The government conducted a study and collected the given data. use the
data to answer the following questions.
speed (mph) 45 55 65 75
fuel (mpg) 43 45 38 32
find the quadratic regression model that represents the relationship
between speed and fuel. round your answer to two decimal places

The composition of the function and its inverse function is always one. Then the correct option is C.

Suppose that the given function will be

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is a reverse operator, that takes back the effect of 'f'

Suppose that f and g are functions that are inverse of each other.

When f is composed of g or vice versa. Then the composition will be

We know that the composition of the function and its inverse function is always one. Then we get

When f is composed of g or vice versa. Then the composition will be 1.

Thus, the correct option is C.

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Answer:

The number is 740

Step-by-step explanation:

Hello!

Let the number that we want to solve for be x.

100% of x is x, but a decrease of 5% if 95% of x.

The number is 740.

The solution is correct.

The balance of the loan at 14 months= $10,561.25

It would take a total 23 months to pay off the loan.

The total amount of money paid for the car is = $9,052.5

The total loan for the car = $8,500

The rate at which the loan is compounded monthly is

= 6.5%

The monthly payment for the loan = $390

Find the simple interest

= P×T×R/100

= 8,500 × 1 × 6.5/100

= 55,250/100

= $552.5

If 12 months = 8,500 + 552.5

14 months = X

make X the subject of formula,

X = 14 × 9052.5/12

X= 126,735/12

X = $10,561.25

The amount paid monthly = $390

The amount to be paid for the loan with interest = 8,500 + 552.5 = $9,052.5

If 1 month = $390

× month = $9,052.5

Make X the subject of formula,

X = $9,052.5/$390

X= 23 months

The total amount of money paid for the car is already calculated which is through the simple interest

= P×T×R/100

= 8,500 × 1 × 6.5/100

= 55,250/100

= $552.5

= 8,500 + 552.5

= $9,052.5

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Answer- 200m

: Right now Sam is 200m far from her starting point

Answer:

Anything more than $13

Step-by-step explanation:

From the information given, the towline must be completely released to enable it to get to the maximum height. This problem is a trigonometry problem because it involves a solution that looks like a right-angled triangle.

In order to determine the maximum height of the parasailer, the length of the rope or towline must be established.

If the length and the height are known, the angle of elevation can be determined using the SOHCAHTOA rule.

SOH - Sine is Opposite over Hypotenuse

CAH - Cosine is Adjacent Over Hypotenus; while

TOA - Tangent is Opposite over Adjacent.

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The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

Then the side length of the pentagon will be

5 x Side length = 21.8 cm

     Side length = 4.36 cm

Then the area of the pentagon, rounded to the nearest tenth will be

Area of pentagon = 5 x area of triangle

Area of pentagon = 5 x 1/2 x 4.36 x 3

Area of pentagon = 32.7 square cm

Thus, the correct option is C.

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Answer:

Graph B

Step-by-step explanation:

Point-line graphs are usually used to compare data over a course of time, and bar graphs are more commonly used to compare statistics between different data sets (in this case it is between different countries)

Based on the number of unit cubes that are fastened together, the number of cubes which will have at least one face painted on is 488 cubes.

The cubes formed one large cube which means that each surface is one cube deep. So two cubes will be painted.

The number of unpainted cubes per surface is therefore:

= 10 - 2

= 8 cubes

Number of unpainted cubes is:

= 8 x 8 x 8

= 512 cubes

Number of cubes with one face painted:

= Total cubes - Number of unpainted cubes

= 1,000 - 512

= 488 cubes.

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Answer:

Determine the equation of the circle.

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

Substitute the given values into the formula to determine the equation of the circle:

[tex]\implies (x-0)^2+(y-0)^2=7^2[/tex]

[tex]\implies x^2+y^2=49[/tex]

Given point:  [tex](-3,2\sqrt{10})[/tex]

Input the x and y values of the given point into the derived circle equation.  If it equals 49, then the point is on the circle:

[tex]\implies (-3)^2+(2 \sqrt{10})^2=9+40=49[/tex]

Therefore, the given point is on the circle centered at the origin with a diameter of 14 units.

Answer:

8

Step-by-step explanation:

To get a fraction of a number, we will simply multiply this fraction by the number.

Answer:

The mean of the data is 70

Step-by-step explanation:

Hope this helps you! :D

Answer:

70

Step-by-step explanation:

Mean-

Add all the numbers to the total = 350

Divide by the amount of numbers (125, 15, 30, 110,70 = 5 numbers)

350/5 = 70

Answer:

Coordinates of the midpoint are ( 9/2 , -6 )

Natalia Net worth will be 550 having Assets= 7285 and liabilities= 6735

Net worth= 550

Assets are the items your company owns that can provide future economic benefit. Liabilities are what you owe other parties.

