Given the following triangle, If Sin F = 3/5 , then find the Cos D: A) 4/5 B) 4/3 C) 3/4 D) 3/5

The general solution to the differential equation dy/dt - 5y = A is y = Ce^(5t) + A/5, where C is a constant of integration. The general solution is y = (A/5) + Ce^(5t). so, the correct answer is D).

The general solution to the differential equation dy/dt - 5y = A, where A is a constant, is

y = Ce^(5t) + A/5

where C is an arbitrary constant determined by any initial or boundary conditions given.

The general solution is a combination of the homogeneous solution y_h = Ce^(5t) (which satisfies the differential equation without the constant term A) and the particular solution y_p = A/5 (which satisfies the differential equation with A but without any initial or boundary conditions).

so, the correct option is D).

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--The given question is incomplete, the complete question is given

" Answer quickly please

Given that A is a constant, the general solution to the differential equation dy/dt -5y = A is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y = Ce^(5t) +A/5 The solution to the exact differential equation"--

Answer:

False.

Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.

The statement is True.

The statement "95% confidence interval (5.623 to 6.377)" means that if we were to repeat this process of taking 100 samples from the population and constructing a confidence interval for each sample, then about 95% of those intervals would contain the true population mean.

This is the definition of a confidence interval at a certain level of confidence (in this case, 95%). Therefore, the statement is true.

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Answer:

-17 and -5

Step-by-step explanation:

-5 x -17 = 85

-5 + -17 = -22

The volume of a triangular prism in question number 3, obtained from the product of the area of a triangle and the thickness of the prism is 1,728 mi³

A triangular prism consists of two triangular bases and three sides that are rectangular.

The solid in the figure in question number 3 is a triangular prism, with the following dimensions.

Base length = 30 mi.

Thickness (depth of the prism) = 8 mi

Shape of the triangles = Right triangles

Leg lengths of the right triangles = 18 miles and 24 miles

The volume of the triangular prism = Area of the cross section of the triangular prism × Depth of the prism

Area of the triangular cross section of the triangular prism = (1/2) × 18 × 24 = 216 mi²

Volume of the triangular prism = 216 mi² × 8 mi = 1728 mi³

The volume of the triangular prism in the figure is therefore; 1,728 mi³

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The possible total number of boys and girls in the class is 21, and

the answer is b).

Let's denote the number of girls in the class as 'g' and the number of

boys as 'b'.

We know that all students in the class study either French or German,

but not both.

Therefore, the total number of students in the class is equal to the sum

of the number of students who study French and the number of students

who study German

From the given information, we can write the following equations:

        study German

Substituting this into the first equation, we get:

Substituting this into the first equation, we get:

Therefore, the total number of students in the class must be a multiple

of 3.

Let's try the answer choices:

a) 15 students (total number of students is not a multiple of 3)

b) 21 students (total number of students is a multiple of 3 and the

number of girls is a multiple of 3, so this is a possible solution)

c) 24 students (total number of students is a multiple of 3 and the

number of girls is not a multiple of 3)

d) 30 students (total number of students is a multiple of 3 but the

number of girls is not a multiple of 3)

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Just-in-time (JIT) delivery is a supply chain management strategy that aims to improve efficiency and reduce inventory costs by having materials and goods delivered exactly when they are needed in the production process.

This approach requires suppliers to be able to respond to the customer's production schedule, ensuring timely deliveries to prevent disruptions. As a result, JIT delivery shifts greater responsibility for physical distribution activities from the supplier to the business customer, who needs to closely monitor inventory levels and maintain efficient communication with suppliers.

However, JIT delivery does not typically lead to larger, less frequent deliveries, nor does it inherently increase physical distribution costs. In fact, it may reduce costs by minimizing inventory storage expenses. Additionally, e-commerce order systems and computer networks are often utilized to facilitate the communication and coordination required for effective JIT delivery.

