In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student the sum of hours in the four activities must be 168. a) Consider the model GPA = β0 + β1study + β2work + β3leisure + β4sleep + u. Interpret the coefficient β1. Does it make sense to hold work, leisure, and sleep fixed, while changing study? b) Explain why this model violates Assumption MLR.3. c) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?
Step-by-step explanation:
Given
GPA = NO + B1Study + B2work + B3leisure + B4sleep + u
1. No it makes no sense. There is an intercorellation between these explanatory variables. Changing study while holding the rest variables constant or fixed would not make sense. If study us changed then one or more of the other predictors should be changed so that they can still be equal to 168
2. Study is a perfect linear function of work, leisure and sleep. There is the problem of multicollinearity among these independent variables. One assumption of the MLR is no multicollinearity.
3. To reformulate model, you have to drop the variable that is having the issue. Let's say that leisure is dropped from the model. After this the assumption is satisfied.
GPA = b0 + B1Study + b2sleep + b3work + u
1 A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10
centimeters. Which measurement is closest to the total surface area of the can in
square centimeters?
Answer:
radius r = 3 cm
height h = 10 cm
volume V = 282.743339 cm^3
lateral surface area L = 188.495559 cm^2
top surface area T = 28.2743339 cm^2
base surface area B = 28.2743339 cm^2
total surface area A = 245.044227 cm^2
In Terms of Pi π
volume V = 90 π cm3
lateral surface area L = 60 π cm^2
top surface area T = 9 π cm^2
base surface area B = 9 π cm^2
total surface area A = 78 π cm^2
Step-by-step explanation:
Cylinder Formulas in terms of r and h:
Calculate volume of a cylinder:
V = πr2h
Calculate the lateral surface area of a cylinder (just the curved outside)**:
L = 2πrh
Calculate the top and bottom surface area of a cylinder (2 circles):
T = B = πr2
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Agenda: r = radius
h = height
V = volume
L = lateral surface area
T = top surface area
B = base surface area
A = total surface area
π = pi = 3.1415926535898
√ = square root
The value of Surface Area of the cylinder is 245.04 cm².
What is Surface Area of a shape ?Surface area is the amount of space covering the outside of a three-dimensional shape.
It is given that the cylinder has
radius r = 3 cm
height h = 10 cm
volume V of the cylinder = πr²h = 282.74 cm³
the lateral surface area of a cylinder
L = 2πrh
lateral surface area L = 188.495559 cm²
the top and bottom surface area of a cylinder (2 circles):
T = B = πr²
top surface area T = 28.2743339 cm²
base surface area B = 28.2743339 cm²
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
total surface area A = 245.044227 cm²
total surface area A = 78 π cm²
Therefore the value of Surface Area of the cylinder is 245.04 cm².
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You had a bag of fruit snacks that you shared with 4 friends. Each of you got 175 or fewer fruit snacks. The inequality x÷4≤175 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Answer:
Step-by-step explanation:
It’s 20
Convert the angle −4.5 radians to degrees, rounding to the nearest 10th
Answer:-257.8
Step-by-step explanation:
you roll two 6-sided number cubes
where is the question I dont see it
A rectangular prism has a width of x^2 inches, A length of xy^2 inches, and a height of y^2 inches. Which expression represents the volume in cubic inches of this rectangular prism
Answer:
[tex]Volume = x^3y^4[/tex]
Step-by-step explanation:
Given
[tex]Length = xy^2[/tex]
[tex]Height = y^2[/tex]
[tex]Width = x^2[/tex]
Required
Determine the volume
The volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = xy^2 * x^2 * y^2[/tex]
This gives:
[tex]Volume = x^3y^4[/tex]
Use distributive property to remove the parenthesis for:
(1-y+x)(-6)
Answer:
Step-by-step explanation:
Multiply -6 to the first bracket so it would be
-6+6y-6x This is the answer
If i put a 100$ into the stock market and the stock market increase by 2% per year. how much money would i have after a year
Answer:
$102
Step-by-step explanation:
2% of $100 = 0.02 * $100 = $2
The increase is $2.
$100 + $2 = $102
Answer: $102
Answer:
100 x 0,2 x 1 year(12/12 months)
=$102 after a year
In triangle ABC, angle C is a right angle. If cos A = 5 8, what is the value of cos B?
Answer:
65
Step-by-step explanation:
What is the correct answer?
