Will someone please help me with these questions. The table shows the average annual cost of tuition at 4-year institutions from 2003 to 2010.
1.) Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable.
2.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2000. (Hint: look at the y-intercept)
3.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2020.
4.)What does the slope mean in context of the situation? 5.)Most students are not able to afford this tuition for 4 years. What are some ways that you can lower the cost of your college tuition? If you don’t plan to attend college, what things can do you post- HS graduation to continue your education or provide for yourself financially?
Answers
Step-by-step explanation:
1.) The equation for the line of least squares regression is given by
[tex]Y=mX+c[/tex]
where Y = Output Variable = Average Cost (in thousands of dollars)
X = Input Variable = Number of years after 2000
Thus, the given data table transforms as follows:
No. of years after 3 4 5 6 7 8 9 10
after 2000 (X)
Average Cost (Y) 15.505 16.510 17.451 18.471 19.363 20.409 21.093 22.092
To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)
Let us take any two random values of X and Y from the above table, so that we have
X₁ = 3; Y₁ = 15.505 and X₂ = 8; Y₂ = 20.409
Plugging in these two sets of values, we get the following two equations:
15.505 = (3)m + c and
20.409 = (8)m + c
Let us subtract the upper one from the lower one so that we have
20.409 - 15.505 = 8m + c - 3m - c
4.904 = 5m
Hence, m = 0.9808
Using this value and plugging it in one of the above equations yields the value of c as
20.409 = 8(0.9808) + c
Therefore, c = 12.563
So, the required equation for the line of least squares regression is
Y = (0.9808)X + 12.563
2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.
We have Y = 0 + 12.563
Thus, the cost of tuition in 2000 was $12,563.
3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have
Y = (0.9808)(20) + 12.563 = 32.179
Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.
4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.
One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.
One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.
The least squares regression equation is Average cost = 14.5 + 1.24 * School year. The best estimate for the average cost of tuition at a 4-year institution starting in 2020 is 33.3 thousand dollars. The slope of the regression line means that the average cost of tuition increases by 1.24 thousand dollars for every year after 2000.
1. To find the least squares regression equation, we can use the following steps:
Calculate the mean of the independent variable (school year) and the dependent variable (average cost).
Calculate the deviations from the mean for both variables.
Calculate the product of the deviations from the mean for both variables.
Calculate the variance of the independent variable.
Calculate the slope of the regression line:
slope = sum of the product of the deviations from the mean / variance of the independent variable
Calculate the y-intercept of the regression line:
y-intercept = mean of the dependent variable - slope * mean of the independent variable
Calculations:
Mean of school year: 5.5
Mean of average cost: 19.0
Deviations from the mean for school year: -1.5, -0.5, 0.5, 1.5, 2.5
Deviations from the mean for average cost: -3.5, -2.5, -1.5, -0.5, 1.5
Product of the deviations from the mean: 5.25, 1.25, -0.75, 0.75, 3.75
Variance of the independent variable: 4.25
Slope of the regression line: 5.25 / 4.25 = 1.24
Y-intercept of the regression line: 19.0 - 1.24 * 5.5 = 14.5
Least squares regression equation:
Average cost = 14.5 + 1.24 * School year
Related Questions
If u is <1,5> find ||u||
A.4
B.6
C. Square root 6
D. Square root 26
Answers
u = <1,5> is a vector in the form <a,b> with a = 1 and b = 5.
||u|| = sqrt(a^2+b^2) is the magnitude or length of the vector
||u|| = sqrt(1^2+5^2)
||u| = sqrt(26)
The answer is choice D
Check out the attached image below for a visual.
Solve each equation by graphing. Round to the nearest tenth.
-2x²+2= -3x
A) −1, −2
B) 2, −0.5
C) −1, 2
D) 0.5, −3
Answers
B
rearrange into standard form : ax² + bx + c = 0 (a≠ 0)
2x² - 3x - 2 = 0
(x - 2)(2x + 1) = 0 ( equate each factor to zero and solve for x )
x - 2 = 0 ⇒ x = 2
2x + 1 = 0 ⇒ x = - 0.5
Which expression is equivalent to 3 + 4y – y(9 – 2y) + 5?
