The 2000 census reported that 66.4% of the households in Alaska were homeowners, and the remainder were renters. During the next decade, 37.2% of the homeowners became renters, and the rest continued to be homeowners. Similarly, 71.5% of the renters became homeowners, and the rest continued to rent. (A) Write the appropriate transition matrix. (B) According to this transition matrix, what percentage of households were homeowners in 2010? (C) If the transition matrix remains the same, what percentage of households will be homeowners in 2030?

You are helping design boxes for game balls that are 1 inch in diameter. Your supervisor wants the balls to be packaged in one rectangular layer of rows and columns. a. Use a table to show all the ways to package 24 balls in rows and columns. b. Plot these points on a graph. c. Do the possible box dimensions represent direct or inverse variation? Explain how you know. d. Represent the situation with an equation. Does the equation have any limitations? If so, what are they?

the product of three integers is 90. the second number is twice the first number. the third number is two more than the first number. what are the three numbers?

Use the method of partial fractions to evaluate the following integrals. $\int \frac { d x } { x ^ { 3 } - x }$

For any triangle, derive the formula $a=b \cos C+c \cos B.$

What is wrong with the following statement: “Given any two bodies, the one with the higher temperature contains more heat.”

A population consists of 600 girls and 400 boys. Jose wanted to investigate what he could expect to happen if he were to take a random sample of 20 people from this population and calculate the proportion of girls in the sample. Jose selected 20 students at random and recorded the following data (B = boy and G = girl):

$$\begin{matrix} \text{G} & \text{G} & \text{B} & \text{B} & \text{G} & \text{B} & \text{G} & \text{B} & \text{B} & \text{B}\\ \text{G} & \text{B} & \text{G} & \text{G} & \text{G} & \text{B} & \text{G} & \text{B} & \text{B} & \text{G}\\ \end{matrix}$$

Jose’s sample proportion was not equal to 0.6, even though 60% of the people in the population are girls. Does this mean that Jose did something wrong when he selected the sample? Explain.

Suppose that a $90-k g$ person walks for 1 hour each day for a year, expending 50,000 extra kilocalories of metabolic energy (in addition to his normal resting metabolic energy use). What approximately is the person’s mass at the end of the year, assuming his food consumption does not change? (a)$57 \mathrm{kg}$ (b)$61 \mathrm{kg}$ (c)$64 \mathrm{kg}$ (d)$66 \mathrm{kg}$ (e)$67 \mathrm{kg}$

A rancher wants to enclose a pen for new calves using 60 ft of fencing. Which shape uses all of the fencing and encloses the greatest area? F. a rectangle that is 12 ft by 18 feet G. a square 15 ft on each side H. a rectangle that is 20 ft by 30 feet I. a circle with an 8-ft radius

Use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. $f(x)=x^{5}-x^{3} \quad (-2,2)$

A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area $A=40,000\ \mathrm{mm}^{2}$ and length $L=2\ \mathrm{m}$. Before the load P is applied, the middle post is shorter than the others by an amount $s=1.0\ \mathrm{mm}$. Determine the maximum allowable load $P_{\text { allow }}$ if the allowable compressive stress in the concrete is $\sigma_{\text { allow }}=$ $20\ \mathrm{MPa}$. (Use $E=30\ \mathrm{GPa}$ for concrete.)

Use the Factor Theorem to prove that x - c is a factor of $x^{n}-c^{n}$ for any positive integer n.

Write each expression in the standard form a + bi. $\left[3\left(\cos 80^{\circ}+i \sin 80^{\circ}\right)\right]^{3}$

A television advertising campaign is conducted during the football season to promote a well-known brand X shaving cream. For each of several weeks, a survey is made, and it is found that each week, 80% of those using brand X continue to use it and 20% switch to another brand. It is also found that of those not using brand X, 20% switch to brand X while the other 80% continue using another brand. (A) Draw a transition diagram. (B) Write the transition matrix. (C) If 20% of the people are using brand X at the start of the advertising campaign, what percentage will be using it 1 week later? 2 weeks later?