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4vir4ik [10]
2 years ago
9

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

tient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
 + 5r = 8
 + 5r = 1
5() = r 
 = 5r
Mathematics
2 answers:
andreyandreev [35.5K]2 years ago
8 0

Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:

<span>Rate of handheld hose = 1 job / 8 minutes                  ---> 1</span>

<span>Rate of lawn sprinkler = r                                             ---> 2</span>

<span>Rate of the two combines = 1 job/ 5 minutes               ---> 3</span>

So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:

1 / 8 + r = 1 / 5

Multiplying both sides by 5:

<span>(5 / 8) + 5 r = 1                                                               ---> ANSWER</span>

mojhsa [17]2 years ago
4 0

Answer:

5/8 + 5r = 1

Step-by-step explanation:

Right on edge!

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A sample of 1714 cultures from individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiot
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Answer:

a) p represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) \hat p=\frac{973}{1714}=0.568 represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.  

Step-by-step explanation:

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".

Part a

Description in words of the parameter p

p represent the real population proportion of people who showed partial or complete resistance to the antibiotic

\hat p represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

z_{\alpha/2} represent the critical value for the margin of error

The population proportion have the following distribution  

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Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

\hat p =\frac{X}{n} where X represent the number of people with a characteristic and n the total sample size selected.

\hat p=\frac{973}{1714}=0.568 represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

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0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545

0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.  

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