1. What are the four key assumptions which are required for multiple linear regression analysis?
2. For each of the four assumptions, please state:
a) the problem they would cause if relaxed/not achieved;
b) the test(s) to identify them;
c) the potential fixes.

My monthly take-home pay would be $2461.16.

My yearly take-home pay would be $29533.92.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

If my take-home pay every Monday is $615.29 then my monthly take-home pay would be,

= (4×615.29).

= $2461.16  (as we have 4 Mondays in a month).

Now, My take-home pay for a year would be,

= (4×12×615.29).         (as we have 4 Mondays in a month and 12 months in a

                                                                                                                      year)                                                 = $29533.92

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Answer:

A: No solution

B: Unique Solution: (0, 0)

Step-by-step explanation:

In System A, you may notice that in both equations the two equations have variables with the same coefficient, and this is ideal for the elimination method of solving the equation. We want to add the equations in a way that cancels out variables. So let's multiply the top equation by negative one: [tex]-1(2x+3y)=-(9)\implies -2x-3y=-9[/tex]

Now from here we want to add the two equations:

[tex]\ \ -2x-3y=9\\+2x+3y=4\\0+0=13[/tex]

And the statement provided is clearly not true, 0 is never equal to 13, meaning the systems of equation has no solution, which occurs when you have two parallel lines.

In this case, we can easily solve this using substitution, since y is equal to 7x that means we can substitute in 7x for y in the second equation:

[tex]y=x\implies 7x=x[/tex]

And from here we subtract x from both sides, and divide by 6 giving us:

[tex]x=0[/tex]

And now we can take this value and plug it into either equation to solve for our y value, and it's most convenient to plug it into the y = x equation... since there's nothing to solve, we just get:

y = 0

So x = 0, and y = 0, meaning there is a unique solution of (0, 0)

However, we can't determine the exact number of participants with this information alone.

an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.

Let's use logic to determine the possible rankings of the participants:

A placed seventh, so at least 6 people ranked higher than A.

B placed sixth, so at least 5 people ranked higher than B.

C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.

D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.

Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.

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Answer:

$57.02

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the values into the simple interest formula and solve for I:

[tex]\implies I=850 \cdot 0.0575 \cdot \dfrac{14}{12}[/tex]

[tex]\implies I=57.0208333...[/tex]

Therefore, the amount of interest is $57.02 (nearest cent).

From the data that teacher described, the following information could be determined:

1. The distribution of midterm and final exam scores for the students. This would allow you to see the range of scores and the overall performance of the students.

2. The average midterm and final exam scores for the students. This would give you an idea of the average performance of the students on each exam.

3. The correlation between final exam and midterm scores. This would indicate if there were a relationship between performance on the midterm and final exams.

4. The distribution of total points calculated for each student. This would allow you to see the range of total scores and the overall performance of the students.

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The area of the given  figure is, 123ft²  .So option c  is correct

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The given figure can be assumed as a trapezoid with the two parallel sides being the bottom side (20.5 feet) and the top side (from the perpendicular to the right vertex to the perpendicular to the left vertex

= 18.4 + 2.1

= 20.5 feet

The height of the trapezoid is given as 6 feet.

The formula for the area of a trapezoid is:

Area = (sum of the parallel sides) * height / 2

So, in this case, the area of the trapezoid would be:

Area = (20.5 + 20.5) x 6 / 2

        = 41 x 3

        = 123 square feet

Therefore, the answer is 123 square feet.

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The first mechanic worked for 5 hours and the second mechanic worked for 15 hours.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two mechanics worked on a car.

The first mechanic charged $55 per hour,

and the second mechanic charged $65 per hour.

The mechanics worked for a combined total of 20 hours,

and together they charged a total of $1250.

Let x be the number of working hours of the First mechanic and y be the

number of working hours of the second mechanic.

So

x + y = 20  {equation 1}

55x + 65y = 1250 {equation 2}

Substituting the value of y from the equation 1 to the equation 2,

55x + 65(20 - x) = 1250

55x + 1300 - 65x = 1250

-10x = -50

x = 5

And y = 15

Therefore, x = 5 and y = 15.

