Recall that the volume of a sphere is given by the formula V = 4/3pi to the 3rd

1. Here is a sphere with radius 4 feet. What is the volume of the sphere? Express your answer in
terms of pi.
2. A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this
balloon holds. Use 3.14 as an approximation for it, and give a numerical answer

Answer:

After next 24 hours, bacterial population would be [tex]1433[/tex]

Step-by-step explanation:

The initial bacterial count at time = 0  was [tex]100[/tex]

At [tex]= 24[/tex] hours, the bacterial count increased up to [tex]305[/tex]

At [tex]= 48[/tex] hours, the bacterial count increased up to [tex]897[/tex]

As we know that

[tex]P = P_0 * e^{rt}[/tex]

The growth rate of bacterial population is equal to

[tex]r = \frac{log\frac{P}{P_0} }{t}[/tex]

Substituting the above values we get -

[tex]r = \frac{log\frac{897}{305} }{24}\\r = 0. 0195[/tex]

Count of bacteria after next 24 hours

[tex]P = 897 * e^{ 0.0195 * 24)\\P = 1433[/tex]

Answer:

[tex]Length = 6x^2 - 2x + 3[/tex]

Step-by-step explanation:

Given

[tex]Area = 42x^3 - 14x^2 + 21x[/tex]

[tex]Width = 7x[/tex]

Required

Determine the length of the aquarium

The area of a rectangular base is calculated as:

[tex]Area = Length * Width[/tex]

Substitute values for Area and Width

[tex]42x^3 - 14x^2 + 21x = Length * 7x[/tex]

Make Length the subject

[tex]Length = \frac{42x^3 - 14x^2 + 21x}{7x}[/tex]

Factorize the numerator

[tex]Length = \frac{7x(6x^2 - 2x + 3)}{7x}[/tex]

[tex]Length = 6x^2 - 2x + 3[/tex]

Step-by-step explanation:

try desmos its a life saver

9514 1404 393

Answer:

  60 cm

Step-by-step explanation:

The model ship will be x feet long, where ...

  x/100 = 1/50

  x = 100/50 = 2

In meters, that is ...

  2(0.3 m) = 0.6 m

A meter is 100 cm, so the length in centimeters is ...

  (0.6)(100 cm) = 60 cm

Answer:

3/4

Step-by-step explanation:

that's as simple as it gets

Answer:

if ur solving for x the answer is x=-1

Step-by-step explanation:

-15 - 4x = -11

=> -4x = -11 + 15

=> -4x = 4

[tex] = > x = \frac{4}{ - 4} [/tex]

=> x = -1 (Ans)

Answer:

10 dollar bill, 5 dollar bill, and one dollar.

Answer:

16 brainliest?

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex](3x+7)8x^2\\ \\ 3x(8x^2)+7(8x^2)\\ \\ 24x^3+56x^2[/tex]

Answer:B

Step-by-step explanation

The slope of the linear relation is -0.0018 and the y-intercept will be 212. The correct option is B.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data in the table is,

Altitude(x)       Boiling point (y)

0                      212.0

500                 211.1

The slope will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 211.1 - 212  ) / (500 - 0 )

Slope = -0.0018

The y-intercept will be calculated as,

y = mx + c

212 = 0 + c

c = 212

Therefore, the slope of the linear relation is -0.0018 and the y-intercept will be 212. The correct option is B.

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ2

Answer:

The answer is C. Quadratic Binomial

Answer:

[tex]Rate = 15[/tex]

Step-by-step explanation:

Given

[tex]R(x) = 56 - 0.020x^2[/tex]

Required

Find the average change from​ 1,000 car seats to​ 1,050 car seats --- Missing information

This is calculated using:

[tex]Rate = \frac{R(b) - R(a)}{b-a}[/tex]

In this case:

[tex]a = 1000[/tex]

[tex]b = 1050[/tex]

Now, we have:

[tex]Rate = \frac{R(1050) - R(1000)}{1050-1000}[/tex]

[tex]Rate = \frac{R(1050) - R(1000)}{50}[/tex]

Calculating R(1050)

[tex]R(1050) = 56 *1050- 0.020*1050^2[/tex]

[tex]R(1050) = 58800-22050[/tex]

[tex]R(1050) = 36750[/tex]

