The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.

Answer:

27

Step-by-step explanation:

Supplementary angles add up to 180 degrees

So to find the measure of an angle supplementary to a given angle, we simply subtract the given angle from 180

The given angle here has a measure of 153 degrees

So the angle's supplement has a measure of 180 - 153 = 27 degrees.

Answer:

3\2 is the marked

y cos x,=2

3\2=0.5

x=0.5*2=3.0

=3.0*2=6.0

[tex]\sf Sine \ Rue : \ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Given following:

Solve for b (distance between school and mall):

[tex]\dashrightarrow \sf \dfrac{\sin 56}{38} = \dfrac{\sin 77}{b}[/tex]

[tex]\dashrightarrow \sf b= \dfrac{38\sin 77}{\sin 56}[/tex]

[tex]\dashrightarrow \sf b= 44.6615 \quad \approx \quad 45[/tex]

Answer:

34 1/2

Step-by-step explanation:

Answer:

D) 65°

Step-by-step explanation:

Use Snell's Law

[tex]n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ[/tex]

Thus, the angle of incidence is D) 65°

It will take 764664.6875 days to empty the water

The given parameters are:

The time is calculated as:

Time = Volume/Rate

So, we have:

Time = 1 cubic mile ÷ 1000 gallons per minute

Convert gallons to cubic mile

Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute

Divide

Time = 1.10111715 × 10^9 minute

Convert to days

Time = 764664.6875 days

Hence, it will take 764664.6875 days to empty the water

Read more about volumes at:

https://brainly.com/question/1972490

#SPJ1

Answer:

  C.  ∆LMN ~ ∆OPQ, because of AA

Step-by-step explanation:

All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.

__

No sides are given as congruent, so no congruences can be proved.

Two pairs of corresponding angles are said to be congruent, so we can say ...

  ∆LMN ~ ∆OPQ, because of AA

The factor of the polynomial function f(x) graphed on the coordinate plane below is x - 1 , Option B is the right answer.

A function in which there is only positive exponents to the variables are called polynomial function.

The missing image is attached with the answer.

It is given in the question

on a coordinate plane, a parabola opens up. it goes through (0, 3), has a vertex at (3.5, 3), and goes through (6, 0)

The zeroes of the polynomial function are the points at which the curve will cut x axis

For the given graph,

the curve cuts the x-axis at x = 1 and x = 6

the  factors will be x - 1 and x - 6

Therefore, a factor of the polynomial function f(x) graphed on the coordinate plane below is x - 1 , Option B is the right answer.

To know more about Polynomial Function

https://brainly.com/question/12976257

#SPJ1

Answer:

B

Step-by-step explanation:

B

Answer:

A.

Step-by-step explanation:

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?

A.

2.8 pounds of apples and 4.8 pounds of grapes

B.

3.3 pounds of apples and 1.3 pounds of grapes

C.

3.8 pounds of apples and 1.8 pounds of grapes

D.

4.5 pounds of apples and 2.5 pounds of grapes

The number of acorns that each animal hid is 48

An equation is formed when two algebraic expressions are equated by an equal sign.

It is asked to calculate the number of acorns that each animal hid.

Total number of acorns hid  =  number of acorns hid per tree * number of trees    

Let   T be the number of trees chipmunk used

For chipmunk:    = 3*T

For squirrel:   = 4*(T-4)

 As both the animals hid same number of acorns.

    3T = 4(T-4)      

    3T = 4T - 16      

      16 = T

Therefore the chipmunk hid 16 * 3 = 48 acorns

and the squirrel hid 4(16-4) = 48 acorns.

To know more about Equation

https://brainly.com/question/2263981

#SPJ1

All the points  The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When we plot all the points on the graph we can see that all the points The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) are located in the solution region.

Therefore all the points  The point (-3.2), The point (-7.5), Point (2.-5), and The point (-14,6) is located in the solution region.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ1

Answer:

true

Step-by-step explanation:

The statement is true because every graph associated a unique x-value for each y - value

Answer:

x = 14

Step-by-step explanation:

given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives

2(3x - 5) = 74 ( divide both sides by 2 )

3x - 5 = 37 ( add 5 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Answer:

[tex]\frac{4}{n^{2} }[/tex]

Step-by-step explanation:

(2nm⁻³) * 2m³n⁻³

First, focus on the coefficients, 2*2 = 4.

Now the n, n * n⁻³ = n⁻²

Now the m, m⁻³ * m³ = m⁰ = 1

Now multiply altogether, 4n⁻²(1) = [tex]\frac{4}{n^{2} }[/tex]

Answer:

[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]

Step-by-step explanation:

Answer:

(3x^2 - 1)(4x - 3)

Step-by-step explanation:

We can use grouping to factor this

12x^3 – 9x^2 − 4x + 3

group into: (12x^3 – 9x^2)(− 4x + 3)

Solve one side at a time:

(12x^3 – 9x^2)

3x^2(4x - 3) factor out a 3x^2

(− 4x + 3)

- 1 (4x - 3) factor out a -1

put the two equations togeth

(3x^2 - 1)(4x + 3)

Step-by-step explanation:

[tex] = 4 + ( - 3) - 2 ( - 6)[/tex]

here ( + ) × ( - ) = ( - )

[tex] = 4 - 3 + 12[/tex]

[tex] = 4 + 12 - 3[/tex]

[tex] = 16 - 3[/tex]

[tex] = 13[/tex]

The correct result of this simplification is 13

To solve this question, we'll just apply the rule of signs - and then we'll calculate the operations.

