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quester [9]
3 years ago
10

A northbound bus and a southbound bus are at a bus stop at the same time. The northbound bus returns to the bus stop every 20 mi

nutes and the southbound bus returns to the bus stop every 25 minutes. How long will it be before both buses are the bus stop at the same time again?
A. 50 minutes
B. 100 minutes
C. 200 minutes
D. 500 minutes

If you could explain how you got the answer that'll be great!
Mathematics
2 answers:
gulaghasi [49]3 years ago
4 0

The question is essentially asking for the least common multiple of 20 and 25. There are several ways you can find the LCM. One easy way is to divide the product by the GCD (greatest common divisor).

GCD(20, 25) = 5 . . . . . see below for a way to find this, if you don't already know

LCM(20, 25) = 20×25/GCD(20, 25)

... = 500/5 = 100

The buses will be there together again after ...

... B. 100 minutes

_____

You can also look at the factors of the numbers:

... 20 = 2²×5

... 25 = 5²

The least common multiple must have factors that include all of these*, so must be ...

... 2²×5² = 100

___

* you can describe the LCM as the product of the unique factors to their highest powers. 20 has 2 raised to the 2nd power. 25 has 5 raised to the 2nd power, which is a higher power of 5 than is present in the factorization of 20. Hence the LCM must have 2² and 5² as factors.

_____

You can also look at the factorization of 20 and 25 to see that 5 is the only factor they have in common. That is the GCD, sometimes called the GCF (greatest common factor).

lukranit [14]3 years ago
3 0

Every 100 minutes. You would need to find the lcm. So 20x5=100 and 25x4=100

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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation o
Mumz [18]

Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that \mu = 2.5, \sigma = 0.2

Sample of 41

This means that n = 41, s = \frac{0.2}{\sqrt{41}}

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}

Z = -9.6

Z = -9.6 has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

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kenny6666 [7]

Answer:

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Read 2 more answers
The disctance between -8 and 5 on the number line can be found by which expression??
Ilia_Sergeevich [38]
It's A.  First of all, one of the only 2 things in math that will NEVER be negative is distances/lengths and times.  You have a distance here, so because one of your 2 numbers is negative, you have to take the absolute value of the difference.  -8-5 = -11, but the absolute value of that is 11.  Put the numbers on a number line and count the units between -8 and +5 and there are 11 units between those 2 numbers.
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3 years ago
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frez [133]

Answer:

0.1

Step-by-step explanation:

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5 0
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vredina [299]
25-29 ok so first do 9-5 equals 4
4 0
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