Math - Numbers & Operations practice

A DVD player is on sale for 15% off the regular price of $135. After the price reduction, a 5% sales tax is added. How much will someone pay for the DVD player after tax? A. $141.75 B. $120.49 C. $114.75 D. $109.01

D. $109.01 Take each step one at a time. Sale: $135 × .15 = $20.25 $135 - $20.25 = $114.75 Tax: $114.75 × .05 = $5.74 $114.75 - $5.74 = $109.01

The diameter of a pollen grain from a flower can range from 0.0000004 inches to 0.00002 inches. Write the equivalent range in scientific notation.

from 4.0 × 10⁻⁷ to 2.0 × 10⁻⁵

A dance committee surveyed some students about suggestions for the next school dance. When they analyzed the results, 45% of those surveyed were seniors, ¹/₄ of those surveyed were juniors, 0.1 of those surveyed were sophomores, and the remainder were freshmen. What fraction of the students surveyed were freshmen?

¹/₅ of the students surveyed were freshmen. To solve, rewrite each group of students as a percent. Subtract this total from 100 (the total percent of students). This percentage is your freshmen. Rewrite as a fraction. Seniors = 45% Juniors = ¹/₄ = 25% Sophomores = .1 = 10% 45% + 25% + 10% = 80% 100% - 80% = 20% 20% = ²⁰/₁₀₀ = ²/₁₀ = ¹/₅

A virus measures 0.000022 mm in length. Write the value in scientific notation.

2.2 × 10⁻⁵

What expression represents 270,000 written in scientific notation?

2.7 × 10⁵

The power output of a nuclear reactor is 2.4 × 10⁷ watts. Write the same number expressed in standard notation.

24,000,000 watts

The diameter of the sun is 864,000 miles. What is this value expressed in scientific notation?

8.64 × 10⁵ miles

Jupiter's diameter is 88,640 miles. What is this measurement expressed in scientific notation?

8.864 × 10⁴ miles

Which of these is equivalent to (¹/₃)³ × (¹/₃)⁴? A. (¹/₃)⁷ B. (²/₃)⁷ C. (¹/₃)¹² D. (¹/₉)¹²

A. (¹/₃)⁷ According to the laws of exponents, you do not multiply exponents. Instead, you add them. (Conversely, when you divide, you really subtract.) Thus, ¹/₃ will remain unchanged, but you will add the exponents 3 and 4, which equal 7.

What is the value of the expression n² - w²/q if n = ¹/₃, w = -6, and q = ²/₃? A. -53 ⁸/₉ B. -23 ⁸/₉ C. 24 ¹/₉ D. 54 ¹/₉

A. -53 ⁸/₉ Substitute the given numbers in for the variables and solve the expression. (¹/₃)² - (-6)²/(²/₃) [Square ¹/₃ and -6] ¹/₉ - 36/²/₃ [Multiply 36 by the reciprocal of the fraction ²/₃ to get rid of it.] ¹/₉ - 54 [Subtract.] = -53 ⁸/₉

Jane has determined that 169 < X < 196. What must be true about √X? A. 13 < √X < 14 B. 84.5 < √X < 98.0 C. 338 < √X < 392 D. 28,561 < √X < 38,416

A. 13 < √X < 14 If X is greater than 169 but less than 196, then the square root of X must be greater than the square root of 169 and less than the square root of 196. √169 = 13 √196 = 14

What is the relationship between these fractions? .75/1, 1.5/2, 3/4, and 9/12 A. The fractions are equivalent. B. The fractions are in ascending order. C. The fractions are in descending order. D. The fractions are doubling from left to right.

A. The fractions are equivalent. You only need to simplify a few of the fractions to determine the relationship. 9/12 = 3/4 Therefore, the only possible answer is A.

