Question 3 In a science class everyone study Physics, Chemistry, Biology or combination of any of the three courses. 22 students study Physics and Biology, 21 students study Chemistry and Biology, 18 students study Chemistry and Physics. If only 6 students study pure Chemistry (15 marl 10 students study pure Physics and 8 students study pure Biology, then; a) Find the total number of students in the class. ​

Answer:

(what is the question).

The slope of a line is a measure of its steepness and is defined as the ratio of the change in y (vertical distance) to the change in x (horizontal distance) between any two points on the line.

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (2, 5) and has a slope of -3. The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Substituting the values we have, we get:

y - 5 = -3(x - 2)

Simplifying this equation, we get:

y - 5 = -3x + 6

Adding 5 to both sides, we get:

y = -3x + 11

Therefore, the equation of the line that passes through the point (2, 5) and has a slope of -3 is y = -3x + 11.

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The job would need to pay $500 to cover Cole's expenses.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let's define some variables to represent the unknowns in this problem:

Let x be the number of hours that the server will work at the next job.

Let y be the total amount of money that Cole will make from the next job.

With these variables, we can set up a system of equations:

The cost of the equipment and server hire is $100 plus the server's hourly wage multiplied by the number of hours worked:

100 + 16x = total cost

The amount that Cole will make from the next job is the base pay of $50 plus the server's hourly wage multiplied by the number of hours worked:

y = 50 + 18x

We want to find the value of y that will make up for the $100 expense. In other words, we want to find the value of x that satisfies the equation:

total cost = y

Substituting the second equation into the first equation, we get:

100 + 16x = 50 + 18x

Solving for x, we get:

x = 25

Substituting x = 25 into the second equation, we get:

y = 50 + 18(25) = 500

Therefore, the job would need to pay $500 to cover Cole's expenses.

We can graph the two equations to visualize the solution:
   y = 50 + 18x          y = 100 + 16x

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

x = 0 |        50      |   |        100      |

    |               |   |               |

    |               |   |               |

    |               |   |               |

    |               |   |               |

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

              25                      25

The point where the two lines intersect is (25, 500), which represents the solution to the system of equations.

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Answer:

[tex]\frac{-2(24t-25)}{45}[/tex]

Step-by-step explanation:

In order to find the expression, you have to read the problem from left to right and make sure to follow PEMDAS.

[tex](-\frac{7}{5} * t+\frac{2}{9})-(-\frac{1}{3}*t+\frac{4}{3})\\\\\\(-\frac{7t}{5} +\frac{2}{9} )-(-\frac{t}{3} +\frac{4}{3} )\\\\(-\frac{7t}{5} *\frac{9}{9} +\frac{2}{9} *\frac{5}{5} )-(\frac{-t+4}{3} )\\\\(-\frac{63t}{45} +\frac{10}{45} )+\frac{t-4}{3} \\\\\frac{-63t+10}{45} +\frac{t-4}{3} \\\\\frac{-63t+10}{45}*\frac{3}{3}+\frac{t-4}{3}*\frac{45}{45}\\\\\frac{3(-63t+10)}{135}+\frac{45(t-4)}{135}\\\\\frac{-189t+30}{135}+\frac{45t-180}{135}\\\\\frac{-189t+30+45t-180}{135}[/tex]

Once you have it combined into only one expression, simplify the expression.

[tex]\frac{-189t+30+45t-180}{135}\\\\\frac{-144t-150}{135}\\\\\frac{-6(24t-25)}{135}\\\\\frac{-2(24t-25)}{45}\\\\[/tex]

Answer:

200ft²

Step-by-step explanation:

SA = 8(15) + (8+15+17) 20

= 120+ (4)(20)

= 120+80

= 200ft²

Answer: x-2

Use A=Lw

A/L=w

if you factor and cancel, you are left wirh x-2.

The right number that fits the sequence 54 , 48 , 18 , 24 , 6 , 12 , is 2

To find the next number in the sequence, we need to look for a pattern in the given numbers.

So, we have

54 .. 18 .. 6 ... division by 3

48 .. 24 .. 12 .. division by 2

So, it seems that we are dividing each pair of consecutive numbers by a certain factor.

So, the factor by which we are dividing each pair of consecutive numbers seems to be decreasing by a factor of 3 each time, for the first sequence.

Therefore, the next number in the sequence should be:

6/3 = 2

So, the complete sequence is:

54, 48, 18, 24, 6, 12, 2

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We need to mix 3.2 units of the 25% orange juice with 0.8 Units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

The first thing we need to do is figure out how much of each type of orange juice we need to mix together to get the desired 25% concentration. Let's call the amount of the 25% orange juice "x" and the amount of the 100% orange juice "y".

We know that the total amount of juice we want to end up with is "4" (since the function f(x) is equal to 4 + 2). So we can write an equation based on that:

x + y = 4

We also know that we want the final concentration to be 25%, which means that the amount of pure orange juice in the mixture should be 25% of the total volume. To calculate that, we can use the formula:

0.25 = (0.25x + y) / 4

Simplifying that equation, we get:

0.25x + y = 1

Now we have two equations with two unknowns (x and y), which we can solve using substitution or elimination. I'll use substitution here:

x = 4 - y (from the first equation)
0.25(4 - y) + y = 1 (substituting for x in the second equation)
1 - 0.25y + y = 1
0.75y = 0
y = 0

Uh-oh, that's not good. It looks like we can't use any of the 100% orange juice, or we'll end up with a concentration greater than 25%. Let's double-check our equations and see if there's a mistake.

x + y = 4
0.25x + y = 1

Hmm, it looks like we made a mistake in the second equation. The 0.25x term should be multiplied by the concentration of the 25% orange juice, which is 0.25 (or 25% as a fraction). So the correct equation should be:

0.25(0.25x) + y = 1

Now let's solve for y:

0.0625x + y = 1
y = 1 - 0.0625x

Substituting that into the first equation, we get:

x + (1 - 0.0625x) = 4
0.9375x = 3
x = 3.2

So we need to mix 3.2 units of the 25% orange juice with 0.8 units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

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Answer:

B

Step-by-step explanation:

Given:

1 furlong has 660 feet

1 yard has 0,5 fathom

Find:

How many fathoms are there in one furlong?

.

We know that 1 yd has 3 ft, that means:

There's 660 ft in one furlong and 3 ft in 0,5 of a fathom (6 ft in one fathom)

Now, in order to find how many fathoms are there in one furlong, we have to divide the number of feet in a furlong by the number of feet in a fathom:

[tex] \frac{660}{6} = 110 \: fathoms[/tex]

Answer:

13

Hope this helps!

Step-by-step explanation:

Answer: 2.4

(Hopefully this helps! If you can, please mark me brainliest tomorrow)

Explanation:

We divide the feet by 5280 to find that amount in miles.

12,672/5280 = 2.4

Therefore, the answer is 2.4 miles.

The cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Let x be the number of units of Food A and y be the number of units of Food B.

The objective is to minimize the cost, which is given by the expression 2x + y.

The constraints are:

50x + 20y >= 2400 (minimum vitamin requirement)

30x + 20y >= 1800 (minimum mineral requirement)

10x + 40y >= 1200 (minimum calorie requirement)

x >= 0, y >= 0 (non-negative quantities)

We can use linear programming to solve this problem. The standard form is:

Minimize: 2x + y

Subject to:

50x + 20y >= 2400

30x + 20y >= 1800

10x + 40y >= 1200

x >= 0, y >= 0

Therefore, the minimum cost is $30, and it is achieved by purchasing 30 units of Food B.

To find the number of units of Food A, we can use one of the constraints, for example:

50x + 20y >= 2400

50x + 20(30) >= 2400

50x >= 1800

x >= 36

So, we need at least 36 units of Food A to meet the vitamin requirement.

Since the cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

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to have $110,000 available for the child's education in 12 years at 6% interest, we need to set aside $54,661.55 now. This assumes that the interest rate remains constant over the 12-year period, which may not be the case in reality.

To calculate how much money must be set aside at 6% interest, we can use the future value formula:

[tex]FV = PV*(1 + r)^n[/tex]

where:
FV = future value (the amount of money we want to have in the future)
PV = present value (the amount of money we need to set aside now)
r = interest rate per period (in this case, per year)
n = number of periods (in this case, the number of years until the child starts college)

In this case, we want to have $110,000 in the future, the child is 6 years old now, and we assume that the child will start college at age 18, which is 12 years from now. The interest rate is given as 6% per year.

So, we can plug in the values into the formula:

[tex]110,000 = PV*(1 + 0.06)^12[/tex]

Simplifying the right-hand side of the equation:

110,000 = PV x 2.012594

Dividing both sides by 2.012594:

PV = 110,000 / 2.012594

PV = $54,661.55 (rounded to the nearest cent)

Therefore, to have $110,000 available for the child's education in 12 years at 6% interest, we need to set aside $54,661.55 now. This assumes that the interest rate remains constant over the 12-year period, which may not be the case in reality.
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Answer:

247277 cubic in

Step-by-step explanation:

To create a 95% confidence interval for the proportion of all U.S. adults living with chronic conditions, we can use the following formula:

CI = p ± zsqrt(pq/n)

where:

p is the sample proportion (0.453)

q is the complement of p (1 - p = 0.547)

z is the z-score associated with a 95% confidence level (1.96)

n is the sample size (unknown)

We need to find the sample size (n) in order to calculate the confidence interval. We can do this by using the margin of error formula:

ME = zsqrt(pq/n)

where ME is the margin of error (0.035)

Solving for n, we get:

n = (z^2 * p * q) / ME^2 = (1.96^2 * 0.453 * 0.547) / 0.035^2 = 580.04

Rounding up to the nearest whole number, the sample size is 581.

Now we can substitute the values into the confidence interval formula:

CI = 0.453 ± 1.96sqrt(0.4530.547/581)

CI = 0.453 ± 0.035

The 95% confidence interval for the proportion of all U.S. adults living with chronic conditions is:

CI = (0.418, 0.488)

So we can say with 95% confidence that the true proportion of all U.S. adults living with chronic conditions is between 0.418 and 0.488.

The article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

Lines 25 and 26 contribute to the development of key ideas in the article "Ideas That Work... And Those That Don't" from "When is a Planet Not a Planet? The Story of Pluto" by providing a comparison between two concepts in the field of astronomy. These lines state, "The IAU's decision to demote Pluto was based on a more nuanced understanding of what constitutes a planet."

Firstly, this statement demonstrates that the International Astronomical Union (IAU) relies on a "nuanced understanding" to define what a planet is, emphasizing the importance of precise criteria in categorizing celestial bodies. The IAU's decision-making process shows that some ideas work, such as establishing clear guidelines for planetary classification, while others don't, like the previous, less accurate definition of a planet.

Secondly, by mentioning the demotion of Pluto, the article highlights the impact of changing scientific perspectives on our understanding of the solar system. This reinforces the idea that knowledge is constantly evolving, and sometimes previously accepted ideas must be reconsidered or discarded to make way for more accurate information.

In summary, lines 25 and 26 contribute to the article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

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The lines are tangent,     The value of x is -7.

To determine the value of x, we need to apply the Tangent-Chord Angle Theorem, which states that the measure of an angle formed by a chord and a tangent line is equal to half the difference of the intercepted arc measures.

In this case, let's call the angle WZY as angle A and angle WYX as angle B. According to the given information, angle A = 2x + 9, and angle B = 3x + 6.

Since , we can apply the Tangent-Chord Angle Theorem:

Angle A = (1/2) * (arc WY - arc ZX)

Substitute the given angle measures:

2x + 9 = (1/2) * ((3x + 6) - (2x + 9))

Multiply both sides by 2 to get rid of the fraction:

4x + 18 = (3x + 6) - (2x + 9)

Simplify the equation:

4x + 18 = x - 3

Subtract x from both sides:

3x + 18 = -3

Subtract 18 from both sides:

3x = -21

Divide both sides by 3:

x = -7

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Answer:

x = 10.20240940

Step-by-step explanation:

[tex]x(2x + 9) = 2x^2 + 9x[/tex]

[tex]2x^2 + 9x = 300[/tex]

- 300 on both sides

[tex]2x^2 + 9x - 300 = 0[/tex]

solve using the quadratic formula

[tex]x = -b +/- \ \text{all root} (b)^2 - 4(a)(c) \ \text{All over} \ 2(a)[/tex]

When all the values are plugged in:

When using "+" in the equation you should get:

x = 10.20240940

When using "-" in the equation you should get:

x = −14.70240940

Now.. you CANNOT have a negative length, so you cross of the negative value leaving you one value for x which is 10.20240940.

Your answer is: x   =  10.20240940

Answer:

B. S(15) - S(10) = -40 means that there were 40 less students in 2010 than there were in 2015. This statement is true because S(15) represents the number of students in the year 2015, and S(10) represents the number of students in the year 2010. Subtracting S(10) from S(15) gives the change in the number of students over that 5-year period.

C. S(0) = 2,000 means that there were no students in the year 2000. This statement is also true because S(t) represents the number of students in terms of the number of years after 2000. Therefore, S(0) represents the number of students in the year 2000, which is the starting point for the function.

Step-by-step explanation:

The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.

A graph of y = f⁻¹(x) is shown below.

An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:

0 < a

Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:

[tex]a^x > a^{x+1}[/tex]

1 > a

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The mean of the remaining stock is 5

To find the mean amount of remaining stock, we need to add up the amounts of remaining stock for each garment and divide by the total number of garments.

So, we can start by adding up the amounts of remaining stock:

5 + 4 + 5 + 3 + 8 + 5 + 5 = 35

Now we can divide by the total number of garments (which is 7) to find the mean:

35 / 7 = 5

Therefore, the mean amount of remaining stock is 5.

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Answer:

3.17

Step-by-step explanation:

First change 63.4 to 634/10

Then simplify

You get 317 over 5 then divide by 20 and get

3.17000

Then round

Answer:

center:(0,0)

Radius:7

Step-by-step explanation:

the equation of circle:

(x-h)^2+(y-k)^2=r^2

the point h and k are the center of the circle
(h,k)  ———-> (0,0)

since r^2 =49

So, the radius will be the square root of that number
[tex]r^{2} =49[/tex]

[tex]\sqrt{r^{2} } =\sqrt{49}[/tex]

[tex]r=7[/tex]

Answer:

Let's start with the distance each person covers in 3 minutes.

Beth's distance = 70 meters/minute x 3 minutes = 210 meters

Liz's distance = 60 meters/minute x 3 minutes = 180 meters

Now we can find their distance apart after 3 minutes.

Distance apart = Initial distance - distance covered

Distance apart = 520 meters - (210 meters + 180 meters)

Distance apart = 520 meters - 390 meters

Distance apart = 130 meters

Therefore, Beth and Liz are 130 meters away from each other after walking towards each other for 3 minutes.

absolute value inequality |x - 2| <= 7 and (x <= 9 or x >= -5)

To create an absolute value inequality that has the solution set x < 9 or x >= -5, we first need to find the midpoint between -5 and 9, which is:

Midpoint = (-5 + 9) / 2 = 2

now, we need to find the distance between the midpoint and either endpoint.

Distance = |9 - 2| = 7

Now we can use the formula:

|x - b| <= c

where b is the midpoint and c is the distance.

putting the values we found,

|x - 2| <= 7

To get the solution set x < 9 or x >= -5, we can split this inequality into two parts:

x - 2 <= 7 or -(x - 2) <= 7

Simplifying each part, we get:

x <= 9 or x >= -5

Combining the two inequalities we get :

|x - 2| <= 7 and (x <= 9 or x >= -5)

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There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

Multiplication is a mathematical operation that involves combining two or more quantities to find their total or product. It is often represented by the "x" symbol or the multiplication sign "⋅". Multiplication is a fundamental operation in arithmetic and is used to calculate the total or result of repeated addition or groups of equal quantities.

The product of the digits being 84 implies that the possible combinations of digits are limited to those whose product is 84. The prime factorization of 84 is 2^2 * 3 * 7. Since the digits must be increasing from left to right and cannot repeat, the possible combinations of digits are:

1, 2, 42

1, 3, 28

1, 4, 21

2, 3, 14

2, 6, 7

So, there are 5 possible combinations for Jacob's lock combination.

Therefore, There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

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1. The each ingredient amount will be multiplied by 2.5.

2. [tex]\frac{5}{8}[/tex] ounces of yeast will make 30 rolls.

3.  [tex]\frac{5}{6}[/tex] cup of powdered milk will make 30 rolls.

4. 15 tablespoons of butter will make 30 rolls.

5.  [tex]\frac{15}{2}[/tex] more cups of bread flour than whole wheat flour will be needed to make 30 rolls.

6. The original recipe has been multiplied by 1.5 and this will serve 18 people.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." Quotient, product, sum, and difference are the mathematical operations that come after division, multiplication, addition, and subtraction.

1. We are given that the given recipe makes 12 rolls.

In order to make 30 rolls, the amount will be multiplied by 2.5 because when 12 is multiplied by 2.5, we get 30.

2. For 12 rolls, [tex]\frac{1}{4}[/tex] ounce package is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{4}[/tex] * 2.5 = [tex]\frac{5}{8}[/tex]

So,  [tex]\frac{5}{8}[/tex] ounces of yeast will make 30 rolls.

3. For 12 rolls, [tex]\frac{1}{3}[/tex] cup of powdered milk is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{3}[/tex] * 2.5 = [tex]\frac{5}{6}[/tex]

So,  [tex]\frac{5}{6}[/tex] cup of powdered milk will make 30 rolls.

4. For 12 rolls, 6 tablespoons of butter is required.

So, using the multiplication operation, we get

⇒ 6 * 2.5 = 15

So,  15 tablespoons of butter will make 30 rolls.

5. 4. For 12 rolls, 3 [tex]\frac{1}{2}[/tex] cups of bread flour is required.

So, using the multiplication operation, we get

⇒ 3 [tex]\frac{1}{2}[/tex]  * 2.5 = [tex]\frac{35}{4}[/tex]

Similarly, for 12 rolls,  [tex]\frac{1}{2}[/tex] cup of wheat flour is required.

So, using the multiplication operation, we get

⇒ [tex]\frac{1}{2}[/tex]  * 2.5 = [tex]\frac{5}{4}[/tex]

Now, using the subtraction operation, we get

⇒ [tex]\frac{35}{4}[/tex] -  [tex]\frac{5}{4}[/tex] =  [tex]\frac{30}{4}[/tex]

⇒ [tex]\frac{35}{4}[/tex] -  [tex]\frac{5}{4}[/tex] = [tex]\frac{15}{2}[/tex]

So, [tex]\frac{15}{2}[/tex] more cups of bread flour than whole wheat flour will be needed to make 30 rolls.

6. Let the number be x.

So,

⇒ [tex]\frac{1}{4}[/tex]x = [tex]\frac{3}{8}[/tex]

⇒ x = 1.5

So, the original recipe has been multiplied by 1.5.

Now,

⇒ Number of people served = 12 * 1.5

⇒ Number of people served = 18

So, this will serve 18 people.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Question:

Recipe:

Cinnamon Rolls

makes 12 rolls

1/4 -ounce package active dry yeast

1 cup warm water

3 tablespoons molasses

1/3 cup powdered milk

1 egg yolk,beaten

1 egg white, beaten

3 1/2 cups bread flour, divided

6 tablespoons butter, melted and divided

1 teaspoon salt

1/2 cup whole wheat flour

1/3 cup raisins

1 large egg, beaten

​​​​​​​1/4 cup water

You will use the recipe above to answer the following questions:

Respond to the questions about the second recipe:

1. This recipe makes 12 rolls, but you need to make 30 rolls. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?

2. How many ounces of yeast will you need to make 30 rolls?

3. How many cups of powdered milk will you need to make 30 rolls?

4. How many tablespoons of butter will you need to make 30 rolls?

5. How many more cups of bread flour than whole wheat flour will you need to make 30 rolls?

6. notice that the original recipe calls for 1/4 cup of water. If you put in 3/8 cup of water, by how much have you multiplied the original recipe? How many people will your new recipe serve?

It would take approximately 1.3 hours for 12 rice to reach the velocity of Earth's orbit at a velocity of 23 km/hr.

The velocity of Earth's orbit around the sun is approximately 30 km/s.

To determine how many hours it takes for 12 rice to reach this velocity, you must use the formula for calculating average speed:

Average Speed = Total Distance/Total Time

Since the total distance is the speed of Earth's orbit (30 km/s) and the total time is the amount of time it takes to reach this speed, then you can solve for the total time by rearranging the equation:

Total Time = Total Distance/Average Speed

Therefore, the total time it takes to reach the velocity of Earth's orbit is:

Total Time = 30 km/s/23 km/hr

= 1.3 hours

It would take approximately 1.3 hours for 12 rice to reach the velocity of Earth's orbit at a velocity of 23 km/hr.

This is because the average speed of the rice is equal to the total distance (30 km/s) divided by the total time (1.3 hours).

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Rounding to the nearest unit, the average annual rate of change during this time period is 10,797.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable that makes the statement true. Equations are used in many areas of mathematics and science, as well as in everyday life, to model relationships and solve problems.

Here,

To find the average annual rate of change, we need to calculate the total change in subscribers over the 6-year period and divide by the number of years. The total change is the final value minus the initial value, or:

335,244 - 270,461 = 64,783

The number of years is 6.

So the average annual rate of change is:

64,783/6 = 10,797.17

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