So, a line parallel to y =ax + c will have a slope of
A. a
B. A number not equal to a
C. 1/a

the volume of the apple would increase by ΔVtotal over the five-week period

The volume of the apple is directly proportional to the cube of its radius. Therefore, if the radius increases by 1/8 inch per week for five weeks, the total increase in radius would be 5/8 inches.

To calculate the change in volume, we can use the formula V = (4/3)πr^3.

Initially, let's assume the radius of the apple is r.

After the first week, the radius would be r + 1/8 inches. Therefore, the new volume would be:
[tex]V_1 = (4/3)\pi(r + 1/8)^3[/tex]

To calculate the change in volume, we can subtract the initial volume from the new volume:

[tex]\DeltaV_1 = V_1 - V_0[/tex]

where V0 is the initial volume of the apple.

Similarly, after the second week, the radius would be r + 2/8 inches, and the new volume would be:

[tex]V2 = (4/3)\pi(r + 2/8)^3[/tex]

The change in volume after the second week would be:

ΔV2 = V2 - V1

We can repeat this process for the remaining three weeks and find the total change in volume by adding all the individual changes:

ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ΔV4 + ΔV5

By simplifying this equation, we get:

[tex]\Delta V_{total }=  (4/3) \pi r^3[(r + 1/8)^3 + (r + 2/8)^3 + (r + 3/8)^3 + (r + 4/8)^3 + (r + 5/8)^3 - 5r^3][/tex]

Therefore, the volume of the apple would increase by ΔVtotal over the five-week period.

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The volume of the apple will increase by [tex](4/3)π[(r0 + 5/8)^3 - r0^3][/tex] during the five-week period.

Assuming that the apple is a perfect sphere, we can use the formula for the volume of a sphere:

[tex]V = (4/3)πr^3[/tex]

where V is the volume of the sphere and r is the radius of the sphere.

Let's start by finding the initial volume of the apple. We are not given the initial radius, so let's assume it to be r0.

[tex]V0 = (4/3)πr0^3[/tex]

After one week, the radius increases by 1/8 inch, so the new radius is r1 = r0 + 1/8. The new volume is:

[tex]V1 = (4/3)π(r0 + 1/8)^3[/tex]

After two weeks, the radius increases by another 1/8 inch, so the new radius is r2 = r0 + 2/8. The new volume is:

[tex]V2 = (4/3)π(r0 + 2/8)^3[/tex]

Similarly, after three weeks, the new radius is r3 = r0 + 3/8 and the new volume is:

[tex]V3 = (4/3)π(r0 + 3/8)^3[/tex]

After four weeks, the new radius is r4 = r0 + 4/8 and the new volume is:

[tex]V4 = (4/3)π(r0 + 4/8)^3[/tex]

Finally, after five weeks, the new radius is r5 = r0 + 5/8 and the new volume is:

[tex]V5 = (4/3)π(r0 + 5/8)^3[/tex]

To find how the volume changes during the five-week period, we need to subtract the initial volume from the final volume:

ΔV = V5 - V0

[tex]ΔV = (4/3)π(r0 + 5/8)^3 - (4/3)πr0^3[/tex]

Simplifying this expression, we get:

[tex]ΔV = (4/3)π[(r0 + 5/8)^3 - r0^3][/tex]

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The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Answer:

40 people are currently planning to attend the reunion.

Step-by-step explanation:

If we don't know how many people are coming, we can call that number x.

If those people split the cost ($200) it will be 200/x.

If 10 more people come, the head count is now x+10.

So the cost becomes 200/(x+10)

The cost when more people pitch in is less money per person. If fewer people split the cost its more per person. They are saying the difference here is $1.

So we can write an equation.

200/x = 200/(x+10) + 1

OR

200/x - 1 = 200/(x+10)

Cross multiply. This gives you a quadratic equation so factor to solve or use Quadratic Formula. See image. It shows how to solve by factoring.

see images. There are 2 images.

The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

Step-by-step explanation:

let's first sort the data points from low to high :

42, 68, 70, 72, 74, 75, 79, 80, 82, 83, 84, 85, 86, 87, 91, 92, 94, 95, 97, 98

67.

the mean score is the sum of all data points divided by the number of data points :

1634/20 = 81.7

=> BC is correct

68.

the median is the number in the sorted list, what half of the data points are lower, and the other half higher.

in case of an even number of data points, it is the mean value of the 2 central data points.

in our case these are 83 and 84. the mean value between these two numbers is 83.5.

