Which pair of functions are inverses of each other?  A. f(x) = \sqrt[3]{{6x}}f(x)= 3 6x​ and g(x) = {\left( {\frac{x}{6}} \right)^3}g(x)=( 6 x​ ) 3  B. f(x) = 10x – 5 and g(x) = \frac{{x + 5}}{{10}}g(x)= 10 x+5​ C. f(x) = \frac{4}{x} - 3f(x)= x 4​ −3 and g(x) = \frac{{x + 3}}{4}g(x)= 4 x+3​ D. f(x) = \frac{x}{8} + 3f(x)= 8 x​ +3 and g(x) = 8x – 3​

Answer:

C

Step-by-step explanation:

The simplified expression of the given expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex] is [tex]w^{16[/tex].

The expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex]  can be simplified as follows:

= -5 * [tex]w^{2 - (-6)[/tex] * [tex]y^{-2 - 2[/tex] / -15 * [tex]w^{-6 - 2[/tex] * [tex]y^{2 - (-2)[/tex]

= -5 * [tex]w^8[/tex] * [tex]y^{-4[/tex] / -15 * [tex]w^{-8[/tex] * [tex]y^4[/tex]

= (-5 / -15) * ([tex]w^8[/tex] / [tex]w^{-8[/tex]) * ([tex]y^{-4[/tex] / [tex]y^4[/tex])

= 1 * [tex]w^{16[/tex] * [tex]y^0[/tex]

= [tex]w^{16[/tex]

Therefore, the simplified expression is w^16.

Here is a breakdown of the steps involved in the simplification:

The powers of w and y are combined using the distributive property of exponents.

The negative exponents are changed to positive exponents by dividing by the same base raised to the power of the negative exponent.

The factors of 5 and 15 are simplified.

The common factors of w and y are simplified.

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Answer:

I'm not completely sure but i'm going to guess on D the domain is 1 < f < 7, the range is 24 < c(f) < 168

Step-by-step explanation:

because 1 cup is < to a cup of Flour (f), and the expression says 7 cups in total so i f is less than or equal to the total number of cups 7. then the range says c(f)=24(f), meaning you get 24 cookies for the input amount "f" of cups of flour. So the range would be 24 is grater of equal to the c(f)which in total (7 x 24) is equal to 168

Answer:

C. y=4x+13

Step-by-step explanation:

To solve this equation first find the slope. Do this by using the slope formula, m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], so plug in the points[tex]\frac{1+3}{-3+4}[/tex] which equals 4/1 or 4. Since now we know the slope is 4 we can put the equation into slope-point form, I will be using (-4,-3) for this equation. y+3=4(x+4), then solve for y. After solving you get y=4x+13.

Answer:

The percentage decrease = 0.9%

Step-by-step explanation:

Using the formula

Percentage Decrease = [ (Initial Value - Final Value) / |Initial Value| ] × 100

                                    = [(9.80 - 9.71 ) / (9.80)] × 100

                                    = [0.09 / 9.80] × 100

                                    = 0.009 × 100  

                                    = 0.9%

Therefore, the percentage decrease = 0.9%

Answer:

Umm !! it's 260

Step-by-step explanation:

Hope I'm right ?!!!!?!??

Answer:

23.8 will be it's answer

Answer:

Step-by-step explanation:

f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

Answer:

∠A = 45°

Step-by-step explanation:

It is given that,

sin A = sin B

∠C is a right angle.

If sin A = sin B, it means

sin 45 = sin 45 = [tex]\dfrac{1}{\sqrt2}[/tex]

It means that angle A and angle B is 45 degrees.

Answer:

28.26 cm^2

Step-by-step explanation:

A = (pi)r^2

A = 3.14 * (3 cm)^2

A = 3.14 * 9 cm^2

A = 28.26 cm^2

Answer:

Each has to work 5 hours and earn $42

Step-by-step explanation:

Let m and h represent hours Nai spends mowing and hauling, respectively. Then (m+h) will be the number of hours Priya spends babysitting. In order for their earnings to be equal, we must have ...

 7m +14h = 8.40(m+h)

 5.60h = 1.40m . . . . . . . . subtract 7m+8.40h

 m = 4h . . . . . . . . . . . . . . divide by 1.40

Then the total number of hours worked by either person is ...

 m + h = (4h) +h = 5h

If only whole numbers of hours are worked, then the smallest number of hours that will make earnings equal is 5h, with h=1, or 5 hours. In that time, each will earn 5×$8.40 = $42.

Each must work 5 hours and earn $42 before they go to the movies.

__

Nai will work 4 hours mowing and 1 hour hauling.

Each must work 5 hours and earn $42 before they go to the movies. Mai will work 4 hours mowing and 1 hour hauling.

Two or more expressions with an Equal sign is called as Equation.

Let m and h represent hours Mai spends mowing and hauling, respectively. Then (m+h) will be the number of hours Priya spends babysitting.

In order for their earnings to be equal, we must have

7m +14h = 8.40(m+h)

subtract 7m+8.40h

5.60h = 1.40m

Divide by 1.40

m = 4h

Then the total number of hours worked by either person

m + h = (4h) +h = 5h

If only whole numbers of hours are worked, then the smallest number of hours that will make earnings equal is 5h, with h=1, or 5 hours. In that time, each will earn 5×$8.40 = $42.

Hence, Each must work 5 hours and earn $42 before they go to the movies. Mai will work 4 hours mowing and 1 hour hauling.

