Which pair of functions are inverses of each other?
O A. f(x) = f and g(x) = 8x?
O B. f(x) = 4 + 9 and g(x) = 4x - 9
O C. Ax) = 5x – 9 and g(x) = 149
O D. f(x) = 3 - 7 and g(x) = 247

Answer:

200 grams

Step-by-step explanation:

80 grams        x grams

-------------- = -------------

6 people        15 people

Using cross products

80 *15 = 6x

1200 = 6x

Divide by 6

1200/6 = 6x/6

200 =x

Answer:

-7

Step-by-step explanation:

63 divided by -9 = y

63 divided by -9 = -7

Check answers :

-9 x -7 = a

a= 63

First let's compute dx/dt

[tex]x = t - \frac{1}{t}\\\\x = t - t^{-1}\\\\\frac{dx}{dt} = \frac{d}{dt}\left(t - t^{-1}\right)\\\\\frac{dx}{dt} = 1-(-1)t^{-2}\\\\\frac{dx}{dt} = 1+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2}{t^{2}}+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2+1}{t^{2}}\\\\[/tex]

Now compute dy/dt

[tex]y = 2t + \frac{1}{t}\\\\y = 2t + t^{-1}\\\\\frac{dy}{dt} = \frac{d}{dt}\left(2t + t^{-1}\right)\\\\\frac{dy}{dt} = 2 - t^{-2}\\\\\frac{dy}{dt} = 2 - \frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2}{t^2}-\frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2-1}{t^2}\\\\[/tex]

From here, apply the chain rule to say

[tex]\frac{dy}{dx} = \frac{dy*dt}{dx*dt}\\\\\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\\\\\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \div \frac{t^2+1}{t^{2}}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \times \frac{t^{2}}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\[/tex]

We could use polynomial long division, or we could add 2 and subtract 2 from the numerator and do a bit of algebra like so

[tex]\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1+2-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{(2t^2+2)-1-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)-3}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)}{t^2+1}-\frac{3}{t^2+1}\\\\\frac{dy}{dx} = 2-\frac{3}{t^2+1}\\\\[/tex]

This concludes the first part of 4b

=======================================================

Now onto the second part.

Since t is nonzero, this means either t > 0 or t < 0.

If t > 0, then,

[tex]t > 0\\\\t^2 > 0\\\\t^2+1 > 1\\\\\frac{1}{t^2+1} < 1 \ \text{ ... inequality sign flip}\\\\\frac{3}{t^2+1} < 3\\\\-\frac{3}{t^2+1} > -3 \ \text{ ... inequality sign flip}\\\\-\frac{3}{t^2+1}+2 > -3 + 2\\\\2-\frac{3}{t^2+1} > -1\\\\-1 < 2-\frac{3}{t^2+1}\\\\-1 < \frac{dy}{dx}\\\\[/tex]

note the inequality signs flipping when we apply the reciprocal to both sides, and when we multiply both sides by a negative value.

You should find that the same conclusion happens when we consider t < 0. Why? Because t < 0 becomes t^2 > 0 after we square both sides. The steps are the same as shown above.

So both t > 0 and t < 0 lead to [tex]-1 < \frac{dy}{dx}[/tex]

We can say that -1 is the lower bound of dy/dx. It never reaches -1 itself because t = 0 is not allowed.

We could say that

[tex]\displaystyle \lim_{t\to0}\left(2-\frac{3}{t^2+1}\right)=-1\\\\[/tex]

---------------------------------------

To establish the upper bound, we consider what happens when t approaches either infinity.

If t approaches positive infinity, then,

[tex]\displaystyle L = \lim_{t\to\infty}\left(2-\frac{3}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2t^2-1}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2-\frac{1}{t^2}}{1+\frac{1}{t^2}}\right)\\\\\\\displaystyle L = \frac{2-0}{1+0}\\\\\\\displaystyle L = 2\\\\[/tex]

As t approaches infinity, the dy/dx value approaches L = 2 from below.

The same applies when t approaches negative infinity.

