119,179,710,145 + 2,195,356,748 + 38,941,733 + 22,093,120 + 33,241,754 +
7,194,542,922 + 100,082,897,068 =

Answer:

Both cultures will have the same population after 11 hours.

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for population growth is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

In which P(0) is the initial population and r is the growth rate, as a decimal.

A culture of 100 bacteria grows at a continuous rate of 20%.

This means that [tex]P(0) = 100, r = 0.2[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P_{1}(t) = 100(1+0.2)^t[/tex]

[tex]P_{1}(t) = 100(1.2)^t[/tex]

The other culture starts to hours later, and we want to take that time as a parameter. So

[tex]P_{1}(2) = 100(1.2)^2 = 144[/tex]

Which means that when culture 2 growth starts, the population size of culture 1 is described by the following equation:

[tex]P_{1}(t) = 144(1.2)^t[/tex]

Two hours later 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate.

This means that [tex]P(0) = 60, r = 0.3[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P_{2}(t) = 60(1+0.3)^t[/tex]

[tex]P_{2}(t) = 60(1.3)^t[/tex]

After how many hours do both cultures have the same population?

This is t for which:

[tex]P_{1}(t) = P_{2}(t)[/tex]

So

[tex]144(1.2)^t = 60(1.3)^t[/tex]

[tex]\frac{(1.3)^t}{(1.2)^t} = \frac{144}{60}[/tex]

[tex](\frac{1.3}{1.2})^t = \frac{144}{60}[/tex]

[tex]\log{(\frac{1.3}{1.2})^t} = \log{\frac{144}{60}}[/tex]

[tex]t\log{\frac{1.3}{1.2}} = \log{\frac{144}{60}}[/tex]

[tex]t = \frac{\log{\frac{144}{60}}}{\log{\frac{1.3}{1.2}}}[/tex]

[tex]t = 11[/tex]

Both cultures will have the same population after 11 hours.

Answer:

x = 7, x = 5

Step-by-step explanation:

[tex]\frac{3x+3}{8}[/tex] = 2x - 11 ( multiply both sides by 8 to clear the fraction )

3x + 3 = 16x - 88 ( subtract 3x from both sides )

3 = 13x - 88 ( add 88 to both sides )

91 = 13x ( divide both sides by 13 )

7 = x

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

[tex]\frac{4x-6}{7}[/tex] = 2 ( multiply both sides by 7 )

4x - 6 = 14 ( add 6 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

3x + 3 / 8 = 2x - 11

Multiply both sides by 8

8 × ( 3x + 3 / 8 ) = 8 × ( 2x - 11 )

3x + 3 = 16x - 88

Add both sides 88

3x + 3 + 88 = 16x - 88 + 88

3x + 91 = 16x

Subtract both sides 3x

3x - 3x + 91 = 16x - 3x

91 = 13x

Divide both sides by 13

91 ÷ 13 = 13x ÷ 13

7 = x

x = 7

_________________________________

4x - 6 / 7 = 2

Multiply both sides by 7

( 4x - 6 / 7 ) × 7 = 2 × 7

4x - 6 = 14

Add both sides 6

4x - 6 + 6 = 14 + 6

4x = 20

Divide both sides by 4

4x ÷ 4 = 20 ÷ 4

x = 5

Answer:

3.15 ft

Step-by-step explanation:      

                                                                                              V

Volume of a cylinder:  πr²h.  Solving for r², we get r² = ---------

                                                                                             πh

Here, we get r² = (117.1 ft³) / (3.14·15 ft) = 2.48 ft² and r = √(2.48 ft²), or

1.58 ft, so that the diameter is 2r, or 3.15 ft

The diameter of the base of the cylinder is 3.15 ft.

