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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please anwser this thank you!!​

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Step-by-step explanation:

v>29 or 29,infinity sign i used an app called and this is what it showed

<3<3<3<3<3<3<3<3<3<3<<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

v >_ 29

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13/4 + c = 3/4 what’s c,?

Answers

Answer:

c = -2.5

Step-by-step explanation:

13/4 + c =3/4

2.5 + c = 0

c=-2.5

DO NOT PRANK!! I NEED HELP PLS (will give brainly)
Use the diagram below for this question. The angle bisectors of triangle ABC meet at G.
If m∠ ABC = (4x + 12) degrees and m∠ GBA = (3x – 4) degrees , find m∠ GBC.
A.26 degrees
B.44 degrees
C.52 degrees
D.36 degrees

Answers

Answer:

b

Step-by-step explanation:

hiiii

I had this same question on a test, I thought it was C and I ended up getting it wrong. It was between that and B and when I was doing the work they both fit so I would say your best choice is

B:44 Degrees

A survey was conducted to investigate whether there is an association between a person's age and their thoughts on what a state senate should do about state parks. Participants selected from "leave state parks the way they are," "increase funding to state parks," or "completely overhaul state parks," and their age was categorized as under 30 years old, between 30 and 50 years old, and over 50 years old. The hypothesis test statistic was calculated to be 15.01. Which of the following is closest to the p- value of the test?
A. 0.0047
B. 0.0103
C. 0.0202
D. 09897
E. 0.9953

Answers

Answer:

E. 0.9953

Step-by-step explanation:

The computation of the p value is shown below:

According to the question

The participant choosen from 3 different state parks, r = 3

And there are 3 different age group, s = 3

So, degrees of freedom is

= (r-1) × (s-1)

= 2 × 2

= 4

And, the Test statistic is 15.01

Now

p-value = P(Chisq < 15.01 )

= 0.9953

In the chisquare table see the degree of freedom i.e. 4

Answer:

0.0047

Step-by-step explanation:

This is what college board says

The value 0.0047 is the probability that χ2 is greater than 15.01 in an χ2 distribution with (3−1)(3−1)=4 degrees of freedom.

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.
Health Insurance
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
c. between .01 and .025
d. between .025 and .05
e. between .05 and .10
f. greater than .10
3. What is your conclusion?
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
4. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %

Answers

Answer:

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

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the employee health insurance coverage is independent of the size of the company

against the claim

Ha: the employee health insurance coverage is not independent of the size of the company

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 3-1) (2-1)=  2 d.f

4) Computations:

Under H0 , the observed frequencies are :

Observed       Expected E        (O-E)         (O-E)²             (O-E)²/E

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              

                                                                                          15.3902    

Expected Values are calculated using the formula :

Row Total * Column Total / sample size

E1= (33+17) (33+ 68+88)/ 50+75+100= 42

E4= (33+17) (17+ 7+ 12)/ 50+75+100=8

E2= (68+7) (33+ 68+88)/ 50+75+100= 63

E5= (68+7)  (17+ 7+ 12)/ 50+75+100= 12

E3= (88+12) (33+ 68+88)/ 50+75+100= 84

E6= (88+12)  (17+ 7+ 12)/ 50+75+100= 16

5) The critical region is χ² ≥ χ² (0.05)2 = 5.99

6) Conclusion:

The calculated χ² =  15.3902    falls in the critical region χ² ≥  5.99  so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.

2. The p value is :_____.

a. less than .005

The p-value is .000385.

3.  Conclusion

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

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

Help me plz! Thank you!

Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

9514 1404 393

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