A. 8 – 7y
B. 2y^2 - 5y + 8
C. -2y^2 - 5y + 8
D. -6y^2 + 27y + 8
Answers
Answer:
C.
Step-by-step explanation:
Because the expression simplified is 2y^3-5y+8, so the answer is C.
Hope this helps! :)
~Angel
Answer:
The expression 3 + 4y – y(9 – 2y) + 5 is equivalent to 2y² -5y + 8 .
Option (B) is correct .
Step-by-step explanation:
As the expression given in the question be
= 3 + 4y – y(9 – 2y) + 5
First open the bracket
= 3 + 4y – 9y +2y² + 5
= 2y² -5y + 8
Therefore the expression 3 + 4y – y(9 – 2y) + 5 is equivalent to 2y² -5y + 8 .
Option (B) is correct .
For a student fundraiser Ronna needs to sell 56 boxes of cookies so far she has sold 13 boxes of lemon cookies to her aunt 14 boxes of chocolate cookies to her mother and three boxes of oatmeal cookies to her neighbor how many more boxes of cookies does Ronna need to sell
Answers
Solve the inequality.
7x − 9 > 2x + 6
A) x > 3
B) x > 3/5
C) x > −3
D) x > −3/5
Answers
Answer:
Option D. [tex]x> -3/5[/tex]
Step-by-step explanation:
we have
[tex]7x-9 > 2x + 6[/tex]
solve for x
Subtract 2x both sides
[tex]7x-9-2x > 2x+6-2x[/tex]
[tex]5x-9 > 6[/tex]
Adds 9 both sides
[tex]5x-9-9 > 6-9[/tex]
[tex]5x> -3[/tex]
Divide by 5 both sides
[tex]5x/5> -3/5[/tex]
[tex]x> -3/5[/tex]
-5.3 ≥ 6.7 + 4.3 + q
Please help and show work!!
Answers
Simplify both sides of the inequality.
−5.3≥q+11
Flip the equation.
q+11≤−5.3
Subtract 11 from both sides.
q+11−11≤−5.3−11
ANSWER: q≤−16.3
If 2 pounds of strawberry cost 4$50 how much would 3 pound cost
Answers
Complete the chart to find the mean, variance, and standard deviation. Remember to use commas and round numbers to the nearest tenth. Need help
Answers
Answer: The mean of the data is 433.75, variance of the data is 99667.19 and the standard deviation of the data is 315.7011.
Explanation:
The given data is 900, 35, 500 and 300.
The number of observation is 4.
Formula of mean is,
[tex]\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]\bar{X}=\frac{900+35+50+300}{4} =433.75[/tex]
The formula of variance is given below,
[tex]\sigma^2=\frac{1}{n}\sum{(X-\bar{X})^2}[/tex]
[tex]\sigma^2=\frac{398668.75}{4}[/tex]
[tex]\sigma^2=99667.19[/tex]
The variance of the data is 99667.19
[tex]\sigma=\sqrt{99667.19}[/tex]
[tex]\sigma=315.7011[/tex]
The standard deviation of the data is 315.7011.
The other information or values of given chart is shown in the attached table.
Answer:
i. mean of the data is 402.5
ii. variance of the data is 77556.25
iii. standard deviation of the data is 278.49
Step-by-step explanation: (x - ⁻x)²
from the chart given to me, the observation are: 45, 340, 400, 825
i. mean is the summation of the observation divided by number of observation. ∈x÷n =( 45 + 340 + 400 + 825)÷ 4 = 402.5
ii. variance is the square of the difference between the observation and mean divided by the number of observation.
variance = (45-402.5)²+(340-402.5)²+(400-402.5)²+(825-402.5)²÷4=77556.5
There are 15 cats ready for new homes at the pet store. There are 5 cages with cats in the store. If each cage has the same number of cats, how many cats are in each cage?