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Answer:

1. 200

2.(1,4)

3.  5

4. (3,1)

5. NO SOLUTION

Step-by-step explanation:

The total sales when the farm stands have 410 customers will be $4326.

To predict the total sales when the farm stand has 280 customers, we need to interpolate between the data points for 254 and 316 customers. First, we can calculate the average growth rate between these two data points:

Average growth rate = (ln(2606) - ln(1995)) / (ln(316) - ln(254)) = 0.3763

Using this average growth rate, we can predict the sales for 280 customers as follows:

ln(y) - ln(1995) = 0.3763 x  (ln(280) - ln(254))

ln(y) = 7.5835

[tex]y = e^{7.5} = 1961.36[/tex]

Rounding to the nearest whole number, we predict that the total sales when the farm stands have 280 customers will be $1961.

To predict the total sales when the farm stands have 410 customers, we need to extrapolate beyond the data points. We can use the same average growth rate calculated above to make this prediction:

ln(y) - ln(2606) = 0.3763 x (ln(410) - ln(316))

ln(y) = 8.4256

[tex]y = e^{8.4256}[/tex] = 4326.46

Rounding to the nearest whole number, we predict that the total sales when the farm stands have 410 customers will be $4326.

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The equation of the line is y=-2x/5 -10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A line that passes through (5,-12) and m=-2/5

Thus using the slope intercept form constructing it we get

y=mx+c

Putting (5,-12) and m=-2/5

-12=-2/5×5+c

c=-12+2

c=-10

The equation of the line is y=-2x/5 -10

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Answer:

see below

Step-by-step explanation:

g(t) = 5t² - 3t+ 6

g(2) = 5*4 - 3*2 + 6  =20

g(-1) = 5*1 -3* (-1) +6 =5+3+6 = 14

g(t+2) = 5(t+2)² - 3(t+2) + 6

= 5*(t²+4t+4) - 3t -6+6

= 5t²+20t+20-3t

= 5t²+17t+20

The value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10 in which arithmetic operations and rearrangement of the given expression is performed.

The term arithmetic stems from the Greek noun arithmos, which means "number," with pauses in Latin, Anglo-French, and Middle English along the route. Even the most elementary math contains a large vocabulary. The study of numbers and their operations, which are relevant to all other fields of mathematics, are part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

Given that, expression: 13 - 7

The steps to determine the value of (13 - 7) by making a group of 10 are as follows:

Step 1 - Breakup 13 into the tens and the ones:

= (10 + 3) - 7

Step 2 - Breakup 7 into the tens and the ones:

= (10 + 3) - (10 - 3)

Step 3 - Rewrite the above expression:

= (10 - 10) + (3 + 3)

Step 4 - Subtraction of 10 by 10:

= (3 + 3)

Step 5 - Addition of 3 by 3:

= 6

So, the value of (13 - 7) is 6 and it can be determined by using the method of making a group of 10.

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The complete question is as follows:

135 and 59 are the values of fog(5) and gof(5) respectively.

Composite functions are also known as function of a function. Given the functions below;

f(x) = x^2 + 6x

g(x) = x + 4

For fog(5)

fog(5) = f(g(5))

f(g(x)) = f(x +4)

f(g(x)) = (x+4)^2 + 6(x+4)

f(g(5)) = (9)^2 + 6(9)

f(g(5)) = 81. + 54 = 135

For gof(5))

g(f(x)) = g(x^2 + 6x)

g(f(x)) = x^2 + 6x + 4

g(f(5)) = 5^2 + 6(5) + 4

g(f(5)) = 59

Hence the value of the composite values fog(5) and gof(5) area 135 and 59

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A. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2] = -5.46 m/s

ii. [1,1.1) = -1.39 m/s

iii. [1,1.01) = -0.138 m/s

iv. [1,1.001) = -0.0138 m/s

(a) To find the average velocity over a time interval, we need to calculate the displacement during that time interval and divide it by the length of the interval. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2]: Δs = y(2) - y(1) = [20(2) - 1.87(2)²] - [20(1) - 1.87(1)²] ≈ -5.46

