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.

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

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.

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?

Complete the following table to compare polynomial approximations of values of cosine x to the actual values of cosine x.

$$\begin{matrix} \text{x} & \ {1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}} & \ {\cos x}\\ \text{0.1} & \text{ } & \text{ }\\ \text{0.2} & \text{ } & \text{ }\\ \text{0.3} & \text{ } & \text{ }\\ \end{matrix}$$

Which aspects of capitalism do you personally appreciate? Which do you find worrisome?

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

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.

Use the formula

$$\sin h+\sin 2 h+\sin 3 h+\cdots+\sin m h =\frac{\cos (h / 2)-\cos ((m+(1 / 2)) h)}{2 \sin (h / 2)}$$

to find the area under the curve y = sin x from x = 0 to $x=\pi / 2$ in two steps: Partition the interval $[0, \pi / 2]$ into n subintervals of equal length and calculate the corresponding upper sum U

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?

Nettles, King, and Tanaka are partners sharing income 3:2:1. After the firm’s loss from liquidation is distributed, the capital account balances were: Nettles, $15,000 Dr.; King,$46,000 Cr.; and Tanaka, $71,000 Cr. If Nettles is personally bankrupt and unable to pay any of the$15,000, what will be the amount of cash received by King and Tanaka upon liquidation?

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.

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

Take $f(x, y)=x+2 y \quad \text { on } \quad R: 0 \leq x \leq 2,0 \leq y \leq 1 .$ and let $P$ be the partition $P=P_1 \times P_2$.

Find $L_f(P)$ and $U_f(P)$ given that $P_1=\left\{0, \frac{1}{2}, 1, \frac{3}{2}, 2\right\}$ and $P_2=\left\{0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1\right\}$.