Will help you prepare for the material covered in the first section of the next chapter. Solve each equation by using rhe cross-products principle to clear fractions from the proportion:

$$\text { If } \frac { a } { b } = \frac { c } { d } , \text { then } a d = b c . ( b \neq 0 \text { and } d \neq 0 )$$

Round to the nearest tenth. Solve for

$$B , 0 < B < 180 ^ { \circ } : \frac { 81 } { \sin 43 ^ { \circ } } = \frac { 62 } { \sin B }$$

How many different ways can change be made for a dollar using only half-dollars, quarters, and/or dimes?

Use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

$$\int _ { 1 } ^ { e } \frac { d y } { y \sqrt { 1 + ( \ln y ) ^ { 2 } } }$$

Alternating current (AC) circuits use complex numbers to represent impedance in ohms. To find the total impedance in a circuit, you need to find the sum of the impedances from each part of the circuit. A circuit has partial impedances of 4.2 + 3i and 5 - 2.2i. What is the total impedance for the circuit?

Three different organic compounds have the formula $\mathrm { C } _ { 3 } \mathrm { H } _ { 8 } \mathrm { O } .$ Only two of these isomers react with $\mathrm { KMnO } _ { 4 }$ (a strong oxidizing agent). What are the names of the products when these isomers react with excess $\mathrm { KMnO } _ { 4 } ?$

Is it possible for a $2 \times 3$ matrix to equal a $3 \times 2$ matrix? Explain.

Each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is written on a piece of paper and all the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even.

Sketch the graph of the equation using extrema, intercepts, symmetry, and asymptotes. y = 1 - 1/x

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

$$\log \left( \frac { x } { 100 } \right)$$

Compute the standard deviation for each set of sample data.

$$85, 75, 62, 78, 100$$

solve the logarithmic equation algebraically. Approximate the result to three decimal places. ln√x+8 = 3

Find T(t) and N(t) at the given point. r(t)=

$$\frac { 1 } { 2 } t ^ { 2 } \mathbf { i } + \frac { 1 } { 3 } t ^ { 3 } \mathbf { j }$$

t=1

Solve the given initial-value problem.

$$\mathbf{X}^{\prime}=\left(\begin{array}{rrr}{1} & {-12} & {-14} \\ {1} & {2} & {-3} \\ {1} & {1} & {-2}\end{array}\right) \mathbf{X}, \quad \mathbf{X}(0)=\left(\begin{array}{r}{4} \\ {6} \\ {-7}\end{array}\right)$$

Meredith wants to go on a trip this summer that costs $375. She paid a deposit of$125 and will save an additional $25 per week to pay for the trip. The equation 125 + 25w = 375 can be used to find the number of weeks Meredith will need to save. Describe the steps needed to solve the equation.