Given that: Assets= 7285, liabilities= 6735

As we know,

Total Net worth=  Total Assets - Total Liabilities

                          =  7285- 6735

                          = 550

The Net worth= 550

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Using the assumed coordinates of point F, the coordinates of point D are (3,3)

The given parameters are:

Ratio, m : n = 2 : 5

E = (3.8, -3)

The coordinates of point D is calculated using:

[tex]D = \frac{1}{m + n} * (mx_2 +nx_1,my_2 +ny_1)[/tex]

So, we have:

[tex]D = \frac{1}{2 + 5} * (2x_2 +5*3.8,2y_2 +5*-3)[/tex]

Evaluate the sum and the products

[tex]D = \frac{1}{7} * (2x_2 +18,2y_2 -15)[/tex]

Assume the coordinates of point F are:

F = (1.5,18);

The equation becomes

[tex]D = \frac{1}{7} * (2*1.5 +18,2*18 -15)[/tex]

Evaluate

[tex]D = \frac{1}{7} * (21,21)[/tex]

This gives

D = (3,3)

Hence, the coordinates of point D are (3,3)

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Answer:

slope m = - [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

At first we should calculate Monthly income by multiplying 2 then After multiplying by 12 to calculate Annual income

Answer:

57/100

Step-by-step explanation: 0.57 can also be written as 57/100 which is equal to 0.57

[tex]( \frac{2}{3} - \frac{3}{4} \times \frac{1}{8} ) \div ( \frac{2}{3} - \frac{3}{4} + \frac{5}{8} )[/tex]

First, solve the brackets.

First bracket:

[tex]( \frac{2}{3} - \frac{3}{4} \times \frac{1}{8} )[/tex]

[tex] = \frac{55}{96} [/tex]

Second bracket:

[tex]( \frac{2}{3} - \frac{3}{4} + \frac{5}{8} )[/tex]

[tex] = \frac{13}{24} [/tex]

Then divide.

[tex] \frac{55}{96} \div \frac{13}{24} [/tex]

[tex] = \frac{55}{52} \: or \: 1\frac{3}{52} [/tex]

answer:

as improper fraction= 55/52

as mixed fraction= 1 3/52

hope this helps

Answer:

949$

Step-by-step explanation:

You get 460$ the first year, then 488 in the second.

Answer:

x=14

Step-by-step explanation:

collect like terms, like so

Answer:4(x−2)−8=4+2x

Use the distributive property to multiply 4 by x−2.

4x−8−8=4+2x

Subtract 8 from −8 to get −16.

4x−16=4+2x

Subtract 2x from both sides.

4x−16−2x=4

Combine 4x and −2x to get 2x.

2x−16=4

Add 16 to both sides.

2x=4+16

Add 4 and 16 to get 20.

2x=20

Divide both sides by 2.

x=

2

20

​

Divide 20 by 2 to get 10.

x=10

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angles labeled with 2x, 4x, and 3x are on a straight line so their sum is equal to 180

2x + 4x + 3x = 180 add like terms

9x = 180 divide both sides by 9

x = 20

The angle represented with 3x - 30 and the angle represented with 2x + 10 are alternate and their measurement is same

3x - 30 = 2x + 10 export like terms to same side of the equation

3x - 2x = 10 + 30

x = 40

to find the angles replace x with the value found for each.

Answer:

-1 ≤ x < 3

Hope this helps ;)

The team-lead gets $2000 if the team of 3 QA testers and l QA team lead is working on a project. The team finishes the job and is paid.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

Let's suppose the team lead salary is x and the team-lead receives, $600 more than the average salary of the entire team then,

The team lead salary:

[tex]\rm x = \dfrac{1200+1200+1200+x}{4} + 600[/tex]

4x = 3600+ x+ 2400

3x = 6000

x = $2000

Thus, the team lead gets $2000 if the team of 3 QA testers and l QA team lead is working on a project. The team finishes the job and is paid.

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Answer:

  17.3 cm³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = 1/3Bh

where B is the area of the base, and h is the height.

__

The volume of a square pyramid with base area 5.5 cm² and height 6.4 cm is ...

  V = 1/3(5.5 cm²)(6.4 cm) ≈ 17.333... cm³

The volume of the pyramid is about 17.3 cm³.

Step-by-step explanation:

x, x+1, x+2 are the 3 consecutive positive integers.

(x+1)(x+2) = 2(x+1) + 2×(x+x+1+x+2)

x² + 3x + 2 = 2x + 2 + 2×(3x + 3)

x² + 3x + 2 = 2x + 2 + 6x + 6 = 8x + 8

x² - 5x - 6 = 0

we can solve this by finding the factoring.

that means we find a, b so that

(x - a)(x - b) = x² - 5x - 6 = 0

because then x = a and x = b are the 2 solutions of the quadratic equation.

we have

x² - ax - bx + ab = x² - (a+b)x + ab = x² - 5x - 6

a+b = 5

ab = -6

that means, either a or b must be 6 and the other -1.

so we get

(x - 6)(x + 1) = 0

x = 6

or

x = -1

since we are only looking for positive integers, the x = -1 solution is invalid, and we get only x = 6 as solution.

therefore the 3 consecutive positive integers are

6, 7, 8

The enthalpy change (ΔH) for the reaction given the data from the question is –900.8 KJ

ΔHrxn = ∑ΔH(products) - ∑ΔH(reactants)

ΔHrxn = ∑[H(H₂O) + H(NO)] - ∑[H(NH₃) + H(O₂)]

ΔHrxn = [(6 × –241.8) + (4 × 91.3)] – [(4 × –46.2) + (5×0)]

ΔHrxn = –1085.6 + 184.8

ΔHrxn = –900.8 KJ

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Answer:

A: –900.8 kJ

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow \dfrac{7513/100\times 5x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75.13(5)x^3}{3x^2}[/tex]

[tex]\\ \rm\Rrightarrow {125.22x}[/tex]