An engineer is interested in the relationship between
the weight of a car (measured in pounds) and the fuel
economy (measured in miles per gallon of gas). To
investigate the relationship, she collects a simple
random sample of 10 cars and records their weight
and fuel efficiency. She finds the equation of the least-
squares regression line to be y=69-0.0114x, where
y is the fuel efficiency (mpg) and x is the weight (in
pounds). The residual plot is shown.

Based on the residual plot, is the linear model
appropriate?

O No, the residuals are relatively large.
O No, there is a clear pattern in the residual plot
O Yes, there is no clear pattern in the residual plot

The sales revenue necessary to generate net income of $100,000 is: $416,667.

Using this formula to find the sales revenue

Sales revenue = Sales revenue + (Sales revenue × Net income / Fixed costs)

Let plug in the formula

Sales revenue =  $250,000 + ($250,000 × $100,000 /$150,000)

Sales revenue = $250,000 + ($250,000 ×0.6666666)

Sales revenue = $250,000 + $166,666.65

Sales revenue = $416,666.65

Sales revenue = $416,667 (Approximately)

Therefore the correct option  is E.

Learn more about sales revenue here:https://brainly.com/question/28390695

#SPJ1

The solution when Kaitlyn has at least five purses using signs and number is N ≥ 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other.

When two expressions are equal, we use the equal sign ( = ). But when we are trying to compare two values or expressions, we use the inequality signs like greater than (>), less than (<), greater than or equal to ( ≥ ) and less than or equal to (≤)  

Given that: Kaitlyn has at least five purses

In order to solve this problem with signs and number, you will make use of the inequality that explains the situation:

Let the number of purses be N

Kaitlyn having at least five purses means she has 5 purses or more. Using inequality, the number of purses is greater than or equal to 5. Thus:

N ≥ 5

Therefore, the solution using signs and number is N ≥ 5

Learn more about expressions with inequalities on:

https://brainly.com/question/25275758

#SPJ1

The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons

Given,

The first brand of antifreeze = 70% pure antifreeze

The second brand of antifreeze =  95% pure antifreeze

The quantity of mixture = 170 gallons contains 80% pure antifreeze

We have to find the quantity of each brand of antifreeze must be used;

Now,

The quantity of first brand = x gallons

The quantity of second brand = y gallons

Then,

x + y = 170

x = 170 - y ....(1)

70x / 100 + 95y / 100 = (80 × 170) / 100

70x + 95y = 13600

Now, putting the value of x from equation 1:

70 (170 - y) + 95y = 13600

11900 - 70y + 95y = 13600

11900 + 25y = 13600

25y = 13600 - 11900

25y = 1700

y = 1700/25

y = 68

Now, putting this value of y in equation 1:

x = 170 - 68

x = 102

Therefore,

The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons

Learn more about quantity here;

https://brainly.com/question/29404995

#SPJ1

The resulting equation after the first step in the solution is: 2v + 4 = 8.

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In this exercise, you're required to describe the steps that should be taken to find a solution to the given equation by solving for v. Therefore, the appropriate and required steps that should be used include the following:

Step 1: Rearrange the equation by collecting like terms.

(v + v) + 4 = 8

Step 2: Add the like terms together.

2v + 4 = 8

Step 3: Subtract 4 from both sides of the equation.

2v + 4 - 4 = 8 - 4

2v = 4

Step 4: Divide both sides of the equation by 2.

v = 4/2

v = 2.

Read more on equation here: brainly.com/question/18912929

#SPJ1

Complete Question:

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

v +4 = 8 – v

v +4 = 8

4 + v = 8 – v

2v + 4 = 8

If the chef follows the recipe proportions, then the true statement is;

A: The chef uses 3/16 cup of flour for every cup of water because 1/8 ÷ 2/3 = 3/16

Fractions can be presented in the form of word problems just like algebraic word problems.

Now, we are told that the chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe.

This means that;

2/3 cup of flour = 1/8 cup of water

Thus;

1 cup of flour = (1 * 1/8)/(2/3) = 3/16 cups of flour for every cup of water

Looking at the given options, we can conclude that the only correct one based on our answer is Option A.

