You are one of 10 students performing in a school talent show. The order of the performances is determined at random. The first 5 performances go on the 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.

Multiply:

$$\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$$

After performing the multiplication, define what happens to the elements in the first matrix.

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.

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

$$\text{value} = 7$$

Given the same initial statements s1 = "spam" s2 = "ni!", show a Python expression that could construct each of the following results by performing string operations on s1 and s2. (a) "NI" (b) "ni!spamni!" (c) "Spam Ni! Spam Ni! Spam Ni!" (d) "spam" (e) ["sp","m"] (f) "spm"

As you flip through The Wall Street Journal, you notice advertisements by investment firms that want to sell you their products. Common among all ads is the claim that the firm has a track record of performing above average. Explain how they can all be above average. Is this inconsistent with the efficient markets theory?

Explain exactly what you would do when performing the following laboratory instructions; that is, write a short procedure.

a. "Wash the organic layer with $1.0 \mathrm{~mL}$ of $1 \mathrm{M}$ aqueous sodium bicarbonate."

b. "Extract the aqueous layer three times with $1-\mathrm{mL}$ portions of methylene chloride."

Determine which value best approximates the length of the arc represented by the integral $\int_{0}^{\pi / 4} \sqrt{1+\left(\sec ^{2} x\right)^{2}} d x$. (Make your selection on the basis of a sketch of the arc and not by performing any calculations.) (a) -2, (b) 1, (c) $\pi$, (d) 4, (e) 3.

Determine whether the statement makes sense or does not make sense, and explain your reasoning.

When performing the division

$$\left(2 x^3+13 x^2+9 x-6\right) \div(2 x+3),$$

I mentally cover up the $+3$, the second term of the binomial divisor, before dividing into the dividend.

Which of the following would be considered a prevention cost of quality?

A. performing a 24-hour burn-in on every item produced to make sure it works before it is shipped
B. inspecting incoming raw materials
C. training workers to perform their jobs
D. issuing a recall of defective product before another customer is injured

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?

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?

Determine which value best approximates the area of the region between the axis and the function $f(x)=\frac{1}{\sqrt{1-x^{2}}}$ over the interval [-0.5, 0.5]. (Make your selection on the basis of a sketch of the region and not by performing any calculations.) (a) 4 (b) -3 (c) 1 (d) 2 (e) 3

Identify the part of speech of each italicized word in the following sentences. If the word is used as an adjective or an adverb, tell what word or words it modifies.

Example:The Mexican artist Diego Rivera was a remarkably talented muralist.

Mexican—adjective—artist remarkably—adverb—talented muralist—noun

Rivera, who was born in Guanajuato, Mexico, in 1886, entered the San Carlos Academy of Fine Arts in Mexico City when he was only eleven.

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) $-100$