A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours​

Answer:

x=8.94 ; y = 1.58; z=2.02

Step-by-step explanation:

solve 10x+4y+12z = 120      →          5x+2y+6z = 60

         8x + 2y +32Z = 160   →           4x+y+16z = 80

To eliminate z multiply first equation by 16 and second equation by 6.

80x+32y+96z = 960

24x+6y+96z =   480

on subtractionwe get 56x+26y = 480

dividing by 2 we get, 28x + 13y = 240

Now we have a given equation 11x + 77y = 220 → x + 7y = 20

solving 28x + 13y = 240 and x + 7y = 20

28x + 13y =240

28x + 216y = 560

subtracting we get, 203y = 320

y = 1.58

x = 8.94

z = 2.02

2[tex]\frac{3}{10\\}[/tex]

Answer: 6y + 5x = 24

Step-by-step explanation:

The formula for calculating  equation of line with two points is given as :

[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = -12

[tex]x_{2}[/tex] = 6

[tex]y_{1}[/tex] = 14

[tex]y_{2}[/tex] = -1

substituting the values into the formula , we have

[tex]\frac{y-14}{x-(-12)}[/tex] = [tex]\frac{-1-14}{6-(-12)}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-15}{18}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-5}{6}[/tex]

cross multiplying , we have :

6(y - 14 ) = -5 ( x + 12 )

6y - 84 = -5x - 60

6y +5x = -60 + 84

6y + 5x = 24

Answer:

y = -5

x = -2

Step-by-step explanation:

x+7y=-37

2x-5y=21

Multiply first equation by -2

-2 × (x + 7y) = -37 ➡ -2x -14y = 74

now add the equation up

2x-5y -2x -14y = 21 + 74 (-2x will eliminate 2x)

-19y = 95 divide both sides by 19

y = -5 we can find the value for x by using this information

x + 7y = -37 replace y by -5

x + 7×(-5) = -37

x = -2

To find out how many times 19 goes into 133, you can perform a simple division. 19 goes into 133 seven times with no remainder.

Dividing 133 by 19 results in 7, which means 19 goes into 133 seven times exactly. This division is a fundamental arithmetic operation, illustrating how many times one number can be evenly divided into another. It's part of the foundation of mathematics and has practical applications in everyday life, from splitting objects into equal groups to determining quantities in various contexts.

In this case, it's evident that 19 is a factor of 133, and understanding this relationship can help in tasks like distributing items evenly or solving problems involving proportions and ratios. Division is a mathematical concept with broad utility and relevance, making it essential in various mathematical, scientific, and real-world scenarios.

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1) 216

2) 1

3) 450 ml

4)15 packs

5)12 sq m

Step-by-step explanation:

Step 1:

1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.

Here we need the 6th term, so the cube of 6 is 216

Step 2 :

2 ) Area of the cube is given as 8000 cubic cm.

Hence side of the cube is 20 cm cube

The radius of the sphere is 20 cm as the diameter is given as 10 cm.

Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1

Step 3 :

3)

Total quantity of the mixture purchased from the chemist is 750 ml

Syrup and alcohol are in the ration 3:2

Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml

Step 4 :

4)

Length and breadth of the given room is 17 m and 15 m

Hence its area is 17 * 5 = 85 sq m.

Size of the tiles is 1 sq m

So for covering 85 sq m we need 85/1 = 85 tiles

Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.

Step 5 :

5)

Surface area of the given  box with length as l, breadth as b and width as w is

2lw+2 lh+2 wh

here we have l,b,w as 3,2,2

so surface area is 3*2*2 = 12 sq m  

Answer:

1) 216

2) 1

3) 450 ml

4)15 packs

5)12 sq m

Step-by-step explanation:

Step 1:

1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.

Here we need the 6th term, so the cube of 6 is 216

Step 2 :

2 ) Area of the cube is given as 8000 cubic cm.

Hence side of the cube is 20 cm cube

The radius of the sphere is 20 cm as the diameter is given as 10 cm.

Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1

Step 3 :

3)

Total quantity of the mixture purchased from the chemist is 750 ml

Syrup and alcohol are in the ration 3:2

Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml

Step 4 :

4)

Length and breadth of the given room is 17 m and 15 m

Hence its area is 17 * 5 = 85 sq m.

Size of the tiles is 1 sq m

So for covering 85 sq m we need 85/1 = 85 tiles

Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.

Step 5 :

5)

Surface area of the given  box with length as l, breadth as b and width as w is

2lw+2 lh+2 wh

here we have l,b,w as 3,2,2

so surface area is 3*2*2 = 12 sq m  

Step-by-step explanation:

Answer: if y is equal to 18 and x is equal to 72

Step-by-step explanation: 18*4=72

Answer: Fills up something like how inflating a ballon fills it with air

Step-by-step explanation:

Hope it helped

Answer:

2:1

Step-by-step explanation:

Answer:60:30

Step-by-step explanation:

90-60=30 so 60 blue to 30 red is 60:30

Answer:

Step-by-step explanation:

The correct fraction is simply 30/7, where 30 is the distance in miles and 7 is the number of days to complete it.

