The length of the escalator is 36 ft and the

vertical height it rises is 9 ft. what is the angle

of elevation?


a. 90

b. 75. 52

c. 14. 48

d. 14. 04

Answer:

B. X4+ 4x2 +8x is the answer

Step-by-step explanation:

Answer:

B        x4 + 4x2 + 8x

Step-by-step explanation:

The appropriate percentages for the Extremely Patriotic group are 19.42% in 1999 and 32.27% in 2010, corresponding to option d: 193/994 compared to 324/1004.

To calculate the appropriate percentages for the Extremely Patriotic group, we need to compare the counts from the 1999 and 2010 samples.

In 1999:

Number of Extremely Patriotic responses: 193

Total number of respondents: 994

In 2010:

Number of Extremely Patriotic responses: 324

Total number of respondents: 1004

Now we can calculate the percentages:

Percentage for 1999: (193 / 994) × 100 = 19.42%

Percentage for 2010: (324 / 1004) × 100 = 32.27%

Therefore, the appropriate percentages as part of the exploratory data analysis for the Extremely Patriotic group are:

19.42% compared to 32.27% (option d: 193/994 compared to 324/1004).

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Answer: Radius=19.2 diameter=38.39

Step-by-step explanation: :DDD

I hope this help you

Answer:

If n is even, then n^2 + 8n + 20 is even.

Let n = 2k (k = 0, 1, 2,...). Then:

(2k)^2 + 8(2k) + 20 = 4k^2 + 16k + 20

= 4(k^2 + 4k + 5)

This expression is even for all k, so if n is even, this expression is even.

So if n^2 + 8n + 20 is odd, then n is odd.

Natural numbers n must be odd for n^2 + 8n + 20 to be odd.

To prove that if n^2 + 8n + 20 is odd, then n is odd for natural numbers n, we can use proof by contradiction.

Assume that n is even for some natural number n. Then we can write n as 2k for some natural number k.

Substituting 2k for n, we get:

n^2 + 8n + 20 = (2k)^2 + 8(2k) + 20
= 4k^2 + 16k + 20
= 4(k^2 + 4k + 5)

Since k^2 + 4k + 5 is an integer, we can write the expression as 4 times an integer. Therefore, n^2 + 8n + 20 is divisible by 4 and hence it is even.

But we are given that n^2 + 8n + 20 is odd. This contradicts our assumption that n is even.

Therefore, our assumption is false and we can conclude that n must be odd for n^2 + 8n + 20 to be odd.

In detail, we have shown that if n is even, then n^2 + 8n + 20 is even. This is a contradiction to the premise that n^2 + 8n + 20 is odd. Therefore, n must be odd for n^2 + 8n + 20 to be odd.

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Answer:

4770 people

Step-by-step explanation:

795*6= 4770

With a frame length of 1, the expectation is 5 seconds and the         standard deviation is approximately 3.464 seconds for the number of seconds between two consecutive connections.

(a) To determine the frame length Δ that gives a probability of 0.15 of an arrival during any given frame, we need to consider the Binomial counting process and its probability distribution.

In a Binomial distribution, the probability of success (an arrival) is given by p, and the probability of failure (no arrival) is given by q = 1 - p. In this case, p = 12 connections per minute.

We can use the cumulative distribution function (CDF) of the Binomial distribution to find the frame length Δ. The CDF gives the probability of having k or fewer arrivals in a given number of frames.

Using a binomial probability table or a calculator, we find that when p = 0.15, the corresponding value of k is 1. Therefore, the frame length Δ that gives a probability of 0.15 of an arrival during any given frame is 1 frame.

(b) With a frame length Δ of 1, we can compute the expectation (mean) and standard deviation for the number of seconds between two consecutive connections.

The average rate of connections is 12 per minute. To find the average time between two consecutive connections, we take the reciprocal of the rate: 1/12 minutes per connection.

To convert minutes to seconds, we multiply by 60: (1/12) * 60 = 5 seconds.

Therefore, the expectation (mean) for the number of seconds between two consecutive connections is 5 seconds.

The standard deviation can be calculated using the formula for the standard deviation of a Poisson process, which is the limit of the Binomial distribution as the number of trials becomes large. For a Poisson process, the standard deviation is equal to the square root of the average rate: √(12) ≈ 3.464 seconds.

