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3 years ago

7

A and B working together can do a work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can

do the work.

1 answer:

svetlana [45]3 years ago

6 0

Answer:

15 days

Step-by-step explanation:

Let x be the number of days needed for B to complete the job. Then x-5 is the number of days needed for A to complete the job.

In 1 day,

A completes $\dfrac{1}{x-5}$ of all work;
B completes $\dfrac{1}{x}$ of all work.

Hence, in 1 day both A and B complete $\dfrac{1}{x-5}+\dfrac{1}{x}$ of all work. A and B working together can do a work in 6 days. Then

$6\cdot \left(\dfrac{1}{x-5}+\dfrac{1}{x}\right)=1.$

Solve this equation:

$\dfrac{6x+6x-30}{x(x-5)}=1,\\ \\12x-30=x^2-5x,\\ \\x^2-17x+30=0,\\ \\D=(-17)^2-4\cdot 30=289-120=169=13^2,\\ \\x_{1,2}=\dfrac{17\pm 13}{2}=2,\ 15.$

If $x=2,$ then $x-5=-3$ that is impossible. So, B needs 15 days to complete the work alone.

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Graph is attached below. Black line is the graph of y=-2

Blue line is the graph of x=3

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A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

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Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

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b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

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Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

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

And if we find the z score for 89 we got:

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Part c

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We can use the z score formula given by:

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And if we find the z score for 75.65 we got:

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Part d

We want this probability:

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$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

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