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The width of Micayla's frame is Wf = (Lf x Wp) / Lp

Let's say that the painting has a length of Lp and a width of Wp, and the frame has a length of Lf and a width of Wf. We want to find the width of the frame, which we can call x. We know that Micayla wants to keep the same ratio of length to width between the painting and the frame, so we can set up the following equation:

Lp/Wp = Lf/Wf

This equation states that the ratio of the length to the width of the painting is equal to the ratio of the length to the width of the frame. We can use this equation to solve for x, the width of the frame. First, we can cross-multiply to get:

Lp x Wf = Lf x Wp

Then, we can solve for x by isolating it on one side of the equation:

Wf = (Lf x Wp) / Lp

This equation tells us that the width of the frame is proportional to the length of the frame and the width of the painting, divided by the length of the painting. By plugging in the appropriate values for Lp, Wp, and Lf, we can solve for x and determine the width of the frame.

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Answer:

radius is 50.95

area is 8158.55

Step-by-step explanation:

cirumference = 2pi×r

or,320.28=2×(22/7)×r

or, r=320.28/(2×(22/7))

r=50.95 cm

area=(22/7)r^2

=8158.55

Answer:

12 is the answer

Step-by-step explanation:

6 y = 6 × 36 in. ( y = yards, in = inches )

do the math:

6(36) ÷ 18 = 12 ( for 18 sections of course )

12 × 18 = 6 × 36

becuase;

12 × 18 = 216 \

                       ——- They are the same

6 × 36 = 216  /

= 216

Divide

216 ÷ 18 = 12

12 being the answer

Answer:

12 inches long

Step-by-step explanation:

One yard is equal to 36 inches, so 6 yards is equal to:

[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]

To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):

[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]

Therefore, each section is 12 inches long.

The production level that will maximize profit is 80 units

To find the production level that will maximize profit given the cost function C(q) = 660 + 5q + 0.03q^2 and demand function p = 10 - q/400, follow these steps:

1. Write down the revenue function: Revenue (R) is the product of price (p) and quantity (q). So, R(q) = p * q.

2. Substitute the demand function into the revenue function: R(q) = (10 - q/400) * q

3. Simplify the revenue function: R(q) = 10q - q^2/400

4. Write down the profit function: Profit (P) is the difference between revenue and cost. So, P(q) = R(q) - C(q).

5. Substitute the revenue and cost functions into the profit function: P(q) = (10q - q^2/400) - (660 + 5q + 0.03q^2)

6. Simplify the profit function: P(q) = 10q - q^2/400 - 660 - 5q - 0.03q^2

7. Combine like terms: P(q) = 5q - q^2/400 - 0.03q^2 - 660

8. Differentiate the profit function with respect to q to find the first derivative: P'(q) = 5 - q/200 - 0.06q

9. Set the first derivative equal to 0 and solve for q: 5 - q/200 - 0.06q = 0

10. Solve for q: q ≈ 80

The production level that will maximize profit is approximately 80 units (rounded to the nearest whole number).

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Answer:

Step-by-step explanation:

The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.

To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,

we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.

This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.

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If t is less than -1.699, we reject the null hypothesis.

To test the claim by the owner of the large dealership, we will use a one-sample t-test with the following hypotheses:

Null Hypothesis: H0: µ >= µ0 (The population mean time of ownership is greater than or equal to µ0)

Alternative Hypothesis: Ha: µ < µ0 (The population mean time of ownership is less than µ0)

where µ is the population mean time of ownership, µ0 is the claimed mean time of ownership by the owner of the dealership.

The significance level is α = 0.05.

We can calculate the t-value as:

t = ([tex]\bar{x}[/tex] - µ0) / (s / √n)

where [tex]\bar{x}[/tex] is the sample mean time of ownership, s is the sample standard deviation, n is the sample size.

Plugging in the values given in the problem, we get:

t = ([tex]\bar{x}[/tex] - µ0) / (s / √n) = (5.7 - µ0) / (1.8 / √n)

Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value from the t-distribution table with n-1 degrees of freedom and a significance level of 0.05. For a sample size of n = 30 (assuming it is large enough), the critical t-value is -1.699.

