From a point 31 meters from the base of a telephone pole the angle of elevation to a worker on the pole is 35 degrees. The angle of elevation to the top of the pole is 68 degrees. Find the distance from the worker to the top of the pole.

Alan made an error in subtracting the x-coordinates without considering their signs. The correct method to find the distance between two points on the same horizontal line is taking the absolute value of the difference of the x-coordinates. Thus, the actual distance from point A to point B is 11 units.

Alan made an error in calculating the distance between point A(-8,-4) and point B(3,-4). The error is in the subtraction, as he should have taken the absolute value of the difference of the x-coordinates of points A and B because the y-coordinates are the same. To find the distance between two points on a coordinate plane, the correct formula when points lie on the same horizontal line (same y-coordinates) is the absolute difference of the x-coordinates. Therefore, the actual distance is calculated as follows:

|x2 - x1| = |3 - (-8)| = |3 + 8| = 11 units

So, the actual distance from point A to point B is 11 units.

Answer:

30 PS4's

Step-by-step explanation:

The manager chose 50/500 PS4's to sample

3/50 were defective

To find how many were defective in all 500, we multiply the fraction by a number that makes the 50 (the sample), into a 500(the total).

That number is 10

Whatever multiplication you do to the bottom of a fraction, you do to the top

3*10 / 50*10

30 / 500 are likely to be defective

Answer:

30

Step-by-step explanation:

Answer:

you live on the 21st floor

Step-by-step explanation:

46-4=42 (level -2 to ground level)

42÷2=21

Answer:

y=50x

Step-by-step explanation:

For every additional 2 hours (x), there are 100 bricks laid.

This means the slope is 50 (100/2)(200/4)etc.

50*2=100

50*4=200

50*6=300

50*8=400

Answer:

82 divided by 5 = 16.4

Step-by-step explanation:

you divide 82 by 5 and get 16.4 or 82 divided by 10= 8.2

They do first they split up the ten bills and it is 8.0.

We have given that,

Five friends are sharing 82 dollars they keep a record

82 divided by 5

[tex]\frac{82}{5} = 16.4[/tex]

You divide 82 by 5 and get 16.4,

After the split up to ten bills is given by,

A split is a situation in a particular frame of a ten-pin bowling game where the player throws the ball and knocks the headpin

82 divided by 10

[tex]\frac{80}{10} =8.0[/tex]

They do first they split up the ten bills.

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Answer:

If  [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

Step-by-step explanation:

According to the information of the problem we know that

[tex]{\displaystyle \frac{dP}{dt} = P(a-bP) }[/tex]

Remember that in general a Bernoulli equation is an equation of the type

[tex]y' + p(x)y = q(x)y^n[/tex]

And the idea to solve the equation is to substitute

[tex]{ \displaystyle v = y^{1-n}}[/tex]

Now for this case

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

Then we substitute

[tex]v = P^{1-2} = P^{-1}[/tex]

Therefore

[tex]P = v^{-1}[/tex]

and if you compute the derivative of that you get that

[tex]{\displaystyle \frac{dP}{dt} = -v^{-2} \frac{dv}{dt}}[/tex]

Now you substitute that onto the original equation and get

[tex]{\displaystyle \frac{dP}{dt} - Pa = -bP^2}[/tex]

[tex]{\displaystyle -v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2}[/tex]

If you multiply everything by  [tex]-v^2[/tex]  you get that

[tex]{\displaystyle \frac{dv}{dt} + v = b }[/tex]

That's a linear differential equation and the solution would be

[tex]v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}[/tex]

Where [tex]K[/tex] is a constant of integration, then

[tex]P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}[/tex]

The given logistic equation is a Bernoulli equation, which can be solved using a substitution of variables method.

The given differential equation is a Bernoulli equation, which is a nonlinear first-order ordinary differential equation of the form dy/dx = P(x)y + Q(x)y^n, where n is a constant. To solve it, we can use a substitution of variables by setting y = u^(1-n). Applying this substitution to the logistic equation, we get du/dx = (1-n)a*u + (1-n)b*u^(2-n), which can be solved using separation of variables method.

