1- Choice D is correct
The correct answer is 9 The line segment is from 1 to - \ 8. Therefore, the line is 9 units. 1 – \ (- \ 8)= 1 \ + \ 8=9
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2- Choice A is correct
The correct answer is 1,350 Use area of rectangle formula. Area = length × width ⇒ A = 30 \ ×\ 45 ⇒ A = 1,350
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3- Choice A is correct
The correct answer is 32 average (mean) = \frac{sum \ of \ terms}{number \ of \ terms}⇒ average =\frac{ 32 \ + \ 35 \ + \ 29}{3} ⇒ average = 32
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4- Choice A is correct
The correct answer is 3 : 2 Peter’s speed = \frac{120}{4} = 30 Jason’s speed = \frac{160}{8} = 20 \frac{The \ average \ speed \ of \ peter}{The \ average \ speed \ of \ Jason}= \frac{30}{20} equals to: \frac{3}{2} or 3 : 2
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5- Choice B is correct
The correct answer is 8 \ (4 \ - \ x)=96 Plug in x=- \ 8 in each equation. A. x \ (2 \ x \ - \ 4)=120→(- \ 8) \ (2 \ (- \ 8) \ - \ 4)=(- \ 8) \ × \ ( - \ 16 \ - \ 4)=160 B. 8 \ (4 \ - \ x)=96→8 \ (4 \ - \ (- \ 8)=8 \ (12)=96 C. 2 \ (4 \ x \ + \ 6)=79→2 \ (4 \ (- \ 8) \ + \ 6)=2 \ (- \ 32 \ + \ 6)=- \ 52 D. 6 \ x \ - \ 2=- \ 46→6 \ (- \ 8) \ - \ 2=- \ 48 \ - \ 2= - \ 50 Only option B is correct.
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6- Choice B is correct
The correct answer is 25.12 The diameter of the circle is 8 inches. Therefore, the radius of the circle is 4 inches. Use circumference of circle formula. C = 2 \ π \ r ⇒ C = 2 \ × \ 3.14 \ × \ 4 ⇒ C = 25.12
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7- Choice B is correct
The correct answer is 15 3 workers can walk 9 dogs ⇒ 1 workers can walk 3 dogs. 5 workers can walk (5 \ × \ 3) \ 15 dogs.
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8- Choice C is correct
The correct answer is (0, \ 0) The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.
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9- Choice C is correct
The correct answer is 435 19 \ + \ (16 \ × \ 26) = 19 \ + \ 416 = 435
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10- Choice D is correct
The correct answer is $38 1 hour: $4.75 8 hours: 8 \ × \ $4.75 = $38
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11- Choice C is correct
The correct answer is 143^° An obtuse angle is an angle of greater than 90^° and less than 180^°. From the options provided, only option C (143 degrees) is an obtuse angle.
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12- Choice A is correct
The correct answer is \frac{23}{9} 6 \ – \ 3 \ \frac{4}{9} = \frac{54}{9} \ - \ \frac{31}{9} = \frac{23}{9}
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13- Choice D is correct
The correct answer is 13.64\% The number of guests that are not present are (220 \ – \ 190) \ 30 out of 220 = \frac{30}{220} Change the fraction to percent: \frac{30}{220} \ × \ 100\%=13.64\%
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14- Choice D is correct
The correct answer is = Each kilogram is 1,000 grams. 18,023 grams = \frac{18,023}{1,000}=18.023 kilograms. Therefore, two amounts provided are equal.
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15- Choice B is correct
The correct answer is $300 Aria teaches 36 hours for three identical courses. Therefore, she teaches 12 hours for each course. Aria earns $25 per hour. Therefore, she earned $300 \ (12 \ × \ 25) for each course.
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16- Choice C is correct
The correct answer is 63\% The number of female students in the class is (60 \ – \ 22) \ 38 out of 60 = \frac{38}{60} Change the fraction to percent: \frac{38}{60} \ × \ 100\%=63\%
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17- Choice C is correct
The correct answer is 114 Write a proportion and solve. \frac{6 \ soft \ drinks}{9 \ guests} = \frac{x}{171\ guests} x =\frac{171 \ × \ 6}{9} ⇒x=114
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18- Choice C is correct
The correct answer is 6 Times Every 90 minutes Emma checks her email. In 9 hours (540 minutes), Emma checks her email (540 \ ÷ \ 90) \ 6 times.