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Answer:

112

Step-by-step explanation:

Sum of interior angles in quadrilaterial = 360

360 - 100 - 104 - 44 = 112

Step-by-step explanation:

Let the 4th angle = x

Now,

x + 100 + 104 + 44 = 360° ( the sum of interior angle of quadrilateral is 360°)

x + 248 = 360°

x = 360° - 248

x = 112

Hence, the fourth angle is 112....

P = 0.75m represents the proportional relationship, therefore, the profit earned for each muffin sold is: $0.75.

If two variables, i.e. P and m are directly proportional to each other, the relationship between them can be represented as P = km, where k is the constant.

Given that P = 0.75m represents the proportional relationship between the profit earned and muffins sold, the constant, k, is 0.75, which is the profit earned for each muffin sold.

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Answer: -4(3x-1)

Step-by-step explanation:

Answer:

The maximum height of the volleyball is 12.25 feet.

Step-by-step explanation:

The height of the volleyball, h(t), is modeled by this equation, where t represents the  time, in seconds, after that ball was set :

....(1)

The volleyball reaches its maximum height after 0.625 seconds.

For maximum height,

Put

Now put t = 0.625 in equation (1)

Hope this helps!!

Answer:

Option D

Step-by-step explanation:

(x + 8) (2x² - 5x - 3)

=> (2x³ - 5x² - 3x) + (16x² - 40x - 24)

=> 2x³ + 11x² - 43x - 24

Hope this helps!

Answer:

Divide each term by  

3

and simplify.

Tap for more steps...

y

=

2

x

3

+

1

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

2

3

y-intercept:  

1

Any line can be graphed using two points. Select two  

x

values, and plug them into the equation to find the corresponding  

y

values.

Tap for more steps...

x

y

0

1

3

3

Graph the line using the slope and the y-intercept, or the points.

Slope:  

2

3

y-intercept:  

1

x

y

0

1

3

3

Step-by-step explanation:

Answer: 28282

Step-by-step explanation:

I think

Answer:

hi

Step-by-step explanation:

Answer:

When four dice are rolled, there are 6 x 6 x 6 x 6 = 1296 possible outcomes, since each die has 6 possible outcomes and the rolls are independent.

To find the probability that each of the four numbers that appear will be different, we need to count the number of outcomes where each die shows a different number. We can do this by breaking it down into cases:

Case 1: The first die shows any number. The second die must show a different number than the first, so there are 5 possible outcomes. The third die must show a different number than the first two, so there are 4 possible outcomes. The fourth die must show a different number than the first three, so there are 3 possible outcomes. Therefore, there are 5 x 4 x 3 = 60 outcomes in this case.

Case 2: The first die shows any number. The second die shows the same number as the first. There is only 1 possible outcome in this case. The third die must show a different number than the first two, so there are 5 possible outcomes. The fourth die must show a different number than the first three, so there are 4 possible outcomes. Therefore, there are 1 x 5 x 4 = 20 outcomes in this case.

Case 3: The first die shows any number. The second die shows a different number than the first. The third die shows the same number as either the first or the second. There are 2 possible outcomes in this case. The fourth die must show a different number than the first three, so there are 4 possible outcomes. Therefore, there are 2 x 4 = 8 outcomes in this case.

To get the total number of outcomes where each die shows a different number, we add up the outcomes from each case:

60 + 20 + 8 = 88

Therefore, the probability that each of the four numbers that appear will be different is:

88 / 1296 = 0.0679, or approximately 6.79%.

The  directed graph for the given values given by the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)} is expained.

The directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)} is shown below:

We can clearly see from the directed graph that there are four vertices: a, b, c, and d.

For the given relation, there are three edges that start and end on vertex a, two edges that start and end on vertex b, one edge that starts from vertex c and ends on vertex b, one edge that starts from vertex c and ends on vertex d, and one edge that starts from vertex d and ends on vertex a.

The vertex a is connected to vertex a and b.

The vertex b is connected to vertices c and d.

The vertex c is connected to vertices b and d.

The vertex d is connected to vertices a and b.

A directed graph is a graphical representation of a binary relation in which vertices are connected by arrows.

Each directed edge shows the direction of the relation.

A directed graph is also called a digraph.

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Answer:

  (0, -2)

Step-by-step explanation:

The solution to a system of equations is the point on the graph where the lines intersect.

Here, both lines have a y-intercept of -2, so intersect there. The solution is ...

