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3 years ago

The seven-digit number 1113A8B can be divided by 4, 5, and 9 What is the sum of the digits A and B?

Mathematics

1 answer:

Gennadij [26K]3 years ago

7 0

Answer:

Step-by-step explanation:

This seven-digit number can be divided by 4, 5 and 9.

This means that 4, 5 and 9 are ALL factors.

Find the least common multiply (LCM) of 4, 5 and 9.

Multiples of 4: 4 , 8 , 12 , 16 , 20

Multiples of 5: 5 , 10 , 15 , 20

Find a multiple of 9 that is also a multiple of 20. All multiples of 20 have the factors 4 and 5.

9 X 20 = 180

The <u>seven-digit number must be a multiple of 180</u> to have the factor 4, 5 and 9. You can find the multiples of 180 until the number looks like 1113A8B, but there are better methods.

All multiples of 180 end in the digit "0". Therefore B = 0.

1113A80

Since 9 is one of the factors, the rules for a number divisible for 3 apply. (9 is a multiple of 3).

You know that a number is divisible by 3 when its digits add to a number divisible by 3.

Find the sum of the digits:

1+1+1+3+A+8+0 = A + 14

A + 14 must be divisible by 3.

Therefore, A has to be either 1, 4, or 7.

If A = 1

1113180 ÷ 180 = 6184.333

If A = 4

1113480÷ 180= 6186

If A = 7

1113780 ÷ 180 = 6187.7

A = 4 because that number is divisible by 180.

Add A = 4 and B = 0.

A + B

= 4 + 0

= 4

The sum of digits A and B is 4.

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3 years ago

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in t

Natali5045456 [20]

Answer:

a) Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

b) Rachel, because her time had the lowest z-score.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The lower the time, the better the runner is. So whoever's time has a lower z-score is a better runner. So initially, we find the z-score of each student's time.

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes.

This means that for Rachel's time, we have that $X = 8, \mu = 11, \sigma = 3$ . So

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

$Z = \frac{8 - 11}{3}$

$Z = -1$

A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.

This means that for Kenji's time, we have that $X = 8.5, \mu = 9, \sigma = 2$ . So

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

$Z = \frac{8.5 - 9}{2}$

$Z = -0.25$

A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.

This means that for Nedda's time, we have that $X = 8, \mu = 7, \sigma = 4$ . So

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

$Z = \frac{8 - 7}{4}$

$Z = 0.25$

(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?

Kenji's time had a lower z-score, which means that he is better compared to other runners on his level, and better to his peers compared to Nedda.

(b) Who is the fastest runner with respect to his or her class? Explain why

Rachel, because her time had the lowest z-score.

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3 years ago

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3 years ago

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Answer:

Step-by-step explanation:

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However, from the question, if he's to run round the circular track once, then he must have run a total of

2πr meters, with r being the radius.

Now, the question says that he ran round the track 10 times, this means that whatever value we get there, for 1 trial, we multiply it by 10, to get the value for 10 trials. Essentially,

10 * 2πr

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3 years ago

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Answer:

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