Average velocity = Δs / Δt = -5.46 / (2 - 1) = -5.46 m/s

ii. [1,1.1): Δs = y(1.1) - y(1) = [20(1.1) - 1.87(1.1)²] - [20(1) - 1.87(1)²] ≈ -1.39

Average velocity = Δs / Δt = -1.39 / (1.1 - 1) = -1.39 m/s

iii. [1,1.01): Δs = y(1.01) - y(1) = [20(1.01) - 1.87(1.01)²] - [20(1) - 1.87(1)²] ≈ -0.138

Average velocity = Δs / Δt = -0.138 / (1.01 - 1) = -0.138 m/s

iv. [1,1.001): Δs = y(1.001) - y(1) = [20(1.001) - 1.87(1.001)²] - [20(1) - 1.87(1)²] ≈ -0.0138

Average velocity = Δs / Δt = -0.0138 / (1.001 - 1) = -0.0138 m/s

(b) The instantaneous velocity at t=1 is given by the derivative of the height function with respect to time, which is:

dy/dt = 20 - 3.74t

So the instantaneous velocity at t=1 is:

dy/dt(1) = 20 - 3.74(1) = 16.26 m/s (approximately)

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A linear equation indicating the number of grades students will receive in Mr. Perez's class is as follows;

Slope: 2.

Y-Intercept: 7.

Equation: y = 2x + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this mathematical expression:

y = mx + b

Where:

From the information provided above, we have the following slope and y-intercept on the line:

Y-intercept = 7

Slope, m = 2

Therefore, the required equation of line is given by:

y = mx + c

y = 2x + 7

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The answer is 10.67 ft. The distance, x, from Player 1 to wall is 10.67 ft.

Given, Two different triangles for player 1 and player 2.

Both triangles have right angle and same angle where they are connected. So other angle is also same. All angles are same so they are similar triangles. smaller triangle is similar to larger triangle.

The distance x in the figure is required.

The required distance is x = 10.65 ft

The given triangles ABC and CDE are similar by Angle.

∠B = ∠D = 90°

∠ACB =∠ECD

The ratio of the sides is:

[tex]\frac{BC}{CD} = \frac{12}{9} = \frac{4}{3}[/tex]

So,

[tex]\frac{AB}{ED} =\frac{4}{3}[/tex]

x/8 = 4/3

x = 4/3 * 8

x = 10.65 ft

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Answer:

B

Step-by-step explanation:

The entry "cash 700000" is listed as a credit in the T account because it represents an increase in the cash balance of the account. In accounting, credits are used to record increases in asset accounts, such as cash. When cash is received, it is recorded as a credit to the cash account, which increases the balance of the account. Therefore, in this case, the entry "cash 700000" is a credit entry because it represents an increase in the cash balance.

Answer:

10 degrees

Step-by-step explanation:

In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.

We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.

Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]

Now from here we can combine the 90 and 80 to get:

[tex]170+A=180[/tex]

Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):

[tex]170-170+A=180-170[/tex]

We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:

[tex]A=10[/tex]

So the other acute angle is 10 degrees.

The equation of line is y = -2x + 9

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 7 )

The slope of the line is m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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The equation of the line of given slope and point is y = 2x + 12. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is the line with m as its slope and b as its y-intercept. The slope-intercept form of the linear equation is used when the values of m and b are real integers.

We are given the slope as 2 and which is passing through the point (6,24).

We need to first find the y-intercept using y = mx + b

⇒y = mx + b

⇒24 = 2(6) + b

⇒24 = 12 + b

⇒b = 12

The equation in the slope-intercept form is

y = mx + b

This gives equation as y = 2x + 12.

Hence, the equation of the line of given slope and point is y = 2x + 12.

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The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0

Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.

(a) sin(28°) = cos(90° - 28°) = cos(62°)

      62° is right answer.

