A mathematics teacher wanted to see the correlation between test scores and
homework. The homework grade (x) and test grade (y) are given in the accompanying
table. Write the linear regression equation that represents this set of data, rounding
all coefficients to the nearest hundredth. Using this equation, find the projected test
grade, to the nearest integer, for a student with a homework grade of 49.
Answers
The linear regression equation that represents this set of data is Y = -12.41 + 1.15x and the projected test grade for a student with a homework grade of 49 is 44 and this can be determined by using the generalized equation of regression.
Given :
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table.The generalized regression equation is given below:
Y = a + bX --- (1)
where b is given by the formula:
[tex]\rm b = \dfrac{N\sum XY-\sum X \sum Y}{N\sum X^2-(\sum X)^2}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'b'.
b = 1.15
and the formula of a is given below:
[tex]\rm a = \dfrac{\sum Y - b \sum X}{N}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'a'.
a = -12.41
Now, substitute the values of a and b in the equation (1).
Y = -12.41 + 1.15x
Now, at x = 49 the value of Y becomes:
Y = -12.41 + 1.15(49)
Y = 43.94
Y [tex]\approx[/tex] 44
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Related Questions
there are only 6 blue pens 5 green pens and 8 red pens in a box one pen is taken randomly from the box write down the probability that this pen is blue
Answers
Answer: 6/19
Step-by-step explanation: six + five+ eight = nine teen so since there are six blue pens the answer would be six/ nine teen as a fraction. It was already simplified and can't be broken down even more.
Which best explains how you know that A(-1,6) is on the same line as a B( -3,10) and C (-5,14)
Answers
Answer:
To get from A to B and from B to C, you move left 2 units and then up 4 units.
Step-by-step explanation:
hope this helps :)
A rectangle has vertices E(-4, 8), F(2, 8), G(2, -2) and H(-4, -2). The rectangle is dilated with the origin as the center of dilation so that G' is located at (5, -5). Which algebraic representation represents this dilation?
Answers
Answer:
The dilation on any point of the rectangle is [tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex].
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
[tex]G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)][/tex] (1)
Where:
[tex]G(x,y)[/tex] - Coordinates of the point G, dimensionless.
[tex]O(x,y)[/tex] - Center of dilation, dimensionless.
[tex]k[/tex] - Scale factor, dimensionless.
[tex]G'(x,y)[/tex] - Coordinates of the point G', dimensionless.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]G(x,y) =(2,-2)[/tex] and [tex]G'(x,y) =(5,-5)[/tex], then scale factor is:
[tex](5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)][/tex]
[tex](5,-5) = (2\cdot k, -2\cdot k)[/tex]
[tex]k = \frac{5}{2}[/tex]
The dilation on any point of the rectangle is:
[tex]P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)][/tex]
[tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex] (2)
The dilation on any point of the rectangle is [tex]P'(x,y) = \frac{5}{2}\cdot P(x,y)[/tex].
Algebraic representation of the dilation will be T'(x, y) → T(2.5x, 2.5y).
Dilation of a rectangle about a point not the origin:Let one of the four vertices of a rectangle is (h, k) is dilated about the origin by the scale factor 'k'.Rule for the transformation will be,
[tex]D_{(o,k)}(x,y)\rightarrow (kx,ky)[/tex]
Following this rule,
If one of the vertices of a rectangle is G(2, -2) and it is dilated by a scale factor 'k', image point will be given by,[tex]D_{(o,k)}(2, -2)\rightarrow (2k, -2k)[/tex]
Since, coordinates of the dilated point are G'(5, -5),
Therefore, (2k, -2k) = (5, -5)
⇒ 2k = 5
⇒ k = 2.5
Hence, algebraic representation defining the dilation of the
triangle will be,
T'(x, y) → T(2.5x, 2.5y)
Algebraic representation of the dilation will be T'(x, y) → T(2.5x, 2.5y).
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It took Mrs. Harpole 35 minutes to grade
four student essays. How long will it take
her to grade all her classes, 80 students?
Answers
Answer:
700 minutes or 11.67 hours
Step-by-step explanation:
35/4=8.75
8.75*80=700
The perimeter of a rectangle is 56 cm. When its length is reduced by 2 cm and its
width is increased by 4 cm, a square is formed. What is the area of the rectangle ?