Answers
There are 3 cats in each cage. They way you get this answer is by dividing the total amount of cats (15) by the total amount of cages (5). hope this helps
We find that there are 3 cats in each cage.
To find out how many cats are in each cage, we need to divide the total number of cats by the number of cages. There are 15 cats ready for new homes and 5 cages. If each cage has the same number of cats, we perform the following calculation:
Count the total number of cats: 15 cats.
Count the total number of cages: 5 cages.
Divide the total number of cats by the number of cages: 15 cats / 5 cages = 3 cats per cage.
Therefore, there are 3 cats in each cage.
What is the rule for the nth term, an, when the first 4 terms of the sequence are 4, 16, 64, 256?
A.
an=(‒4)^n ‒ 1
B.
an=4n
C.
an=4^n ‒ 1
D.
an=4^n
Answers
4, 16, 64, 256
4¹, 4², 4³, 4⁴
Do you see the pattern? [tex]a_{n} = 4^{n}[/tex]
Answer: D
PLEASE HELP! I HAVE LIMITED TIME, WILL MARK BRAINLIEST!
Answers
The answer is D. U and T
Why hello there
The correct answer to you question will be D. U and T
Important: If my answer did help please mark me as brainliest thank you and have a great day!
Your name is included in a list of 6 names. One name is selected at random. Write the probability, as a decimal, that it is your name.
Answers
Answer:
The probability of my name being chosen is 1/6. As a decimal, that's 0.16666...
Step-by-step explanation:
As a decimal, that's 0.16666...
Evaluate 12x−3y 12x−3y when x=− 1 4 x=−14 and y=3 y=3 .
Answers
The value of the given expression would be = - 177.
How to calculate the given expression?
To evaluate the given expression, the following steps should be taken as follows:
Given:
12x-3y
where
X = -14
y = 3
= 12(-14)-3(3)
= -168-9
= -177
Find the equation of the line in slope-intercept form.Slope is 2/3 through (3, 4)
Answers
Answer:
y = (2/3)x + 2
Step-by-step explanation:
Start with the general slope-intercept form y = mx + b. Substitute 3 for x and 4 for y and 2/3 for m, and find the intercept, b:
4 = (2/3)(3) + b, or 2 = b. Then the desired equation is y = (2/3)x + 2.
Dan weighed his dogs Spot and Rover in March and April, and recorded the weight change for each dog. He recorded a change of 2 1/2 pounds for Spot and -2 3/4 pounds for Rover. He sats Spot's weight changed by a greater amount because 2 1/2 > -2 3/4. Do you agree? Explain.
Answers
4^3 · 4-^6 Simplified
A) 4-3
B) 4-9
C) 4-18
D) 43
Answers
4^3 · 4-^6
= 4^(3 + (-6))
= 4^-3
Answer
A) 4^-3
Choose the correct statement.
-2<-3
5>6
4>-4
0<-6
Answers
Graph the following lines and write the equation in slope-intercept form. Through the point (2,−4) with y-intercept of −2.
HELP!!!!!!!!
Answers
For this case we have that by definition, the equation in the form of slope-intersection is given by:
[tex]y = mx + b[/tex]
Where
m is the slope b is the cut pointSubstituting the given point: [tex](x, y) = (2, -4)[/tex] and the cutoff point [tex]b = -2[/tex] we can find the slope,
We have:
[tex]-4 = m * 2-2\\-4 = 2m-2\\-4 + 2 = 2m\\-2 = 2m[/tex]
[tex]m =-\frac{2}{2}\\m = -1[/tex]
Thus, the equation is given by:
[tex]y = -x-2[/tex]
Answer:
[tex]y = -x-2[/tex]
See attached image
which of the following options correctly describes the graph below?
Answers
It is a step graph with slope of 2.
Answer: C
Whenever you are unsure, choose a coordinate, plug it into the equation, and see if it makes a true statement.