Read more about Fraction Word Problems at; https://brainly.com/question/24132459

#SPJ1

An equation in standard form is written as y = 80x - 40

Let the cost of books Ahmad bought be represented by m

let the flat cost by c (c reduction at the fair)

Information given in the question is interperted as

ahmad bought 2 books for 120 at a book fair

2m + c = 120

Another time he bought 4 books for 280

4m + c = 480

The required equation leads to 2 simultaneous equation with 2 unknown

2m + c = 120

4x + c = 480

solving the 2 equations gives

m = 80 and y = -40

representing the equation as 1 we have

y = mx + c

Definition of variables to suit the problem to be solved

y = Total cost

m = cost per book

x = number of books

c = flat cost

writing the equation

y = 80x - 40

Learn more about linear functions for costing at:

https://brainly.com/question/29213643

#SPJ1

Answer:

295

Step-by-step explanation:

he has 379 less apples now so you have to subtract 379 from 674

674 - 379 = 295

The coordinate pairs that could represent the equation 3x - 2y = 12 are

( x₁ , y₁ ) = ( 2 , -3 )

( x₂ , y₂ ) = ( 4 , 0 )

( x₃ , y₃ ) = ( 0 , -6 )

What is an Equation?

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 equation be A

3x - 2y = 12

Now , Substituting the values of x and y in the above equation , we get

a)

The coordinate pair ( 2 , -3 )

So , the equation becomes

3 ( 2 ) - 2 ( -3 ) = 12

6 + 6 = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

b)

The coordinate pair ( 4 , 0 )

So , the equation becomes

3 ( 4 ) - 2 ( 0 ) = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

c)

The coordinate pair ( 0 , -6 )

So , the equation becomes

3 ( 0 ) - 2 ( -6 ) = 12

12 = 12

Therefore , the coordinate pair satisfies the given equation

Hence , the coordinate pairs that satisfies the the equation 3x - 2y = 12 are

( 2 , -3 ) , ( 4 , 0 ) and ( 0 , -6 )

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ1

Answer:

$1701.75

Step-by-step explanation:

34535-500=34035

34035/20=$1701.75 per year

Answer:

7

Step-by-step explanation:

Exponent law:

        [tex]\sf a^m * a^n = a^{m+n}\\\\\dfrac{a^m}{a^n}=a^{m-n}[/tex]

In exponents multiplication, when bases are same add the powers.

In exponents division, if bases are same subtract the powers.

[tex]\sf \dfrac{7^8*7^3*7^4}{7^9*7^5}=\dfrac{7^{8+3+4}}{7^{9+5}}[/tex]

                  [tex]\sf =\dfrac{7^{15}}{7^{14}}\\\\=7^{15-14}\\\\=7^1\\\\=7[/tex]

After 10 years students in both schools are same.

Algebra is a branch of mathematics that uses mathematical expressions to represent problems. To form a meaningful mathematical expression, variables such as x, y, and z are combined with mathematical operations such as addition, subtraction, multiplication, and division. It teaches you how to solve a problem by following a logical path. As a result, you will have a better understanding of how numbers function and interact in an equation. You will be able to do any type of math better if you have a better understanding of numbers.

There are two high schools in a small town.

High school A has currently 900 students and is projects to grow by 30 students each year

Similarly

High school B has currently 750 students and is projected to grow by 45 students each year.

To find the equation for each situation in terms of t years.

also in how many years t' the number of students in both high schools would be same?

Given

The initial strength of school A = 900

the increasing rate of students = 30 students per year

i.e students in 1 year = 30

students in t years = 30t

Total students of school A after 't' years = 900+ 30t

⇒ A = 600+ 65t

The initial strength of school B = 750

increasing rate of students = 45 per year

i.e. student in 1 year = 45

⇒ student in 't' years = 45t

Total students of school B in 't' years = 950 + 30t

=> B=950+30t

Now to find no. of years 't' when students in both schools are the same i.e. A =B

⇒ 900+ 30t = 750 + 45t

⇒ 45t-30t = 900-750

⇒ 15t = 150

⇒t= 150 /15

⇒t=10

Therefore after 10 years, students in both schools are the same.

To learn more about algebra visit

https://brainly.com/question/28795935

#SPJ1

If the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

it is given that, A 35-tooth gear on a motor shaft drives a larger gear having 63 teeth and the motor shaft rotated at 900 rpm.

The number of teeth on the smaller gear,n₂ = 35

The number of teeth on the larger gear,n₁ = 63

The gear ratio is obtained as,

n₁/n₂=63/35

n₁/n₂=9:5

If the motor shaft rotated at 900 rpm, The speed of the larger gear is,

=900 rpm / 9

=100 rpm

Thus, if the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ1

a = F/m

because F = ma

The equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.