So we see that [tex]\frac{dy}{dx} < 2[/tex]

---------------------------------------

Since [tex]-1 < \frac{dy}{dx} \text{ and } \frac{dy}{dx} < 2[/tex], those two inequalities combine into the compound inequality [tex]-1 < \frac{dy}{dx} < 2[/tex]

So dy/dx is bounded between -1 and 2, exclusive of either endpoint.

no te puedo contestarte yo no hablo inglés

Answer:

Test Statistic = 10

Critical Value = 9.488

Step-by-step explanation:

Given :

Grade A _ B _ C _ D _ F

_____14 _ 18 _32_ 20_16

H0 : distribution of grade is uniform

H1 : Distribution of grade is not uniform

Using the Chisquare statistic :

χ² = (observed - Expected)² / Expected

The expected value :

(14+18+32+20+16) / 5 = 20

χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20

χ² statistic = 10

The χ² critical at df = (n - 1) = 5 - 1 = 4

χ² Critical(10, 4) = 9.488

9514 1404 393

Answer:

  x = A/y

Step-by-step explanation:

Divide both sides of the equation by y

  A = xy

  A/y = (xy)/y . . . . . . divide by y

  A/y = x . . . . . . . . . .simplify

  x = A/y . . . . . . . . . write with x on the left

The product that provides the better value per sheet is Angel Soft toilet paper.

Each sheet of Angel Soft costs $0.20 whereas each sheet of Charmin costs $0.36.

Data and Calculations:

Charmin has 18 rolls, each with 200 sheets, for $12.97

Angel Soft has 24 rolls, each with 425 sheets, for $19.98

Product      Rolls  Sheets   Total Sheets      Total Cost    Cost per Sheet

                           in a Roll  (rolls x sheet)                   (Total cost/No. Sheets)

Charmin      18     200      3,600 (18 x 200)   $12.97  $0.36 ($12.97/3,600)

Angel Soft  24    425     10,200 (24 x 425)  $19.98  $0.20 ($19.98/10,200)

Thus, Rebecca should go for Angel Soft toilet paper because it provides a better value per sheet than Charmin toilet paper.

Learn more about better product values here: https://brainly.com/question/14920077

Answer:

30 new residents

Step-by-step explanation:

Find how many new residents they will have by finding 1.2% of the current population.

2500(0.012)

= 30

So, Hawkville will have 30 new residents

Answer:

f(x)=15x+5

thanks

Step-by-step explanation:

p=2(length +width)

p=f(x)=2(5x+2+2x)

=f(x)=10x+4+5x

collecting like terms,we get;

f(x)=15x+5

The expression that represents the perimeter P as a function of x is 14x + 14

The perimeter can simply be defined as the part or portion surrounding a shape or boundary. The formula for calculating the perimeter of the rectangular yard is expressed as:

The perimeter of the rectangular yard = 2(L+W) where:

L is the length

W is the width

Given the following parameters

Length = 5x + 2

Width = 2x

Substitute the given parameters into the formula above:

Perimeter = 2(5x+2+2x)

Perimeter = 2(7x + 2)

Perimeter = 14x + 4

Hence the expression that represents the perimeter P as a function of x is 14x + 14

Learn more: https://brainly.com/question/10452031

Answer:

R x 1= price of 1 locker

Step-by-step explanation:

it would continue the same way. Just multiply R and the number of lockers.

Is there a certain situation it was asking about?

Answer:

(C) The value of r indicates that the number of sales decreases as the price increases.

ED2021.

The best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

A negative correlation coefficient has a negative sign, and implies a negative relationship between two variables.

This means that, as one variable decreases, the other variable increases.

Thus, a correlation coefficient of -0.63 shows a negative relationship between prices of smartphones and the number of sales.

Therefore, the best statement, given the correlation coefficient of -0.63 is: value of r indicates that the number of sales decreases as the price increases.

Learn more about correlation coefficient on:

https://brainly.com/question/4219149

Answer:

20kg

Step-by-step explanation:

Let the weight of one duck be x and the weight of one duckling be y

ATQ, 3x+2y=32 and 4x+3y=44, solving for x and y we get, weight of one duck is 8kg and one duckling is 4kg. The weight of two ducks and one duckling is 20kg

36 different value meal packages are possible

Step-by-step explanation:

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

Answer:

Perimeter: 3/4

Area: 9/16

Step-by-step explanation:

The ratio of the perimeters is equal to the ratio of the sides so:

18/24 = 3/4

Ratio of Area = (Ratio of Sides)^2

(3/4)^2 = 9/16

I wasn't sure about the answer so I used Gauthmath

Answer:

w = -46/5

Step-by-step explanation:

Answer:

w=-9.2

Step-by-step explanation:

7(w+8)=2w+10

7w+56=2w+10

7w-2w=10-56

5w=-46

w=-9.2

Answer:

a

Step-by-step explanation:

Answer:

There are 28 beads

Step-by-step explanation:

Total ratio:

[tex]{ \sf{ (4 + 7) = 11}}[/tex]

let total beads be x:

[tex]{ \sf{ \frac{4}{11} \times x = 16 }} \\ \\ { \sf{x = \frac{11 \times 16}{4} }} \\ x = 44 \: beads[/tex]

Blue beads:

[tex] = 44 - 16 \\ = 28 \: \: beads[/tex]

Statements? At least look for one that says it is equivalent to positive 5.

Answer:

1.09c

Step-by-step explanation:

The clothes cost c before tax.

The tax is 9% of the price of the clothes, or 9% of c.

To find a percent of a number, change the percent to a decimal and multiply by the number.

9% as a decimal is 0.09

9% of c = 9% * c = 0.09c

The amount of tax is 0.09c.

Now we add the amount of tax to the original price, c.

c + 0.09c = 1.09c

Answer: 1.09c

Answer: (7, -4)

Concept:

For each rotation angle, there is a specified rule that could be applied. Please refer to the attachment below for the list of rotation rules.

Solve:

Given point = (-7, 4)

Given rotation rule = (x , y) ⇒ (-x, -y)

(-7, 4) ⇒ (7, -4)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

the write answer to your question is tan 25 degree

9514 1404 393

Answer:

  perimeter ratio = dilation factor

Step-by-step explanation:

In general, all linear dimensions are scaled by the dilation factor. This includes lengths of sides, perimeter, circumference, diameter, radius, or any other 1-dimensional (length) measure of a figure.

The ratio of perimeters is equal to the ratio of side lengths.

https://www.chegg.com/homework-help/questions-and-answers/contractor-susan-meyer-haul-gravel-three-building-sites-purchase-much-18-tons-gravel-pit-n-q8579741

Answer:

3*sqrt(2) and 3pi/4

Step-by-step explanation:

tan(theta)=y/x and r^2=y^+x^2.

tan(theta)=-3/3=-1, theta=3pi/4

r=sqrt(3^2+3^2)=3*sqrt(2)

First concert mixed fractions to normal Form

[tex]\\ \sf\longmapsto 1\dfrac{1}{4}=\dfrac{5}{4}[/tex]

[tex]\\ \sf\longmapsto 1\dfrac{3}{4}=\dfrac{7}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{4}-\dfrac{1}{4}=\dfrac{5}{4}-\dfrac{3}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3-1}{4}=\dfrac{5-3}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{2}{4}=\dfrac{2}{4}[/tex]

Hence it's true

Answer: True

Explanation:

1/4, 3/4, 1 1/4, 1 3/4

1 1/4 = 5/4

1 3/4 = 7/4

1/4, 3/4, 5/4, 7/4

= 0.25, 0.75, 1.25 , 1.75

This is arithmetic

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Answer:

x = 14

Step-by-step explanation:

Vertical angles are equal

5x+2 = 6x-12

Subtract 5x from each side

5x+2-5x = 6x-12-5x

2 = x-12

Add 12 to each side

2+12 = x-12+12

14 =x

Answer:

17.62%

Step-by-step explanation:

z→   ρ

0.93 (L)0.82381 (R)0.17619

17.62% / 82.38%

The area in the right tail more extreme than z=0.93 in standard normal distribution is 17.62% rounded to three decimal places.

A normal distribution of data occurs when the majority of data points are relatively similar and the data set has a small range of values.

We need to find the area in the right tail more extreme than z=0.93 in standard normal distribution.

Here, z=0.93

z→  ρ

The mean ( the population mean, at 0.93 standard deviation units, and it represents an area that is, 17.619% of the total area of the standard distribution).

In this normal distribution, every given score is a z-score. A z-score explain us the distance from the mean in standard deviation units.

A = 17.62% / 82.38%

Hence, The area in the right tail more extreme than z=0.93 in standard normal distribution is 17.62% rounded to three decimal places.

Learn more about standard deviation and variance:

https://brainly.com/question/11448982

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Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

12

,

67.45

)

Equation Form:

x

=

12

,

y

=

67.45

Answer:

a

Step-by-step explanation:

1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't