A population of bacteria doubles every 15 hours. initially, the population of bacteria is 40. What is the population of bacteria after 40 hours? Enter your answer, rounded to the nearest whole number, in the box.

Answer:

Circumcenter O (0.5 , 5)

Step-by-step explanation:

Circumcenter O (x , y)

OA = OB = OC

OA² = (x + 4)² + (y - 3)²

OB² = (x - 5)² + (y - 7)²

OC² = ( x + 4)² + (y - 7)²

OA² = OC² : (x + 4)² + (y - 3)² = ( x + 4)² + (y - 7)²

(y - 3)² = (y - 7)²        y² - 6y + 9 = y² -14y + 49

8y = 40

y = 5

OB² = OC² : (x - 5)² + (y - 7)² = ( x + 4)² + (y - 7)²

x² - 10x + 25 = x² + 8x + 16

18x = 9

x = 0.5

Circumcenter O (0.5 , 5)

The height of a randomly chosen basketball player is a continuous random variable since height is measured and can take on an infinite range of values.

The random variable described, the height of a randomly chosen basketball player, is a continuous random variable. This is because height can take an infinite number of possible values within a range and is measured rather than counted. Unlike discrete random variables, which have countable values such as the number of heads in a coin toss, continuous random variables like height are measured and can include values such as 6'1" or 6'1.5". The values are on a continuous scale, and therefore the probability distribution of a continuous random variable is concerned with the probability of the variable falling within a certain range, rather than taking specific countable values.

Answer: 2

Step-by-step explanation:    Edge 2023

Final answer:

To find the average number from a list of numbers, add up all the numbers and then divide the sum by the total number of numbers.

Explanation:

The question asks for the average number from a given list of numbers. To find the average, you add up all the numbers in the list and then divide the sum by the total number of numbers in the list.

In this case, the average of the numbers 1, 0, 1, 5, 6, 3, and 4 can be found by adding those numbers together (1 + 0 + 1 + 5 + 6 + 3 + 4) and then dividing the sum by 7 (the total number of numbers in the list). So, the average is 4.

Answer:

3R

Step-by-step explanation:

Answer:

B is the answer. ........

Answer:

B

Step-by-step explanation:

it intercepts the y line at -1 and the rise over run is 3

Answer:

187 people

Step-by-step explanation:

340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.

Answer:

187 people

Step-by-step explanation:

340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.

Answer: 3

Step-by-step explanation:

10 had sprinkles and 2 did not which mean there are 12.

So would it be 3 that not have a sprinkles?

I think so.

Answer:

Step-by-step explanation:

Answer: 72 ft

Step-by-step explanation:

We can solve this problem using geometry, if we draw two righ triangles (figure attached):

-One formed by you, assuming you are 6 ft tall, and the ground

-The other formed by the height  of the cliff, the bottom of the cliff and the ground.

Both triangles are congruent, having the mirror as a common vertex, hence we can use the following relation to find :

[tex]\frac{6 ft}{y}=\frac{5 ft}{60 ft}[/tex]

Isolating :

[tex]y=\frac{(60 ft)(6 ft)}{5 ft}=72 ft[/tex] This is the height of the cliff

The calculated height of the cliff is 72 feet.

To determine the height of the cliff, we use a mirror and the property of the reflection of light. Here are the steps to solve the problem:

height of cliff / 60 feet = 6 feet / 5 feet.

    5. Solve for the height of the cliff:

height of cliff = (6 feet / 5 feet) * 60 feet = 72 feet.

Thus, the height of the cliff is 72 feet.

Answer:

24 degrees

Step-by-step explanation:

The distance from 15 degrees to 0 degrees is 15, and the distance from 0 degrees to -9 degrees is 9, so then the total distance from 15 degrees to -9 degrees is (15+9 degrees) which adds up to be 24 degrees

Answer: He left a 27.27272727% tip

To calculate f(-5) for the function f(x)=-x+2, we substitute -5 in place of x, which gives us f(-5) = 7.

To find the value of f(-5) for the function f(x)=−x+2, we simply substitute x with -5:

f(-5) = −(-5) + 2

Now, we perform the operations:

f(-5) = 5 + 2

f(-5) = 7

Therefore, the answer is 7.

