You are one of the 10 students performing in a school talent show. The order of the performance is determined at random. The first 5 performers go on stage before the intermission. a. What is the probability that you are the last performer before the intermission and your rival performs immediately before you? b. What is the probability that you are not the first performer?

The band director at a high school wants to know what percentage of parents supports a decrease in the budget for fine arts. Because many parents attend the school's annual musical, the director surveys the first 30 parents who arrive at the show. Explain why this sampling method is biased. Is the proportion of parents in the sample who support the decrease likely greater than or less than the proportion of all parents in the school who support the decrease?

Ben has been accepted into a 2-year culinary arts program at the Greenfield Career Institute. He has been approved for a $5,000 unsubsidized 10-year federal loan at 4.29%. He knows he has the option of beginning repayment of the loan in 2.5 years. He also knows that during this nonpayment period, interest will accrue at 4.29%. How much interest will Ben accrue during the 2.5-year nonpayment period?

An athlete performing the long jump tries to achieve the maximum distance from the point of takeoff to the first point of touching the ground. After the jump, rather than land upright, she extends her legs forward as in the photo. How does this affect the time in the air? How does this give the jumper a longer range?

Determine which value best approximates the volume of the solid between the $x y$-plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.)

$$f(x, y)=\sqrt{x^2+y^2}$$

$R$ : circle bounded by $x^2+y^2=9$ $(a)$ $50$ $(b)$ $500$ $(c)$ $-500$ $(d)$ $5$ $(e)$ $5000$

Determine which value best approximates the volume of the solid between the $x y$-plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.) \

$$f(x, y)=x+y$$

$R$ : triangle with vertices $(0,0),(3,0),(3,3)$
(a) $\dfrac{9}{2}$ (b) $5$ (c ) $13$ (d) $100$ (e) $-100$

Consider the overall effects on Global Cleaning Service from selling and performing services on account for $6,400 and paying expenses totaling$ 2,500. What is Global Cleaning Service's net income or net loss? a. Net income of $3,900 c. Net income of$ 6,400 b. Net loss of $3,900 d. Net income of$ 8,900

Determine which value best approximates the volume of the solid between the $x y$-plane and the function over the region. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.)
$f(x, y)=15-2 y ; R$ : semicircle: $x^2+y^2=16, y \geq 0$
(a) $100$ (b) $200$ (c ) $300$ (d) $-200$ (e) $800$

A system undergoes a process consisting of the following two steps: Step 1: The system absorbs 72 J of heat while 35 J of work is done on it. Step 2: The system absorbs 35 J of heat while performing 72 J of work. Calculate ΔE for the overall process.

Determine which value best approximates the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Make your selection on the basis of a sketch of the solid and not by performing any calculations.) $y=2 e^{-x}, y=0, x=0, x=2$ (a) $\frac{3}{2}$, (b) $-2$, (c) $4$, (d) $7.5$, (e) $15$

In this exercise, determine which value best approximates the area of the region between the $x$-axis and the graph of the function over the given interval. (Make your selection on the basis of a sketch of the region and not by performing any calculations.)

$$f(x)=\sec x, \quad[0,1]$$

(a) 6

(b) $-6$

(c) $\frac{1}{2}$

(d) $1.25$

(e) 3

Mario has a 500-page novel which he is required to read during the summer for his upcoming language arts class. a. If Mario reads 24 pages each day, write and graph a function to represent the number of pages that Mario has left to read p after d days. b. Estimate the zero of the function. Justify your response. c. Solve the related function to find the zero and interpret its meaning in the context of the situation.

Use inductive reasoning to find the solution to the problem; then check it by performing the calculation.

$$\begin{aligned} &0 \cdot 9+8=8 \\ &9 \cdot 9+7=88 \\ &98 \cdot 9+6=888 \\ &987 \cdot 9+5=8,888 \\ &\vdots \\ &9,876,543 \cdot 9+1=? \end{aligned}$$

Solve each system using a graphing calculator capable of performing row operations. Give solutions with values correct to the nearest thousandth.

$$\begin{aligned} \sqrt{5} x-1.2 y+z &=-3 \\ \frac{1}{2} x-3 y+4 z &=\frac{4}{3} \\ 4 x+7 y-9 z &=\sqrt{2} \end{aligned}$$