According to the question,

We have the following information:

We have a diagram where seed yield is given.

Now, the required equation represents the difference in seed yield between beans without treatment and beans with treatment will be:

(seed yield with treatments-seed yield without treatment)

(300+310-270)

(610-270)

340

Hence, the equation that represents the difference in seed yield between beans without treatment and beans with treatment is (seed yield with treatments-seed yield without treatment) whose value will be 340.

To know more about equation here

https://brainly.com/question/10413253

#SPJ1

Answer:

(-5/48)

Step-by-step explanation:

-5     ×    1           -5

------- × ------- =   -------

  6    ×    8           48

Multiply the numerators together (top numbers) to get the new numerator

Multiply the denominators together (bottom numbers) to get the denominator.

I hope this helps!

The value of 2,850,000,000 in scientific notation is 2.85*[tex]10^{9}[/tex], so option A is correct.

Given:

= 2,850,000,000

= 2850,000 * [tex]10^{3}[/tex]

= 2850 * [tex]10^{3}[/tex] * [tex]10^{3}[/tex]

= 2850 * [tex]10^{6}[/tex]

= 285*[tex]10^{7}[/tex]

= 28.5*[tex]10^{8}[/tex]

= 2.85*[tex]10^{9}[/tex]

Therefore the value of 2,850,000,000 in scientific notation is  2.85*[tex]10^{9}[/tex], so option A is correct.

Learn more about the scientific notation here:

https://brainly.com/question/18073768

#SPJ1

           [ 9(a + h) - 3 - 9a + 3]/h =

          9h /h = 9

Answer:

[tex]\textsf{(d)} \quad \boxed{9a+9h-3}[/tex]

[tex]\textsf{(e)} \quad \boxed{9a+9h-6}[/tex]

[tex]\textsf{(f)} \quad \boxed{9}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x) = 9x - 3[/tex]

Part (d)

To find f(a + h), substitute x = a + h into the function:

[tex]\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}[/tex]

Part (e)

Find f(a) by substituting x = a into the function:

[tex]\implies f(a)=9a-3[/tex]

Find f(h) by substituting x = h into the function:

[tex]\implies f(h)=9h-3[/tex]

Therefore:

[tex]\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}[/tex]

Part (f)

[tex]\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}[/tex]

Answer:

He would have detailed 16 cars.

Step-by-step explanation:

912/57=16

" I hoped I helped you matey : - ) "

When 15 milliliters of pure drug are in 500 mL of solution, the percent strength of the solution is

information from the problem

15 milliliters of pure drug are in 500 mL of solution

the percent strength of the solution = ?

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

= volume of pure drug / volume of solution * 100

= 15 milliliters / 500 milliliters  * 100

= 0.03

= 3%

Learn more about percent here:

https://brainly.com/question/29230566

#SPJ1

Answer:

Each gets 14 cards.

Step-by-step explanation:

7*8=56

56 Is the total amount of cards

56/4 equals 14

We divide 56 by 4 since 4 is the total number of friends.

Answer:

1,296 miles

Step-by-step explanation:

to answer this question, we have to apply the next formula:  

Distance = Speed rate x time

speed rate = 54 miles per hour

time = 24 hours

Replacing with the values given and solving for D (distance)

D = 54 mph x 24 h = 1,296 m

The car traveled 1,296 miles

Hope this helped! :)

The building is  76.545 m tall.

Given:

A pole that is 2.5 m tall casts a shadow that is 1.65 m long. At the same time, a nearby building casts a shadow that is 50.25 m long.

Let x be the height of the building.

2.5/1.65 = x/50.25

2.5*50.25 = x * 1.65

25/10*5025/100 = x*165/100

25*5025/10 = 165x

25*5025 = 1650x

126300 = 1650x

x = 126300/1650

x = 76.545 m.

Therefore the building is  76.545 m tall.

Learn more about the building and shadow here:

https://brainly.com/question/26277943

#SPJ1

The slope of the line is 2 whose equation is given by y = 2x.

The given equation is y = 2x

The general equation of the line is given by

y = mx +c  where m is the slope and c is the intercept of the line.

The slope of line a line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run."

The intercept of the line is a  point on the y-axis known as an intercept is where the line's slope passes.

