For each pair of functions and below, find and .
Then, determine whether and are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all in the domain of the composition.
You do not have to indicate the domain.)
f(x)=3/x,x=/= 0
g(x)=3/x, x=/=0
f(g(x))=
g(f(x))=
f and g are inverses of each other
f and g are not inverses of each other
f(x)=x+4
g(x)=-x+4
f(g(x))=
g(f(x))=
f and g are inverses of each other
f and g are not inverses of each other

Answer:

The intercepts of the line: 9x - 7y = 14

For x-intercept, in this case: y = 0, => 9x = 14 => x = 14/9

=> x-intercept (14/9, 0)

For y-intercept, in this case: x = 0, => -7y = 14 => y = -2

=> y-intercept (0, -2)

Hope this helps!

:)

Answer:

The real solutions are

[tex]x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]

Step-by-step explanation:

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

To find the real solutions of the equation [tex]5x^6=30[/tex]:

[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x^6}{5}=\frac{30}{5}\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35[/tex]

Step-by-step explanation:

[tex](3x-2)(5x^2-3x+4)[/tex]

[tex]15x^3-9x^2+12x-10x^2+6x-8[/tex]

Now, combine like terms.

[tex]15x^3-19x^2+18x-8[/tex]

Answer:

Option C is correct

Step-by-step explanation:

The equation, when graphed with the given  equation (y = -x + 4), will form a system that has an infinite number of solutions MUST have same form as given equation.

y = (-1/2)(2x - 8) = (-1/2)*2x + (-1/2)*8 = -x + 4 (same form as given equation)

Hope this helps!

:)

Answer:

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Step-by-step explanation:

Given sample size 'n' =n₁ = n₂ = 40

The mean of the first sample  (x₁⁻) = 5.69 hours

The standard deviation of the first sample (S₁)= 2.42 hours

The mean of the second sample( x₂⁻) = 4.32 hours

The standard deviation of the second sample (S₂)= 1.83 hours

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

where

The standard error of the difference between two means

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{S^{2} _{1} }{n_{1} }+\frac{S^{2} _{2} }{n_{2} } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{(2.42)^2 }{40 }+\frac{(1.83)^2 }{40 } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{0.2301325} = 0.47972[/tex]

Degrees of freedom γ = n₁ +n₂ -2 = 40+40 -2 =78

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025}[/tex]

t₀.₀₂₅ = 1.992

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

(5.69 -4.32)- 1.992(0.47972)), (5.69-4.32)+1.992(0.47972))

(1.37 -0.9556 , 1.37+0.9556)

(0.4144 , 2.3256)

Conclusion:-

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Following are the calculation to the confidence interval:

Given:

[tex]\bar{x_1}= 5.69\\\\\bar{x_2}= 4.32\\\\s_1=2.42\\\\s_2=1.83\\\\n_1=40\\\\n_2=40\\\\[/tex]

To find:

confidence interval=?

Solution:

[tex]\to a=0.1\\\\ \to Z(0.05)=1.645[/tex]            (from standard normal table)

Calculating the confidence interval when its value is [tex]95\%[/tex]:

[tex]\to (\bar{x_1}-\bar{x_2}) \pm Z \times \sqrt{(\frac{s^2_{1}}{n_1}+ \frac{s^2_{2}}{n_2})}[/tex]  

[tex]\to (5.69-4.32)\pm 1.645 \times \sqrt{(\frac{2.42^2}{40}+\frac{1.83^2}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564}{40}+\frac{3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564+3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{9.2053}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{0.2301325}\\\\\to (1.37)\pm 1.645 \times 0.4797212 \\\\\to (1.37)\pm 0.789\\\\\to (2.159, 0.581 )[/tex]

Therefore, the final answer is "(2.159 and 0.581)".

Learn more about the confidence interval:

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Answer:

$0.08

Step-by-step explanation:

Take 0.23 and divide it by 3 to get an individual cost and round to the nearest tenth.

Answer:

Step-by-step explanation:

.23 ÷3=.076

Rounded up .08

Answer:

  7 years

Step-by-step explanation:

We expect your equation is ...

  200e^(.08t) = 350

Dividing by 200 and taking the natural log, we have ...

  0.08t = ln(1.75)

  t = ln(1.75)/.08 ≈ 7.0

The money has been invested 7 years.

