Improve Your Algebra Skills with Practice Problems

Divide
${\displaystyle \frac{3+2i}{5-i}}$

The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following.
$\begin{array}{|cccccc|}\hline x& 1& 2& 4& 8& 16\\ p(x)& 0.05& 0.10& 0.30& 0.45& 0.10\\ \hline\end{array}$
a) Compute E(X). (Enter your answer to two decimal places.) GB
b) Compute V(X) directly from the definition. (Enter your answer to four decimal places.) ${\displaystyle G{B}^2}$
c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB
d) Compute V(X) using the shortcut formula. (Enter your answer to four decimal places.) ${\displaystyle G{B}^2}$

${\displaystyle \frac{x^2+3x-28}{x^2+4x+4}+\frac{x^2-5x-14}{x^2-49}}$

The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8.
a) What is the ideal efficiency of the engine? Use ${\displaystyle \gamma =1.40}$
b) The engine in a Dodge Viper GT2 has a slightly higher compression ratio of 9.6. How much increase in the ideal efficiency results from this increase in the compression ratio?

To find the Gear ratio of the Driving gear, 40 teeth; driven gear, 5 teeth.

The results of a survey of 39 students and the foreign language they are studying are shown in the two-way frequency table.
$\begin{array}{|ccccc|}\hline Gender& Chinese& French& Spanish& Total\\ Girl& 3& 8& 13& 24\\ Boy& 2& 2& 11& 15\\ Total& 5& 10& 24& 39\\ \hline\end{array}$
What fraction of girls are studying French? Use decimals to answer, and round to 3 places.
The fraction of girls that are studying French is ______.

One way to find the formula of a line passing through (15,16) and (30,25) is by using a table, as shown below. Complete parts (a) and (b) below.
a) Complete the box in the first row.
$\begin{array}{|cc|}\hline x& y\\ 0& \\ 15& 16\\ 30& 25\\ \hline\end{array}$
b) Report the formula of the line in slope-intercept form.
$y=$___$+x$___

Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.
${\displaystyle 5^{x-3}=3^{2x}}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ______.
B. The solution is the empty set.

Write and algebraic equation for the following problem and then solve it.
Creekside dormitory just purchased a new sofa on sale $456. The sale price was ${\displaystyle 60\mathrm{\%}}$ of the original price. What was the original price of the sofa?
Let ${\displaystyle x=}$ original price of the sofa, Write an equation for the statement "the sale price was $60\mathrm{\%}$ of the original price"

.___$=456$
(Use integers or decimals for any numbers in the expression.)
The original price was $___.
(Simplify your answer.)

Your instructor had 24 marbles. She lost 3. What fractional part of her marbles does she still have? Make sure your answer is simplified.

A truck rental company rents a moving truck for one day by charging $27 plus $0.10 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 187 miles? 439 miles?
Type the linear equation that relates the cost C, in dollars, of renting the truck to the number of x miles driven.
${\displaystyle C=}$
What is the cost of renting the truck if the truck is driven 187 miles?
${\displaystyle C=\mathrm{\$}?}$
What is the cost of renting the truck if the truck is driven 439 miles?
${\displaystyle C=\mathrm{\$}}$

Two pizzas are the same size. One is cut into 6 pieces and the other is cut into 24 pieces. Is 1 out 6 pieces the same amount of pizza as 3 out of 24 pieces? If they are not equal, which piece is larger? Justify your answer.

The future value $5000 invested for 3 years at a rate r compounded annually is given by ${\displaystyle S=5000{(1+r)}^3}$. Complete parts (a) through (d).
a) Complete the table below to determine the future value of $5000 at certain interest rates.
$\begin{array}{|ccccc|}\hline Rate& 4\mathrm{\%}& 5\mathrm{\%}& 7.25\mathrm{\%}& 10.5\mathrm{\%}\\ \text{Future Value}& \$?& \$?& \$?& \$?\\ \hline\end{array}$
(Type integers or decimal rounded to the nearest hundredth.)

The inverse notation ${\displaystyle f^{-1}}$ used a pure mathematics problem is not always used when finding inverses of applied problems. Rether, the inverse of a function such as ${\displaystyle C=C\left(q\right)}$ will be ${\displaystyle q=q\left(C\right)}$. The following problem illustrates this ideal.
The ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the following functions.
a) What is the ideal weight of a 6-foot male?
b) Express the height h as a function of weight W. Verify your answer by cheking that ${\displaystyle W\left(n\left(W\right)\right)=W=h}$
c) What is the height of a male who is at his ideal weight of 80 killograms?

Write the following fraction proportions as ratio proportions.
${\displaystyle \frac{5}{7}=\frac{15}{21}}$

Write the decimals in words. Write the money amounts in words for dollars and fractions for cents. Write the words in decimals. 7.8

To calculate: The solution of absolute value inequality ${\displaystyle -9\le 4-|2k-1|}$ and write solution set in interval notation.

Determine ${\displaystyle z\alpha }$ for the following. (Round your answer to two decimal place)
a) ${\displaystyle \alpha =0.0089}$
b) ${\displaystyle \alpha =0.09}$
c) ${\displaystyle \alpha =0.707}$

An electric utility company determines the monthly bill by charging 85.4 cents per​ kilowatt-hour (kWh) used plus a base charge of ​$17.55 per month.​ Thus, the monthly charge is given by the function ${\displaystyle f\left(W\right)=0.854W+17.55}$ ​dollars, where W is the number of​ kilowatt-hours.
a. Find f (6000​) and explain what it means.
b. What is the monthly charge if 9500 kWh are​ used?
a. Select the correct choice below and fill in the answer box to complete your choice.
​(Simplify your answers. Type integers or​ decimals.)
A. ${\displaystyle f\left(6000\right)=}$ nothing.
The charge for 6000 kWh is $nothing.
B. ${\displaystyle f\left(6000\right)=}$ nothing.
The charge for nothing kWh is ​$6000.
b. The monthly charge is ​$nothing if 9500 kWh are used.
​ (Simplify your answer. Type an integer or a​ decimal.)

Even though housing prices have been declining in many parts of the country, in Lara's neighborhood, they have been increasing steadily since Lara bought her home in 2006. Lara purchased her home in 2006 for $120,000, and it steadily increases its value by $4100 a year. Let V represent the market value (in dollars) of her home; x, the length of time she has lived there (in years). Complete parts a through d below.
a. Complete the following table.
$\begin{array}{|ccc|}\hline Year& x& \text{V, Market value}\\ 2006& & \$\\ 2011& & \$\\ 2014& & \$\\ \hline\end{array}$
b. Write a symbolic rule that expresses V in terms of x.
c. Determine the expected value of her home in 2016. (Simplify your answer)
d. In which year is the value of her home expected to reach $177,400?