If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.

If the calculated t-value is greater than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.

So, if we assume that the sample is representative of the population and meets the assumptions of the t-test, we can calculate the t-value as:

t = (5.7 - µ0) / (1.8 / √30)

If t is less than -1.699, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Note that we don't have any information about the claimed mean time of ownership by the owner of the dealership, so we cannot calculate the t-value or make any conclusions.

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68.2% confidence of the students drink between: 131 and 175 bottles of water per day.

We can use the empirical rule, also known as the 68-95-99.7 rule, to determine the range of values that contain 68.2% of the data in a normal distribution. According to the rule, approximately 68.2% of the data falls within one standard deviation of the mean.

We know that the mean amount of bottled water consumed is 153 bottles, with a standard deviation of 22 bottles. Therefore, one standard deviation below the mean is 153 - 22 = 131 bottles, and one standard deviation above the mean is 153 + 22 = 175 bottles.

Thus, we can say with 68.2% confidence that the number of bottled water consumed by students each day falls between 131 and 175 bottles.

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To find dy/dt, we need to use implicit differentiation.

First, we differentiate both sides of the equation with respect to t:

2x(dx/dt) + 2y(dy/dt) = 2(dx/dt) + 4(dy/dt)

Next, we plug in the given values for x, y, and dx/dt:

2(3)(7) + 2(1)(dy/dt) = 2(7) + 4(dy/dt)

Simplifying, we get:

42 + 2(dy/dt) = 14 + 4(dy/dt)

Subtracting 2(dy/dt) and 14 from both sides:

28 = 2(dy/dt)

Finally, we divide both sides by 2 to solve for dy/dt:

dy/dt = 14
To find dy/dt, first differentiate the given equation x^2+y^2=2x+4y with respect to time t. Use the chain rule:

2x(dx/dt) + 2y(dy/dt) = 2(dx/dt) + 4(dy/dt).

Now substitute the given values, x = 3, y = 1, and dx/dt = 7:

2(3)(7) + 2(1)(dy/dt) = 2(7) + 4(dy/dt).

Solve for dy/dt:

42 + 2(dy/dt) = 14 + 4(dy/dt).

Rearrange and solve:

2(dy/dt) - 4(dy/dt) = 14 - 42,

-2(dy/dt) = -28.

Finally, divide by -2:

dy/dt = 14.

So the value of dy/dt is 14 when x = 3, y = 1, and dx/dt = 7.

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(a) The minimum number of hikers who could have walked between 7 miles and 18 miles: at least 5 hikers and at most 13 hikers.

(b) The maximum number of hikers who could have walked between 7 miles and 18 miles:  at most 15 hikers.

According to the question and given conditions, we need to find the cumulative frequency of the distance intervals that fall within the range of 7 miles and 18 miles, to find the minimum number of hikers and the maximum number of hikers who could have walked between 7 miles and 18 miles.

The sum of the frequencies up to a certain point in the data is the cumulative frequency. By adding the frequency of the current interval to the frequency of the previous interval, we can calculate the cumulative frequency.

a) To find the minimum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 5 miles to 10 miles and then from 10 miles to 15 miles.

Cumulative frequency for 5 < x <= 10: 2 + 3 = 5

Cumulative frequency for 10 < x <= 15: 5 + 8 = 13

Therefore, we find that at least 5 hikers and at most 13 hikers could have walked between 7 miles and 18 miles.

b) To find the maximum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 10 miles to 15 miles and from 15 miles to 20 miles.

Cumulative frequency for 10 < x <= 15: 8

Cumulative frequency for 15 < x <= 20: 8 + 7 = 15

Therefore, we can conclude that at most 15 hikers could have walked between 7 miles and 18 miles.

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The complete question is "a) work out the minimum number of hikers who could have walked between 7 miles and 18 miles b) work out the maximum number of hikers who could have walked between 7 miles and 18 miles."

Answer:

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

The two smaller right triangles are similar by AA property.