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Answer:

x=0 i think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I took the quiz

Answer:

  π/2 or 1.57 square units

Step-by-step explanation:

The area of a sector with central angle θ is given by the formula ...

  A = (1/2)r²θ

Filling in the given value, we find the area to be ...

  A = (1/2)(3²)(π/9) = π/2 . . . . square units

Using 3.14 for π, this is ...

  A = 3.14/2 = 1.57 . . . . square units

Answer:

is D

Step-by-step explanation:

for egny

Answer:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

Step-by-step explanation:

Information given

[tex]p_1[/tex] represent the real population proportion of males with tattoos

[tex]\hat p_1 =\frac{190}{1231}=0.154[/tex] represent the estimated proportion of males with tattos

[tex]n_1=1231[/tex] is the sample size for males

[tex]p_2[/tex] represent the real population proportion of female with tatto

[tex]\hat p_2 =\frac{143}{1067}=0.134[/tex] represent the estimated proportion of females with tattos

[tex]n_2=1067[/tex] is the sample size of female

[tex]z[/tex] represent the critical value

Confidence intrval

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]  

For the 90% confidence interval the value of [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2=0.05[/tex], and the critical value for this case would be:  

[tex]z_{\alpha/2}=1.64[/tex]  

Replacing the info given we got:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

Answer:

-3x + 8 = y

-3x = y - 8

3x = 8 - y

x = (8-y)/3

Now interchanging x and y:-

y = (8-x)/3

Here, y is inverse function i.e. f⁻¹(x)

Hence, f⁻¹(x) = (8-x)/3

Since f⁻¹(x) is a linear expression of x, therefore it is a function.

Step-by-step explanation:

Answer:

Look at the answer of the pic

Answer:

1) A. H0: μ ≥ 7.2; H1: μ < 7.2

2) D. Reject H0 if z < –1.645

3) [tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]  

4) [tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Step-by-step explanation:

Information provided  

[tex]\bar X=6.2[/tex] represent the sample mean for the number of movies watched last month

[tex]\sigma=0.9[/tex] represent the population deviation

[tex]n=35[/tex] sample size selected

[tex]\mu_o =7.2[/tex] represent the value that we want to test    

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

1) System of hypothesis

We want to check if college students watch fewer movies a month than high school students, and the best system of hypothesis are:

Null hypothesis:[tex]\mu \geq 7.2[/tex]      

Alternative hypothesis:[tex]\mu < 7.2[/tex]      

A. H0: μ ≥ 7.2; H1: μ < 7.2

2) Decision rule

For this case we are ocnduting a left tailed test so then we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the left and we got:

[tex]z_{crit}= -1.645[/tex]

And the rejection zone would be:

D. Reject H0 if z < –1.645

3) Statistic

Since we know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing we got:

[tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]      

4) P value

We have a left tailed test then the p value would be:      

[tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Final answer:

The correct null and alternate hypotheses are H0: μ ≥ 7.2 and H1: μ < 7.2, respectively. Reject the null hypothesis if z < -1.645. The computed test statistic is approximately -7.378, suggesting a p-value near zero and thus, we can conclude that college students watch fewer movies on average.

Explanation:

In order to determine whether college students watch fewer movies a month than high school students, we should set up a hypothesis test comparing the college students' mean number of movies watched to the known population mean for high school students.

Step 1: State the null and alternate hypotheses.

The correct hypotheses would be A. H0: μ ≥ 7.2; H1: μ < 7.2 since we are testing if the college students watch fewer movies, which is a one-tailed test.

Step 2: State the decision rule.

The correct decision rule at the 0.05 significance level for a left-tailed test would be D. Reject H0 if z < – 1.645.

Step 3: Calculate the test statistic.

Using the formula for the z-test, z = (sample mean - population mean) / (population standard deviation / √ sample size), we calculate z = (6.2 - 7.2) / (0.9 / √35) ≈ – 7.378. Thus, the test statistic z is approximately -7.378.

