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3 years ago

12

Chantal is building a fence around her swimming pool. The pool is 25 ft long and12 ft wide, and she wants a 6-ft wide rectangula

r walkway around the entire pool.How much fencing will she need?

1 answer:

Alex_Xolod [135]3 years ago

4 0

25 /12*6 =12.5 or thats what i got

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Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these

avanturin [10]

Answer:

We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%

Step-by-step explanation:

-From the given information, $\hat p=0.65$ .

-We calculate the confidence interval using this value at 95% confidence level:

$CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585]$

So, the 95% confidence interval is (0.6515,0.6585).

Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.

6 0

3 years ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

The line plot below shows the weight of each of 15 ostrich eggs . What is the total weight of the 3 heaviest eggs

erica [24]

Answer:

D). 6 3/4

Step-by-step explanation:

Given,

The three eggs with the heaviest weights are;

$2\frac{1}{2}$ ounces

$2\frac{1}{4}$ ounces, &

2 ounces

To find,

The total weight of the three heaviest eggs = $2\frac{1}{2}$ ounces + $2\frac{1}{4}$ ounces + 2 ounces

= 5/2 + 9/4 + 2/1

Taking the L.C.M. of 2, 4, and 1,

= 10/4 + 9/4 + 8/4

= (10 + 9 + 8)/4

= 27/4 or 6 3/4

4 0

3 years ago

On a number line 8.63 would be located where

Oksanka [162]

Answer:

It would be slightly higher than 8.5 and lower than 9.

Step-by-step explanation:

8.6 is bigger than 8.5, but it's smaller than 9, so you would place it in between the two but closer to the 8.5 mark.

4 0

4 years ago

Caroline’s cell phone plan costs $32 per month. Which table shows the sum of the amounts that Caroline will pay for her cell pho

Greeley [361]

Answer:

the answer is j

Step-by-step explanation:

32 plus 32 is 64 and 32 plus 64 is 96 so foth and so on

5 0

3 years ago

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