Answer:

x = 2, y =7

Step-by-step explanation:

4x - 2y = -6

-6x + 2y = 2

Add the equations together

4x - 2y = -6

-6x + 2y = 2

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

-2x = -4

Divide each side by -2

-2x/-2 = -4/-2

x = 2

now find y

-6x+2y =2

-6(2) +2y =2

-12+2y =2

Add 12 to each side

-12+12+2y = 2+12

2y =14

Divide by 2

2y/2 =14/2

y =7

Answer:

The sum of the first nine terms of the sequence is 74.44.

Step-by-step explanation:

Geometric sequence concepts:

The nth term of a geometric sequence is given by the following equation.

[tex]a_{n+1} = ra_{n}[/tex]

In which r is the common ratio.

This can be expanded for the nth term in the following way:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

Or even:

[tex]a_{n} = a_{m}r^{n-m}[/tex]

The sum of the first n terms of a geometric sequence is given by:

[tex]S_{n} = \frac{a_{1}(1 - r^{n})}{1 - r}[/tex]

Finding the common ratio:

[tex]a_{3} = 3.645, a_{8} = 15[/tex]

[tex]a_{n} = a_{m}r^{n-m}[/tex]

[tex]a_{8} = a_{3}r^{8-3}[/tex]

[tex]a_{3}r^{5} = a_{8}[/tex]

[tex]3.645r^{5} = 15[/tex]

[tex]r^{5} = \frac{15}{3.645}[/tex]

[tex]r = \sqrt[5]{\frac{15}{3.645}}[/tex]

[tex]r = 1.327[/tex]

Finding the first term:

[tex]a_{3} = a_{1}r^{2}[/tex]

[tex]a_{1} = \frac{a_{3}}{r^{2}}[/tex]

[tex]a_{1} = \frac{3.645}{(1.327)^{2}}[/tex]

[tex]a_{1} = 2.07[/tex]

Sum of the first nine terms:

[tex]S_{9} = \frac{2.07*(1 - (1.327)^{9})}{1 - 1.327} = 74.44[/tex]

The sum of the first nine terms of the sequence is 74.44.

Answer:

S₉ = 9.84

Step-by-step explanation:

In a geometric series, the general formula for nth term is:

an = a₁rⁿ⁻¹

where,

an = nth term

a₁ = first term

r = common ratio

From this formula, we have:

a₃ = a₁r² = 3.645   --------- equation (1)

a₈ = a₁r⁷ = 15    ----------- equation (2)

dividing both of these equations, we get:

a₁r⁷/a₁r² = 15/3.645

r⁵ = 4.115

r = (4.115)^1/5

r = 1.33

Now, put this value in equation (1), we get:

a₁(1.33)² = 3.645

a₁ = 0.27

Now, the formula for the sum of geometric series upto nth term is:

Sn = a₁(rⁿ - 1)/(r - 1)

therefore,

S₉ = (0.27)(1.33⁹ - 1)/(1.33 - 1)

S₉ = 9.84

Answer:

  B.  5x^2 -4

Step-by-step explanation:

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

  = (4x^2 +1) +(x^2 -5) . . . . . . substitute for f(x) and g(x)

  = x^2(4 +1) +(1 -5) . . . . . . . . collect terms

(f+g)(x) = 5x^2 -4

Answer:

Yes 0 is a natural number

Step-by-step explanation:

I googled it

Step-by-step explanation:

Zero is not positive or negative Even though zero is not a positive number it is still considered a whole number yes it is a natural number because it is on the number line

Answer:

-2+2x=y

Step-by-step explanation:

got it correct on imagine math

Answer:

38

Step-by-step explanation:

Range= highest number - lowest number

Range= 43-5

=38

Step-by-step explanation:

Step 1:  Find the highest number and the lowest number

Highest Number → 43

Lowest Number → 5

Step 2:  Find the range by subtract the lowest number from the highest number

Highest Number - Lowest Number

43 - 5

38

Answer:  The range is 38

Answer:

[tex]32[/tex]

Step-by-step explanation:

[tex] {2}^{5} \\ 2 \times 2 \times 2 \times 2 \times 2 \\ 4 \times 4 \times 2 \\ 16 \times 2 \\ = 32[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is 32.

Look at the attached picture

hope it will help you

good luck on your assignment

Answer:

The central angle measure of the sector in radians is [tex]\theta=\frac{13}{9}[/tex].

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.

The area of a sector when the central angle is in radians is given by

                                                    [tex]A=(\frac{\theta}{2})\cdot r^2[/tex]

where

r = radius

θ = central angle in radians

We know that the area of the sector is [tex]26 \:cm^2[/tex] and the radius is 6 cm. Applying the above formula and solving for the central angle ([tex]\theta[/tex]) we get that

                                                   [tex]26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}[/tex]

Answer:

  7,854 cm squared

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

Filling in the given radius gives you ...