30/7 = 4.286miles daily but since you've asked to have this as a fraction, 30/7miles is good.

Final answer:

To achieve his goal of running 30 miles in a week, Raul should run 30 miles divided by 7 days, which is approximately 4 2/7 (⅔) miles every day.

Explanation:

If Raul wants to run 30 miles this week and he wants to run the same number of miles each day, we need to divide the total miles by the number of days in a week. There are 7 days in a week, so we will divide 30 miles by 7 days.

Using division: 30 miles ÷ 7 days = ⅔ miles per day. The fraction ⅔ represents the number of miles Raul plans to run each day to meet his goal of running 30 miles in a week.

Answer:

96 blueberries

Step-by-step explanation:

x = number of muffins

Since each blueberry is going to contain 12 blueberries, we can multiply 12 by the number of muffins to get the total number of blueberries.

12x

12(8)

96

Answer:

Step-by-step explanation:

-3 3/4, -3, 3 1/10, and then 3 1/3 i think this is correct...sorry if it is wrong though.

Answer:

58/48 to 29/24

Step-by-step explanation:

An easy way that I always remember is that if both the numbers are even, divide by 2. Keep dividing until you get a odd number and then you know that you have your lowest form.

Answer:

Square root of 8.

Step-by-step explanation:

Given:

Number given : 2 to the power of 3 over 2 equal ...

Using the laws of exponent:

We know that:

⇒ [tex]\sqrt{a} = (a)^1^/^2[/tex]  and

⇒ [tex]\sqrt[3]{a}=(a)^1^/^3[/tex]

So,

According to the question:

2 to the power of 3 over 2  = [tex](2) ^3^/^2[/tex]

Using fractional exponent concept where :  [tex]\sqrt[y]{a^x} = (a)^x^/^y[/tex]

This can be re-written as:

⇒ [tex](2^3)^1^/^2[/tex] and [tex]\sqrt{2^3}[/tex] that is equivalent to [tex]\sqrt{8}[/tex]    as  ...[tex]2^3=2\times 2\times 2=8[/tex]

Square root of 8 is our final answer.

Answer:

(48 m^12)/n^8

Step-by-step explanation:

Simplify the following:

3 ((2 m^3)/(n^2))^4

Multiply each exponent in (2 m^3)/(n^2) by 4:

3×2^4 m^(4×3) n^(-2×4)

4 (-2) = -8:

3×2^4 m^(4×3) n^(-8)

4×3 = 12:

(3×2^4 m^12)/(n^8)

2^4 = (2^2)^2:

(3 (2^2)^2 m^12)/(n^8)

2^2 = 4:

(3×4^2 m^12)/(n^8)

4^2 = 16:

(3×16 m^12)/(n^8)

3×16 = 48:

Answer: (48 m^12)/n^8

Answer:

On the screen shot

Step-by-step explanation:

pretty basic. you can't evaluate it to a single digit if there are 2 variables. lmk which variable you are solving for.

Answer:

x = 8

y = 10

Step-by-step explanation:

We are given the equations;

-3x + 4Y = 16

3x - y =14

We are required to solve the two equations simultaneously using elimination

In this case, we will eliminate one unknown;

We eliminate x by adding the two equations;

That is;

-3x + 4Y = 16

3x - y =14

.............................

     3y = 30

       y = 10

Solving for x

3x - (10) = 14

3x = 14 +10

  3x = 24

   x = 8

Therefore, the solution of the equation is x=8 and y=10

Answer:

84m2

Step-by-step explanation:

it is not b because that is only the area of the square inside of the parallelogram i know that for a FACT sorry i answered late.

Answer:

The answer is m = 5

Step-by-step explanation:

Let's solve the proportional equation, this way:

3/m-2 = 7/m+2

3 * (m + 2) = 7 * (m - 2) [Lowest common denominator (m + 2) * (m - 2)]

3m + 6 = 7m - 14

-4m = -14 - 6 (Like terms)

-4m = -20

m = -20/-4

m = 5

The answer is m = 5

The initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]

Suppose you have the following problem:

The population of Naguanagua in 2019 is estimated to be 20,000 people with an annual rate of increase of 4%. Which equation models the population of Naguanagua in t years?