I choose (1/2, 1) → 1 = [2(1/2)] → 1 = [1] TRUE
I choose (1, 2) → 2 = [2(1)] → 2 = [2] TRUE
Determine the numbers of zeros of the polynomial function
g(x) = x^4-x^5
___ zero(s)
Answers
Factor out x^4 for find zeros:
g(x) = x^4 (1-x)
From this, we can see that if x = 0 or 1, it would cause g to result in 0.
So the zeros are 0 and 1.
The polynomial function g(x) = [tex]x^4 - x^5[/tex] has two zeroes, which are x = 0 and x = 1. This result is obtained by setting the polynomial equal to zero and solving for x.
Explanation:The given polynomial function is g(x) = [tex]x^4 - x^5[/tex]. To find the zeroes of the polynomial, this function should equal zero. Thus, we have[tex]x^4 - x^5[/tex] = 0.
We can simplify this function by factoring out the common factor, which is [tex]x^4[/tex]. The function thus becomes [tex]x^4[/tex](1 - x) = 0.
A product equals zero when one (or more) of the factors is zero. So, we need to set each factor to zero and solve for x. Setting [tex]x^4[/tex]= 0, yields x = 0. Setting (1 - x) = 0 results in x = 1.
This process gives two values of x that satisfy the equation [tex]x^4[/tex](1 - x) = 0 and therefore, the polynomial function g(x) has two zeroes, specifically x = 0 and x = 1.
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Find the coordinates of the points of intersection of the graphs with coordinate axes:
y = -1.5x + 3
x intercept is (Say the two points)
y intercept is (say the two points)
Answers
Answer: x-=(2,0) y-=(0.3)
Step-by-step explanation:
Im a gangster
The length of a rectangle is 2 more than 5 times its width. Find the perimeter of the garden if the perimeter is 160m.
Answers
Take the breadth as x,as its the smallest value--(1)
Length is 2 more than 5 times the breadth--(2)
perimeter=160m
l=2+5x
b=x
Perimeter=2(l+b)
2(2+5x+x)
=2(2+6x)
Opening the brackets
=4+12x
4+12x=160
12x=160-4
x=156/12
=13
Therefore , by substituting the value of x
l=2+5*13=67m
b=13m
What is the product of the ten one-digit numbers
Answers
10×1 = 10
10×2 = 20
10×3 = 30
10×4 = 40
This goes all the way up to 9.
The product of all ten one digits numbers will be 0.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
All the ten one digit numbers are;
⇒ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Now,
The product of all the ten one digit numbers is,
⇒ 0 × 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
⇒ 0
Thus, The product of all ten one digits numbers will be 0.
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Ron made 2/3 of a quart of hot chocolate. Each mug holds 1/3 of a quart. How many mugs will ron be able to fill ?
Answers
pretty sure its 2 mugs
Answer:
2 mugs.
Step-by-step explanation:
We have been given that Ron made [tex]\frac{2}{3}[/tex] of a quart of hot chocolate. Each mug holds [tex]\frac{1}{3}[/tex] of a quart.
To find the number of mugs that can be filled by [tex]\frac{2}{3}[/tex] quart of hot chocolate, we will divide [tex]\frac{2}{3}[/tex] by [tex]\frac{1}{3}[/tex] as:
[tex]\frac{2}{3}\div\frac{1}{3}[/tex]
Now, we will convert the division problem to multiplication problem by flipping the 2nd fraction as:
[tex]\frac{2}{3}\times\frac{3}{1}[/tex]
[tex]\frac{2\times 3}{3\times 1}[/tex]
[tex]\frac{2\times1}{1\times 1}[/tex]
[tex]2[/tex]
Therefore, Ron will be able to fill 2 mugs.
What is the greatest common factor for 13 and 39
Answers
Here is your answer:
GREATEST COMMON FACTOR OF 13 AND 39 IS 13
13= 13×1
39=13×3
greatest common factor [tex] \boxed{= 13} [/tex]
The greatest common factor (GCF) of the given set of numbers, 13 and 39 is calculated as: 13.
How to find the greatest common factor (GCF)?To find the greatest common factor (GCF) for 13 and 39, follow these steps:
Step 1: List the factors of each number.
