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.
Find an equation in slope-intercept form of the line that has slope 2 and passes through point A(-3. - 1)
Answer:
Step-by-step explanation:
m = 2 ; x1 = -3 ; y1 = -1
Slope- point form: y - y1 = m(x -x1)
y - [-1] = 2(x - [-3])
y + 1 = 2(x + 3)
y + 1 = 2x + 3*2
y + 1 =2x + 6
y = 2x + 6 - 1
y = 2x + 5 This is slope intercept form : y = mx + b
Pls help 10 ptsssssssssssss
NO LINKS
Answer:
the answer is 16
Step-by-step explanation:
8/2=4
4*4=16
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
Answer:
b
Step-by-step explanation:
hiiii
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
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.
I need some help! Will give brainliest!!!
Answer:
Positive 7 on the line pointing up (y axis) is where you start (where your first dot goes when graphing). Then down two and right one. (Your second dot will end up on (5,1))
Step-by-step explanation:
LOOK AT THE PHOTO HELP ME PLEASE
Answer:
30°
Step-by-step explanation:
[tex] m\angle 2=m\angle 3[/tex]
(Alternate angles)
[tex] \because m\angle 3 =30\degree [/tex] (Given)
[tex] \therefore m\angle 2 =30\degree [/tex]
Solve for q: 2q- 12 = -40
Answer:
q = -14
Step-by-step explanation:
2q - 12 = -40
Add 12 to both sides
2q - 12 + 12 = - 40 + 12
2q = - 28
Divide both sides by 2
2q/2 = -28/2
q = - 14
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 %
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
Luna's dining room is 19 feet wide and 22 feet long. Luna wants to install wooden trim
around the top of the room. The trim costs $0.06 per foot. How much will it cost Luna to buy
enough trim?
9514 1404 393
Answer:
$4.92
Step-by-step explanation:
The cost is found by multiplying the number of feet by the cost per foot. The number of feet is the perimeter of the dining room, the sum of the lengths of all the sides.
There are two sides of the rectangular room that are 19 feet, and two sides that are 22 feet, so the total length of trim is ...
P = 2(L +W) = 2(22 ft + 19 ft) = 2(41 ft) = 82 ft
The cost is then ...
cost = ($0.06/ft)(82 ft) = $4.92
It will cost Luna $4.92 to buy enough trim.
please do this thanks
Answer:
225 in²
Step-by-step explanation:
First you have to find the ∛3,375 since it is a cube you know that all the dimensions are the same so when 15 comes out all you have to do is multiply the height by the length to get the area of one of its sides to get the answer.
Use the box plots for 3 and 4. What are the two medians. Pls help me
Answer:
C
Step-by-step explanation:
Answer:
C. 40 and 50
Step-by-step explanation:
The median marks the mid-point of the data and is shown by the line that divides the box into two parts (sometimes known as the second quartile). Half the scores are greater than or equal to this value and half are less.
please anwser this thank you!!
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
<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
Simplify, then write the answer in the standard form
(2x3 - X + 8) + (- X3 + x - 3)
Answer: x^3+5
Step-by-step explanation: You add the terms with similar exponents.
2x^3 + (-x^3) = x^3 -x+x = 0 8 + (-3) = 5
Is it monomial binomial or trinomial or non polynomial
Answer: Trinomial
Step-by-step explanation: The expression has 3 terms.
The perimeter of the base of a right square pyramid is 32 cm. The height of the pyramid is 8 cm. What is the volume of the pyramid?
If 43x-2=4 x+1, then x
Answer:
Step-by-step explanation:
Picture has the answer, not a bad picture I promise.
Step-by-step explanation:
43x-4x=1+2
39x/39=3/39
x=0.076
Help me plz! Thank you!
Answer:
the vertical line test proves that it is not a function because there are two y values for 1 x value
Step-by-step explanation:
8 The circle graph below shows the number of votes each candidate received in a recent student
council election.
Student Council Election
Votes Received
Jacob
60
Elias
25
Jade
40
What percentage of the votes did Jacob receive?
F 36%
G 44%
H 48%
J 60%
Answer:
60%
Step-by-step explanation:
What’s the volume of 9 cm 6 cm 4 cm
Answer:
bro tell me the shape
Step-by-step explanation:
Select all numbers that have an absolute value of 4.
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
angle 8 and 4
Step-by-step explanation:
it is shown by the picture I had just provided you
Answer:
A
Explination:
Hope this helps ^-^
A game comes with a deck of cards with each card
showing one of the numbers 2, 3, 4, 5, 6, or 8. Each
card occurs one time in red, one time in purple, and
one time in blue. Given that a blue card is drawn, what
is the probability the card is a 4?
Select one:
4/9
1/18
1/3
1/6
Aasf;kbdaihhakufnsdo;fgaoudghosaugbolfbodbfaifjla;db;ihjlksabd;ohipn
Step-by-step explanation:
Answer:
k
Step-by-step explanation:
which description is paired with its correct expression
Answer:
The answer is C.
Step-by-step explanation:
Select two days on which mike ran a total of 6 5/6 miles.
Saturday and sunday.............
13/4 + c = 3/4 what’s c,?
Answer:
c = -2.5
Step-by-step explanation:
13/4 + c =3/4
2.5 + c = 0
c=-2.5
What if the value of <5
Answer:
any number from -infinity to 4 is the value less then 5
which expression is equivalent to 6^4x6^3
Answer:
C - (6x6x6x6)(6x6x6)
Step-by-step explanation:
need help with math its a struggle
Answer:
(1,4)
(0,0)
Step-by-step explanation:
smarts
Answer:
1,4
0,0
Step-by-step explanation:
whatever is in the purple is valid and the closed line is inclusive so anything on it counts but the dotted line is exclusive
Help me please sjsjdjs it’s due in a few minutes
Answer:
The answer is the 3rd dot.
Step-by-step explanation:
hope this helps
Answer:
The one right below 8
Step-by-step explanation:
4. What is the volume of the triangular pyramid?
10 in
6 in
8 in
Will Mark brainliest
Answer:
V=6240 in^3
Step-by-step explanation:
I am not sure what the base is but here is my guess:
V=13Ah
V=13(48)(10)
V=6240 in^3