Answers
Based on rectangle:
2L + 2W = 56
Draw the square and name your sides the following:
(W+4) , (L-2), (W+4), (L-2)
Because it’s a square, all sides are equal and we can remove and solve for one of the variables but keep in mind the parameter changed..
The new parameter is 56 minus 4cm + 8cm...keep in mind I used 4cm and 8cm because we have a 2 Lengths and 2 Widths.
Solving 60= 4 (w+4)
W= 11
So the side of our square is 11+4=15
L-2 = 15
L=17
So the area of the Rectangle is 11*17=187 cm squared.
Please let me know if it’s correct !
A nest of ants has been growing exponentially in such a way that it's population,P, as a function increasing on average more or less than 1600 ants per week? Enter the value per week to the nearest tenth.
Answers
Not sure question is complete, assumptions however
Answer and explanation:
Given the above, the function of the population of the ants can be modelled thus:
P(x)= 1600x
Where x is the number of weeks and assuming exponential growth 1600 is constant for each week
Assuming average number of ants in week 1,2,3 and 4 are given by 1545,1520,1620 and 1630 respectively, then we would round these numbers to the nearest tenth to get 1500, 1500, 1600 and 1600 respectively. In this case the function above wouldn't apply, as growth values vary for each week and would have to be added without using the function.
On one hand, the function above could be used as an estimate given that 1600 is the average growth of the ants per week hence a reasonable estimate of total ants in x weeks can be made using the function.
If f(x) = 3x + 4(x + 1) + 2 then f (4x) =?
Answers
Answer:
3×+4(×+2 then f (4×)=21
The expression for f(4x) is 28x + 6. When you evaluate the function f at 4x, you obtain 28 times x + 6. For every value of x, you can plug it into the equation 28x + 6 to get f(4x).
To find the expression for f(4x), we substitute 4x for every occurrence of x in the original function f(x).
Given f(x) = 3x + 4(x + 1) + 2, we have to replace every x with 4x:
f(4x) = 3(4x) + 4(4x + 1) + 2
Now, simplify the expression:
f(4x) = 12x + 4(4x + 1) + 2
f(4x) = 12x + 16x + 4 + 2
f(4x) = 28x + 6
Therefore, the expression for f(4x) is 28x + 6.
This means that when you evaluate the function f at 4x, you get 28 times the value of x plus 6. So, for any given value of x, you can plug it into the expression 28x + 6 to get the corresponding value of f(4x).
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In the input/output rule: y = -2x - 5 What
would be the output of an input of -1? Write
only the number.
Answers
Answer:
-3
Step-by-step explanation:
(-2)*(-1) - 5
2 - 5 = -3
find the measure of the acute angles pls help
Answers
Answer:
60 degrees
and
52 degrees
angle C and angle D are a linear pair. angle C is four times larger than angle D. What is the measure of angle C?
Answers
By using the fact that the angles form a linear pair, we will see that the measure of angle C is 144 degrees.
How to determine the measures of angles C and D?
Well, we know that these are a linear pair, which means that the angles are supplementary, thus, their measures add up to 180°.
So we can write:
C + D = 180°
Now, we also know that C is four times larger than D, so we can write:
C = 4*D
Replacing that in the equation above we get:
4*D + D = 180°
5*D = 180°
D = 180°/5 = 36°
Then we know that the value of D is 36°, and C is 4 times that, so:
C = 4*36° = 144°
The measure of angle C is 144 degrees.
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write down 45 in the Scientific Notation
Answers
Answer:
4.5x10^1
The first value should be less than 10
How to write vertex form when given to choices of “a” in a question ex: write the vertex form of the function where a=1 or a= -1 and H and K are integers? And the vertex is (-1,4)
Answers
Answer:
Step-by-step explanation:
Vertex form of quadratic equation is
[tex]y = a(x-h)^2 + k[/tex]
where h and k are the x and y coordinates of the vertex, respectively.
so in this problem
if a=1 and Vertex is (-1,4) means h= -1 and k = 4
the equation will be
[tex]y = 1 (x-(-1))^{2} + 4[/tex]
[tex]y = (x+1)^2 + 4[/tex]
if a=-1 and Vertex is (-1,4) means h= -1 and k = 4
the equation will be
[tex]y = -1 (x-(-1))^{2} + 4[/tex]
[tex]y = -(x+1)^2 + 4[/tex]
Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine
m
m, the number of miles in the taxi ride.
