What is the inverse of the function f(x) = 2x – 10?

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Answer:

Step-by-step explanation:

Step 1

Calculate the slope of the dashed line

The slope between two points is computed with the formula:

We consider

(-3,1) and (0,3)

and substitute into it:

Step 2

Determine the equation of the dashed line in slope-intercept form:

The equation we established is:

---> associated problem

Substituting yields:

Step 3

Establish the inequality corresponding to the graph

Given that it is represented by a dashed line, the area to the left of this line is shaded.

Thus,

Refer to the attached diagram for enhanced understanding of the problem.

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: y = 2/5 --> y = 0.4

Step-by-step explanation:

The equation 5y = 2 represents a horizontal line at y = 2/5.

This means that the y-coordinate holds the value of 2/5 = 0.4 for any x-coordinate.

<span><span>Center coordinates: (x0, y0, z0)</span></span> and radius r.

<span>The equation of the sphere is:</span>
<span>(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2</span>