Step 4: Find the p-value.

With a z-score as extreme as – 7.378, the p-value is near zero, implying strong evidence against the null hypothesis.

Answer:

The center is located at (2, –1).  

The major axis is 8 units long.

The vertices are 4 units above and below the centre.

The foci are √7 units above and below the centre.  

Step-by-step explanation:

Assume the ellipse looks like the one below.

The properties of a vertical ellipse are

[tex]\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}[/tex]

A. Centre

TRUE. The centre is at (2,-1).

B. Major axis

TRUE

Length of major axis = 3 - (-5) = 3 + 5 = 8

C. Minor axis

False

Length of minor axis = 5 - (-1) = 5 + 1 = 6

D. Vertices

TRUE

Distance between vertices = 8 = 2a

a - 8/2 = 4

Vertices at (h, k ± a) = (2, -1 ± 4)

E. Foci

TRUE

c² = a² - b² = 4² - 3² = 16 - 9 = 7

c = √7

The foci are √7 above and below the centre.

F. Foci

False.

The foci are on a vertical line.

Answer:

percentage error = 11.11 %

Step-by-step explanation:

Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.

percentage error = approximate value - exact value/exact value × 100

approximate value = 32 ounces

exact value = 36 ounces

percentage error = |32 - 36| / | 36 | × 100

note we used the absolute value to eliminate negative signs

percentage error = 4/36 × 100

percentage error = 400/36

percentage error = 11.11 %

Answer:

In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Answer:

In geometry, the  theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Answer:

(a)

The average length of the project is 33.9 weeks

The standard deviation of the project length is 2.8 weeks

(b)

The estimated probability that the project will be completed in 35 weeks or less is 0.65

Step-by-step explanation:

(a)

The average length of the project is;

E(P) = E(A+B+C+D)

      = 6.3 + 5.1 + 13.7 + 8.8

      = 33.9

The standard deviation of the project length;

SD(P) = √V(P)

         = √V(A+B+C+D)

         = √1.01 + 1.79 + 4.11 + 0.96

         = √7.87

         = 2.8

(b)

Normal distribution with mean 33.9 weeks and variance of 2.8² weeks.

The estimated probability that the project will be completed in 35 weeks or less is;

[tex]P(P \leq 35) = P( \frac{P-E(P)}{SD(P)} \leq \frac{35-33.9}{2.8} )[/tex]

[tex]P(P \leq 35) = P(z\leq0.3929)[/tex]

                 = 0.65  → Using Excel command (NORM.S.DIST(0.3929,TRUE))

To estimate the average length and standard deviation of a project, use a spreadsheet simulation model. Calculate the expected completion time and standard deviation for each activity. To find the probability of completing the project in a certain time frame, sum up the probabilities of activities that can be completed within that timeframe.

To estimate the average length of the project and the standard deviation of the project length, you can use a spreadsheet simulation model. Here are the steps you can follow:

For part (b), to find the estimated probability that the project will be completed in 35 weeks or less, you'll need to sum up the probabilities of all activities that can be completed within 35 weeks or less.

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Answer:

[tex]P(E1/R)= 0.15[/tex]

Step-by-step explanation:

Hola!

La comañía en cuestión usa 4 empresas de transporte para realizar envios. Llamemos "E" al evento de que la empresa haya sido seleccionada para un envío:

E1: La empresa A1 realiza el envío ⇒ P(E1)= 0.15

E2: La empresa A2 realiza en envío ⇒ P(E2)= 0.30

E3: La empresa A3 realiza el envío ⇒ P(E3)= 0.35

E4: La empresa A4 realiza el envío ⇒ P(E4)= 0.20

Y también conoces las probabilidades de que un envío llegue con retraso, sabiendo cual es la empresa que realizó el envío. Llamemos "R" al evento que el envío llegó con retraso. Las probabilidades mencionadas son condicionales y se simbolizan de la siguiente manera:

P(R/E1)= 0.07

P(R/E2)= 0.08

P(R/E3)= 0.05

P(R/E4)= 0.09

Tienes que calcular la probabilidad de que un embarque que ha sido entregado con retraso, haya sido enviado por la empresa A1.