Answers
Solve the following system of equations:
x − 2y = 14
x + 3y = 9
Answers
EXPLANATION:
you set both equations equal to each other by subtracting the sum and adding it to the equation. once you set them equal to eachother (x-2y-14=x+3y-9)
you can solve by moving everything to one side by subtracting. once you get it all to one side you can start adding common numbers and variables and solve
Answer:
(12, - 1)
Step-by-step explanation:
x - 2y = 14 ......... (1)
x + 3y = 9 ......... (2)
(2) - (1)
(x - x) + (3y - ( - 2y)) = 9 - 14
5y = - 5 ⇒ y = - 1
x + 3( - 1) = 9 ⇒ x = 12
(12, - 1)
ISSS THIS CORRECT??????please help
Answers
Answer:
I think that is correct, sorry if i get it wrong
Answer:
Step-by-step explanation:
(4,1) you are correct
thhe solution is the intersection of thhe 2 graphs because that point of intersection belongs to both lines in the same time
Last year, the school library had a total of x books. Over the summer, the library acquired another 40 books and now has a total of 1,795 books. Which equation could be used to find x, the number of books the library had last year?
Answers
Answer:
1794-40=x?
Step-by-step explanation:
this is genuine answer but a little bit unsure
Last year = x books
This year = x + 40 books
The needed equation is x + 40 = 1,795.
what is 2414 divided by 8
Answers
Answer:
301.75
Step-by-step explanation:
I hope this helps
Answer:
301.75
Check:
301.75 * 8 = 2414 Correct!
Place these number in order from greatest to least.
-7/5, 16, -1, 3.2, -6.5, 0, 3/4,
Answers
Answer:
Step-by-step explanation:
First, change the fractions into decimals, then use the knowledge of the number line system to know which is greater or smaller than who.
-7/5 -1.4
3/4 0.75
so the numbers are -1.4, 16, -1, 3.2, -6.5, 0, 0.75
from greatest to least:
= 16, 3.2, 0.75, 0, -1, -1.4, -6.5
Whats the answer for number 11?
Answers
Answer:
Option 4
Step-by-step explanation:
y = -5x + 2
-8 = -5(2) + 2
-8 = -10 + 2
Correct! :)
HELP ASAP ILL GIVE You 5 stars
What is the solution to this inequality?
7x + 25<=11
Answers
Answer:
Step-by-step explanation:
smplifying
7x + 11 = 25
Reorder the terms:
11 + 7x = 25
Solving
11 + 7x = 25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + 7x = 25 + -11
Combine like terms: 11 + -11 = 0
0 + 7x = 25 + -11
7x = 25 + -11
Combine like terms: 25 + -11 = 14
7x = 14
Divide each side by '7'.
x = 2
Simplifying
x = 2
Answer: Inequality form: x<=-2
Interval notation: (-infinity,-2]
$650,000 was stolen from 1st Trust American Bank during a heist. The bank robbers got away clean and sped away traveling at a constant rate of 70 miles per hour. What the robbers did not realize is that one of the bank bags had a GPS tracking device inside of it. Once the police locked on to the signal of the tracking device they took off after the robbers traveling at a constant rate of 90 miles per hour. If the robbers already had a 30 mile head start, how long will it take the police to pass them and force them off the road to be arrested?
