| Problem |
Solution |
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1) Julian has scored 93 and 96 on his first two tests. With one test remaining, what is the least score
Julian needs to average 90 or better on his three tests?
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This is actually an algebra problem.
The equation for the average (mean) is:
(93 + 96 + N) / 3 = 90.
93 + 96 + N = 270
189 + N = 270
N = 81
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2) Four students form a line to use a water fountain. How many different ways can they arrange
themselves in line? |
This is a permutations problem.
1. The number of ways to pick the first student is 4
2. After picking that student, how many students are left? 3
3. After picking that student, how many students are left? 2
4. How many are left after that pick? 1
5. Multiply these together to get the total number of ways to arrange the students = 4 x 3 x 2 x 1 = 24
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3) Tammy and two of her friends are flipping coins. Tammy guesses 7 of 15 coin flips correctly.
Colin guesses 14 of 25 coin flips correctly. Winona guesses 12 of 20 coin flips correctly. Who was
the best at guessing coin flips?
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1. Compute the fraction of each person's guesses that were right and convert to decimals:
Tammy: 7/15 = .4667 , Colin: 14/25 = .56, Winona: 12/20 = .6
2. The best one was Winona.
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4) A factor of 90 is chosen at random. What is the probability that the chosen factor has both 3 and
5 as factors?
(Express your answer as a fraction in lowest terms ) |
1. Write out all the factors of 90:
45 30 18 15 10 9 6 5 3 2
There are 10 of them.
2. Find the number of these factors that also have 3 and 5 as factors:
45, 30, 15 = 3 factors.
3. Divide this number by the total number of factors = 3/10.
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5) Find the mean and mode of the following set of numbers:
60, 68, 74, 70, 59, 68, 76, 64, 57, 73, 68
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1. The mode is the one that shows up the most = 68.
2. Add up all the scores and divide by the number of scores to get the mean = 67.
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