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evablogger [386]

4 years ago

9

Mia worked 40 hours at her two jobs last week. She earns $20 per hour at her weekday job and $18 per hour at her weekend. She ea

rned $770 in all. How many hours did she work at each job?

1 answer:

11111nata11111 [884]4 years ago

7 0

Answer:

x = 25

Step-by-step explanation:

x = # of hrs he worked at his weekday job

w = # of hours he worked at his weekend job

25+ x = 40y = 40 - 25 = 15.

Therefore, Mia worked for 25 hours at his weekday job and 15 hours at his weekend job.

w + x = 40

20x + 18w = 770

18(x + w = 40) = 18x + 18w = 720

(20x + 18w = 770) - (18x + 18w = 720)

2x=50

x=25

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3 years ago

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The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the

Vikki [24]

Answer:

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

Previous concepts

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".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,35)".And we see that $t_{\alpha/2}=2.03$

Now we have everything in order to replace into formula (1):

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

5 0

3 years ago

Mathematics please help...

galben [10]

Answer:

the answer is B

Step-by-step explanation:

area of the minor arc is teter all over 360 times 2 pie r square.

that is

$\frac{?}{360} \times 2\pi {r}^{2}$

= but because the question said for length AB, youvhave to use only one radius.

$\frac{160}{360} \times 2 \times \pi \times 9$

You the use 40 to cancel 160 and 360 to get 4 all over 9 times 2 pie times 9.

$\frac{4}{9} \times 2 \times \pi \times 9$

You then cancel 9 with 9 to get 4 times 2 times pie

$4 \times 2 \times \pi$

this is equal to

$8\pi$

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3 years ago