Answer:
6 units to the right, 3 units down
Step-by-step explanation:
Three points are coplanar
sometimes
Never
Always
Answer:
Never:
Step-by-step explanation:
because its more understandable we know this because it wouldnt be always
Find x.
2x + 40
3x
4x
X + 50
x = [?]
y
Answer:
x=27
Step-by-step explanation:
Hey there!
the exterior angles of a quadrilateral add up to equal 360
so 360=2x+40+4x+3x+x+50
step 1 combine like terms
2x+4x+3x+x=10x
50+40=90
now we have
360=10x+90
step 2 subtract each side by 90
360-90=270
90-90 cancels out
now we have 270=10x
step 3 divide each side by 10
270/10=27
we're left with
x=27
HELP please my friend needs help with his MATH homework, see picture for problem TY :)
What is 5/9=14c-5/12
Answer:
c=5/72
Step-by-step explanation:
5/9=14c-5/12
Switch sides
14c-5/12=5/9
Add 5/12 tp both sides
14c-5/12+5/12=5/9+5/12
Simplify;
14c-5/12+5/12
=14c
Simplify;
5/9+5/12
LCM of 9, 12;
36
The least common multiplier of a, b is the smallest positive number that is divisible by both a and b.
Prime factorization of 9;
3*3
Prime factorization of 12;
2*6
=2*2*3
=3*3*2*2
=36
5/9=5*4/9*4=20/36
5/12=5*3/12*3=15/36
=20/36+15/36
20+15/36
=35/36
14c=35/36
14c/14=35/36/14
14c/14=c
35/36*14
=35/504
=5/72
Answer c=5/72
Answer to the following question is as follows;
Value of C = 5 / 72
Step-by-step explanation:
Given:
[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]
Find:
Value of C
Computation:
[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]
By taking 5/12 to LHS Side
[tex]\frac{5}{9} + \frac{5}{12} = 14c\\\\[/tex]
By taking LCM;
[tex]\frac{(4)(5) + (3)(5)}{36} = 14c\\\\[/tex]
[tex]\frac{20 + 15}{36} = 14c\\\\[/tex]
[tex]\frac{35}{36} = 14c\\\\[/tex]
By transfer 14 to LHS side
[tex]\frac{35}{36 \times 14 } = c\\\\[/tex]
[tex]\frac{5}{36 \times 2 } = c\\\\[/tex]
[tex]\frac{5}{72} = c\\\\[/tex]
Value of C = 5 / 72
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Linda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 13/20. Find the odds in favor of her character unlocking the treasure chest.
Answer:
65 percent chance right
Step-by-step explanation:
so she opens it 13 out of 20 times, so divide 13 by 20 and you get it
need help geometry question
Answer:
okay the answer 13.02 enjoy
Solve. -x < 20
Graph on a number lin
Answer:
x > -20
Step-by-step explanation:
-x < 20
When dividing by negative numbers, flip the inequality.
x > -20
inclusive -> open circle
greater than -> to the right
open circle at -20 going to the right
Find the measure of 46.
70*110°
46
o
66 = [?]
Answer:
angle 6 is equal to 70° vertically opposite angle on the same side of transeversal.
A jewelry store offers its own brand of customizable charm bracelets. You are able to choose from 9
different charms for your bracelet.
How many different charm bracelets is it possible to create?
Answer:
By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.
Hope this helps(and also if you have a more refined wording please put it in the comments)!
Answer:
By the way that it is worded, I believe that you are only allowed to put 1 charm on the bracelet, so there are 9 ways to pick a charm.
The midpoints of the hexagon are connected to form another hexagon, this pattern continues indefinitely. If the area of the 99th hexagon formed by this pattern is 1, what is the area of the original hexagon?
Answer:
(4/3)⁹⁸ units²Step-by-step explanation:
Regular hexagons have a property that cutting off the triangles obtained by joining the midpoints of consecutive sides leaves a hexagon of 3/4 of the area.This means the area of each hexagon inside out starting from the one with unit area is 4/3 of the previous one.
99 ⇒ 198 ⇒ 1*4/397 ⇒ 1*(4/3)²...1 ⇒ (4/3)⁹⁹⁻¹The original hexagon has the area of:
(4/3)⁹⁸ units²Answer:
(4/3)^98units.
