An inheritance of $24,000 is to be divided among three trusts with the second trust receiving twice as much as the first trust. The three trusts pay interest at the rates of 9%, 10%, and 6% annually, respectively, and return a total in interest of$2210 at the end of the first year. How much was invested in each trust?

If 10 pens and 12 pads cost $42, and 5 of the same pens and 10 of the same pads cost$29, find the cost of a pen and a pad.

Does the area enclosed by the cycle on a T-s diagram represent the net work input for the reversed Carnot cycle? How about for the ideal vapor-compression refrigeration cycle?

Solve each equation or inequality. Round to the nearest ten-thousandth. $2^{3 x}<5^{x-1}$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $(8.25, 3.5)$

Write each expression as a single natural logarithm. $\ln a-2 \ln b+\frac{1}{3} \ln c$

Work cooperatively. Solve each equation. Round to the nearest tenth if necessary. $x^{2}+8 x+16=0$

Find the amount of an annuity that consists of 16 quarterly payments of $300 each into an account that pays 8% interest per year, compounded quarterly.

An axially symmetric space station (principal axis

$$e_3$$

, and

$$λ_1 = λ_2)$$

is floating in free space. It has rockets mounted symmetrically on either side that are firing and exert a constant torque Γ about the symmetry axis. Solve Euler's equations exactly for ω relative to the body axis) and describe the motion. At t = 0 take

$$ω = (ω_{10}, 0, ω_{30}).$$

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z>d)=0.9922, find d.

Evaluate the expression using properties of numbers. Name the property used in each step. 5.3 + 2.8 + 3.7 + 6.2

Given a polynomial and one of its factors, find the remaining factors of the polynomial.

$$x^3-x^2-10x-8; x+2$$

Suppose that in Example discussed before there were three rival companies $R, S$, and $T$ so that the pattern of customer retention and switching is given by the information in the matrix $A$ where

$$A=\left[\begin{array}{ccc} R & S & T \\ \frac{1}{3} & \frac{1}{2} & \frac{1}{4} \\ \frac{2}{3} & \frac{1}{4} & \frac{1}{3} \\ 0 & \frac{1}{4} & \frac{1}{4} \end{array}\right] \begin{aligned} &R \\ &S \end{aligned}$$

(a) If the initial market distribution is given by

$$\mathbf{x}_0=\left[\begin{array}{c} \frac{1}{3} \\ \frac{1}{3} \\ \frac{1}{3} \end{array}\right] .$$

then determine the market distribution after I year; after 2 years. (b) Show that the stable market distribution is given by

$$\mathbf{x}=\left[\begin{array}{c} \frac{21}{53} \\ \frac{24}{51} \\ \frac{8}{53} \end{array}\right]$$

(c) Which company $R, S$, or $T$ will gain the most market share over a long period of time (assuming that the retention and switching patterns remain the same)? Approximately what percent of the market was gained by this company?

Suppose that x and y vary inversely. Write a function that models each inverse variation. Graph the function and find y when x=10. x=2.5 when y=100