Building A is 165 feet tall and Building B is 210 feet tall. If the angle of depression from the top of Building B to the top of Building A is 52°, how far apart are the buildings?

help please

The correct test statistic for this hypothesis test is t = -2.88, not z = -2.65 or z = 2.65.

To perform a hypothesis test, we start by stating the alternative hypotheses:

H0: μ = 62 (the population temperature is 62 degrees F)

Ha: μ < 62 (the population  temperature is less than 62 degrees F)

X is the sample temperature, μ is the population temperature, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (59 - 62) / (6.21 / √(30)) = -2.88

Finally, we compare the test statistic to the critical value from the t-distribution with n - 1 f and an alpha level of 0.05. Since the alternative hypothesis is one-tailed (μ < 62), we use a one-tailed test and look up the critical value for a t-distribution with 29 f and an alpha level of 0.05. The critical value is -1.699.

Since the test statistic of -2.88 is smaller than the critical value of -1.699, we reject the null hypothesis and conclude that there is convincing evidence at the alpha = 0.05 level that the  temperature in fall and winter months in southwest is less than 62 degrees F.

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Answer: 72

800/11 = 72.272727272

11 is 6ft plus 5 feet in between each barricade since you need 5 ft for each barricade including the 6ft itself.

Therefore, 800ft can have no more than 72 barricades.

Answer:

61

Step-by-step explanation:

triangles add up to 180

56+63 is 119

180-119 to find the missing angle is 61

hope this helped

Answer:

2816 ft^3

Step-by-step explanation:

Solution Given:

Radius(r)=8ft.

Height(h)=14 ft.

Now

To find the volume of a cylinder, you can use the formula:

[tex]\boxed{\bold{Volume = \pi * r^2 * h}}[/tex]

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

[tex]Volume = \pi * r^2 * h\\Volume=3.14*8^2*14\\Volume=2816 ft^3[/tex]

Answer:

A

Step-by-step explanation:

We can factor 625x^4 - 81 by recognizing it as the difference of two squares:

625x^4 - 81 = (25x^2)^2 - 9^2

This can be further simplified using the formula for the difference of squares, which states that:

a^2 - b^2 = (a + b)(a - b)

In this case, a = 25x^2 and b = 9, so we have:

(25x^2 + 9)(25x^2 - 9)

We can then use the difference of squares formula again to factor 25x^2 - 9:

25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)

Substituting this into our original expression, we get:

625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)

Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)

Vertical Angles

---Vertical angles are congruent and can often be found where two lines intersect and make an "X" shape.

The vertical angles in this figure are XAW and UAY.

Adjacent angles that are neither complementary nor supplementary

---Adjacent angles are angles that share a line and are, as a result, next to each other.

Two adjacent angles in this figure that are neither complementary nor supplementary are XAW and ZAY.

Supplementary Angles

---Supplementary angles form a straight line, or 180 degree angle.

The supplementary angles in this figure are XAW and WAU.

Complementary Angles

---Complementary angles form a right, or 90 degree angle.

The complementary angles in this figure are XAW and XAZ.

Hope this helps!

Step-by-step explanation:

See image

You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.

(a) The two points you selected are (6,9) and (10,13). This is correct.

(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.

(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.

(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.

(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.

We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.

Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.

(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.

The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.

To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:

(c) The equation of the linear model in point-slope form: y - 9 = x - 6.

(d) The slope-intercept form of the equation: y = x + 3.

(e) The equation for the least squares regression line: y = 1x + 3.

(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.

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The equations to have infinite solutions and no solutions are 3x + 5 = 3x + 5 and 3x + 5 = 3x + 6

Infinite many solutions

From the question, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have infinite many solutions, both sides must be equal

So, we have

[1] x + 2x + 5 = [3] x+ [5]

Evaluate

3x + 5 = 3x + 5

No solution

Here, we have:

[ ] x + 2x + (-4 + 9) = [] x+ []

This gives

[ ] x + 2x + 5 = [] x+ []

For an equation to have no solutions, both sides must be unequal

So, we have

[1] x + 2x + 5 = [3] x+ [6]

Evaluate

3x + 5 = 3x + 6

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The required equation of the function with the given characteristics is y = (2/9)|x| whose height will be compressed to 2/9 of the original height.

As per the question, the absolute value function y = |x| looks like a "V" shape with its vertex at the origin and opening upward.

To shrink it vertically by a factor of 2/9, we need to multiply the function by this factor.

Thus, the equation of the function with the given characteristics is:

y = (2/9)|x|

The resulting graph will still have a "V" shape, but its height will be compressed to 2/9 of the original height.

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The number of ways to choose the letters is given as follows:

First we must decide which formula to use, depending if the order matters, as follows:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P(n,x) = \frac{n!}{(n-x)!}[/tex]

Hence, if the order matters, the number of ways is given as follows:

P(3,2) = 3!/(3 - 2)! = 6.

The combination formula is given as follows:

[tex]C(n,x) = \frac{n!}x!{(n-x)!}[/tex]

Hence, if the order does not matter, the number of ways is given as follows:

C(3,2) = 3!/(2! x 1!) = 3.

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The equation subject to p is P = (n - 7/2)/q.

To solve for p, we need to isolate it on one side of the equation.

Starting with:

Pq+7/2=n

Subtract 7/2 from both sides:

Pq = n - 7/2

Divide both sides by q:

P = (n - 7/2) / q

Therefore, the solution for p is:

P = (n - 7/2) / q

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The values of the probabilities are P(5) = 1/8 and P(Number > 2) = 75%

From the question, we have the following parameters that can be used in our computation:

The spinner

There are 8 sections on the spinner

So, we have

Section = 8

One of the sections is 5

So, we have

P(5) = 1/8

There are 6 sections greater than 2

So, we have

P(Number > 2) = 6/8

Evaluate

P(Number > 2) = 75%

Hence, the probabilities are 1/8 and 75%

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The probability that the husband has more than $150,000 of insurance is 1.4577

Looking at the row where the husband's insurance is between $50,000 and $100,000, we can see that there are a total of 329 policies.