  A = π(50 cm)^2 = 2500π cm^2 ≈ 7854 cm^2

Answer:

wheres the info

Step-by-step explanation:

Answer:

A: 10.5 m

Step-by-step explanation:

i think it's A, i may be wrong! hope this helps!!~

Answer:

Athena = 10,265 km

Vesta = 102,650 km

Juno = 102,650 km

Ceres = 2,053,000 km

Apollo = 1,026,500 km

Step-by-step explanation:

Athena = 20,530 / 2 = 10,256

From there, you can work out the rest by multiplying accordingly.

Hope this helps and made sense! :)

Look at the attached picture

Hope it will help you

Answer:

Step 1: Write down the decimal divided by 1, like this: decimal 1.

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction.

Answer:

The answer is D. Range Hopefully this helps!

Answer:

D

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

The current endpoints are ...

  V = (-9, 2)

  W = (-3, 6)

Put each of these in the translation formula to see where the image points are.

  (x, y) ⇒ (x+5, y-1)

  (-9, 2) ⇒ (-9+5), 2-1) = (-4, 1) . . . . point V ⇒ V'

  (-3, 6) ⇒ (-3+5, 6-1) = (2, 5) . . . . . point W ⇒ W'

The new end points are (-4, 1) and (2, 5), matching choices A and B.

Answer:2k-13

Step-by-step explanation:

Answer:

2k-13.

Step-by-step explanation:

We can simplify this equation using the Distributive Property:

-3(2 + 4k) + 7(2k-1) becomes

-6 - 12k + 14k -7

Combining like terms gets us:

2k-13.

Answer:

(x-8)(x^2-2)

Step-by-step explanation:

take x common from the first 2 terms and take -2 common from the last two terms. Then, take (x-8) common.

x^2(x-8)-2(x-8) = (x-8)(x^2-2)

the percent difference is 60%

Answer:

  y +9 = 15(x -2)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . for slope m and point (h, k)

Here, you are given m=15 and (h, k) = (2, -9). Putting these values into the form gives the equation ...

  y +9 = 15(x -2)

Answer:

Mean, m = 72

Step-by-step explanation:

It is given that, Carl earned grades of 62, 78, 59, and 89 on four math tests.

It is required to find the mean of his grades.

Mean of a data is given by :

[tex]m=\dfrac{\text{sum of observations}}{\text{total no of observations}}[/tex]

Sum of observations is 62 + 78 + 59 + 89 = 288

Total no of observations are 4

So, mean of his grades is :

[tex]m=\dfrac{288}{4}\\\\m=72[/tex]

So, the mean of his grades is 72.

Option C is correct. If Carl earned grades of 62, 78, 59, and 89 on four math tests, the mean of his grades is 72

Mean is the average of the given data. It is expressed mathematically as:

[tex]\overlibe x=\frac{\sum x}{N}[/tex]

[tex]\sum x[/tex] is the sum of the variables

N is the total test taken

[tex]\sum x = 62 + 78 + 59 + 89\\\sum x = 288\\\\N = 4[/tex]

Substitute the resulting values into the mean formula:

[tex]\overline x = \frac{288}{4}\\ \overline x =72[/tex]

This shows that the mean of his grades is 72

Learn more here:https://brainly.in/question/2401311

Answer:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Step-by-step explanation:

The correct situation is the third one, this is because the expression we have is:

[tex]30+4x=70+2x[/tex]

let's take the left side as the charge of the company limo A, and the left side as the charge of limo B.

Since 'x' is the number of people, the left side tells us that limo A charges $4 per person (hence the 4x) and adds an additional $30 (hence the 30 added on the left side).

And the right side tells us that limo B charges $2 per person (hence the 2x) and adds an additional $70 (hence the 70 added on the right side).

And since we have an equal sign this means that the expression represents the number of people that can ride and will pay an equal amount in each company.

This is the situation that the third option describes:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Answer:

Volume of the mold is [tex]6.93\ \text{yards}^3[/tex].

Step-by-step explanation:

The volume of the mold is 186 cubic feet concrete. It is to be sold by cubic yard. It means that we need to convert cubic feet to cubic yard.

1 feet = 0.334 yards

[tex]186\ \text{feet}^3=186\times (0.334\ \text{yards})^3\\\\V=6.93\ \text{yards}^3[/tex]

So, the volume of the mold is [tex]6.93\ \text{yards}^3[/tex].