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xxMikexx [17]
3 years ago
8

Please answer thx so much

Mathematics
1 answer:
const2013 [10]3 years ago
6 0

Answer: E

Step-by-step explanation:

length: 3w

width: ?

perimeter: 20 inches

Formula: P=2(l+w)

Plug your values into the formula.

20=2(3w+w)

Divide by 2.

\frac{20}{2}=3w+w

Combine like terms and simplify.

10=4w

Divide by 4

\frac{10}{4}=w\\\frac{5}{2}=w

Now determine the length, replacing the value of w.

3(\frac{5}{2})=\frac{15}{2}

Now, to find the area, use the following formula: A=l*w

A=(\frac{15}{2})(\frac{5}{2})\\A=\frac{75}{4}\\ A=18.75in^2

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Answer: (2.54,6.86)

Step-by-step explanation:

Given : A random sample of 10 parking meters in a beach community showed the following incomes for a day.

We assume the incomes are normally distributed.

Mean income : \mu=\dfrac{\sum^{10}_{i=1}x_i}{n}=\dfrac{47}{10}=4.7

Standard deviation : \sigma=\sqrt{\dfrac{\sum^{10}_{i=1}{(x_i-\mu)^2}}{n}}

=\sqrt{\dfrac{(1.1)^2+(0.2)^2+(1.9)^2+(1.6)^2+(2.1)^2+(0.5)^2+(2.05)^2+(0.45)^2+(3.3)^2+(1.7)^2}{10}}

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The confidence interval for the population mean (for sample size <30) is given by :-

\mu\ \pm t_{n-1, \alpha/2}\times\dfrac{\sigma}{\sqrt{n}}

Given significance level : \alpha=1-0.95=0.05

Critical value : t_{n-1,\alpha/2}=t_{9,0.025}=2.262

We assume that the population is normally distributed.

Now, the 95% confidence interval for the true mean will be :-

4.7\ \pm\ 2.262\times\dfrac{3.0265}{\sqrt{10}} \\\\\approx4.7\pm2.16=(4.7-2.16\ ,\ 4.7+2.16)=(2.54,\ 6.86)

Hence, 95% confidence interval for the true mean= (2.54,6.86)

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