Out of these policies, the number of policies where the husband has more than $150,000 of insurance is 249+30+25+176 = 480.

Therefore, the probability that the husband has more than $150,000 of insurance given that his insurance is between $50,000 and $100,000 is:

480/329 ≈ 1.4577

Rounded to four decimal places, the probability is 1.4577.

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1) The translation made is 2 units up, 1 units left.

2) The translation made is 2 units right, 1 unit up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Chess player moves a knight from the location (3,2) to (5,1) on a chessboard.

And, the player moves the knight from (5,1) to (6,3),

Since, Translation for (3,2) to (5,1|) is,

⇒ 2 units up, 1 units left.

And, Translation for (5,1) to (6,3) is,

⇒ 2 units right, 1 units up.

Hence, When a player moves a knight from the location (3, 2) to (5, 1) on a chessboard the translation made is 2 units up, 1 units left.

And, When the player moves the knight from (5, 1) to (6, 3), the translation made is 2 units right, 1 units up.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 7} \implies \boxed{A \approx 3969.39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2800\\ r=rate\to 5.2\%\to \frac{5.2}{100}\dotfill &0.052\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A = 2800\left(1+\frac{0.052}{4}\right)^{4\cdot 7}\implies A=2800(1.013)^{28} \implies \boxed{A \approx 4019.97} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 4019.97 ~~ > ~~ 3969.39 \end{array}}~\hfill[/tex]

The set of results that could not have been drawn from the bag is 3, 5, 5.

Let's assume there are three balls in the bag, labeled A, B, and C. The possible combinations are:

ABC, ACB, BAC, BCA, CAB, CBA

Now, let's analyze each set of results:

2, 3, 7: This set of results could have been drawn from the bag. For example, if A = 2, B = 3, and C = 7, the results would be 2, 3, 7.

10, 4, 3: This set of results could have been drawn from the bag. For example, if A = 10, B = 4, and C = 3, the results would be 10, 4, 3.

3, 5, 5: This set of results could not have been drawn from the bag, because there is only one ball labeled 3 in the bag. Therefore, it is impossible to draw two balls labeled 5 and one ball labeled 3.

8, 6, 10: This set of results could not have been drawn from the bag, because there is no ball labeled 8 in the bag. Therefore, it is impossible to draw a ball labeled 8.

So, the set of results that could not have been drawn from the bag is 3, 5, 5.

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Answer:

1×1=1

2×2=4

3×3=9

4×4=16

Answer:

62.25

Step-by-step explanation:

Rectangle Area Formula: A=l•w

7.5•5=37.5

=hbb/2=7.5·4.2/2=15.75

=hbb/2=7.5·2.4/2=

Add all three =62.25

Answer:

18 more sessions

Step-by-step explanation:

Her goal is to practice 800 minutes.

She already did 175 minutes.

That means she has 800 - 175 = 625 minutes remaining, and she says that she will only practice in 35 minute sessions.

To determine the number of sessions she has left, just divide 625 by 35.

[tex]\frac{625}{35}[/tex]

= 17.85714

However, you can't have a portion of a session, as she only does 35 mins every session. Therfore, she must do 18 more sessions.

~~~Harsha~~~

The solution of the expression is,

⇒ - 37/14

We have to given that;

Expression to solve is,

⇒ 6 - 5/4 × 6 - 8/7

Now, We can simplify the expression as,

⇒ 6 - 5/4 × 6 - 8/7

⇒ 6 - 5/2 × 3 - 8/7

⇒ 6 - 15/2 - 8/7

⇒ (12 - 15)/2 - 8/7

⇒ - 3/2 - 8/7

⇒ (- 21 - 16) / 14

⇒ - 37/14

Thus, The solution of the expression is,

⇒ - 37/14

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The required length is 11 units for the given triangle.

The sine rule defines the side length ratios of triangles to their opposing angles. This proportion is true for all three sides and opposing angles.

a/sinA = b/sinB = c/sinC

The triangle is given in the question, as follows:

In ΔABC, ∠A=120°, ∠B=37°, and c = 5 units

Here, ∠C= 180° - 120° - 37° = 23.

We have to determine the length of a.

As per the sine rule, the required solution would be as:

a/sin∠A = c/sin∠C

Substitute the known values and we get

a/sin 120° = 5/sin 23°

a = (18/sin 1240°) × sin 23°

k ≈ 11

Thus, the length of c is 11 units.

Hence, the number that belongs in the green box is 11.

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The total area of the figure formed by the congruent triangles and the square is 60 sq in

For square

A = s²

where s is the side

Given:

s = 6 in

Area = 6 * 6

= 36 sq in

Area of triangle = 0.5bh

where b is the base

h is the height

Given:

b = 6 in

h = 4 in

A = 0.5 * 6 * 4

= 12 sq in

Total area of the figure = 2 * Area of triangle + area of square

= 2 * 12 + 36

= 24 + 36

= 60 sq in

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Answer:

8 more red counters

Step-by-step explanation:

It would make it 9:3, which, when simplified, is 3:1.

Answer: 260(0.962)^8

Step-by-step explanation:

Pretty simple. We have a base of 260, which all of the answers include. Then for a decay rate of 3.8, we reduce to percentage form ( 0.038 ) and subtract that from 1 ( or 100 in standard form ). Then we get 0.962. We choose the second option because it includes both these terms and 8 ( which I'm assuming is an exponent )