PLEASE HELP!!!!!!!!! I NEED IT The angle of elevation from a point on the ground to the top of a tower is 18°. The base of the tower is 100 feet from the point on the ground. Find the height of the tower. Round to the nearest tenth of a foot.

Answers

Answer 1

Answer:

Answer:

32.5 feet

Step-by-step explanation:

This situation forms a right triangle. We are given the distance from the base of the tower (long leg of the triangle) and are asked to find the height (short leg of the triangle).

With this information, we can use the tan ratio, opposite over adjacent, to find the height of the tower.

tan 18 = $(x)/(100)$

Multiply each side by 100:

(100) tan 18 = x

Simplify and round to the nearest tenth:

32.49 = x

32.5 = x

So, the height of the tower is approximately 32.5 feet

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An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the claim, 35 randomly selected individuals were given the product; the average time until relief was 9.25 minutes. From past studies, the standard deviation of the population is known to be 2 minutes. Can you conclude that the claim is justified? Find the P-value and let a = 0.05.

Answers

Answer:

$z=(9.25-10)/((2)/(√(35)))=-2.219$

$p_v =P(z<-2.219)=0.0132$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.

Step-by-step explanation:

Data given and notation

$\bar X=9.25$ represent the sample mean

$\sigma=2$ represent the population standard deviation

$n=35$ sample size

$\mu_o =10$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 10 minutes, the system of hypothesis would be:

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

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:

$z=(\bar X-\mu_o)/((\sigma)/(√(n)))$ (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:

$z=(9.25-10)/((2)/(√(35)))=-2.219$

P-value

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

$p_v =P(z<-2.219)=0.0132$

Conclusion

-4= -(x-8)
negative four equals negative (parentheses x minus 8 parentheses)

Answers

-4=-x-8
+4. +4
—————
0=-x-4
x=-4

Suppose you wanted to estimate the difference between two population means correct to within 4.8 at the 92% confidence level. If prior information suggests that both population variances are approximately equal to 12 and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?Critical Value: 1.75
The sample sizes should be: n1=___n2=_____?

Answers

Answer: $n_1=n_2=4$

Step-by-step explanation:

Given : Margin of error : E= 4.8

Confidence level : 92%

Significance level : $1-0.92=0.08$

$\sigma_1^2=\sigma_1^2\approx12$

Two-tailed critical value :-

$z_(\alpha/2)=z_(0.08/2)=z_(0.04)=1.75$

If we want to select independent random samples of equal size from the populations,

Formula for the sample size :

$n_1=n_2=((z_(\alpha/2))/(E))^2(\sigma_1^2+\sigma_2^2)$

Then buy using given values , we have

$n_1=n_2=((1.75)/(4.8))^2(12+12)$

Simplify ,

$n_1=n_2=((1.75)/(4.8))^2(12+12)=3.190\approx4$ [Round to the next integer.]

Hence, the The sample sizes should be: $n_1=n_2=4$

Which equation represents the polar form of x2 + (y + 4)2 = 16?

Answers

The polar form of equation is r = -8sinθ.

What is polar form of complex number?

The combination of the complex number's modulus r and argument is how complex numbers are shown in polar form z = r cosθ + i r sinθ = r (cosθ + i sinθ), is the polar form of a complex number with coordinates (x, y). In the coordinate system, polar coordinates of real and imaginary numbers are used to represent the polar form.

Given x² + (y + 4)² = 16

here The following is the relationship between (r, θ) and (x, y) if they are in Cartesian form:

x = rcosθ, y = rsinθ and r² = x² + y² ad tanθ = y/x

x² + (y + 4)² = 16

x² + y² + 16 + 8y = 16

x² + y² + 8y = 0

r² + 8rsinθ = 0

r(r + 8sinθ) = 0

r =0 and r = -8sinθ

Hence the polar form of equation is r = -8sinθ.

Learn more about polar form of complex number;

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