Answer:

$24.75  

Step-by-step explanation:

Find the unit rate for 1 gallon, to dothis divide $22 by the 8 gallons of gas. 22/8 is $2.75. now that we know the unit rate, multiply it by 9 for our answer. 2.75*9=24.75,the cost for 9 gallons.

Trevin puts 8 gallons of gas in his car and pays $22. The cost of 9 gallons of gas at this rate is $24.75

Word problems in mathematics involve a careful understanding of the question. It is usually written or expressed in one or more sentences and it requires pupils to apply their arithmetic skills to a real-life issue.

From the information given:

i.e

We are to determine the rate he will pay for 9 gallons. i.e.

From the above two expressions, by cross multiplying, we have:

[tex]\mathbf{x = \dfrac{9 \ gallons \times \$22 }{8 \ gallons}}[/tex]

x = $24.75

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Answer:

At the donut shop, Karley and 24 of her co-workers have split the tip jar. There is $42.48 in the tip jar. How much money does each worker get from the jar?

Answer:

(4+1+2)3= 21

Step-by-step explanation:

you add the cost of snacks then multiply by 3 because there are 3 people to get total cost.

Answer:

4+4+4+1+1+1+2+2+2=25

1. The possible solution for x + y is 8 ⇒ d

2. The possible solution for m - n is 16 ⇒ a

Step-by-step explanation:

Lets explain some notes about the even numbers

1.

∵ x and y are both even whole numbers

∴ Their sum is even whole number

∵ 5 and 9 are odd numbers ⇒ impossible

∵ 4.6 is not a whole number ⇒ impossible

∵ 8 is an even whole number ⇒ possible

∴ x + y could be 8

The possible solution for x + y is 8

2.

∵ n and m are both even whole numbers

∵ m > n

∴ m - n must be positive even whole number

∵ 1/2 is not a whole number ⇒ impossible

∵ 0 is not a positive number ⇒ impossible

   (zero is not positive nor negative)

∵ -2 is not a positive number ⇒ impossible

∵ 16 is a positive even whole number ⇒ possible

∴ m - n could be 16

The possible solution for m - n is 16

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Answer:

250x^26/y^9

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Given

2x - 2y ← factor out 2 from each term

= 2(x - y) ← substitute x - y = 3 into the expression

= 2(3)

= 6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

x - y = 3

2x - 2y

The value of 2x - 2y is 6.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x - y = 3  _____(1)

The value of 2x-2y.

= 2x - 2y

Taking 2 as common.

= 2 (x - y)

From (1) we get,

= 2 x 3

= 6

Thus,

The value of 2x - 2y is 6.

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Expression that gives the ticket cost in dollars for a group of g girls and b boys is (8g + 8b) dollars

Solution:

Given that tickets to play cost $ 8 each

To find: Expression that gives the ticket cost in dollars for a group of g girls and b boys

From given,

cost of 1 ticket = $ 8

Number of girls = g

Number of boys = b

Thus the expression can be framed for total cost as:

Total cost = (number of girls + number of boys)(cost of 1 ticket)

[tex]Total\ Cost = (g + b) \times 8\\\\Total\ Cost = 8g + 8b[/tex]

Thus the expression that gives total cost is (8g + 8b) dollars

Answer:A $35 decrease followed by a $25 increase is less than the original.

A 50% decrease then 33.333% increase is the same.

A 30% increase then 15% decrease is more.

A 50% decrease then 100% increase is the same.

A 70% increase then 50%decrease is less.

Step-by-step explanation:

The solutions are - 0.8 and 1

Step-by-step explanation:

In the quadratic equation ax² + bx + c = 0

Assume that the solutions of the equations are m and n

∵ 5x² - x - k = 0

- By comparing it by the form above

∴ a = 5, b = -1 , c = -k

- Use the rule of the sum of the two solutions above

∵ The sum of the two solutions = [tex]\frac{-b}{a}[/tex]

∴ The sum of the two solutions = [tex]\frac{-(-1)}{5}=0.2[/tex]

∵ The two solutions are m and n

∴ m + n = 0.2 ⇒ (1)

∵ The difference of the two solutions is 1.8

∴ m - n = 1.8 ⇒ (2)