Use ratios of corresponding sides to get:

Simplify and solve for y:

The answer is that the town's percentage growth rate is approximately 3% per year.

To find the town's percentage growth rate, we can use the formula:

growth rate = (final population - initial population) / initial population * 100%

Let P be the initial population of the town, and let t be the time it takes for the population to double, which is 23 years in this case. We know that:

final population = 2P (since the population doubles)

t = 23 years

Substituting these values into the formula, we get:

growth rate = (2P - P) / P * 100% / 23

= P / P * 100% / 23

= 100% / 23

≈ 4.35%

However, this is the annual growth rate that would result in a doubling of the population in exactly 23 years. Since the question asks for the approximate percentage growth rate per year.

We need to find the equivalent annual growth rate that would result in a doubling time of approximately 23 years.

One way to do this is to use the rule of 70, which states that the doubling time (t) of a quantity growing at a constant percentage rate (r) is approximately equal to 70 divided by the growth rate:

t ≈ 70 / r

In this case, we want t to be approximately 23 years, so we can solve for r:

23 ≈ 70 / r

r ≈ 70 / 23

r ≈ 3.04%

Therefore, the town's percentage growth rate is approximately 3% per year.

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To find the slope of the tangent line to the polar curve, we need to find the derivative of the equation with respect to θ.

First, we can convert the polar equation into rectangular coordinates using the conversions rcos(θ) = x and rsin(θ) = y:
rcos(θ) = (1-2sin(θ))cos(θ)
r = x/cos(θ)
x/cos(θ) = 1 - 2sin(θ)
x = cos(θ) - 2sin(θ)cos(θ)
y = sin(θ) - 2sin^2(θ)

Next, we can find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dθ = cos(θ) - 4sin(θ)cos(θ)
dx/dθ = -sin(θ) - 2cos^2(θ)
Plugging in the value of e for θ, we get:
dy/dθ = cos(e) - 4sin(e)cos(e)
dx/dθ = -sin(e) - 2cos^2(e)

Finally, we can find the slope of the tangent line by taking the ratio of dy/dθ to dx/dθ:
slope = (cos(e) - 4sin(e)cos(e)) / (-sin(e) - 2cos^2(e))
This is the slope of the tangent line to the polar curve at the point specified by the value of e.
Hi! I'd be happy to help you with your question. To find the slope of the tangent line to the polar curve r = 1 - 2sin(θ) at a specific value of θ, we'll first need to convert the polar equation into Cartesian coordinates.
Let's recall the conversion formulas:
x = r*cos(θ)
y = r*sin(θ)

Now, substitute the polar curve equation into these formulas:
x = (1 - 2sin(θ))*cos(θ)
y = (1 - 2sin(θ))*sin(θ)
To find the slope, we need the derivative of y with respect to x, which is dy/dx. To do this, we'll first find dy/dθ and dx/dθ.
Differentiating both x and y with respect to θ:
dx/dθ = -2cos(θ)^2 + 2sin(θ)cos(θ)
dy/dθ = -2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)
Now, we find the derivative of y with respect to x:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (-2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)) / (-2cos(θ)^2 + 2sin(θ)cos(θ))

Now, you can plug in the specific value of θ for which you want to find the slope of the tangent line to the polar curve, and simplify the expression to obtain the final answer.

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1.  The proportion of students at the school who write with their left hand is 2/15 OR 13.3%

2. The estimated number of students who write with their left hand is 77 students

3. The estimated number of students in the different class of 18 students who write with their left hand is 2

From the question, we are to estimate the proportion of students who write with their left hand

To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.

From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:

2/15 = 0.133

OR

13.3%

2.

To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school

That is,

2/15 x 580 = 77.33

Thus, about 77 students write with their left hand

3.

To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:

2/15x 18 = 2.4

Hence, about 2 students in the different class write with their left hand.