If x is even and y is odd, which expression will produce an even number? A. x+2y B. 2x+y C. x²+y² D. (x+y)²

A. x + 2y Use the substitution method by plugging in any even number for x and any odd number for y. Try out each formula and compare the results. If x=2 and y=3 then (2) + 2(3) = 2 + 6 = 8 8 = even number

Three-fifths of a city's population is registered to vote. In the last election, 75% of the registered voters cast a ballot. What fractional part of the city's population voted in the last election? A. ⁹/₂₀ B. ³/₄ C. ⁴/₅ D. ²⁷/₂₀

A. ⁹/₂₀ To solve, you must multiply the number of people registered to vote by the number of people who voted. Convert both numbers to fractions and multiply across. Three-fifths = ³/₅ 75% = ³/₄ ³/₅ × ³/₄ = ⁹/₂₀

Which number is NOT a perfect square? A. 729 B. 1,280 C. 3,600 D. 5,329

B. 1,280 A perfect square is a number that has a whole number for its square root. In other words, a whole number multiplied by itself will equal a perfect square. Ex: 3×3=9, 4×4=16, 5×5=25, etc. The square root of 729 is 27. The square root of 1,280 is 35.77708... The square root of 3,600 is 60. The square root of 5,329 is 73.

Tina plays on the Lakewood High softball team. During her first season, she went to bat 27 times and got 6 hits. If she continues to hit at about the same rate, how many total hits will she have after she bats 40 times? A. 4 B. 9 C. 15 D. 19

B. 9 You can solve this with a proportion. 6 hits out of 27 times at bat is equal to how many hits out of 40 times at bat? H stands for hits. Cross multiply and solve for H. ⁶/₂₇ = H/₄₀ 240 = 27H H = 8.888888...

Which number is irrational? A. -2 B. √8 C. 3 D. ²²/₈

B. √8 = 2.82842712474619

The area of Alaska is about 6 × 10⁵ square miles. The area of Rhode island is about 1.5 × 10³ square miles. What is the difference between the area of Alaska and the area of Rhode Island? A. 4.5 × 10² square miles B. 4.5 × 10⁵ square miles C. 5.985 × 10⁵ square miles D. 5,985 × 10⁵ square miles

C. 5.985 × 10⁵ 6 × 10⁵ = 600,000 1.5 × 10³ = 1,500 600,000 - 1,500 = 598,500 598,500 = 5.985 × 10⁵

A state game warden has been observing deer during a particular severe winter. She recorded that 14 of the 96 deer she observed throughout the state appeared to be suffering from malnutrition. The state has an estimated deer population of 600,000. Approximately how many deer can she predict are suffering from malnutrition? A. 14,000 B. 72,000 C. 88,000 D. 96,000

C. 88,000 Set up a proportion. Cross multiply and solve. D stands for deer. ¹⁴/₉₆ = D/₆₀₀₀₀₀ 96D = 8,400,000 D = 87,500

Which expression is equivalent to 8¹²/8³? A. 1⁹ B. 8⁴ C. 8⁹ D. 5¹²

C. 8⁹ The laws of exponents tell us when exponents are being divided in an expression, we really subtract them. 12 - 3 = 9. So, 8⁹.

Earth has a surface area of 1.97 × 10⁸ square miles. Another planet has a surface area 13 times the surface area of Earth. What is the surface area of the planet? A. 1.515 × 10⁷ B. 2.10 × 10⁸ C. 2.56 × 10⁸ D. 2.56 × 10⁹

D. 2.56 × 10⁹ 1.97 × 10⁸ = 197,000,000 197,000,000 × 13 = 2,561,000,000 2,561,000,000 = 2.5 × 10⁹ The shortcut is to forget the 0's. Multiply 197 by 13 = 2,561. Now add the zeros back on. You will have the same amount of zero's (8) and one added decimal place because 2,561 is one digit larger than 197. 8 + 1 = 9. So, 10⁹.

