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BARSIC [14]
3 years ago
11

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right,

with a mean of 30 minutes and a standard deviation of 15 minutes. the distribution of z-scores for those times is
Mathematics
1 answer:
dezoksy [38]3 years ago
5 0
<span>Answer: Skewed to right with mean 0 and S.D. 1 Explanation: Let's assume the z-scores as a linear transformation. then z=(x-mean)/S.D. = (x-30)/15 z(mean) = (30-30)/15= 0 z(sigma) = 15/15 = 1 Note: Shape does not change.</span>
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2 years ago
What is the square root of m^6?
Nastasia [14]
Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3

==============================

Explanation:

There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative. 

---------------------------

A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative

sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative

------------------------------

If we allow m to be negative, then the final result would be either |m^3| or |m|^3. 

The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.

Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2

4 0
3 years ago
Kacey had 48 tickets for games at the school carnival. She used 1/3 of her tickets to play the spin-the-wheel game. She used hal
vovangra [49]

Answer:

32 tickets.

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First, 1/3 of 48 is 16. So 48-16= 32. Usually, people think the remaining half is half of 48, but it's supposed to be half of 32. So half of 32 is 16. So Kacey used 32 tickets for those 2 games.

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