The figure below shows a shaded circular region inside a larger circle:

Working together, it takes 2 computers 12 minutes to send out emails. If it takes the slower 30 minutes to the job on its own, h

artcher [175]

Answer:

The faster computer can do the job in 20 mins on it own.

Step-by-step explanation:

Given:

Time taken by slower computer to do job on its own =30 minutes.

Time taken by both the computers to do the job = 12 mins.

We need to find the Time taken by faster computer to do job on its own.

Solution:

Let the the Time taken by faster computer to do job on its own be 'x'.

Now we know that;

Rate to complete the job is equal to number of jobs divided by time taken to complete the job.

Rate of faster computer = $\frac1x$

Rate of slower computer = $\frac{1}{30}$

Rate of both the computers = $\frac{1}{12}$

Now we can say that;

Rate of both the computers is equal to sum of Rate of faster computer and Rate of slower computer.

framing in equation form we get;

$\frac{1}{12}=\frac{1}{30}+\frac{1}{x}\\\\\frac{1}{x} = \frac{1}{12}-\frac{1}{30}$

Now we will take the LCM to make the denominator common we get;

$\frac{1}{x}=\frac{5}{12\times5}-\frac{2}{30\times2}\\\\\frac1x=\frac{5}{60}-\frac{2}{60}$

Now denominator are same so we will solve the numerator.

$\frac1x=\frac{5-2}{60}\\\\\frac1x=\frac{3}{60}\\\\\frac1x=\frac{1}{20}\\\\x=20\ mins$

Hence The faster computer can do the job in 20 mins on it own.

4 0

3 years ago

Help asap with math evaluate expression

madam [21]

Answer:

14

Step-by-step explanation:

you can simplify it by turning a²+b²/a-b

into

(a-b)²+2ab / a-b

eliminate the fraction

a-b +2ab

a=-1

b=-5

-1-(-5)+2*-1*-5

-1+5+10 = 14

5 0

2 years ago

Simplify the expressions <br> -8(5r+6)+9(6r+3)

nirvana33 [79]

7 0

2 years ago

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: