The measures of the length, width, and height of a rectangular prism are in the ratio 2:6:5. If the volume of the prism is 1, 620 mm3, what is the width of the prism?
Answer(s): D
The volume of a prism is equal tolwh, where is the length of the prism, w is the width of the prism, and is the height of the prism:The length of the prism is2(3) = 6 mm, the width of the prism is6(3) = 18mm, and the height of the prism is5(3)=15mm.
A box contains five blue pens, three black pens, and two red pens. If every time a pen is selected, it is removed from the box, what is the probability of selecting a black pen followed by a blue pen?
Answer(s): A
At the start, there are 5 + 3 + 2 = 10 pens in the box, 3 of which are black. Therefore, the probability of selecting a black pen is3/10After the black pen is removed, there are nine pens remaining in the box, five of which are blue. The probability of selecting a blue pen second is5/9To find the probability that both events will happen, multiply the probability of the first event by the probability of the second event:
In the diagram above, lines NO and PQ are parallel to each other and perpendicular to lines JK and LM. Line JK is parallel to line LM. If angle CBD is 70 degrees, what is the measure of angle ZBK?
Answer(s): B
AngleCBDand anglePBZare alternating angles--their measures are equal. AnglePBZ= 70 degrees.AnglePBZ+ angleZBKform anglePBK. LinePQis perpendicular to lineJK; therefore, anglePBKis a right angle (90 degrees). AngleZBK= anglePBK anglePBZ= 90 70 = 20 degrees.
Monica sells pretzels in the cafeteria every school day for a week. She sells 14 pretzels on Monday, 12 pretzels on Tuesday, 16 pretzels on Wednesday, and 12 pretzels on Thursday. Then, she calculates the mean, median, and mode of her sales. If she sells 13 pretzels on Friday, then
Answer(s): C
For the first four days of the week, Monica sells 12 pretzels, 12 pretzels, 14 pretzels, and 16 pretzels.The median value is the average of the second and third values: IfMonica sells 13 pretzels on Friday, the median will still be 13. She will have sold 12 pretzels, 12 pretzels, 13 pretzels, 14 pretzels, and 16 pretzels. The median stays the same.
What is the tenth term of the pattern below?
The denominator of each term in the pattern is equal to 2 raised to the power given in the numerator. The numerator decreases by 1 from one term to the next. Since 10 is the numerator of the first term, 10 9, or 1, will be the numerator of the tenth term.21= 2so the tenth term will be1/2.
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