Esta probabilidad también es condicional, queremos saber la probabilidad de E1 sabiendo que ya ha pasado R, se simboliza de la siguiente manera:

[tex]P(E1/R)= \frac{P(E1nR)}{P(R)}[/tex]

Para poder calcularla necesitas averiguar el valor de la probabilidad de intersección entre E1 y R, P(E1∩R), y el valor de la probabilidad de R, P(R).

La probabilidad de R es una probabilidad marginal y es igual a:

P(R)= P(E1∩R)+P(E2∩R)+P(E3∩R)+P(E4∩R)

Para calcular los valores de las intersecciones debes aplicar la definición de probabilidad condicional:

[tex]P(A/B) = \frac{P(AnB)}{P(B)}[/tex] entonces P(A∩B)= P(A/B)*P(B)

Entonces:

[tex]P(R/E1)= \frac{P(RnE1}{P(E1)}[/tex] ⇒ P(E1∩R)= P(R/E1)*P(E1)= 0.07*0.15= 0.0105

P(E2∩R)= P(R/E2)*P(E2)= 0.08*0.30= 0.024

P(E3∩R)= P(R/E3)*P(E3)=0.05*0.35= 0.0175

P(E4∩R)= P(R/E4)*P(E4)= 0.09*0.20= 0.018

Ahora puedes calcular la probabilidad de que el envío llegue con retraso:

P(R)= 0.0105+0.024+0.0175+0.018= 0.07

Por último queda calcular la probabilidad solicitada:

[tex]P(E1/R)= \frac{0.0105}{0.07}= 0.15[/tex]

Espero que tengas un buen día!

you will need

2 gallons lime soda

1 gallon icecream

and 4 gallons lemonade

Answer:

10,000

Step-by-step explanation:  

10 x 10 = 100 when you do the power of 2, you multiply that number by itself.

Answer:

positive 5.5

Step-by-step explanation:

Answer:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

Step-by-step explanation:

Data provided

3.6​, 3.1​, 4.0​, 4.9​, 3.0​, 4.3​, 3.6​, 4.6​, 4.6​, 4.0​, 4.4​, 3.6​, 3.3​, 4.2​, 3.7

The sample mean and deviation can be calculated with the following formulas

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex]

[tex]\bar X=3.93[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s=0.574 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the true mean is given by:

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

The degrees of freedom, given by:

[tex]df=n-1=15-1=114[/tex]

The Confidence is 0.99 or 99%, the significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value would be[tex]t_{\alpha/2}=2.977[/tex]

Replacing we got:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

Answer:

1.12 meters

Step-by-step explanation:

Answer:

1.12

Step-by-step explanation:

each week it grows 0.16 m

so,in 7 weeks it will grow 0.16*7m

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for detailed and step by step solution of the given problem.

a. The critical number of f is -5

b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

c.  There is no relative extremum at x = -5.

d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

(a) To find the critical numbers of the function,  find where the derivative is 0 or undefined.

To find the derivative of f(x):

[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]

The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.

So -5 is a critical number of f.

(b) To find the intervals on which the function is increasing or decreasing,  examine the sign of the derivative on each interval.

Since f'(x) is always positive (except at x = -5, where it is undefined),

The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.

The derivative is undefined at x = -5, so the test is not applicable

Therefore, there is no relative extremum at x = -5.

Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

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Answer:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Step-by-step explanation:

Information provided

4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9

We can find the sample mean and deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=3.76[/tex] represent the sample mean

[tex]s=0.241[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\mu_o =3.5[/tex] represent the value to check

[tex]\alpha=0.01[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test  if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 3.5[/tex]  

Alternative hypothesis:[tex]\mu > 3.5[/tex]  

Since we don't know the deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Principal Balance: 2000

Compound Interest: 3%

Type: Yearly

2000 x 1.03 = 2060

Year 1 : £2060

2060 x 1.03 = 2121.8

Year 2: £2121.8

There will be £2,121.80 in the account after 2 years.

