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gayaneshka [121]
3 years ago
10

Solve for b: 16b = 12

Mathematics
1 answer:
Zina [86]3 years ago
5 0

Answer:

b = 3/4

Step-by-step explanation:

Hi!!!

You want the value of B. To get that, we have to divide both sides by 16:

\frac{16}{16}b =\frac{12}{16}

\frac{12}{16} = \frac{3}{4}

Thus the answer to your question is $\boxed{b = \frac{3}{4} }.

<u>Check:</u>

3/4 * 16 = 3 * 4 = 12.

12 = 12

So we are correct!!!

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A company considers buying a machine to manufacture a certain item. When tested, 28 out of 600 items produccd by the machine wer
weqwewe [10]

Answer:

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject H_0, as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

Step-by-step explanation:

The null and alternate hypothesis are:

H0:p≥0.03

Ha:p<0.03

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis:

This means that \mu = 0.03, \sigma = \sqrt{0.03*0.97}

28 out of 600 items produced by the machine were found defective.

This means that n = 600, X = \frac{28}{600} = 0.0467

Value of the test-statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.0467 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{600}}}

z = 2.4

P-value of the test:

The p-value of the test is the probability of finding a sample proportion below 0.0467, which is the p-value of z = 2.4.

Looking at the z-table, z = 2.4 has a p-value of 0.9918.

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject H_0, as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

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Step-by-step explanation:

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If the cone and the square pyramid have the same volume, find the radius of the cross section of the cone. Round your answer to
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Pi r^2= 8.7^2

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6 0
3 years ago
Do you tailgate the car in front of you? About 35% of all drivers will tailgate before passing, thinking they can make the car i
Vesna [10]

Answer:

(a) The histogram is shown below.

(b) E (X) = 4.2

(c) SD (X) = 2.73

Step-by-step explanation:

Let <em>X</em> = <em>r</em><em> </em>= a driver will tailgate the car in front of him before passing.

The probability that a driver will tailgate the car in front of him before passing is, P (X) = <em>p</em> = 0.35.

The sample selected is of size <em>n</em> = 12.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 12 and <em>p</em> = 0.35.

The probability function of a binomial random variable is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x}

(a)

For <em>X</em> = 0 the probability is:

P(X=0)={12\choose 0}(0.35)^{0}(1-0.35)^{12-0}=0.006

For <em>X</em> = 1 the probability is:

P(X=1)={12\choose 1}(0.35)^{1}(1-0.35)^{12-1}=0.037

For <em>X</em> = 2 the probability is:

P(X=2)={12\choose 2}(0.35)^{2}(1-0.35)^{12-2}=0.109

Similarly the remaining probabilities will be computed.

The probability distribution table is shown below.

The histogram is also shown below.

(b)

The expected value of a Binomial distribution is:

E(X)=np

The expected number of vehicles out of 12 that will tailgate is:

E(X)=np=12\times0.35=4.2

Thus, the expected number of vehicles out of 12 that will tailgate is 4.2.

(c)

The standard deviation of a Binomial distribution is:

SD(X)=np(1-p)

The standard deviation of vehicles out of 12 that will tailgate is:

SD(X)=np(1-p)=12\times0.35\times(1-0.35)=2.73\\

Thus, the standard deviation of vehicles out of 12 that will tailgate is 2.73.

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