For the following situation, find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. The word counts of five essays are \( 503,637,553,615 \), and 586 . Use a sample size of 2 . M. \( 615,637, \bar{x}=561.5 \) P. \( 637,553, \bar{x}=595 \) S. \( 615,503, \bar{x}=559 \) V. \( 503,637, \bar{x}=570 \) y. \( 503,553, \bar{x}=528 \) N. \( 586,586, \bar{x}=586 \) Q. \( 586,553, \bar{x}=569.5 \) T. \( 615,553, \bar{x}=584 \) W. \( 637,586, \bar{x}=611.5 \) 2. \( 615,586, \bar{x}=600.5 \) 0. \( 553,637, \bar{x}=595 \) R. \( 553,553, \bar{x}=553 \) U. \( 553,615, \bar{x}=584 \) \( 615,615, \bar{x}=615 \) \( 586,615, \bar{x}=600.5 \) The mean of the sampling distribution is \( \square \). (Round to two decimal places as needed)

Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) \[ 25 x^{3}-125 x^{2}-25 x+125=0 \] \( x=\square \)

Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated list.) \[ 9 x^{2}-6 x+226=0 \] \( x=\square \)

Solve the equation below and express your answers in the form \( \mathrm{a}+\mathrm{b} \sqrt{\mathrm{c}} \) where \( a, b \) and \( c \) are integers \( \begin{array}{l}2 x^{2}-8 x-1=0 \\ \left(x^{2}+(-6 x)+(-1)=0\right. \\ 1^{2}+(-8)(x)(x+(-1)=0\end{array} \)

Consider the product \( \left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right) \ldots \) Each factor in the product is of the form \( \left(1+\frac{1}{n}\right) \) for \( n \geq 2 \). Determine ALL the values of \( n \) for which the product will be an integer value.

st Prep A new mobile device has a value of \( \$ 256.25 \). Its value changes by \( -22 \frac{1}{2} \% \) each year. What is the value of the phone after two years? \( \begin{array}{ll}\text { (A) } \$ 140.93 & \text { (C) } \$ 153.91 \\ \text { (B) } \$ 198.59 & \text { (D) } \$ 57.66\end{array} \)