A large set of data was collected and analyzed for the majors of college seniors in the US From the scatter plots produced the f
ollowing associations were observed the linear model P(1) - 2,376 + 73,219 can
be used to estimate the number of college seniors who graduated with a bachelor's degree in psychology, tyears after 2000. The linear model B(l) 2,4140 + 56, 545 can be used to estimate the number of college
seniors who graduated with a bachelor's degree in biology, years after 2000
Which of the following statements are true?
The number of psychology degrees increases by about 73,219 each year after 2000
The number of biology degrees increases by about 2,414 each year after 2000,
About 73,000 students graduated with degrees in psychology in 2000.
About 2,400 students graduated with degrees in biology in 2000.
In 2000, more students graduated with psychology degrees than biology degrees.
be used to estimate the number of college seniors who graduated with a bachelor's degree in psychology, tyears after 2000. The linear model B(l) 2,4140 + 56, 545 can be used to estimate the number of college
seniors who graduated with a bachelor's degree in biology, years after 2000
Which of the following statements are true?
The number of psychology degrees increases by about 73,219 each year after 2000
The number of biology degrees increases by about 2,414 each year after 2000,
About 73,000 students graduated with degrees in psychology in 2000.
About 2,400 students graduated with degrees in biology in 2000.
In 2000, more students graduated with psychology degrees than biology degrees.
1 answer:
Using linear function concepts, it is found that the correct statements are given by:
- The number of biology degrees increases by about 2,414 each year after 2000.
- About 73,000 students graduated with degrees in psychology in 2000.
- In 2000, more students graduated with psychology degrees than biology degrees.
A linear function is modeled by:
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.
In this problem, the number of college seniors who graduated with a bachelor's degree in psychology, in t years after 2000, is modeled by:
P(t) = 2,376t + 73,219.
For biology, the amount is given by:
B(t) = 2,414t + 56,545.
Then, the true statements are given by:
- The number of biology degrees increases by about 2,414 each year after 2000.
- About 73,000 students graduated with degrees in psychology in 2000.
- In 2000, more students graduated with psychology degrees than biology degrees.
More can be learned about linear function concepts at brainly.com/question/24808124
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The average squared distance between the points is their variance
The average squared distance is 8/3
<h3>How to determine the average squared distance?</h3>The given parameters are:
R={(x,y): 0<=x<=2, 0<=y<=2}
The point = (2,2).
f(x,y) = (x-2)² + (y-2)²
The squared distance is calculated as:
D² = f(x,y) = (x-2)² + (y-2)²
Where the area (A) is:
A = xy
Substitute the maximum values of x and y in A = xy
A = 2 * 2
A = 4
The minimum values of x and y are 0.
So, the limits for the integrals are 0 to 2
The integral becomes
Expand
Evaluate the inner integral with respect to x from 0 to 2
Expand
Simplify
Expand
Evaluate the integral with respect to y from 0 to 2
Expand
D² = 32/3
The average squared distance (AD²) is calculated as:
AD² = D²/A
So, we have:
AD² = 32/3 4
Evaluate the quotient
AD² = 32/12
Simplify
AD² = 8/3
Hence, the average squared distance is 8/3
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