Ask question

Ask question

All categories

3 years ago

10

a reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

n the side along the building. the third side is 7 feet longer than the side along the building. find the length of all three sides of the reflecting pool

2 answers:

Eva8 [605]3 years ago

5 0

a^2 + b^2 = c^2

9^2 + 7^2 = get the answer then find the square root of it

almond37 [142]3 years ago

4 0

Answer: The length of all three sides of the reflecting pool are 8 feet , 17 feet and 16 feet.

Step-by-step explanation:

Let sides along the building be 'x', then the measure of hypotenuse = x+9 and the measure of third side = 7+x

Since , the reflecting pool is shaped like a right triangle.

Then , by using Pythagoras theorem , we have

$(x+9)^2=x^2+(x+7)^2\\\\\Rightarrow\ x^2+81+18x=x^2+x^2+49+14x\ \ [\text{Using }(a+b)^2=a^2+b^2+2ab ]]\\\\\Rightarrow\ x^2+81+18x=2x^2+49+14x\\\\\Rightarrow\ x^2-4x-32=0\\\\\Rightarrow\ x^2-8x+4x-32=0\\\\\Rigtarrow\ x(x-8)+4(x-8)=(x-8)(x+4)\\\\\Rightarrow\ x=8\ or -4$

But length cannot be negative , it means x= 8

Now, the length of side along building = 8 feet

Length of hypotenuse = 9+8 =17 feet

Length of third side = 8+7= 16 feet

You might be interested in

Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a

tigry1 [53]

Answer:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

$\bar X =237$ represent the sample mean

$\sigma = 47$ represent the population deviation

$n =30$ represent the sample size selected

$\mu_0 = 247$ represent the value that we want to test.

The standard error for this case is given by:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

For the 90% confidence the value of the significance is given by $\alpha=1-0.9 = 0.1$ and $\alpha/2 = 0.05$ so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

$z_{\alpha/2}= 1.64$

And the margin of error would be:

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

The confidence interval for this case would be given by:

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

5 0

3 years ago

An account earns simple interest. Find the principal.

Alexandra [31]

Answer:

$ 900

Step-by-step explanation:

Simple interest = Principle * Time * Rate / 100

Now by substituting :

27 = Principle * 2 * 1.5 / 100

Principle = 27 * 100 / 2 * 1.5

Principle = 2700 / 3

So Principle = $ 900

Hope it helps

5 0

3 years ago

14+14p=21 solve for p

11Alexandr11 [23.1K]

Answer: 0.5

Step-by-step explanation: In this problem, we're asked to solve the following equation for <em>p. </em>Let's first switch 14 and 14p around so we have 14p + 14 = 21.

<em />

To solve this equation for <em>p</em>, we must first isolate the term containing <em>p</em> which in this case is 14p.

Since 14 is being added to 14p, we need to subtract 14 from both sides of the equation.

14p + 14 = 21

-14 -14

On the left side of the equation, the positive 14 and negative 14 cancel each other out and we have 14p. On the right side of the equation, we hav 21 - 14 which gives us 7.

Now we have the equation 14p = 7.

Since <em>p</em> is being multiplied by 14, to get <em>p</em> by itself, we divide both sides of the equation by 14.

On the left side of the equation the 14's cancel and we are left with <em>p</em>. On the right side of the equation, 7 divided by 14 is 0.5 which is our answer.

Therefore, p = 0.5 which is the solution for our equation.

Remember, you can always check your solution by substituting a number in for a variable to make sure the equation is true.

6 0

3 years ago

The midpoint of (3,4) and (5.5,0)

meriva

Answer:

(4.25,2)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates and divide by 2

x = (3+5.5) /2 = 8.5/2 =4.25

To find the y coordinate of the midpoint, add the y coordinates and divide by 2

y = ( 4+0)/2 = 4/2 =2

8 0

3 years ago

kodGreya [7K]

Answer:

(-2,3)

Step-by-step explanation:

For the point to be 2/3 of the way; it means it divides AB into the ratio 2 to 1

Now, we can use the internal section formula to get the coordinates of this point

(x,y) = (nx1 + mx2)/(m + n), (ny1 + my2)/(m + n)

where (m,n) = (2,1)

(x1,y1) = (-4,-1)

(x2,y2) = (5,5)

(x,y) = (1(-4) + 2(-1)/(1+2), (1(-1)+2(5)/(1+2)

(x,y) = (-4-2)/3, (-1 + 10)/3

(x,y) = (-2,3)

4 0

3 years ago