  (x, y) = (0, -2)

Answer:

jsjdkfnfnfkdkfkfkfkidkffbgngngkgk

To convert grams per tablespoon to grams per pint, we need to know the conversion factor between tablespoons and pints.

Since there are 2 tablespoons in 1 fluid ounce (oz), and there are 16 fluid ounces in 1 pint, we can calculate the conversion factor as follows:

Conversion factor = (2 tablespoons/1 fluid ounce)  (1 fluid ounce/16 fluid ounces) = 1/8

Given that the solution is 1 gram per tablespoon, we can multiply this value by the conversion factor to find the grams per pint:

Grams per pint = (1 gram/tablespoon)  (1/8)  2 pints = 0.25 grams

Therefore, there are 0.25 grams in 2 pints of the solution.

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The standard error for the sample proportion is 0.3995.

Standard Error: What Is It?

The standard error of the mean, or simply standard error, indicates how likely it is that the population means will differ from a sample mean. It demonstrates how much the sample means would vary if the same study were conducted again using new samples taken from the same population.

given:

n= 200

and possible outcomes= 80

Standard deviation = √(80²/200)= 5.65

Now, standard error = σ / √n

                                 = 5.65/√200

                                  = 0.3995

Hence, the standard error for the sample proportion is 0.3995.

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The value of x is the vertex of an angle with angles measuring 120 degrees and 240 degrees.

To solve this problem, we need to use the fact that the sum of the angles around a point is 360 degrees. This means that the angles formed by the two lines at the point of intersection add up to 360 degrees.

Let's call the two angles A and B. Then we can set up the following equation:

A + B = 360

Now, we need to use some information about the angle with vertex x to solve for one of the angles. Depending on the information given in the problem, we may need to use additional equations.

If we are given that one of the angles is twice the size of the other angle, we can write:

A = 2B

Now we can substitute this into our equation:

2B + B = 360

Simplifying, we get:

3B = 360

Dividing both sides by 3, we get:

B = 120

Now that we know the value of one of the angles, we can use our equation to find the value of the other angle:

A + 120 = 360

Subtracting 120 from both sides, we get:

A = 240

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Complete Question:

Two lines meet at a point that is also the vertex of an angle. Set up and solve an equation to find the value of x. Explain why your answer is reasonable.

Answer:

  a) 6 7/8 days

  b) 105 miles

Step-by-step explanation:

Given that L(d) = 209 -8d miles of road remain to be paved after d days, you want to know (a) the number of days paving if 154 miles remain, and (b) remaining miles after 13 days.

We want to find d such that L(d) = 154.

  L(d) = 154

  209 -8d = 154 . . . . . . substitute for L(d)

  209 -154 = 8d . . . . . add 8d-154

  55/8 = d = 6 7/8 . . . divide by 8

The crew has been paving for 6 7/8 days if 154 miles remain.

After 13 days, the remaining miles will be ...

  L(13) = 209 -8·13 = 209 -104

  L(13) = 105

After 13 days, the crew has 105 miles left to pave.

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Answer:

Step-by-step explanation:

Required equation is:

The graph is attached

Possible combinations are:

Answer:

C

Step-by-step explanation:

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution.

To simulate the emergency calls for 3 days, we need to use a cumulative hourly clock and generate random numbers to determine when the calls will occur. Let's use the following table of random numbers:

Random Number Call Time

57 1 hour

23 2 hours

89 3 hours

12 4 hours

45 5 hours

76 6 hours

Starting at 12:00 AM on the first day, we can generate the following sequence of emergency calls:

Day 1:

12:00 AM - Call

1:00 AM - No Call

3:00 AM - Call

5:00 AM - No Call

5:00 PM - Call

Day 2:

1:00 AM - No Call

2:00 AM - Call

4:00 AM - No Call

7:00 AM - Call

8:00 AM - No Call

11:00 PM - Call

Day 3:

12:00 AM - No Call

1:00 AM - Call

2:00 AM - No Call

4:00 AM - No Call

7:00 AM - Call

9:00 AM - Call

10:00 PM - Call

The average time between calls can be calculated by adding up the times between each call and dividing by the total number of calls. Using the simulated data from part a, we get:

Average time between calls = ((2+10+10+12)+(1+2+3)) / 7 = 5.57 hours

The expected value of the time between calls can be calculated using the probability distribution:

Expected value = (1/6)x1 + (1/6)x2 + (1/6)x3 + (1/6)x4 + (1/6)x5 + (1/6)x6 = 3.5 hours

The results are different because the simulated data is based on random numbers and may not perfectly match the probability distribution. As more data is generated and averaged, the simulated results should approach the expected value.