(b) cos (33°) = sin (90° – 33°) = sin (57°)

      57° is correct answer.

(c) cos (31°) = sin(90° - 31°) = sin (59°)

      59° is correct answer

(d) cos(90° - 0) = sin0

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The equations for the amount of ingredients is

The amount of pasta = 33 parts pasta

The amount of tomato = 16 parts tomato

The amount of cucumber = 10.5 parts cucumber

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of pasta , tomato and cucumber required to make 6 servings be represented as P , T and C respectively

Now , the equation will be

The amount of pasta for 1 servings = 5 1/2

The amount of pasta for 6 servings P = 6 x ( 5 1/2 )

On simplifying the equation , we get

The amount of pasta for 6 servings P = 33 parts pasta

And ,

The amount of tomato for 1 servings = 2 2/3

The amount of tomato for 6 servings T = 6 x ( 2 2/3 )

On simplifying the equation , we get

The amount of tomato for 6 servings T = 16 parts tomato

And ,

The amount of cucumber for 1 servings = 1 3/4

The amount of cucumber for 6 servings C = 6 x ( 1 3/4 )

On simplifying the equation , we get

The amount of cucumber for 6 servings C = 10.5 parts cucumber

Hence , the equations are solved

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The surface area of rectangular prism above is 2738 in².

At the picture above is a rectangular prism with the sides 29 in, 36 in and 5 in.

The question is want to know The are

The surface area of a rectangular prism is given by this formula: 

A = 2 (lh +wh + lw )

Substitute the sides of the shapes to the formula

A = 2 (lh +wh + lw )

A= 2( 36.5 + 29.5 + 36.29)

A= 2(180+145+1044)

A= 2(1369)

A=2738 in²

Therefore the surface area is 2738 in².

A right-angle prism is a three-dimensional shape with six faces, where all faces of the prism (top, bottom, and sides) are rectangular and all pairs of opposing faces are congruent. Like all three-dimensional shapes, right-angled prisms have a volume and a surface area. A right angle prism is also called a cuboid 

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Answer:

Step-by-step explanation:

This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:

y = 2sinx

The number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

Cubic form is defined as the shape of a cube. Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped.

According to the prism, the cube at the center has no stickers.

Stickers on 0 side = 1

The face of the prism contains cube that would have stickers on one side. The center cubes on each face will have stickers on one side:

Stickers on 1 side = 6

The edges of the prism will have cubes at the center that contain stickers on both sides:

Stickers on 2 side = 4 (3) = 12

Every vertices on the prism will have sticker on three sides.

Sticker on three side = 8

Hence, the number of cubes in the prism with stickers 0 - 1, 1 - 6, 2 - 12, and 3 - 8.

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The correct question is:

The interest rate of the account that Steve invested in after the given number of years would be = 16%

The total amount of money invested (p) = $2,807

The time of investment= 13 years

The interest generated at the end of the given years = 9,044.13-2807 = $6,237.13

Therefore the rate = ?

The formula for simple interest:

= P×T×R/100

6,237.13= 2,807× 14 ×r/100

Make r the subject of formula;

r= 6,237.14×100/2807×14

r = 623714/39298

r= 15.87139294

r= 16%

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The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

rectangular dining room floor, which has a length of 12 feet and a width of 9 feet.

The cost to install the carpet is $5 per square foot.

so, area of the floor = A= l. w

                                     = 108 ft^2

so, total cost = 108* 5

                     =$ 540

i.e. Sarah rounded the area of the floor to 100 square feet.

because, 100*5 = $500

Hence, The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

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Answer:

1/7

Step-by-step explanation:

Absolute value is the distance from zero. 7 and -1/7 and their distance from zero is not the same, but the distance from zero with the numbers -1/7 and 1/7 are the same. The absolute value, the distance from zero, is both 1/7.

Answer:

0.65*10=6.5

10*0.35=3.5

10-3.5=6.5

So, it is decreasing by 35%

Step-by-step explanation: