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Jen walked 10 laps. Which measurement could show how far she walked?

1 lap = 400 meters.

1. 4 centimeters
2. 4 meters
3. 4 kilometers

The answer is... 4 kilometers

a) The initial size of the culture was approximately 255.5.

b) The doubling period is approximately 6.1 minutes.

c) The population after 120 minutes is approximately 26967.

d) The population will reach 14000 after approximately 114.2 minutes.

We can use the formula for exponential growth, N(t) = N0 * \(e^{(kt)}\), where N(t) is the population at time t, N0 denotes the population at the beginning, k denotes the growth rate, and e denotes the natural logarithm base.

a) To solve for the initial size of the culture, we can use the fact that the count was 600 after 15 minutes and 2000 after 30 minutes. We know that after 15 minutes, N(15) = 600, and after 30 minutes, N(30) = 2000. We can use these values to solve for N0 and k:

N(15) = N0 *\(e^{(k15)}\)

600 = N0 * \(e^{(k15)}\)

N(30) = N0 * \(e^{(k30)}\)

2000 = N0 *\(e^{(k30)}\)

Dividing the second equation by the first, we get:

2000/600 =\(e^{(k30)}\) /\(e^{(k15)}\)

3.33 = \(e^{(k*15)}\)

After calculating the natural logarithm of both sides, we arrive at:

ln(3.33) = k*15

Solving for k, we get:

k = ln(3.33) / 15

k ≈ 0.1136

Substituting k into either of the original equations, we can solve for N0:

600 = N0 * \(e^{(0.1136*15)}\)

N0 ≈ 255.5

Therefore, the initial size of the culture was approximately 255.5.

b) To find the doubling period, we can use the fact that the population doubles when t increases by a certain amount. Let T be the doubling period so that N(2T) = 2N0. Substituting into the formula for exponential growth, we get:

2N0 = N0 * \(e^{(k2T)}\)

2 = \(e^{(k2T)}\)

When we take the natural logarithm of both sides, we obtain:

ln(2) = k*2T

T = ln(2) / (2k)

T ≈ 6.1 minutes

Therefore, the doubling period is approximately 6.1 minutes.

c) To find the population after 120 minutes, we can use the formula for exponential growth:

N(120) = N0 * \(e^{(k120)}\)

N(120) ≈ 255.5 * \(e^{(0.1136120)}\)

N(120) ≈ 26967

Therefore, the population after 120 minutes is approximately 26967.

d) To find when the population will reach 14000, we can set N(t) = 14000 and solve for t:

14000 = 255.5 * \(e^{(0.1136*t)}\)

t = ln(14000/255.5) / 0.1136

t ≈ 114.2 minutes

Therefore, the population will reach 14000 after approximately 114.2 minutes.

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Using division, we can prove that there are models that we can use to prove 7 divided by 2 is = 7/2.

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many groups will be created, for instance, if a sports event requires that 30 students be divided into groups of 5 students. The division operation makes it simple to tackle such issues. Divide 30 by 5 in this case. The outcome is 30 x 5 = 6. There will thus be 6 groups, each with 5 pupils. By multiplying 6 by 5, which yields the initial figure of 30, you can confirm this value.

Here in the question,

We have to model to find 7 divided by 2 = 7/2.

For the two math classes, 7 pizzas have been delivered.

Half of the first pizza is distributed to each class.

A half of the second pizza is distributed to each class.

Third pizza, cut in half, with half going to each class.

Continue until each class receives 7 halves, or 7/2, of the pizzas that were delivered.

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ANSWER:

-11

STEP-BY-STEP EXPLANATION:

We have that the winner has a score of -3, and the second place, 8 points behind, therefore, the score of the second place would be:

Therefore:

The score is -11

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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When 1 gallon of gas has been used, the car will travel 30 miles as per the graph - speculation.

The unit rate is 30miles/gallon as per the graph speculation which is given in the question.

In order to speculate the graph, look at the units at the x-axis and y-axis,, and with the help of the relation given between the axis, you can speculate the graph.

Now, on the graph when the value of gallons used is 1/2, the miles traveled by car is 15 miles.

Therefore, with the help of the unitary method if 1/2 gallon is used for 15 miles, then 1 gallon is used for 30 miles ie. doubling both units.

Now, since the unit rate is defined as miles/gallon and in the above step, we derived that 30 miles are used for a gallon, hence, the rate is 30 miles/gallon.

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Answer:

32%

Step-by-step explanation:

The employer has paid 68% of you premium, so there is 100%-68% = 32% remaining

The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given are two sets of ratios 2, _, _ and 3, 1, 8.

If we observe the first value of the first and second ratio we see that

The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.

So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.

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4/10 or 2/5 simplified

Hope this helps you out!

Answer:

The rule: Adds twice as much as the previous number added

Next number: 38

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The rule is every time you add 2 so 6 plus 2 equals 8 them you would do 8+4=12. your counting by 2 as u go up the line.

Answer:

neither

Step-by-step explanation:

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

Answer:

slope=2

Step-by-step explanation:

y-y=m(4-3)

5-3=m(4-3)

2=m(1)

2/1=m

m=2

Answer:

\(-8,+735\)

Step-by-step explanation:

The lowest point in New Orleans is 8 feet below sea  level.

This can be represented numerically using \(-8\)

(negative sign denotes below sea level)

The highest point in Chicago is 735 feet above sea  level.

This can be represented numerically using \(+735\)

(positive sign denotes above sea level)

Answer:

This is correct but if some people are confused it’s a negative integer and a positive integer

Step-by-step explanation:

Answer:

the larger number is 50

Step-by-step explanation:

3:5

×10

30:50

30+50=80

Answer:

I think the larger number would be 50

Step-by-step explanation:

I could be wrong but im pretty sure the larger number is 50.

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Have a GREAT day!!!

Answer:

0.85714286

Step-by-step explanation:

Answer:

x = 1.4

Step-by-step explanation:

6 - 2x = 8(x -1)

6 - 2x = 8x - 8

collecting like terms

-2x - 8x = -8 - 6

-10x = -14

10x = 14

dividing both sides by 10

x = 14/10

x = 1.40 (2d.p)

please mark brainliest

Answer:In my opinion B.0.005 is the correct answer

Step-by-step explanation:

hope it will help you

The three numbers before 1022₅ are 1014₅, 1020₅, 1021₅ while the three numbers after 1022₅ are 1023₅, 1024₅, 1030₅

The number is given as

1022₅

As a general rule in number base.

If the base of a number is n

The highest digit in any number in that base is n - 1

This means that the highest digit in base 5 is 4

Using the above as a guide, the three numbers before 1022₅ are 1014₅, 1020₅, 1021₅ while the three numbers after 1022₅ are 1023₅, 1024₅, 1030₅

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Answer:

\( 14y + 9 \)

Step-by-step explanation:

Perimeter of the given triangular above = sum of all its sides.

\( = (y + 9) + 2y + (4y - 1) = y + 9 + 2y + 4y -1 \)

Collect like terms

\( = y + 2y + 4y + 9 - 1 \)

\( = 7y + 8 \)

If Bob creates a new triangle that is 7 less than twice of the perimeter of the triangle above, the expression of the new triangle would be:

\( 2(7y + 8) - 7 \)

Simplify

\( 2*7y + 2*8 - 7 \)

\( 14y + 16 - 7 \)

New perimeter = \( 14y + 9 \)

The correct answer will be option b

let x= 5.764764               (1)

multiply both the sides by 1000

1000x = 5764.764              (2)

now substract equation one from equation (2)

999x =  5764

x = 5764/999  

In mathematics, a rational number is a number that can be expressed as the quotient or fraction

p

/

q

of two integers, a numerator p and a non-zero denominator q.[1] For example,

−3

/

7

is a rational number, as is every integer (e.g. 5 =

5

/

1

). The set of all rational numbers, also referred to as "the rationals",[2]

A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example:

3

/

4

= 0.75), or eventually begins to repeat the same finite sequence of digits over and over (example:

9

/

44

= 0.20454545...).[6] This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones

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Answer:

16383

Step-by-step explanation:

El primer término de la progresión geométrica es 3 y lo llamaremos \(a\).

Se tiene que una progresión geométrica es de la forma:

\(a, ar, ar^2, ar^3, ar^4, \cdot \cdot \cdot\)

Donde \(r \neq 0\) y es la proporción es común. Por lo tanto si el séptimo número de la sucesión es 12.288 este se puede re-escribir como:

\(ar^6 = 12.288\)

Si se resuelve la ecuación para hallar \(r\) se tiene

\(r = \sqrt[6]{\frac{12.288}{a} } = \sqrt[6]{\frac{12.288}{3} } = \sqrt[6]{ 4096} = 4\)

Ahora se halla cada número de la progresión geométrica entre 1 y 7 para finalmente sumarlos

\(ar^0+ar^1+ar^2+ar^3+ar^4+ar^5+ar^6\)

\(3+12+48+192+768+3072+12288\) = 16383

Por lo tanto la sumatoria de los primeros \(7\) términos de la sucesión son 16383

Answer:

3/5=0.6

_

4/9=0.4

_

11/12=0.916

Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.

To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.

Let's calculate the daily balances for each day:

Day 1: Closing Balance = $850

Day 8: Closing Balance = $300

Day 16: Closing Balance = $500

Day 24: Closing Balance = $650

To calculate the daily balances, we need to consider the activities that occurred on each day.

On Day 1, there was no activity recorded, so the closing balance remains at $850.

On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.

On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.

On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.

Now, let's calculate the average daily balance:

Sum of daily balances = $850 + $300 + $500 + $650 = $2300

Number of days in the billing period = 31

Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19

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Answer:

5.4 = 7.56

1.5 = 2.1

Step-by-step explanation:

Just find the answer for 40% of the given meters.

Answer:

The LCM of 3,4,5 3 , 4 , 5 is 2⋅2⋅3⋅5=60 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 .

Step-by-step explanation:

Answer: 60

3 x 4 x 5 = 60

The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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