The __________ statement causes one or more statements to execute only when a Boolean expression is __________. a. else, false b. if, true c. if, false d. else, true

In the following exercise, use the expression $1+\frac{z}{3}+2 w$.

Which part of the expression is a product of two factors? Describe its parts.

A bag contains $2$ red, $6$ blue, $7$ yellow, and $3$ orange marbles. Once a marble is selected, it is not replaced. Find each probability.

$P(2$ yellows in a row then orange $)$

In given problem, $R=\{(x, y): 0 \leq x \leq 6,0 \leq y \leq 4\}$ and P is the partition of R into six equal squares by the lines x=2, x=4, and y=2. Approximate $\iint_R f(x, y) d A$ by calculating the corresponding Riemann sum $\sum_{k=1}^6 f\left(\bar{x}_k, \bar{y}_k\right) \Delta A_k$, assuming that $\left(\bar{x}_k, \bar{y}_k\right)$ are the centers of the six squares.

$$f(x, y)=\frac{1}{6}(48-4 x-3 y)$$

Hilliard, Downey, and Petrov are partners sharing income $3$:$2$:$1$. After the firm’s loss from liquidation is distributed, the capital account balances were: Hilliard, $\$24,000$ Dr.; Downey, $\$90,000$ Cr.; and Petrov, $\$64,000$ Cr. If Hilliard is personally bankrupt and unable to pay any of the $\$24,000$, what will be the amount of cash received by Downey and Petrov upon liquidation?

The diameter of Mars is about 6800 km. Approximate the surface area of Mars using the formula for the surface area of a sphere, $S=4 \pi r^{2}$. Write your answer in scientific notation.

A group of junior high students will be touring Washington, D.C. Their chaperons will have the $1,810 cost of the tour reduced by$15.50 for each student they personally supervise. How many students will a chaperon have to supervise so that his or her cost to take the tour will be $1,500?

Piecewise functions can sometimes be differentiable at a point where two pieces meet. For the function $f$, use one-sided limits to find the values of $a$ and $b$ that make $f$ differentiable at $x=2$.

$$f(x)=\left\{\begin{array}{l} a x^2+1, \quad \text { if } x<2 \\ -x^2+6 x+b, \quad \text { if } x \geq 2 \end{array}\right.$$

Plot the graph using Boolean variables to restrict the domain, and sketch the result.

In the independent and subordinate clauses in the given sentences, underline the subjects once and the verbs twice.

In 1909, funding was approved for this statue, which is located between Plymouth, Indiana, and the Yellow River.

Have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing rectangle to deter- mine which possible rational roots are actual roots of the equation.

$$6 x ^ { 3 } - 19 x ^ { 2 } + 16 x - 4 = 0 ; [ 0,2,1 ] \text { by } [ - 3,2,1 ]$$

A train's horn produces a $148-\mathrm{Hz}$ sound while moving at $32.0 \mathrm{~m} / \mathrm{s}$. What frequencies are heard by a person standing still beside the tracks as the train approaches and after it passes?

For the underlined phrase or sentence, choose the revision that most improves the writing. Personally, I would rather read $\underline{\text{a poem without rhyme than with a tired old rhyme.}}$ A. a poem without rhyme than a tired old rhyming idea. B. a poem without rhyme than a tired old one C. a poem without rhyme than one with a tired old rhyme. D. Correct as is

According to the Old Farmer's Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice is $13.65$ and the number of hours of sunlight on the winter solstice is 9.067. Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac and compare the actual hours of daylight to the results found in the previous part.

Answer each question about the surface area S on a surface given by a positive function z = f(x, y) over a region R in the xy-plane. Explain each answer. (a) Is it possible for S to equal the area of R?