Let:

[tex]P:Population \ of \ Naguanagua \\ \\ t:Number \ of \ years \ since \ 2019 \\ \\ r:Rate \ of \ increase[/tex]

So the population of Naguanagua can be modeled by the following equation:

[tex]P=P_{0}(1+r)^t \\ \\ P_{0}=20,000 \\ \\ r=4\%=0.04 \\ \\ \\ P=20,000(1+0.04)^t \\ \\ P=20,000(1.04)^t[/tex]

So the initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]

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Answer:

15

Step-by-step explanation:

you work it out

Answer:

midpoint (5,4)

Step-by-step explanation:

The midpoint(M) of a segment with endpoints (x₁ , y₁) and ( x₂,  y₂) is

where x₁ = 2 and x₂ = 8

y₁ = 0 and y₂ = 8

M = [tex]\frac{x_1 + x_2}{2} ,\frac{y_1 + y_2}{2}[/tex]

M = [tex]\frac{2 + 8}{2} ,\frac{0 + 8}{2}[/tex]

M = 5 , 4

Based on the number of people dying from both causes and their relationship with each other, we can calculate that the number of people dead from cancer was 300,000 and those from accidents was 60,000.

Assuming x number of people died from accidents, the number that died from cancer would be 5 times that:

= 5x

The number of people dead from accidents is:

360,000 = 5x + x

6x = 360,000

x = 60,000 people

The number dead from cancer is:

= 5x

= 5 × 60,000

= 300,000 people

In conclusion, 60,000 died from accidents and 300,000 people died from cancer.

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Final answer:

To solve the problem, we created two equations: c = 5a and c + a = 360,000. After substituting and solving these equations, we found that 300,000 people died from cancer and 60,000 from accidents.

Explanation:

The question refers to a situation where the number of people dying from cancer is five times the number who died from accidents, and the total deaths from these two causes amounted to 360,000. To solve this, we can set up a system of equations. Let ‘c’ be the number of cancer deaths and ‘a’ the number of accident deaths. We are given:

Substituting the first equation into the second, we get:

Then we substitute the value of ‘a’ back into the first equation to find ‘c’:

Therefore, 60,000 people died from accidents and 300,000 from cancer.

Answer:

9 3/4, 9 3/4, 9.5, 9.125

Step-by-step explanation:

*I converted to decimal form*

9 3/4= 9.75

9.75 is greater than both 9.5 and 9.125, so therefore it is first on the list.

Next, since 9.5 is greater than 9.125, it is arranged next on the list.

9.125 is the only number left, and is clearly the smallest out of all of the numbers shown.

We want to order the given set of numbers from greatest to lest.

The correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

Let's see how to get that.

The given set is:

{9.5, 9 3/4, 9.125, 9 3/4}

Here we can see that we have two times the mixed number (9 3/4).

This can also be written as:

9 + 3/4

And we know that 3/4 = 0.75

Then:

9 + 3/4 = 9.75

Then the mixed number is the largest number.

Then comes the 9.5, and finally the 9.125

Then the correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

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Answer:

49.6 or 49 3/5

Step-by-step explanation:

62/100*80

Simplify the 62/100 (meaning to make it to its simplest terms as possible).

62/100= 31/50

Now we can solve:

31/50*80= 49.6 or 49 3/5

Answer:

Step-by-step explanation divide 62 by 100 and multiply by 80

= 49.6

Answer:

[tex]remainder=2802[/tex]

Step-by-step explanation:

Remainder Theorem: When a polynomial [tex]f(x)[/tex] is divided by [tex](x-a)[/tex] the remainder will be [tex]f(a)[/tex]

[tex]Here \ \ f(x)=x^3+6x^2-20x+450[/tex]

[tex]It\ is\ divided\ by\ (x-12)[/tex]

[tex]Then\ remainder =f(12)\\\\remainder=(12)^3+6(12)^2-20\times12+450\\\\remainder=1728+6\times144-240+450\\\\remainder=1728+864-240+450\\\\remainder=3042-240\\\\remainder=2802[/tex]

Final answer:

To find the remainder of the polynomial f(x) = x³ + 6x² - 20x + 450 when divided by (x - 12), we evaluate f(12) using the Remainder Theorem, which yields a remainder of 2802.

Explanation:

To find the remainder when the function f(x) = x³ + 6x² - 20x + 450 is divided by (x - 12), we use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by (x - a) is f(a). Therefore, to find the remainder of f(x) divided by (x - 12), we evaluate f(12).

Substitute x with 12 into the function:

f(12) = (12)³ + 6(12)² - 20(12) + 450

f(12) = 1728 + 864 - 240 + 450

f(12) = 2802

Thus, the remainder is 2802.

Answer:

time  |   distance

2       | 50

1.5     | 37.5

t        | 25*t

2       | 50

12      | 300

d/25 | d

Step-by-step explanation:

Answer:

Explanation:

The ball is dropped from a height of 900 centimeters.

Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:

Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:

            [tex]a_n=800(0.7)^{n-1}[/tex]

With that formula you can find any term:

             [tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]

Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.

Answer C seams like a likely answer ssa

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You will move the 7 to 18 but bc there is a equal sign you will change the positive sign to negative and just solve -7 plus 18 you will get 11 and that’s b

Answer:

Step-by-step explanation:

18 = 7/b

18b=7

b=7/18