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Answer:

E,F,H

Step-by-step explanation:

Answer:

B = 2 (could be 4, like with this font)

E = 4

F = 3

H = 4

P = 0 (could be 3, like this this font)

R = 0 (could be 3, like with this font)

X = (could be 4)

Other right angles:

D = 0 (could be 2, like with this font)

L = 1

T = 2

Y = (could be 1)

The missing step in solving the inequality 4(x – 3) /4 < 10/6x is to divide both sides by 2.

Apply the distributive property to get 4x - 12 /4 < 10/6x.

Combine like terms to obtain 4x - 3 < 5/3x.

Add 3/3x to both sides to get 4x < 8/3x + 3.

Subtract 8/3x from both sides to get 4/3x < 3.

Divide both sides by 4/3 to get x < -9/4.

Simplify the result by dividing both sides by 2 to get x < -9/2 or x > -4/3.

Therefore, the missing step is to divide both sides by 2, which gives x < -9/2 or x > -4/3.

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The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.

1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22

2. Determine the median (Q2):

The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:

Median = (8 + 12) / 2 = 10

Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:

Q1 = (4 + 4) / 2 = 4

Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:

Q3 = (18 + 18) / 2 = 18

3. Find the lower quartile (Q1):

The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.

4. Find the upper quartile (Q3):

The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1

= 18 - 4

= 14.

The interquartile range (IQR) for the given data is 14.

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The measure of the angle x in the circle is 65 degrees

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

The circle

On the circle, we have the angle at the vertex of the triangle to be

Angle = 100/2

Angle = 50

The sum of angles in a triangle is 180

So, we have

x + x + 50 = 180

Evaluate the like terms,

2x = 130

So, we have

x = 65

Hence, the angle is 65 degrees

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6.6,your answer is correct.

As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.

To solve you must take

10^2+b^2=12^2

100+b=144

144-100=44

Since b^2 is 44 you must find the square root [tex]\sqrt{44}[/tex]=6.6

a. The cost for a 100-mile radius for 3 weeks is $585, and there are 98 resumes within this radius, so the average cost per resume would be:

$585 / 98 = $5.96 per resume

b. The cost for a 150-mile radius for 3 weeks is $675, and there are 208 resumes within this radius, so the average cost per resume would be:

$675 / 208 = $3.25 per resume

c. If an employer opts for the 150-mile radius option instead of the 100-mile radius option, they would pay an extra $90 ($675 - $585) to see an additional 110 resumes (208 - 98).

The average cost to the employer for looking at each extra resume would be:

$90 / 110 = $0.82 per resume

d. An advantage of opting for the more expensive plan is that the employer would have access to a larger pool of potential candidates, which could increase the likelihood of finding a qualified applicant.

A disadvantage is that the employer would have to pay more money, which could be a significant expense for smaller businesses or those with limited budgets.

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The correct answer is (C) -8x12.

To simplify (4x^4)^-3, we use the power of a power rule which states that (a^m)^n = a^(mn), where a is a non-negative number and m and n are integers. Applying this rule, we get:

(4x^4)^-3 = 4^(-3) x^(4 x -3) = (1/64)x^(-12) = -8x^12 (using the negative exponent rule, which states that a^(-n) = 1/a^n)

Therefore, the simplified form of (4x^4)^-3 is -8x^12.

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Susan earns $9.50 per hour. This is found by dividing her earnings by the number of hours worked for each corresponding row in the table.

To find how much money Susan earned per hour, we need to divide the total earnings by the total number of hours worked. For finding the Total earnings we need to add the money earned in every hour,

Total earnings = $47.50 + $66.50 + $85.50 + $104.50 = $304

Total hours worked = 5 + 7 + 9 + 11 = 32

Money earned per hour = Total earnings / Total hours worked

= $304 / 32

= $9.50

Therefore, Susan earned money of $9.50 per hour.

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Answer:

Baltimore Train: 1,020 mi/12 hr = 85 mph

Pennsylvania Train: 75 mph

So the correct answer is A.

Answer: 35 + 25 + 50 / 2 = 85

Step-by-step explanation: You would have to add them all together and then divide them by 2.