A student has a tennis ball can with a flat top and bottom containing three tightly fitting tennis balls. To the student’s surprise, the circumference of the top of the can is longer than the height of the can. The student wants to know if this fact can be explained without performing any measurements. How do you respond?

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?

Determine which value best approximates the arc length represented by the integral. Make your selection on the basis of a sketch of the arc, not by performing calculations.

$$\int_0^2 \sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x$$

$$\text{value} = 5$$

Two skaters are performing on ice. One skater is gripping the other's hand and spinning her in an arc around his body. The distance between the skaters' grip and the outer edge of the arc is $3.0 \mathrm{~m}$. The skater is being swung around at $2.0 \mathrm{rpm}$ and has a mass of $54 \mathrm{~kg}$. Calculate the centripetal force.

Marco's Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $\$2.50$ each and he has $\$14.75$ to spend, hw many tickets can he buy? (A) 4 tickets (B) 0 tickets (C) 6 tickets (D) 5 tickets

Determine which value best approximates the arc length represented by the integral. Make your selection on the basis of a sketch of the arc, not by performing calculations.

$$\int_0^2 \sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x$$

$$\text{value} = 1$$

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.

$$\begin{array}{c} 0.3 x+2.7 y-\sqrt{2} z=3 \\ \sqrt{7} x-20 y+12 z=-2 \\ 4 x+\sqrt{3} y-1.2 z=\frac{3}{4} \end{array}$$

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

Write your own function $\operatorname{sim}(A, C)$ for performing a similarity transformation $B=C^{-1} A C$. The function should be on your own disc, call matrices $A$ and $C$ from the matrix command window, and return $B$ to the command window. Check your function out on the similarity transformations of just the previous exercise.

In this exercise, determine which value best approximates the length of the arc represented by the integral. (Make your selection on the basis of a sketch of the arc and not by performing any calculations.)

$$\displaystyle\int_0^2\sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x$$

$$-4$$

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?

Set up an equation that can be used to solve the prob lem. Solve the equation and determine the desired value(s).
MODELING - Scholarship Donation Each year, Andrea Choi donates a total of $\$1000$ for scholarships at Mercer County Commun ity College . This year, she wants the amount she donates for scholarships for liberal arts to bethree times the amount she donates for scholarships for business. Determine the amount she will donate for each type of scholarship.