A college has an acceptance rate of 17%. If 3,240 students apply, about

Answer:

Step-by-step explanation:

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!

Answer:

16 cubic feet per hour

Step-by-step explanation:

This involves a straightforward conversion from inches to feet.

Step 1: Establish the conversion scale

---> the volume of water in 1 minute is 462 cubic inches

--->1 cubic foot = 1728 cubic inches

--->1 hour consists of 60 minutes,

Step 2: Determine the volume in feet per hour

Volume of water in one hour =  0.0347 x 462

---> the amount of water in 1 hour =  = 16.0314 cubic feet

---> Rounded to--> 16 cubic feet

Thus, 462 cubic inches per minute equates to 16 cubic feet of water on an hourly basis

Answer:

The correct choice is option D.

Detailed explanation:

Any fraction where m > n can be represented as a/b

where a = quotient

b = remainder.

The specified number is given as m/n.

3)4( 1 ← quotient

- 3

____

   1 ← remainder

In this case, quotient= 1, remainder=1, and n=3.

.

Answer:

a. i) Please refer to the attached graph representing the equation $10·x + $12·y = $300

ii) The intercepts indicate the maximum number of short-sleeve (at the x-intercept) and long-sleeve shirts (at the y-intercept) that can be ordered.

Step-by-step explanation:

The details provided are as follows:

Cost of each short-sleeve shirt = $10

Cost of each long-sleeve shirt = $12

Total budget available = $300

The equation for total spending is given by $10·x + $12·y = $300

Where;

x = Number of short-sleeved shirts

y = Number of long-sleeved shirts

Rearranging the equation into slope-intercept form, we have:

$10·x + $12·y = $300

$12·y = $300 - $10·x

y = $300/$12 - $10·x/$12

y = 25 - 5/6·x

Attached is the graph produced using Microsoft Excel

The coordinates that can be used for graph plotting are as follows:

x, y

(0, 25)

(5, 20.83)

(15, 12.5)

(20, 8.33)

(25, 4.17)

(30, 0)

The x-intercept denotes the quantity of short-sleeve shirts purchasable with a $300 budget, while the y-intercept signifies the quantity of long-sleeve shirts achievable under the same budget.