answered] $2-(-8)+(-3)=$ A) 14 B) 7 C) 1 D) 12

[Answered] If [tex]$\log \frac{M}{N}=4$[/tex] and [tex]$\log \frac{P}{N}=5$[/tex], what can you say about the relationship between [tex]$M$[/tex] and [tex]$P$[/tex]? A. [tex]$P=0.1 M$[/tex] B. [tex]$P=100 M$[/tex] C. [tex]$M=10 P$[/tex] D. [tex]$P=10 M$[/tex]

[Answered] What is the range of [tex]$y=-3 \sin (x)-4$[/tex]?

[Answered] Select the correct answer. What is the end behavior of this radical function? [tex]$f(x)=-2 \sqrt[3]{x+7}$[/tex] A. As [tex]$x$[/tex] approaches negative infinity, [tex]$f(x)$[/tex] approaches negative infinity. B. As [tex]$x$[/tex] approaches positive infinity, [tex]$f(x)$[/tex] approaches negative infinity. C. As [tex]$x$[/tex] approaches negative infinity, [tex]$f(x)$[/tex] approaches 0. D. As [tex]$x$[/tex] approaches positive infinity, [tex]$f(x)$[/tex] approaches positive infinity.

[Answered] Solve $\frac{1}{4}\left(4^{x-1}\right)+3=12$ $x=$ (round your answer to two decimal places)

[Answered] Which shows one way to determine the factors of $x^3+4 x^2+5 x+20$ by grouping? A. $x(x^2+4)+5(x^2+4)$ B. $x^2(x+4)+5(x+4)$ C. $x^2(x+5)+4(x+5)$ D. $x(x^2+5)+4 x(x^2+5)$