=> BE is correct

69.

the mode is the most frequent number among the data points.

but all scores appear only once.

so, some say, the mode is the set of all data points.

or, others say, there is no mode (like your teacher, apparently)..

=> ABC is correct.

70.

mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean.

so, now we are creating a new data set : the individual distances of the original data points to their mean value :

39.7, 13.7, 11.7, 9.7, 7.7, 6.7, 2.7, 1.7, 0.3, 1.3, 2.3, 3.3, 4.3, 5.3, 9.3, 10.3, 12.3, 13.3, 15.3, 16.3

the man value for these is the MAD of the original data points :

187.2/20 = 9.36

=> B is correct

71.

the range is the difference between the highest and lowest values in a set of numbers.

so, in our case that is

98 - 42 = 56

=> AD is correct

72.

quartiles are the values that divide a list of numbers into quarters (4 equally long parts).

we have here 20 numbers, so all Qs are between 2 numbers.

Q1 is between the 5th and the 6th number (and again, the mean value between these two numbers is the result) :

Q1 = (74 + 75)/2 = 74.5

=> AE is correct

73.

as above, just for Q3 it is between the 15th and 16th number :

Q3 = (91 + 92)/2 = 91.5

=> DE is correct

74.

the interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

while the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set - so, between Q1 and Q3 :

91.5 - 74.5 = 17

=> E is correct

75.

outliers are extreme values that differ from most other data points in a dataset (much lower or higher than the others).

outliers are therefore values at the extreme ends of a dataset.

often we see at least some of them right away, like 42 in our set.

but are there any others ?

there are some guidelines like building an upper and lower "fence" (or limit), and any value beyond these limits are great candidates for being outliers.

upper fence = Q3 + 1.5 × IQR = 91.5 + 1.5×17 = 117

we have no values higher than 117.

lower fence = Q1 - 1.5 × IQR = 74.5 - 1.5×17 = 49

we have one value (as expected) lower than that (42), which makes this a confirmed outlier.

=> AB is correct.

Answer:

29 cm

Step-by-step explanation:

We Know

Pinocchio’s nose is 9cm long.

His nose grows by 6cm if he lies.

His nose shortens by 2cm if he tells the truth.

He lies 4 times and truth 2 times.

We Take

9 + (6 x 4) - (2 x 2) = 29 cm

So, Pinocchio's nose now is 29 cm.

Answer:

29 cm

Step-by-step explanation:

(6x4) + 9

(6x4) = 24 cm

24 + 9 = 33 cm

(2x2) - 33

(2x2) = 4 cm

4 - 33 = 29 cm

I hope this helps!

The wheel does 1,184 revolutions in the 1700 meters.

To find the number of revolutions we need to take the quotient between the distance and the circumference of the wheel.

The circumference of a circle of diameter D is:

C = 3.14*D

So here we have:

C = 3.14*18in = 56.52 in

And we know that:

1 meter ≈ 39.3701 inches

Then the circumference in meters is:

C = 56.52/39.3701 m = 1.435m

The number of revolutions is:

1700m/1.435m = 1,184

That is the correct answer.

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Answer:

Step-by-step explanation:

First find the circumference:

π × 18 = 3.14 × 18 = 56.52"

56.52÷ 39.3701 inches in one meter = 1.4356 meters for the circumference.

Divide 1700 meters by 39.3701 = 1184.173

round to 1184 revolutions

If a 36-oz bottle of water costs $2. 88, then the cost per ounce is $0.08

Unitary method is a mathematical method used to find the value of a single unit of a quantity, by dividing the total value of the quantity by the number of units.

To find the cost per ounce, we can use the unitary method which involves dividing the total cost by the total number of ounces:

Cost per ounce = Total cost ÷ Total ounces

Total cost of a 36-oz bottle of water = $2.88

Total ounces in a 36-oz bottle of water = 36 oz

Therefore, the cost per ounce of water can be calculated as

Cost per ounce = $2.88 ÷ 36 oz

Cost per ounce = $0.08 per ounce

So the cost per ounce of water is $0.08

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The total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

To calculate how many oranges are used in Bertha's pyramid, we first need to find out how many oranges are in each

layer of the pyramid. Since the base of the pyramid is a rectangle that is 4 oranges by 6 oranges, there are a total of 4 x 6 = 24 oranges in the base layer.

For the second layer of the pyramid, each orange rests on 4 oranges below it.

Since the base layer has 24 oranges, there will be 24 / 4 = 6 oranges in the second layer.

For the third layer, each orange again rests on 4 oranges below it.