- In the sign rule - when both signs are equal, the result will be positive. If the signs are different, the result is negative.

4 + ( - 3 ) - 2 · ( - 6 )

4 - 3 - ( - 12 )

4 - 3 + 12

1 + 12

13

Therefore, the alternative value will be 13

By solving the two quadratic equations we found the values (0,-1).

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equations are;-

The two equations are solved by equating them and finding the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

6x ( x+1 ) = 0

6x  = 0 so x = 0

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

Therefore solving the two quadratic equations we found the values (0,-1).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

Answer:

[tex]\left(12x^5-3x^1+2x-5\right)+\left(8x^1-3x^3+4x+1\right)[/tex]

=> Expand

[tex]12x^5-3x^1+2x-5+8x^1-3x^3+4x+1[/tex]

=> simplify and group like terms

[tex]12x^5-3x^3+5x^1+6x-4[/tex]

=> simplify further

[tex]12x^5-3x^3+11x-4[/tex]

Answer:

a) 13

b) 1/3

c) -2

d) 1

Step-by-step explanation:

This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:

For example:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

________

f(-3) = 3x + 7

f(-3) = 3(-3) + 7

f(-3) = -9 + 7

f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.

f(-3) = -2

The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:

For example:

f(x) = 8

f(x) = 3x + 7

8 = 3x + 7

8 - 7 = 3x

1 = 3x

x = 1/3

f(x)= 10

f(x) = 3x + 7

10 = 3x + 7

10 - 7 = 3x

3 = 3x

3/3 = x

1 = x

I hope this helps!

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

[tex]= \rm \dfrac{\left(14x^4y^6\right)}{\left(7x^8y^2\right)}[/tex]

[tex]\rm =\dfrac{7\cdot \:2x^4y^6}{7x^8y^2}[/tex]

[tex]\rm =\dfrac{2x^4y^6}{x^8y^2}[/tex]

[tex]\rm =\dfrac{2y^4}{x^4}[/tex]

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

Learn more about the integer exponent here:

brainly.com/question/4533599

#SPJ1

Answer:

A

Step-by-step explanation:

imagine explaining

In 15 years, the average car releases 458.7 kilograms of nox.

We know that the average vehicle releases 1.39 grams per mile driven.

And, in average, that car drives 22,000 miles per year.

So in a year, a car releases:

M = (22,000)*1.39 g  = 30,580 g = 30.58 kg

In one year, the average car releases around 30.58 kilograms of nox.

Then in 15 years, the car releases 15 times that amount, then we have the product:

T = 15*30.58 kg = 458.7 kg

In 15 years, the average car releases 458.7 kilograms of nox.

If you want to learn more about products:

https://brainly.com/question/10873737

#SPJ1

Based on the preferred dividends, the dividends for preferred and common stock in each year are:

Preferred stock dividends:

Common stock dividends:

Preferred shares have a specific dividend, and as these are cumulative shares, the dividends that are not paid in one year, will be paid in the next.

Dividends per year:

= 20,000 x 2% x 150

= $60,000

20y1 dividend per share:

= 60,000 / 20,000

= $3.00 per share

20y2 dividend per share:

= 24,000 / 20,000

= $1.20 per share

20y3 dividend per share:

The remaining dividend from 20y2 will have to be paid here:

= (60,000 + (60,000 - 24,000)) / 20,000

= 96,000 / 20,000

= $4.80 per share

Preferred dividends are paid first:

Common dividends are:

= (Amount distributed as dividends - Preferred dividends) / Number of common shares

In 20y1:

= (120,000 - 60,000) / 50,000

= $1.20

In 20y2:

= (45,000 - 45,000) / 50,000

= $0 per share

In 20y3:

= (180,000 - 96,000) / 50,000

= $1.68 per share.

Find out more on preferred dividends at https://brainly.com/question/1416151.

#SPJ1

Answer:

Step-by-step explanation:

ohn will need to sleep for 10.3 hours before his second exam so that the

he average of his two exam scores is an 80.

We were given

8 hours of sleep = 70

To get an average of 80

70+ x = 80

2

Cross multiply:

70+x = 160

x= 160-70

= 90.

If 8 hours of sleep = 70

x hours of sleep = 90

Cross multiply

8× 90 = 70 × x

720 = 70x

x = 720/70

x = 10.2857

≈ 10.3 hours of sleep

Answer:

Approx. 2140.16 cubic centimeters

Step-by-step explanation:

[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]

The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.

The domain means all the possible values of x and the range means all the possible values of y.

The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.

The graph is given below.

We know that the exponential function is given as

y = abˣ

For x = 0, y will be 250,000

250,000 = a

For x = 40, y will be 400,000

400,000 = 250,000b⁴⁰

           b = 1.0118

Then we have

y = 250,000 (1.0118)ˣ

Then the range of the exponential function will be y ≥ 250,0003.

More about the domain and range link is given below.

https://brainly.com/question/12208715

#SPJ4

The value of f(3) is 9

The table that completes the question is added as an attachment.

From the complete table, we have:

When x = 3, the value of the function is 9

This means that:

f(3) = 9

Hence, the value of f(3) is 9

Read more about functions at:

https://brainly.com/question/20896994

#SPJ1