Now we have a system of equations to solve

Add Equations (1) and (2) to eliminate n

∴ 2m = 2

- Divide both sides by 2

∴ m = 1

- Substitute the value of m in equation (1) to find n

∴ 1 + n = 0.2

- Subtract 1 from both sides

∴ n = -0.8

The solutions are - 0.8 and 1

If you want to find the value of k

∵ The product of the solutions is [tex]\frac{c}{a}[/tex]

∴ The product of the solutions = [tex]\frac{-k}{5}[/tex]

∵ m × n = 1 × (-0.8) = - 0.8

- Equate  [tex]\frac{-k}{5}[/tex]  by - 0.8

∴ [tex]\frac{-k}{5}=-0.8[/tex]

- Multiply both sides by -5

∴ k = 4

∴ The equation is 5x² - x - 4 = 0

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Answer:

x = 1; x = -0.8

Step-by-step explanation:

Here is a simpler approach if needed for future students:

5x^2-x-k = 0,

System of Equations: x1 - x2 = 1.8 & x1 + x2 = 1/5 = 0.2 (if x1 and x2 are roots)

Now let's add the two:

x1 - x2 = 1.8

+ x1 + x2 = 0.2

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

2x1 = 2,

x1 = 2/2 = 1

- x2 = 1.8 - 1 = 0.8 => x2 = -0.8

The system of equation is:

x + y = 20

x - y = 4

She has 12 dimes and 8 nickels

Step-by-step explanation:

The given is:

We need to write a system of equations that represents the problem and how

many of each coin she has

Assume that she has now x dimes and y nickels

∵ She has x dimes and y nickels

∵ She has a total of 20 coins

- Add x and y, then equate the sum by 20

∴ x + y = 20 ⇒ (1)

∵ One dime = 10 cents

∵ One nickels = 5 cents

- Multiply x by 10 and y by 5 to find how many cents she has now

∵ She has now (10x + 5y) cents

∵ The dimes were nickels and the nickels were dimes

- Multiply x by 5 and y by 10 to find how many cents she has

   after the change

∴ She had after the change (5x + 10y) cents

∵ The value after the change is less than the value now by

   20 cents

- Subtract (5x + 10y) from (10x + 5y) and equate the difference

   by 20

∴ (10x + 5y) - (5x + 10y) = 20

- Add the like terms in the left hand side

∴ (10x - 5x) + (5y - 10y) = 20

∴ 5x - 5y = 20

- Divide both sides by 5

∴ x - y = 4 ⇒ (2)

The system of equation is:

x + y = 20

x - y = 4

Now we have a system of equations to solve it

Add equations (1) and (2) to eliminate y

∴ 2x = 24

- Divide both sides by 2

∴ x = 12

- Substitute the value of x in equation (1) to find y

∵ 12 + y = 20

- Subtract 12 from both sides

∴ y = 8

She has 12 dimes and 8 nickels

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Answer:

12

Step-by-step explanation:

Answer: 4,690.33

Step-by-step explanation:

The formula for calculating amount is given by :

A = P [tex](1+r)^{n}[/tex]

Where :

A = amount = ?

P = Principal = 3500

r = rate = 0.05

n = number of years  = 6

substituting the given values into the formula , we have

A = 3500[tex](1+0.05)^{6}[/tex]

A = 3500 [tex](1.05)^{6}[/tex]

A = 3500 (1.340095640625)

A = 4690.3347421875

A = 4,690.33

Final answer:

To calculate Colin's investment with compound interest after 6 years, we use the formula for compound interest and determine that he will have £4690.33 to the nearest penny.

Explanation:

To calculate how much Colin will have after 6 years with compound interest, we use the formula for compound interest:

A = P(1 + r/n)nt

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In Colin's case, we have:

P = £3500

r = 5% or 0.05

n is not mentioned, so we assume it is compounded once per year, thus n = 1

t = 6 years

Plugging these values into the formula:

A = £3500(1 + 0.05/1)1×6 = £3500(1 + 0.05)6

A = £3500 × (1.05)6 = £3500 × 1.340095

A = £4690.3325

To the nearest penny, Colin will have
£4690.33 after 6 years.