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Nikolay [14]
3 years ago
10

A number is selected randomly from the integer from 10to30 what is the probability of picking a multiple of 4or5​

Mathematics
1 answer:
arlik [135]3 years ago
6 0

Answer:

\frac{3}{7}

Step-by-step explanation:

Start by finding how many integers there are from 10-30...

30-10+1=20+1=21

Note we have to add 1 since it is inclusive.

Now, let's find how many multiples of 4 or 5 there are from 10-30...

4*3=12

4*4=16

4*5=20

4*6=24

4*7=28

5*2=10

5*3=15

5*4=20

5*5=25

5*6=30

5+5-1=9

Note we have to subtract 1 since 20 is counted twice.

The probability would be...

\frac{Multiples\ of\ four\ and\ five\ from\ 10-30}{Amount\ of\ integers\ between\ 10-30}=\frac{9}{21}=\frac{3}{7}

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Answer:

a=\frac{13}{11}   b =\frac{-2}{11}

Step-by-step explanation:

  • By equating coefficients on both sides of respective terms.

Given,

\frac{x-4}{x^2+7x-18} = \frac{a}{x+9} + \frac{b}{x-2}

<u>Now take  </u><u>lcm</u><u> on right hand side </u>

\frac{x-4}{x^2+7x-18} =\frac{a(x-2)+b(x+9)}{x^2+7x-18}

By equating coefficients of respective terms

x-4 = a(x-2)+b(x+9)

a+b=1  -----1 ; 9b-2a=-4  -----2

Substitute b=1-a in 2

9(1-a)-2a=-4

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As b=1-a=1- \frac{13}{11}=\frac{-2}{11}

3 0
3 years ago
In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distributi
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Answer:

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.

Step-by-step explanation:

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

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.

3.41 kg with a standard deviation of 0.55 kg.

This means that \mu = 3.41, \sigma = 0.55

What proportion of baby boys in the United States are born with low birth weight?

This is the pvalue of Z when X = 2.5. So

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

Z = \frac{2.5 - 3.41}{0.55}

Z = -1.65

Z = -1.65 has a pvalue of 0.0495

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.

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