Improve Your Algebra Skills with Practice Problems

David worked $7\frac{1}{3}$ hours today and planted I I trees. It takes him about the same amount of time to plant each tree. How long did it take him to plant each tree? It took him ___________. hour to plant each tree.

Write three ratios that are equivalent to the one given. The ratio is 18:4.

Let A={1, 2, 3, 4, 5, 6, 7, 8, 9}
a) If five integers are selected from A, must at least one pair of the integer have a sume of 9?

Doug entered a canoe race. He rowed 3 ${\displaystyle \frac{1}{2}}$ miles in ${\displaystyle \frac{1}{2}}$ hour. What is his average speed in miles per hour?

Find the median of -4, 11, -12, 11, and -7.

Why can a null measurement be more accurate than one using standard voltmeters and ammeters?
What factors limit the accuracy of null measurements?

Find the missing digits in the number below if the number is the product of two equal factors. 2, _ _ 5

A standard piece of paper is 8.5 inches by 11 inches. A piece of legal-size paper is 8.5 inches by 14 inches. By what scale factor k would you need to dilate the standard paper so that you could fit two pages on a single piece of legal paper?

A restaurant has a ${\displaystyle \frac{3}{4}}$ -full pan of lasagna. If the cost is $20 per ${\displaystyle \frac{1}{3}}$ pan, how much will the restaurant charge for the ${\displaystyle \frac{1}{3}}$-full pan of lasagna?
A. $20
B. $45
C. $60
D. $125

Find z, given the following. (Give your answer correct to two decimal places.)
$x=233,\mu =223,\sigma =12.2$
$z=?$

Define rational and irrational number. Give examples.

Consider the following annuity: $1,000 due at the end of each year for three years, and $2,000 due thereafer at the end of each year for three years. Assume an interest rate of 2% compounded annually to find the present value of the annuity.

Answer this question and show the steps. ${\displaystyle \sqrt{x}+\sqrt{y}=3}$, find the value of ${\displaystyle \frac{dy}{dx}}$ at the point (4,1)

Ms. Donahue rents a space in the mall for her store. The mall owner just increased the amount of her rent. As a result, Ms. Donahue decided to raise all the prices in her store by 5%. What is the new price of an item that had an original price of $80?
A. $84
B. $85
C. $120
D. $160

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The stardard deviation of lab measurements made by students is $\sigma =10$ milligrams. Juan repeats the measurement 3 times and records the mean xbar of his 3 measurements.
(a) What is the standard deviation of Juan's mean result? (That is, if Juan kept making sets of 3 measurements and averaging them, what would be the standard deviation of all his xbar's?)
(b) How many times must juan repeat the measurement to reduce the standard deviation of xbar to5? Explain to someone who knows nothing about statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.

a student is speeding down route 11 in his fancy red Porschewhen his radar system warns him of an obstacle 400 ft ahead. heimmediately applies the brakes, starts to slow down and spots askunk in the road directly ahead of him. the "black box" in thePorsche records the cars

What is the improper fraction for ${\displaystyle \frac{9}{6}}$

What is the square root of 16

A car traveling at a certain speed will travel 76 feet per second. How many miles will the car travel in 3.1 hours if it maintains the same speed? Round to the nearest tenth. (Hint: There are 5,280 feet in one mile)

Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that $\mu <7$ hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of beta and interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)