A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school

Given the specified angles, one is 90 degrees, indicating that the triangle is a right triangle. With provided angles and one side representing the hypotenuse (the longest side), the area is determined using the formula: Area = 1/2 * base * height. Let's compute the height and base:

From sin 75, we derive height = 1.67.
And from cos 75, we obtain base = 0.45.

Calculating area gives us Area = (0.45 * 1.67) / 2, resulting in 0.37 square units.

Thus, the triangle's area is approximately 0.37 square units.

You can easily calculate the result for each segment and then sum them to determine the perimeter of triangle MNK.

It's false due to the squares being reduced to their minimum values.

Answer:

Step-by-step explanation:

<pGreetings!

a. The variable X represents the height of a Goomba, which follows a normal distribution with a mean of μ= 12 inches and a standard deviation of δ= 6 inches.

To find the probability that a Goomba picked at random has a height between 13 and 15 inches, you express it as:

P(13≤X≤15)

Considering that standard normal probability tables provide cumulative values, you can express this range as the cumulative probability up to 15 minus the cumulative probability up to 13. You'll first need to standardize these variable heights to obtain corresponding Z values:

P(X≤15) - P(X≤13)

P(Z≤(15-12)/6) - P(Z≤(13-12)/6)

P(Z≤0.33) - P(Z≤0.17)= 0.62930 - 0.56749= 0.06181

b. Now we have Y as the variable indicating the height of a Koopa Troopa. This variable also follows a normal distribution, with a mean μ= 15 inches and a standard deviation δ=3 inches.

The query concerns the probability that a Koopa Troopa stands taller than 75% of Goombas.

First step:

You need to determine the height of a randomly chosen Koopa Troopa that exceeds 75% of the Goomba population.

This entails determining the value of X corresponding to the limit below which 75% of the population falls, denoted by:

P(X ≤ b)= 0.75

Step 2:

Search the standard normal distribution for the Z value that has 0.75 beneath it:

Next, you will reverse the standardization to solve for "b"

Z= (b - μ)/δ

b= (Z*δ)+μ

b= (0.674*6)+12

b= 16.044 inches

Step 3:

With the height that identifies a Koopa Troopa taller than 75% of the Goomba population determined, compute the probability of selecting that Koopa Troopa:

P(Y≤16.044)

This time, utilize the Koopa’s average height and standard deviation to find the probability:

P(Z≤(16.044-15)/3)

P(Z≤0.348)= 0.636

The likelihood of randomly selecting a Koopa Troopa that is taller than 75% of Goombas is 63.6%

I hope this information is useful!

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by in grams, is defined by the differential equation,

which is linear. Shift the term to the right side, then multiply both sides by :

Next, integrate both sides and solve for :

Initially, the tank contains 5 g of salt at time , so we have

The duration required for the tank to contain 20 g of salt is , such that