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Daily Quiz #5: March 26, 2014

The scores as of this morning are as follows: Srikhar, 130 points; Caroline, 180 points. Johnum is starting off with us at 20 points. Again, keep up the good work and have fun with today’s quiz!

Solution to yesterday’s quiz.

16. We write an equation representing the new class average after the 7 students make up the test: \frac{1638+7x}{25} = 93. Solving this equation, we find that x = 98.1.

17. To find the lowest common multiple of the three expressions, all we need to do is list the factors and include the greatest number of each that exists in any one factor. For example, a factor of 2 appears once, x appears up to twice, 3 appears once, and y appears up to twice. Multiplying these together, we get 6x2y2.

18. The number of possible magnets that could have fallen on the floor is 10 x 9 = 90. I know we didn’t account for reversed arrangements, but it’s okay because we’ll also not account for them in the numerator of the probability. The numerator, then, is 4 x 3 = 12 vowel arrangements. So the answer is 12/90 or 2/15.

19. To solve this problem, we can write an equation that represents all the students in the class. Let x represent the number of students with freckles: x + 2x + x + 4 – 7 – 3 = 30. We subtracted 7 and 3 because, like in #12, those were repeats in the hat of names. The solution is 9.

20. Using Pascal’s triangle, we can immediately tell that the coefficients of the expansion of (a + b)6 are 1, 6, 15, 20, 15, 6, 1. The probability of selecting an odd number from this list is 4/7.

Today’s quiz.

21. What is the smallest integer with exactly 15 distinct factors? (10 pts.)

22. The new iPad has a screen shaped like a parallelogram with side lengths 6 in and 2 in and angle measures 60° and 120°. What is the area of this screen? Express your answer in simplest radical form. (10 pts.)

23. The new MacBook Pro uses multiple cores to achieve the most performance; however, due to strikes in their factory in China, the cores don’t all work at the same speed. One core processes 1.6 million floating point operations in a second, and the other processes 3 million computations in two seconds. If Call of Duty requires 8 million floating point operations to load on your computer, how long will it take the computer when both cores work together? Express your answer as a decimal to the nearest tenth. (10 pts.)

24. Bonus. Each pool at the Hyperbola Hotel is planned to have a 5-foot wide sunbathing deck surrounding it. The pool will be 4 feet longer than it is wide. If 1,440 square feet of floor space have been set aside for both the pool and deck, what is the perimeter of the pool? (20 pts.)

25. Bonus. Ms. Clements, the chemistry teacher at Magnet, needs 250 mL of 20% hydrochloric acid for a Chem I lab. Her chemical cabinet has a bottle of 80% hydrochloric acid. How many mL of the stronger hydrochloric acid should she put in the volumetric flask, which she will then fill with water to the 250 mL mark? Express your answer as a decimal to the nearest tenth. (20 pts.)

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7 thoughts on “Daily Quiz #5: March 26, 2014

  1. 21. 30030
    22. 6 square root 2 (Did we have to use trigonometry, b/c I didn’t)
    23. 2.6 sec.
    24. 112 ft.
    25. ——-

  2. Sorry for the replies, but best of luck for Srikhar, Caroline, and the other Matheletes for the competition Friday (I heard they are leaving tomorrow, so yeah)

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