Answer:

$1.59

Step-by-step explanation:

monthly finance charge = average daily balance x monthly interest

monthly interest = 14,99% / 12 = 1.249%

1.249% x $127.50 = $1.59

Answer:

lateral area = pi x radius x slant height

slant height = 40^2 + 30^2 = 1600 + 900= [tex]\sqrt{2500}[/tex] = 50

3.14 x 30 x 50 = 4710m^3

Hope that answers your question

Don't hesitate to leave a comment if you are confused about something

Step-by-step explanation:

Answer:

(5y+3) x (y-2)

Step-by-step explanation:

5y^2-7y-6

5y^2+3y-10y-6

y(5y+3(-2(5y+3)

(5y+3) x (y-2)

Answer:

the answer is this! understand

Answer:

Step-by-step explanation:

7

3 = 7 - 4

-1 = 3 - 4

-5 = -1 - 4

so the 5th:  -5 - 4 = -9

     the 6th:   -9 - 4 = -13

and the 7th:   -13 - 4 = -17

Answer:

1/3

Step-by-step explanation:

Take the second term and divide by the first

9/27 = 1/3

Take the third term and divide by the second

3/9 = 1/3

Check each subsequent ratio, we can see the common ratio is 1/3

Answer:

Negative correlation.

Step-by-step explanation:

Negative correlation means that as x increases, y decreases

Positive correlation means that as x increases, y also increases.

No correlation means that neither of the two above cases happens.

In the graph, we can see that on the right (when x is negative) the general y values are larger.

As x increases, the y-values decrease.

(Particularly, we could adjust these data with a linear equation with a negative slope)

Then this is a negative correlation.

Answer:

4 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The additive inverse is the value that must be added to the number to give zero.

- 4 [tex]\frac{1}{4}[/tex] + 4 [tex]\frac{1}{4}[/tex] = 0

           ↑ additive inverse

Answer:

100%

Step-by-step explanation:

Answer:

1.55

Step-by-step explanation:

Answer:

1331 ft³

Step-by-step explanation:

The volume of a cube = (edge length)³

From the above question,

Edge length = 11 ft

The volume of the cube = (11 ft)³

= (11 ft × 11 ft × 11 ft)

= 1331 ft³

The volume of the cube = 1331 ft³

Answer:

74.5

Step-by-step explanation:

Answer:

The second, 16^3/2

Step-by-step explanation:

The first is equal to 16

The second is equal to 64

The third is equal to 16

The fourth is equal to 16

The required, greatest volume among the given number is [tex]16^{3/2}[/tex].

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
The given number,
∛64² simplified to 16,
[tex]16^{3/2}[/tex] simplified to 64.
√16² simplified to 16
∛8⁴ simplified to 16

Thus, the required, greatest volume among the given number is [tex]16^{3/2}[/tex].

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ3

Answer:the photo is to bleary

Step-by-step explanation:

Answer: It’s UNBIASED!

Step-by-step explanation:

Answer:

7/12 < 2/3 < 17/24 < 3/4

Step-by-step explanation:

least to greatest

Answer:

8.375

Step-by-step explanation:

5.75,6, 6.5, 6.75, 7, 7.5, 8, 8, 8.25, 8.25, 8.5, 8.75, 9, 9.25, 9.25, 9.5, 10, 10.25, 11, 13.75

8.25 + 8.5 = 16.75

16.75/2 = 8.375

Answer:

x = 31

Step-by-step explanation:

The two triangles are similar, so [tex]\triangle{NPO} \sim \triangle{YZO}[/tex].

Vertex N matches up with vertex Y.

Vertex P matches up with vertex Z.

Vertex[tex]\frac{NO}{YO}=\frac{1}{4}\\\\\frac{x}{124}=\frac{1}{4}\\\\4x=124\\\\x=31[/tex] O matches up with itself.

Corresponding sides are in proportion.  To find the proportion between the two triangles, you use known sides from each.

[tex]\frac{NP}{YZ}=\frac{23}{92}=\frac{1}{4}[/tex] meaning the small triangle is 1/4 the size of the large one.

To find  x , notice that it is side NO which corresponds to side YO from the large triangle.

Answer:

2.4 pounds

Step-by-step explanation:

19.2 pounds÷ 8 bags= 2.4 pounds per bag

Answer:

keep 5 dollars spending and 1 dollar charity

Step-by-step explanation:

the rest don't add up to 6 dollars and that is all the money he has.

Answer: Isaiah is correct because you can never be sure whether it’s gonna be a queen but you can be sure that the card could be red

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The slope of the line through (-3, 2) and (1,10) can be found by lining up the point's vertically and subtracting then putting 2nd difference on top of first.

(1,10)

Minus

(-3,2)

-------

8/4=2

The slope is 2.