Which expression is NOT equivalent to 7? A. |−7| B. √49 C. 7¹ D. ⁷/₄₉

D. ⁷/₄₉ All the others simplify to 7. However, this fraction simplifies to ¹/₇.

Jerry is planning to buy a stereo system priced at $840 through an installment plan. This plan requires him to make a down payment of $190 and make 24 monthly payments of $32.35. How much more will Jerry pay for the stereo system through the installment plan rather than paying cash outright?

Installment Plan: Down payment $190 Monthly payments $32.35 × 24 = $776.40 Down payment + monthly payments = $966.40 Subtract the price of the stereo system in cash from the price through the installment plan to find the difference. $966.40 - $840.00 = $126.40

Adam was going to buy a new lawn mower from Lawn Care Depot for $169, less a 10% discount. He saw the same mower on sale at Tractors-R-Us. Their mower originally cost $210 and was on sale for ¹/₃ off. Which store would be the most economical place to purchase the mower?

Lawn Care Depot: $169(.10) = $16.91 $169 - $16.91 = $152.09 Tractors-R-Us: ²¹⁰/₁ × ¹/₃ = ²¹⁰/₃ = $70 $210 - $70 = $140.00 The mower costs less at Tractors-R-Us.

Explain which of the three opinion polls shows the greatest favorable result for Candidate A. Poll 1: Nine of every 20 voters are expected to vote for Candidate A. Poll 2: The percentage of voters expected to vote for Candidate A is 52%. Poll 3: There are 130,000 people expected to vote, and of these, 55,000 are expected to vote for Candidate A.

Poll 2 is the best because it shows the greatest amount of possible votes for Candidate A. Poll 1: ⁹/₂₀ = .45 = 45% Poll 2: 52% Poll 3: ⁵⁵⁰⁰⁰/₁₃₀₀₀₀ = ⁵⁵/₁₃₀ ≈ .42 = 42%

Joel has a 50-meter roll of copper wire that weighs 7.5 kilograms. Approximately how many meters of wire will be in a new shipment that weighs 502.5 kilograms?

Set up a proportion. The top values of the fractions will stand for weight. The bottom values will stand for meters of wire. Cross-multiply and solve for x. 7.5/502.5 = 50/x [cross multiply] 7.5(x) = 502.5(50) [combine terms] 7.5x = 25125 [isolate x] x = 3350 meters

An organization distributes money to various groups in the Toledo area. This organization expects to receive a gift of 15% of a $5.8 million grant. Sixty-seven percent of this gift will be distributed to the Toledo Arts Festival. Explain how to find the amount the Toledo Arts Festival will receive.

Since the Toledo Arts Festival receives the money from the organization, we first have to determine how much money the organization will receive. $5,800,000 × .15 = $870,000 Sixty-seven percent of this amount is gifted to the Toledo Arts Festival. $870,000 × .67 = $582,900

Carmella has a coupon that allows her to buy one pair of shorts at the regular price and get a second pair for half off. The shorts cost $25.50 a pair. When Carmella arrives at the store, she finds that the shorts are on sale for 30% off. She cannot use the coupon with the sale. Should Carmella choose to use her coupon to buy the shorts or buy them at the sale price?

The 30% sale price is the better option. Coupon: Multiply a pair of shorts by .50 or ¹/₂ to find its half-off price. $25.50(.5) = $12.75 $25.50 + $12.75 = $38.25 Sale: Multiply a pair of shorts by .30 or ³⁰/₁₀₀ to find 30%. $25.50(.3) = $7.65 $25.50 - $7.65 = $17.85 $17.85(2) = $35.70

Order these numbers from least to greatest: ³¹/₄, 7 ⁵/₈, √50, 7.82

√50, 7 ⁵/₈, ³¹/₄, 7.82 Put each number in the same form. Decimals will be the most clear. Then, rewrite from the smallest to the largest. ³¹/₄ = 7.75 (2nd largest) 7 ⁵/₈ = 7.625 (2nd smallest) √50 ≈ 7.07 (smallest) 7.82 (largest)