A small town has two local high schools. High School A currently has 700 students and is projected to grow by 65 students each year. High School B currently has 900 students and is projected to grow by 40 students each year. Let A(t) represent the number of students in High School A in t years, and let B(t) represent the number of students in High School B after t years. Write the equation for each function and determine how many students would be in each high school in the year they are projected to have the same number of students. A(t) = B(t) =

Answers

Answer 1

Answer:

1. A(t) = 65t + 700

2.B(t) = 40t + 900

3. High School A and High School B will both have 1,220 students in the 8th year

Step-by-step explanation:

1. The equation for the number of students in High School A represents a linear function.

⭐ What is a linear function?

A linear function is a type of equation where every y-value increases by a constant, additive amountOne way to write the equation for a linear function is: [tex]y = mx+b[/tex], where m is the constant, additive amount, and b is the y-intercept, or the initial value.

Let's write the equation for High School A in the [tex]y = mx+b[/tex] format, known as slope-intercept form:

The constant, additive amount for High School A is 65 (m)The initial value for High School A is 700 (b)

∴ High School A: [tex]y = 65x + 700[/tex]

2. Let's write the equation for High School B in the [tex]y = mx + b[/tex] format, known as slope-intercept form:

The constant, additive amount for High School B is 40 (m)The initial value for High School B is 900 (b)

∴ High School B: [tex]y = 40x + 900[/tex]

3. To find at what year High School A and High School B will have the same number of students, we need to solve a system of linear equations.

What is a system of linear equations?

A system of linear equations is two or more linear equations that intersect at one point (x,y)

For this problem, let's set both linear equations equal to each other to see at what point will the high school populations be the same.

[tex]A(t) = B(t)[/tex]

[tex]65t + 700 = 40t + 900[/tex]

[tex]25t = 200[/tex]

[tex]t = 8[/tex]

Now we know that in the 8th year, High School A will have the same population as High School B.

We need to find what the population will be in year 8.

Thus, substitute the value of t into one of the functions and solve.

I am choosing to substitute t into A(t), but you can also do B(t).

[tex]A(8) = 65(8) + 700[/tex]

[tex]A(8) = 520 + 700[/tex]

[tex]A(8) = 1,220[/tex]

⚠️!!! CAUTION !!! ⚠️

Some people may stop at this point and write that in the 8th year, both high schools will have a population of 1,220 students.

However, you should also substitute 8 into the other function you didn't substitute it into to make sure that 8 is correct.

[tex]B(8) = 40(8) + 900[/tex]

[tex]B(8) = 320 + 900[/tex]

[tex]B(8) = 1,220[/tex]

∴ In the 8th year, both high schools will have a population of 1,220 students.


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With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.
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Size of Company Yes No Total
Small 33 17 50
Medium 68 7 75
Large 88 12 100
Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
1. Compute the value of the 2 test statistic (to 2 decimals).
2. The p value is :_____.
a. less than .005
b. between .005 and .01
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d. between .025 and .05
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a. health insurance coverage is not independent of the size of the company
b. Cannot reject the assumption that health insurance coverage and size of the company are independent
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Medium %
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Answers

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1.  χ² =  15.3902

2. The p value is :_____.a. less than .005

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

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Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

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against the claim

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2) the significance level alpha is set at 0.05

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33                   42                      -9               81                    1.928  

68                  63                         5              25                  0.3968

88                  84                         4               16                  0.1904

17                    8                           9              81                  10.125

7                     12                          -5             21                    1.75

12                    16                         -4              16                     1              

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