Answers
Answer:
The time taken before the police force the robbers off the road is 1.5 hours
Step-by-step explanation:
The speed with which the robbers were travelling = 70 miles per hour
The speed with which the police went after the robbers = 90 miles per hour
The distance with which the robbers were in front of the police before the police came after them = miles
Let t represent the time in hours the police force the robbers off the road, we have;
30 + 70 × t = 90 × t
30 = 90 × t - 70 × t = (90 - 70) × t = 20 × t
30 = 20 × t
20 × t = 30
t = 30/20 = 1.5
t = 1.5 hours
The time taken before the police force the robbers off the road = t = 1.5 hours
Answer:
The time taken before the police force the robbers off the road is 1.5 hours
Step-by-step explanation:
solve the following equation 3(x+6) =4(2x-8)
Answers
Answer:
x=10
Step-by-step explanation:
3(x+6)=4(2x-8)
3x+18=8x-32
8x-3x=18+32
5x=50
x=10
Answer:
3x+18=8x-32
18+32=8x-3x
50=5x
x=10
HELP ASAP!! ILL GIVE BRAINLIEST
y=2.36x+4.29
A) Identify the slope. Describe what the slope means in the context of the problem.
B) Identify the y-intercept. Describe what the y-intercept represents in the context of the problem.
Answers
and the y intercept is 4.29 or (0,4.29)
i can’t answer the second part of each question because i don’t know the context!!
identify the population being studied and the sample chosen. the heights of 4 out of the 36 pepper plants at mr. lonardo's greenhouse.
Answers
The sample = 4 pepper plants
The population = 36 pepper plants
We have to identify the sample and the population from the instance that heights of 4 out of 36 pepper plants are chosen.
Statistical studies are carried out on populations. So here there may be a study related to the heights of the pepper plants.
Sometimes, when the population is very large, studies are carried out on the samples taken from the population which gives not the exact but an approximately same result.
Hence in this case, the sample is the 4 plants chosen from the population of 36 plants at Mr. Lonardo's greenhouse.
Population: Population is the entire and broader group considered for collecting data on a statistical study.
Sample: Sample is the specific, comparatively small group selected from the population from which the data used for study is collected.
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What is the value of the expression below when w=7 and x=2?
3w - 4x
Answers
Answer:
13
Step-by-step explanation:
3(7)-4x
3(7)-4(2)
21-8
=13
sarah reads 6 stories in 8 day
salma reads 11 stories in 8 days
how many stories can salma read more than sarah in 24 days?
Answers
Sarah by 24 days will have 18 stories read
Salma by 24 days will have 33 stories read
33 - 18 = 15
Write a two-column proof
Given: ∠1 and ∠2 are supplementary, m∠1 = 135°
Prove: m∠2 = 45°
Answers
Notice:
Unfortunately I’ve never written a two-column proof before. So I can’t do that. Let me know if what I can do helps at all though.
Step-by-step explanation:
A supplementary angle is an angle made up of two angles that have measures that add up to 180°. m∠2 = 45° because 45° added to 135° equals 180°. Therefore making it a supplementary angle. Meaning that m∠2 = 45° is true. Sorry if this doesn’t help. I tried my best.
What is the length of segment AB? (1 point)
Coordinate grid shown from negative 8 to positive 8 on both x axis and y axis at intervals of 1. A straight line labeled AB is drawn. A is the ordered pair 0, 6 and B is the ordered pair 7, 0.
Group of answer choices
Square root of 13
Square root of 85
14
13
Answers
Answer:
Square root of 85
Step-by-step explanation:
We can envision the segment AB as the hypotenuse of a right triangle with a height of 6 units and a length of 7 units. We can use the Pythagorean Theorem to solve for the length of segment AB which is similar to distance formula.
6^2 + 7^2 = c^2
36 + 49 = c^2
c^2 = 85
c = Square root of 85.
45 Points- Geometry
HELP ME
Answers
S<--->T
T<--->S
Same thing
4Both sides a equivalent therefore both triangle areas are also equivalent
9514 1404 393
Explanation:
The missing reasons are ...
3. Reflexive property of congruence. A segment is congruent to itself.
4. SSS postulate. The three corresponding sides are shown congruent, so the triangles are congruent.
Nellle has her hair styled by her hair stylist. The styling costs $85 and Nellie wants to leave a 30% tip. There is a tax rate of 6%.
and tip?
Answers
Answer:
115.60
Step-by-step explanation:
for a tip 85x 0.30=25.50
tax 85x0.06=5.10
total extra money 5.10+25.50=30.60
total money payed 85+30.60=115.60
Hope this helped
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