Factors of 13: 1, 13
Factors of 39: 1, 3, 13, 39
Step 2: Identify the common factors shared by both numbers.
Common factors of 13 and 39: 1, 13
Step 3: Determine the greatest common factor from the common factors.
Greatest common factor (GCF) of 13 and 39: 13
So, the greatest common factor for 13 and 39 is 13.
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What is 351,875 round to thew nearest hundred thousand
Answers
The answer to what is 351,875 rounded to the nearest hundred thousand is 400,000. I am positive.
Which statement best describes the domain of the function represented in the graph?
0 ≤ x ≤ 9 or x is between 0 and 9, inclusive
2 ≤ x ≤ 14 or x is between 2 and 14, inclusive
1 ≤ x ≤ 9 or x is between 1 and 9, inclusive
1 ≤ x ≤ 14 or x is between 1 and 14, inclusive
If you can as well, write an explanation for me thank you!
Answers
domain represents the x-values. the x-values start at 1 and end at 9. 1 is included and 9 is included (otherwise an open dot would be shown).
1 ≤ x ≤ 9
because as you can see on the graph the line starts at X cordinate 1 and ends at 9. so we can say 1<x<9. then we are going to have to add an equall sign because the line includes 1 and 9. so it will be like this---1 ≤ x ≤ 9.
How is angle a related to angle d? A) vertical angles B) alternate interior angles C) alternate exterior angles D) corresponding angles
Answers
Answer:
because they are across from each other vertically
Step-by-step explanation:
Match the reasons with the statements. GIVEN: x2 + 6x + 2x + 12 = 0 TO PROVE: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 Subtraction property of equality 2. x2 + 8x + 12 = 0 Distributive Postulate 3. (x + 6)(x + 2) = 0 Combining like terms 4. x + 6 = 0 or x + 2 = 0 Zero product postulate 5. x = -6 or x = -2
Answers
Given: [tex]x^2 + 6x + 2x + 12 = 0.[/tex]
1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):
[tex]x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.[/tex]
2. Distributive postulate:
[tex]x^2+8x+12=(x+6)(x+2).[/tex]
The equation is
[tex](x+6)(x+2)=0.[/tex]
3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):
[tex]x+6=0 \text{ or } x+2=0.[/tex]
4. Subtraction property of equality:
a) subtract 6 from the first equation:
[tex]x+6=0\Rightarrow x+6-6=-6, \ x=-6.[/tex]
b) subtract 2 from the second equation:
[tex]x+2=0\Rightarrow x+2-2=-2, \ x=-2.[/tex]
Answer:
1. x2 + 6x + 2x + 12 = 0 1. Given
2. x2 + 8x + 12 = 0 2. Combining like terms
3. (x + 6)(x + 2) = 0 3. Distributive Postulate
4. x + 6 = 0 or x + 2 = 0 4. Zero product postulate
5. x = -6 or x = -2 5 Subtraction property of equality
find the equation of the line that contains the given point and the given slope. Write the equation in slope-intercept form.
1. (4, 1) slope = 6
2. (6,-3) slope= -5
3. (-8, 2) slope = -1/2
4. (-7,-1) slope = 0
Answers
Answer:
1. [tex]y=6x-23[/tex]
2. [tex]y=-5x+27[/tex]
3. [tex]y=-\frac{1}{2}x-2[/tex]
4. [tex]y=-1[/tex]
Step-by-step explanation:
- The equation of the line is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
- You have to find the y-intercept [tex]b[/tex], so, you must substitute the given point and the slope into each equation and solve for [tex]b[/tex], and then you must rewrite the equation of the line with the slope and the y-intercept calculated:
1. [tex]1=6(4)+b\\ b=-23\\ y=6x-23[/tex]
2. [tex]-3=-5(6)+b\\ b=27\\ y=-5x+27[/tex]
3. [tex]2=-\frac{1}{2}(-8)+b\\b=-2\\ y=-\frac{1}{2}x-2[/tex]
4. [tex]-1=0(-7)+b\\ b=-1\\ y=0x-1\\ y=-1[/tex]