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19- Choice C is correct
The correct answer is 59\% There are 44 students in the class. 18 of the are male and 26 of them are female. 26 out of 44 are female. Then: \frac{26}{44}=\frac{x}{100}→ 2,600=44 \ x→ x=2,600 \ ÷ \ 44 \approx 59\%
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20- Choice C is correct
The correct answer is 43 Divide the number flowers by 12: \ 516 \ ÷ \ 12 = 43
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21- Choice A is correct
The correct answer is 24 average (mean) = \frac{sum\ of \ terms}{number \ of\ terms}⇒ average =\frac{2 \ + \ 5 \ + \ 22 \ + \ 28 \ + \ 32 \ + \ 35 \ + \ 35 \ + \ 33}{8} ⇒ average = 24
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22- Choice B is correct
The correct answer is 5,231.5 Rounding decimals is similar to rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they are dropped, and the tenths place does not change. For example, rounding 0.843 to the nearest tenth would give 0.8. Therefore, 5,231.48245 rounded to the nearest tenth is 5,231.5.
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23- Choice D is correct
The correct answer is 748 square feet Perimeter of rectangle formula: P = 2 (length + width) ⇒112 =2 \ (l \ + \ 22) ⇒ l= 34 Area of rectangle formula: A = length × width ⇒ A = 34 \ × \ 22 ⇒ A = 748
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24- Choice D is correct
The correct answer is 120 ft^3 Use volume of rectangle prism formula. V = length × width × height ⇒ V= 6 \ × \ 4 \ × \ 5 ⇒ V= 120
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25- Choice D is correct
The correct answer is \frac{1}{10} , \ \frac{1}{8}, \ \frac{1}{6}, \ \frac{1}{3} In fractions, when denominators increase, the value of fractions decrease and as much as numerators increase, the value of fractions increase. Therefore, the least one of this list is: \frac{1}{10} and the greatest one of this list is: \frac{1}{3 }
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26- Choice E is correct
The correct answer is 110^° All angles in every triangle add up to 180^°. Let x be the angle ABC. Then: 180 = 25 \ + \ 45 \ + \ x ⇒ x=110^°
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27- Choice C is correct
The correct answer is 30 miles per gallon Write a proportion and solve. 15 gallons: 450 miles 1 gallon: 450 \ ÷ \ 15 = 30 miles
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28- Choice C is correct
The correct answer is 2.5\% 0.025 = \frac{25}{1000} = \frac{2.5}{100} = 2.5\%
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29- Choice A is correct
The correct answer is 4,896 1 acre: 153 pine trees 32 acres: 153 \ × \ 32 = 4,896 pine trees
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30- Choice A is correct
The correct answer is \frac{5}{6} The students that had to go to summer school is 5 out of 30 = \frac{5}{30} = \frac{1}{6} Therefore \frac{5}{6} students did not have to go to summer school.
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31- Choice D is correct
The correct answer is \frac{5}{7} \frac{2}{5} = 0.4 \frac{1}{3} = 0.33 \frac{6}{9} = 0.67 \frac{5}{7} = 0.71 \frac{5}{7} is the largest.
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32- Choice D is correct
The correct answer is 10 4 garbage trucks can collect the trash of 28 homes. Then, one garbage truck can collect the trash of 7 homes. To collect trash of 70 houses, 10 \ (70 \ ÷ \ 7) garbage trucks are required.
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33- Choice C is correct
The correct answer is $33.00 4 steak dinners = 4 \ × \ $8.25 = $33
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34- Choice D is correct
The correct answer is $92.90 $3.45 per mile for the first 22 miles. Therefore, the cost for the first 22 miles is: 22 \ × \ $3.45 = $75.9 $4.25 per mile for each mile over 22, therefore, 4 miles over 22 miles cost: 4 \ × \ $4.25 = $17 In total, David pays: $75.9 \ + \ $17 = $92.90
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35- Choice A is correct
The correct answer is 3 Write a proportion and solve. \frac{6 \ soft \ drinks}{10 \ guests} = \frac{x}{5 \ guests} x =\frac{5 \ × \ 6}{10} ⇒x=3
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36- Choice B is correct
The correct answer is 216 The number of candies should be a whole number! Check each option provided. A. 167 \ ÷ \ 8 = 23.375 B. 216 \ ÷ \ 8 = 27 C. 243 \ ÷ \ 8 = 30.375 D. 223 \ ÷ \ 8 = 27.875 Only option B gives a whole number.
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37- Choice C is correct
The correct answer is $39.95 They contributed: $10.25 \ + \ $11.25 \ + \ $18.45 = $39.95 in total, so the maximum amount that they can spend is the sum of their contribution.
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38- Choice C is correct
The correct answer is 32,000 Use area of rectangle formula. Area = length × width ⇒ A= 160 \ × \ 200 ⇒ A= 32,000
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39- Choice B is correct
The correct answer is 80 12 cups: 1 hour 960 cups: 960 \ ÷ \ 12 = 80 hours
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40- Choice D is correct
The correct answer is 250 Write a proportion and solve. \frac{\frac{1}{5}}{50} = \frac{1}{x}⇒ x = 50 \ × \ 5=250
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