Step-by-step explanation:
By hexagonal property in which cut off the triangles obtained be the joining of m.p of adjacent sides which left 3/4 of total area.
PLEASE HELP!!!
Which expression are equal to 6³×2 6÷2³?
O12 6
O12³
O6³
O2 6×3³
O2³×3³
Answer:
(6³×2^6)÷2³=6³×2^(6-3)=6³×2³=(6×2)³=12³is your answer(1728)
help me please, please
Jill wants to solve the following system using the elimination method:
Y = X + 8
y = 3x - 11
What number should the equation = x + 8 be multiplied by to eliminate x?
3
Answer:
3
Step-by-step explanation:
y= x + 8..... (1)
y= 3x - 11..... (2)
y - x = 8..... (3)
y - 3x = -11..... (4)
eliminating x:
(3) × 3: 3y - 3x = 24 ........ (5)
(4) × 1: y - 3x = -11 ......... (6)
(5) - (6): 2y = 35
Divide both sides by 2, therefore, y = 17.5
substitute the value of y into (3)
y - x = 8
17.5 - x = 8
17.5 - 8 = x
9.5 = x
I hope it'll help
im super confused pls help
in an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are __________.
A. On the same line
B. Unequal
C. Imaginary
D. The same point
Answer:
D. The same point
Step-by-step explanation:
An equilateral triangle can be defined as a type of triangle that has all of its sides being equal in length.
This ultimately implies that, an equilateral triangle comprises of three (3) congruent sides and as such creates three (3) congruent angles that measures 60° each. Also, the sum of the congruent angles of an equilateral is always equal to 180°.
Hence, in an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are the same point i.e all of the three (3) centers fall on the same point or spot.
Solve for x. 5000(2)^x = 3500(3)^x
Answer:
0.887966
Step-by-step explanation:
1. Divide by 3500
(5000/3500)(2^x) = (3^x)
2. divide by 2^x and simplify
10/7 = (3/2)^x.
3. apply 'ln' function
ln(10/7) = xln(3/2)
4. divide ln(3/2)
ln(10/7) / ln(3/2) = x
x = 0.87966
the equation of a line that is perpendicular to y = 2x + 1 passes through the point (4,-3)
Step-by-step explanation:
perp. -1/2
y + 3 = -1/2(x - 4)
y + 3 = -1/2x + 2
y = -1/2x - 1
What is the image point of (7,0) after a translation right 2 units and up 1 unit?
Answer: (9,1)
Step-by-step explanation: This is because x (7) moves left and right, and y (0) moves up and down. the formula would be (x, y) --->(x+2, y+1)
Which systems of equations have the same solutions?
L (3x+y = 8
1x - 4y = -6
m{$*=*=230
NS 4x – 3y = 2
12% -8y = -12
Answer:
B. L and N
Step-by-step explanation:
Let's solve each system
✔️System L:
3x + y = 8 => Eqn. 1
x - 4y = -6 => Eqn. 2
x = -6 + 4y
Substitute x = (-6 + 4y) in eqn. 1
3(-6 + 4y) + y = 8
-18 + 12y + y = 8
-18 + 13y = 8
13y = 8 + 18
13y = 26
y = 26/13
y = 2
Substitute y = 2 into Eqn. 2
x - 4y = -6
x - 4(2) = -6
x - 8 = -6
x = -6 + 8
x = 2
Solution to system L = (2, 2)
✔️System M:
4x - 3y = 2 => Eqn. 1
5x - 4y = -30 => Eqn. 2
Multiply eqn 1 by 5, and eqn. 2 by 4
20x - 15y = 10
20x - 16y = -120
Subtract
y = 130
Substitute y = 130 into eqn. 1
4x - 3(130) = 2
4x - 390 = 2
4x = 2 + 390
4x = 392
x = 392/4 = 98
Solution to system M = (98, 130)
✔️System N:
4x - 3y = 2 =>Eqn. 1
2x - 8y = -12 => Eqn. 2
Multiply Eqn. 1 by 2, and eqn. 2 by 4
8x - 6y = 4
8x - 32y = -48
Subtract
26y = 52
y = 52/26
y = 2
Substitute y = 2 into eqn. 1
4x - 3(2) = 2
4x - 6 = 2
4x = 2 + 6
4x = 8
x = 8/4
x = 2
Solution to system N = (2, 2)
Someone help me
Right now.