Calculating R(1000)

[tex]R(1000) = 56 *1000- 0.020*1000^2[/tex]

[tex]R(1000) = 56000- 20000[/tex]

[tex]R(1000) = 36000[/tex]

So:

[tex]Rate = \frac{R(1050) - R(1000)}{50}[/tex]

[tex]Rate = \frac{750} {50}[/tex]

[tex]Rate = 15[/tex]

The average rate of change is 12

Answer:

it was a 2 year loan with $210 contributed each year

Step-by-step explanation:

you take 7 percent of 300 which is 210 and see how many times it goes into the total interest amount and then your answer is how many years the loan was for

Answer:

multiplication

Step-by-step explanation:

whenever a number and a variable are together it means they are being multiplied together

Answer:

6y represents Multiplication.

Souljem

Step-by-step explanation:

souljem yes yes yes

Given:

Brianna had a garden Box that is 8' by 12'.

She decided to reduce it by a scale factor of [tex]\dfrac{1}{2}[/tex].

To find:

The area of her new garden.

Solution:

Let the length and width  of the original garden are 8 ft by 12 ft respectively.

Reduce the dimensions by a scale factor of [tex]\dfrac{1}{2}[/tex].

Length of the new garden is

[tex]\dfrac{8\ ft}{2}=4\ ft[/tex]

Width of the new garden is

[tex]\dfrac{12\ ft}{2}=6\ ft[/tex]

Now, the area of the new garden is

[tex]Area=Length\times Width[/tex]

[tex]Area=(4)\times (6)[/tex]

[tex]Area=24[/tex]

Therefore, the area of the new garden is 24 sq. ft.

Answer:

1,137.24

Step-by-step explanation:

Every worksheet is made up of thousands of rectangles, which are called cells. A cell is the intersection of a row and a column—in other words, where a row and column meet. Columns are identified by letters (A, B, C), while rows are identified by numbers (1, 2, 3).

So all you do is multiply like if you were finding the area:

35.1 x 32.4 = 1137.24.

Answer:

plot it 2 higher ticks then the zero. hope this helps

Step-by-step explanation:

it should look like this

Answer:

-17

Step-by-step explanation:

-17/4 = -4.25

and 4 is greater than that, so i think

K = -17

Step-by-step explanation:

log x = 1 + a

a = log x - 1

log y = 1 - a

a = 1 - log y

So

log x - 1 = 1 - log y

log x + log y = 2

log (xy) = 2

xy = 100

Answer: 3y+5

Step-by-step explanation: 4y+3−(y−2)

4y+3+−1(y−2)

4y+3+−1y+(−1)(−2)

4y+3+−y+2

(4y+−y)+(3+2)

3y+5

Answer:

See below, please!

Step-by-step explanation:

There are infinite number of ratios equivalent to 3:8 because both numbers can be multiplied by a common number or divided by a common number.

For example, 9:24 would still be equivalent to 3:8 because the common number in our case is 3. See what I mean?

Hope this helped!

Answer:

8. 548.9       9.349.3

Step-by-step explanation:

10% of 499 is 49.9

30% of 499 is 3*49.9=149.7

499+49.9=548.9

499-149.7=349.7

Answer:

[tex]Rate = 0.13[/tex]

Step-by-step explanation:

Given

[tex]y = \sqrt[3] x[/tex]

Required

Determine the average rate of change over [2,7]

This is calculated as:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]b = 7[/tex] and [tex]a = 2[/tex]

So, we have:

[tex]Rate = \frac{f(7) - f(2)}{7-2}[/tex]

[tex]Rate = \frac{f(7) - f(2)}{5}[/tex]

From the table:

f(7) = 1.91

f(2) = 1.26

[tex]Rate = \frac{1.91 - 1.26}{5}[/tex]

[tex]Rate = \frac{0.65}{5}[/tex]

[tex]Rate = 0.13[/tex]

Answer:

Explanation:

Area = width · length

The length of the rug is 9 feet. We need to find the width.

72 ÷ 9 = 8

Check to see if this is correct: width (8) · length (9) = area (72)

Now add the length and width together two times since a rug has 4 sides

8 + 8 + 9 + 9 = 34

The perimeter of the rug is 34 ft.²