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The total distance traveled is approximately 207.948 miles and the average speed is approximately 53.48 mph.

To find the total distance traveled, we need to calculate the distance traveled during each segment of the journey and then sum them up.

Distance traveled during the first segment:

```

d1 = v1 * t1

  = 65.6 mph * 2.08 hours

```

Distance traveled during the stop:

Since the car comes to a stop, the distance traveled during this time is zero.

Distance traveled during the second segment:

```

d2 = v2 * t2

  = 57.2 mph * 1.25 hours

```

Now we can calculate the total distance traveled:

```

d = d1 + d2

```

Let's calculate the values:

```

d1 = 65.6 mph * 2.08 hours = 136.448 miles

d2 = 57.2 mph * 1.25 hours = 71.5 miles

d = d1 + d2 = 136.448 miles + 71.5 miles = 207.948 miles

tstop = 33.6 min = 33.6/60 hours = 0.56 hours

= 207.948 miles / (2.08 hours + 0.56 hours + 1.25 hours) = 207.948 miles / 3.89 hours ≈ 53.48 mph

```

Therefore, the total distance traveled is approximately 207.948 miles and the average speed is approximately 53.48 mph.

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1. The solution to the first differential equation is given by e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. The general solution to the second differential equation is x(3x - y^2) = C, where C is a positive constant.

To solve the first-order differential equations, let's solve them one by one:

1. (e^2y - ycos(xy))dx + (2xe^2y - xcos(xy) + 2y)dy = 0

We notice that the given equation is not in standard form, so let's rearrange it:

(e^2y - ycos(xy))dx + (2xe^2y - xcos(xy))dy + 2ydy = 0

Comparing this with the standard form: P(x, y)dx + Q(x, y)dy = 0, we have:

P(x, y) = e^2y - ycos(xy)

Q(x, y) = 2xe^2y - xcos(xy) + 2y

To check if this equation is exact, we can compute the partial derivatives:

∂P/∂y = 2e^2y - xcos(xy) - sin(xy)

∂Q/∂x = 2e^2y - xcos(xy) - sin(xy)

Since ∂P/∂y = ∂Q/∂x, the equation is exact.

Now, we need to find a function f(x, y) such that ∂f/∂x = P(x, y) and ∂f/∂y = Q(x, y).

Integrating P(x, y) with respect to x, treating y as a constant:

f(x, y) = ∫(e^2y - ycos(xy))dx = e^2yx - y∫cos(xy)dx = e^2yx - ysin(xy) + g(y)

Here, g(y) is an arbitrary function of y since we treated it as a constant while integrating with respect to x.

Now, differentiate f(x, y) with respect to y to find Q(x, y):

∂f/∂y = e^2x - xcos(xy) + g'(y) = Q(x, y)

Comparing the coefficients of Q(x, y), we have:

g'(y) = 2y

Integrating g'(y) with respect to y, we get:

g(y) = y^2 + C

Therefore, f(x, y) = e^2yx - ysin(xy) + y^2 + C.

The general solution to the given differential equation is:

e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. x(yy' - 3) + y^2 = 0

Let's rearrange the equation:

xyy' + y^2 - 3x = 0

To solve this equation, we'll use the substitution u = y^2, which gives du/dx = 2yy'.

Substituting these values in the equation, we have:

x(du/dx) + u - 3x = 0

Now, let's rearrange the equation:

x du/dx = 3x - u

Dividing both sides by x(3x - u), we get:

du/(3x - u) = dx/x

To integrate both sides, we use the substitution v = 3x - u, which gives dv/dx = -du/dx.

Substituting these values, we have:

-dv/v = dx/x

Integrating both sides:

-ln|v| = ln|x| + c₁

Simplifying:

ln|v| = -ln|x| + c₁

ln|x| + ln|v| = c₁

ln

|xv| = c₁

Now, substitute back v = 3x - u:

ln|x(3x - u)| = c₁

Since v = 3x - u and u = y^2, we have:

ln|x(3x - y^2)| = c₁

Taking the exponential of both sides:

x(3x - y^2) = e^(c₁)

x(3x - y^2) = C, where C = e^(c₁) is a positive constant.

This is the general solution to the given differential equation.

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