What is the average rate of change for this function for the interval from x= 2
to x = 4?

The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term:

Last term:

To find the probability that at least six students will graduate in four years, we can use the binomial probability formula.

The first and last terms of the expanded expression for this probability can be determined using the binomial coefficients.

The binomial probability formula is given by:

Where:

P(X ≥ k) is the probability that X is greater than or equal to k,

n is the number of trials (students in this case),

k is the desired number of successes (six or more students graduating),

p is the probability of success in a single trial (probability of graduating in four years).

In this case, the number of trials (n) is 10, and the probability of success (p) is 0.63.

To find the first term, we substitute k = 6 into the formula:

C(10, 6) represents the binomial coefficient, which can be calculated as:

C(10, 6) = 10! / (6! * (10 - 6)!)

To find the last term, we substitute k = 10 into the formula:

C(10, 10) = 10! / (10! * (10 - 10)!)

Hence, The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term:

Last term:

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Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = to find the angle that the ramp makes with the ground.

The angle is equal to

Final answer:

The angle that the ramp makes with the ground can be found using the concept of tangent in trigonometry. By dividing the height of the loading platform by the length of the ramp and taking the inverse tangent of the result, we find the angle to be approximately 11.3 degrees.

Explanation:

This question can be solved by using trigonometric principles, specifically the tangent of an angle in a right triangle. The tangent of an angle θ (theta) can be defined as the ratio of the side opposite the angle to the side adjacent to it.

In this scenario, the ramp forms a right triangle with the ground and the vertical line from the loading platform to the ground directly below it. The height of the platform, or the 'opposite' side, is 3 1/2 feet, and the ramp, or the 'adjacent' side, is 17 1/2 feet.

Therefore, we can say that: tan θ = (3.5 / 17.5)

To find the value of θ, we take the inverse tangent (or arc tangent) of the quotient. Using a calculator to do this (remember to set your calculator to degree mode), we find θ to be approximately 11.3 degrees.

Thus, the angle that the ramp makes with the ground is about 11.3 degrees.

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