Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). Her work is shown below. Let (x2, y2) be (–

Establish a proportion.

8/127=15/x

Cross multiply

8x=1,905

Divide each side by 8

x=238.125

The greatest of the actual distances is 238.125 km.

Hope this clarification helps:)

Answer:

a. Alpha equals 3.014 while beta equals 12.442

b. The likelihood that the data transfer duration surpasses 50ms is 0.238

c. The chance that data transfer time falls between 50 and 75 ms is 0.176

Step-by-step explanation:

a. Given the data, the mean and standard deviation for the random variable X are 37.5 ms and 21.6, respectively.

Thus, E(X)=37.5 and V(X)=(21.6)∧2  

To find alpha, we need to apply the formula:

alpha=E(X)∧2/V(X)

alpha=(37.5)∧2/21.6∧2

alpha=1,406.25 /466.56

​alpha=3.014

To determine beta, the following formula is employed:

β=  V(X) ∧2/E(X)

β=(21.6)  ∧2/37.5

β=466.56 /37.5

β=12.442

b. With E(X)=37.5 and V(X)=(21.6)∧2,  

Hence, P(X>50)=1−P(X≤50)

To find the probability of data transfer time exceeding 50ms, we use the formula:

P(X>50)=1−P(X≤50)

=1−0.762

=0.238

The chance of data transfer time exceeding 50ms is 0.238

c. With E(X)=37.5 and V(X)=(21.6)∧2,  

Thus, P(50<X<75)=P(X<75)−P(X<50)  

To find the probability that data transfer time is between 50 and 75 ms, we apply the formula:

P(50<X<75)=P(X<75)−P(X<50)

=0.938−0.762

=0.176

​

The probability that data transfer time falls between 50 and 75 ms is 0.176

Answer: The correct formulation is option A.)A = x(x − 4) − 0.5(8)(x − 4) − 4(8)

Step-by-step explanation:

To calculate the area that needs painting in the theater room in square feet, follow these steps:

1. Calculate the area of the theater room

Length: x

Width: x-4

A (area of theater room) = x (x-4)

2. Calculate the area of the right triangle

Height: x-4

Base: 8

A (area of right triangle) = 0.5 (8) (x-4)

3. Calculate the area of the rectangle designated as a closet

Length: 8

Width: 4

A (closet) = 8 (4)

4. The painted area is calculated by subtracting the areas of the right triangle and the closet from the total area of the theater room:

A= A(theater room) - A(right triangle) - A (closet)

A = x (x-4) -0.5 (8) (x - 4) - 4 (8)

Thus, the proper equation to compute the area is option A.