On Comparing the given equation with the general equation, we have:

m = slope = 2

Thus the slope of the line is 2.

To read more about slopes, visit https://brainly.com/question/3605446

#SPj1

The equation of the time that it took Tara to get to the store is; x + 4x = 25

We know that in this case, the task that we have is to form an equation that would reflect the total time that Tara took in moving to the store. We have to factor in that the variable here is the time.

We are told that she ran 4 times as long as she walked and the total time spent walking and running was 25 minutes. Let us designate the time taken to walk as x. This implies that the time that she ran is 4x.

The equation would now be; x + 4x = 25

Learn more about equation:https://brainly.com/question/10413253

#SPJ1

The equation of the given straight line is y = 3x.

We are given a graph. The graph shows a straight line. Several points are marked on the line in the graph. The coordinates of two such points are (1, 3) and (2, 6). We need to find the equation of the straight line.

The equation of the straight line can be found using the two-point form of a line. The equation is solved below.

(y - y1) = [(y2 - y1)/(x2 - x1)]×(x - x1)

(y - 3) = [(6 - 3)/(2 - 1)]×(x - 1)

y - 3 = 3(x - 1)

y = 3x - 3 + 3

y = 3x

Hence, the equation of the line shown in the graph is y = 3x.

To learn more about equations, visit :

https://brainly.com/question/10413253

#SPJ1

The equation of the line parallel to the line, [tex]y=\frac{3}{2} x-6[/tex] through the point (-6,5) is [tex]3x-2y+28=0[/tex]

What are Parallel Lines?

What is Point-Slope Equation of Line?

Here, it is given that the equation of the line parallel to the given straight line is [tex]y=\frac{3}{2} x-6[/tex]  ----(1)

We know that the slope of parallel lines is equal.

So, the slope of (1) will be equal to the given line.

Writing (1) in the form of [tex]y=mx+c[/tex], we get

Slope, [tex]m=\frac{3}{2}[/tex]

Using the Point-Slope Equation of the line, we have

[tex]y-y_{1}=m(x- x_{1})[/tex]

Now, substituting the point (-6,5) in the place of [tex](x_{1}, y_{1})[/tex], we get

[tex]y-5=\frac{3}{2} (x- (-6))\\\implies 2(y-5)=3(x+6)\\\implies 2y-10=3x+18[/tex]

Simplifying, we get

[tex]3x-2y+18+10=0\\\implies 3x-2y+28=0[/tex]

Therefore, the equation of the given line is [tex]3x-2y+28=0[/tex]

Correct Question: Write an equation for the line parallel to the line y=3/2x-6 through the point (-6, 5).

To learn more about the Point-Slope Equation from the given link

https://brainly.com/question/24907633

#SPJ1

Answer:

(x+1)(x-1)

Step-by-step explanation:

The solutions 1 and - 1 is given when

x = 1 or x = - 1

hence; (x - 1) = 0 or (x + 1) = 0

(x - 1)(x + 1) = 0

x² -1 = 0

Mark as brainliest answer please. Thanks

Answer:

-1/5

Step-b-1/5y-step explanation:

The rule for a perpendicular slope of a line is -1/s

In this case, we find the slope of the line first.
5x - y = -7
-y = -5x - 7
y = 5x + 7

The slope is 5, so -1/(5) is the slope of the perpendicular line.

The height of the cone is 580.36 cm.

The curved surface area of the cone is given by,

[tex]A = \pi \sqrt{h^{2} +r^{2} }[/tex]

Squaring both sides, we get :

[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]

Now, it is given that the height of the cone is h,

The area of the cone = 550 [tex]cm^{2}[/tex]

And the radius of the cone = 7cm,

Putting these values in the given formula, we get,

[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]

[tex]550^{2} = \pi ^{2} * ( h^{2} +7^{2} )\\[/tex]

3,36,875 = [tex]h^{2}+49[/tex]

[tex]h^{2}[/tex] = 3,36,875 - 49 = 3,36,826

h = 580.36 cm

To read more about cone, visit https://brainly.com/question/16394302

#SPJ1

Answer: [tex]\frac{0}{24}[/tex]

Step-by-step explanation:

The slope is [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex], or reverse: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

If we substitute, we get that [tex]\frac{2-2}{6-(-18)}[/tex].

Simplify to get [tex]\frac{0}{24}[/tex].