Answer:okStep-by-step explanation:

Answer: 8.5%

Step-by-step explanation:

This is simple interest.

The formula fie finding simple interest is

I = principal × rate × time

-------------------------------

100

I = PRT/100

From the given values,

P = $5,500, T = 4years, R = ?, I = $1,870

Now we shall change the formula which is fundamental or in situ to suit the rate R.we now have

I = PRT

----

100

PRT = I × 100

R. = I × 100

---------

P × T

= 1,870 × 100

---------------

5,500 × 4

= 1,870 × 25

------------

5,500

= 187000/4

-----------

5500

= 46750/5500

= 8.5%

Therefore, the imtetest rate at which the loan was calculated is

8.5%.

Answer:

If you mean how much is left after he ate 1/4 from the 2/3 then 5/12 of the pizza is left.

Step-by-step explanation:

Final answer:

Wakami ate 1/6 of the entire pizza by consuming 1/4 of the 2/3 of the pizza that was left.

Explanation:

To find out how much of the pizza Wakami ate, we need to calculate 1/4 of the 2/3 of the pizza that was left. This requires multiplying the two fractions together:

2/3 of the pizza left times 1/4 that Wakami eats = 2/3 times 1/4

To multiply fractions, you simply multiply the numerators (top numbers) and then multiply the denominators (bottom numbers):

(2 times 1) / (3 times 4) = 2 / 12

Now we simplify the fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 2:

2 / 12 = 1/6

So, Wakami ate 1/6 of the entire pizza.

Answer:

[tex]Length\hspace{3}of\hspace{3}the\hspace{3}beam=y=21.3ft[/tex]

Step-by-step explanation:

Look the picture I attached you. As you can see the beam against the wall form a right triangle. The trigonometry functions on a right triangle are:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\hspace{10}csc(\theta)=\frac{hypotenuse}{opposite}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\hspace{10}sec(\theta)=\frac{hypotenuse}{adjacent} \\\\tan(\theta)=\frac{opposite}{adjacent} \hspace{20}cot(\theta)=\frac{adjacent}{opposite}[/tex]

The problem give us the following data:

[tex]y=9sec(\theta)[/tex]

Using the previous information about the trigonometry functions on a right triangle and the data provided by the problem you can conclude:

[tex]y=Hypotenuse\\Adjacent=9\\\theta=65^{\circ}[/tex]

Therefore:

[tex]y=9sec(65^{\circ})=9*(2.366201583)=21.29581425\approx21.3ft[/tex]

The length of the beam for the given situation is 21.3 ft.

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.

Here, given function

y = 9. sec θ

put, θ = 65⁰

then, y = 9 X sec 65⁰

        y = 9 X 2.366

        y = 21.294 ft. ≈ 21.3 ft.

Thus, the length of the beam for the given situation is 21.3 ft.

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Answer: The type is Retrospective.

Step-by-step explanation: Observational Study is a type of research which measures determined characteristics of a population by studying individuals in a sample, without interfering or influencing the variables. There are 3 types of observational study:

According to the description given, the study above is a case-control study and the type is called Retrospective because it asks the individuals to tell about past habits, exposure to sunshine in this case. This type of study is not very reliable because it depends on the memory and the ability of the individuals to be honest and it can only prove association, not causation.

The type of observational study described in the question is a case-control study. The researcher selected women with and without osteoperosis, collected data on their exposure to sunshine, and compared the amount of exposure between the two groups.

The type of observational study described in the question is a case-control study. In a case-control study, the researcher selects subjects based on their disease status (in this case, women with or without osteoperosis) and compares their exposure to a risk factor (in this case, lack of exposure to sunshine). The researcher collected data on the exposure to sunshine over the previous twenty years for both groups and compared the amount of exposure between the two groups.

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