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Answer: Yes

Step-by-step explanation:

Answer:

yesh it does :>

Step-by-step explanation:

9514 1404 393

Answer:

  453.6 g

Step-by-step explanation:

The mass of 80 quarters will be 80 times the mass of 1 quarter:

  80 × 5.67 g = 453.6 g

The mass of two rolls of quarters is 453.6 grams.

_____

Additional comment

That's about 1.0000 pounds.

Answer: 7 ; 26 ; 123

Step-by-step explanation:

Min __Q1 __ Median ___ Q3 __ Max

7____ 72 ____79 ______86__ 123

Given the 5 number summary information :

The Outlier :

Lower bound : Q1 - (1.5 * IQR)

Upper bound : Q3 + (1.5 * IQR

IQR = Q3 - Q1 = (86 - 72) = 14

Lower = 72 - (1.5 * 14)

Lower boundary = 51

Upper boundary = 86 + (1.5 * 14)

Upper boundary = 86 + 21 = 107

Values below 51 and values greater Than 107 are outliers.

Hence, 7, 36 and 123 are outliers

Answer:

6

Step-by-step explanation:

s=9, t=12

2s-t = 2*9 -12 = 18 -12 = 6

Answer:

the answer is 6

Step-by-step explanation:

Because you do 2 times 9 = 18 then 18 - 12 = 6

Answer:

4

Step-by-step explanation:

7+7+7+7 or 28/7 =4

Answer:

x ≠ 5

Step-by-step explanation:

x ≠ 5

The reason for this is because if we use the input 5, this will be the result:

f(x) = 3/(5) - 5

f(x) = 3/0 = Undefined

Answer:

The calculated mean price is a sample mean and it is denoted by x.

Step-by-step explanation:

Given that

Mean price of paintings = $3550

Number of paintings = 20

In order to decide whether it is a population mean or a sample mean we have to understand the terms first.

Population:

Population is the overall collection from which a sample or observations are taken.

Sample:

The small or less number of observations that we take from a large population to perform data analysis is called sample.

In the given scenario, all the paintings at the art fair are population while the number of paintings that the art collector bought is a sample.

Hence,

The calculated mean price is a sample mean and it is denoted by x.

Answer:

1. is Line C

2. is line A

(slope, y-intercept)

4. (1, 4)

6. (-5/7, -2)

8. (6, 2)

9. (1/2, -7)

10.

a) you've already done this

b)-4200

c)21000

d) 5

11.

draw a line between the intercepts and add arrows to each end to graph the line easily

y- intercept is -6 ( at 0, -6)

x intercept is 2 ( at 2, 0)

Answer:

the oldest sister spent 2.70$ (given)

the middle sister spent 10.80$

and the youngest sister spent 7.12$

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

-3 * (x-11) = -51

x-11 = 17

x = 28

Answer:

8.04

Step-by-step explanation:

Answer:

If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .

Step-by-step explanation:

Answer:

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Step-by-step explanation:

T = k * sqrt(d), where k is a real constant.

When d = 6, T = 5.

k = T / sqrt(d) = 5 / sqrt6.

Therefore when d = 3, T = (5 / sqrt6) * sqrt3 = 3.53.

Answer:

762 days

Step-by-step explanation:

Given

[tex]Rate = 200 + 10t + 13t^2[/tex]

Let the rate be R.

So the rate change with time is represented as:

[tex]\frac{dR}{dt} = 200 +10t + 13t^2[/tex]

So:

[tex]dR = (200 + 10t + 13t^2)\ dt[/tex]

To get the number of insects between day 0 and day 3, we need to integrate dR and set the bounds to 0 and 3

i.e.

[tex]dR = (200 + 10t + 13t^2)\ dt[/tex] becomes

[tex]\int\limits^3_0 {dR} \, =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]

[tex]R =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]

Integrate

[tex]R = 200t + \frac{10t^2}{2} + \frac{13t^3}{3} [3,0][/tex]

Solve for R by substituting 0 and 3 for t

[tex]R = (200*3 + \frac{10*3^2}{2} + \frac{13*3^3}{3}) - ( 200*0 + \frac{10*0^2}{2} + \frac{13*0^3}{3})[/tex]

[tex]R = (200*3 + \frac{10*9}{2} + \frac{13*27}{3}) - (0 + \frac{10}{2} + \frac{0}{3})[/tex]

[tex]R = (200*3 + 5*9 + 13*9) - (0)[/tex]

[tex]R = 600 + 45 + 117 - 0[/tex]

[tex]R =762[/tex]

The population of insect between the required interval is 762

The required change in the population of insects between day 0 and day 3 is 762.

Given that,

A population of insects increases at the rate of 200++ 10t + 13t2.

We have to determine,

What is the change in the population of insects between day 0 and day 3.

According to the question,

The rate change with time is represented as:

[tex]\frac{dr}{dt} = 200+10t+13t^{2}[/tex]

To determine the change in the population of insects between day 0 and day 3,

Integrating the given function with respect to time with limit 0 days to 3 days.

[tex]\int\limits^3_0 dr = \int\limits^3_0 (200+10t+13t^{2} ). dt\\\\\int\limits^3_0dr =\int\limits^3_0 \, 200dt + \int\limits^3_0 10tdt +\int\limits^3_0{13t^{2} dt\\\\\\\\R = [200t]^3_0 + [5t^{2} ]^3_0 + [\frac{13t^{3} }{3} ]^3_0\\\\R = 200[(3) - (0)] + 5 (3^{2} - 0^{2} ) + \frac{13}{3} [ 3^{3} - 0^{3} ]\\\\R = 200(3) + 5 (9) + \frac{13}{3}(27)\\\\R = 600+45+117\\\\R = 762[/tex]

Hence, The required change in the population of insects between day 0 and day 3 is 762.

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