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2#3 = 6
5#4 =
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The correct answer is D. Because 2#3 = 6, the # symbol indicates multiplication. Therefore, 5#4 = 5 × 4 = 20.
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Four-fifths of the seats in a movie theater are filled and two-thirds of the people in the theater are children. What fraction of the total seats are filled with children?
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Multiply the fraction of the seats that are filled by the fraction of the people that are children:
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An isosceles triangle always has
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An isosceles triangle is a triangle with two equal sides and two equal angles. It can have one right angle, one obtuse angle, or one angle measuring 45°, but it doesn't always.
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Contest participants are each assigned a ticket in one of the following colors: red, blue, or orange. There are 8 red tickets assigned, 20 blue tickets assigned, and 12 orange tickets assigned. If one participant is to be selected at random, what is the likelihood that the selected person's assigned ticket will be orange?
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There are 8 + 20 + 12, or 40 total tickets assigned. There are 12 orange tickets assigned. The probability that the selected person's ticket will be orange is
 which can be reduced to  |
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A restaurant had C customers in 2000, with K orders for pizza. What is the restaurant's monthly average number of pizza orders for 2000?
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The number of customers is irrelevant because the question asks for the monthly average number of orders. There are 12 months in a year, so divide the number of orders by 12:
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If k = –2, then k + k(k) =
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Plug –2 in for k in the given equation: –2 + –2(–2) = –2 + 4 = 2.
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If 2x – 7 = 3, then 3x + 1 =
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Solve the first equation for x:
Then plug that value of x into the second equation to find its value: 3(5) + 1 = 15 + 1 = 16. |
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What is the measure of an angle whose supplementary angle is 150°?
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Two angles are said to be supplementary if the sum of their measures is 180°. 180 – 150 = 30. Therefore, the measure of the angle described in the question is 30°.
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If four boxes of books each weighing at least 20 pounds have an average weight of 60 pounds, and if one of the boxes weighs 80 pounds, what is the maximum possible weight of the heaviest box in pounds?
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There are four boxes and the average weight is 60 pounds, so the total weight of all four boxes is 4 × 60, or 240 pounds. One of the boxes must weigh 80 pounds, so the remaining three boxes total 240 – 80, or 160 pounds. To find the maximum weight of the heaviest remaining box, the two others must be the minimum weight, which is 20 pounds. Therefore, the maximum possible weight of the heaviest box is 160 – 20 – 20, or 120 pounds.
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If a = 2b and 4b = 6c, then a =
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The second equation can be written as 2(2b) = 6c. Because 2b = a, you can plug a into the equation to get 2a = 6c. Then divide both sides by 2 to get a = 3c.
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Given that 3x + 8y = 43 and 3x – 7y = 13, find the value of y.
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. Subtract the second equation from the first equation to get rid of the x variable. Subtracting the y terms gives you 15y (8y – (–7y)) and subtracting the numbers gives you 30 (43 – 13). The equation then becomes 15y = 30. Divide both sides by 15 to get y = 2.
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The expression 4! is equal to
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The expression 4! is a factorial. To find the value, multiply the number by every positive whole number beneath it: 4 × 3 × 2 × 1 = 24.
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Find the factors of x3 – 2x2 – 35x.
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First, factor out an x to get x(x2 – 2x – 35). Then factor the quadratic. It factors to (x – 7)(x + 5). Therefore, the factors of the expressions are x(x – 7)(x + 5).
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The difference between the surface area and the volume of a cube with a side of 4 is
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Find the surface area first. The area of one face is 4 squared, or 16. Multiply this by 6 because there are six faces: 16 × 6 = 96. Next find the volume: 4 × 4 × 4 = 64. Now subtract to get the difference: 96 – 64 = 32.
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