So there will be 6 / 4 = 1.5 oranges in the third layer.

Since we cannot have half an orange, we round up to 2 oranges.

Finally, the top layer of the pyramid will consist of a single orange.

Therefore, the total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

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Answer:

40-m=21

40-40-m=21-40

m=21-40

m=-19

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

The value of x in the expression is 3 / 2.

The value of x in the expression can be found as follows:

Therefore, the quotient rule can be used to find the value of quotient x in the expression as follows:

q⁵ × q²ˣ = q¹⁰ ×  q⁶ / q⁸

Using the quotient rule

[tex]A^{x} X A^{y} = A^{x + y}[/tex]

Therefore,

q⁵ × q²ˣ = q¹⁰ ×  q⁶ / q⁸

q⁵⁺²ˣ = q¹⁶ / q⁸

q⁵⁺²ˣ = q⁸

cancel the base

5 + 2x = 8

2x = 8 - 5

2x = 3

divide both sides of the equation by 2

x = 3 / 2

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Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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Answer:

The answer for anle X is 66°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

<x=<y

<x+<y+<w=180

let<x=X

Remember <X=<Y

X+X+48=180

2X+48=180

2X=180-48

2X=132

divide both sides by 2

X=66°

<X=X

<X=66°

Thus, the values of x,y, and z for the similar triangles are obtained:

Part A: y = 6.70; z = 13.41 and x = 6.

Part B: z = 17.88 ; y = 35.77 and x = 32.

Congruent triangles and similar triangles are two distinct but closely related concepts. There are two different kinds of similar triangle problems: those that ask you to determine whether a set of triangles is similar and those that ask you to determine the angles and side length of similar triangles that are missing.

Part A: using similarity of the triangle, taking the ratios of corresponding side.

y/15 = x/z = 3/y

Consider

y/15 = 3/y

y² = 15*3

y² = 45

y = 6.70

Now,

applying Pythagorean theorem:

y² = 3² + x²

x² = y² - 3²

x² = 45 - 9

x² = 36

x = 6

And,

z² = 12² + x²

z² = 144 + 36

z² = 180

z = 13.41

Part B:using similarity of the triangle, taking the ratios of corresponding side.

z/(x + 8) = 16/y = 8/x  ... eq 1

applying Pythagorean theorem:

z² = 16² + 8²

z² = 256 + 64

z² = 320

z = 17.88

Now, from eq 1

z² = 8(8 +x)

320 = 64 + 8x

8x = 320 - 64

x = 256/8

x = 32

Now,

applying Pythagorean theorem:

y² = 16² + x²

y² = 256 + 32²

y² = 1280

y = 35.77

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True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.

An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).

Let's verify the given conditions:

f(x) > 0:

Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.

f'(x) < 0:

To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative

[tex]f'(x) = -e^(-x)[/tex] is  always negative for all x.

f"(x) > 0:

To find the second derivative, apply the chain rule again:

[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.

Thus, it is true that there exists a function f with the given conditions.

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The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.

True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:

1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.

Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.

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A number multiplied by itself.

What is square?

In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.

Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.

The better definition of squares is:

A number multiplied by itself.

In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.

While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.

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The sine ratio of for angle A is 4/5 and the right option is B. 4/5.

Sine ratio is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The formula for the sine ratio of angle A is given in the formula below

Formula:

From the diagram.

Given:

Substitute these values into equation 1

Hence, the right option is B. 4/5.

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The value of the given expression -0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g ) in the simplest form  is equal to  1.8g + 2.6h.

The expression is equal to,

-0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g )

Apply distributive law multiplication over addition.

A ( B + C ) = A × B + A × C

Simplify the expression by first distributing the -0.4 and -0.2 coefficients to the terms inside the parentheses,

= (-0.4 × -6g  + 0.4 × 9h ) -2h - ( 0.2 × -5h  + 0.2 × 3g )

= 2.4g + 3.6h - 2h + h - 0.6g

Combine like terms,

= (2.4g - 0.6g) + (3.6h - 2h + h)

= 1.8g + 2.6h

Therefore, the simplest form of the expression is 1.8g + 2.6h.

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The above question is incomplete, the complete question is:

Rewrite in simplest terms:

− 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g )

Okay, here are the steps:

1) For the new drug group, the mean reduction is 25 points and standard deviation is 3.1.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 25 ± (1.645 * 3.1)

= 24.584 to 25.416

2) For the placebo group, the mean reduction is 18 points and standard deviation is 2.8.

To get the 90% CI, we calculate:

Mean ± (1.645 * SD)

= 18 ± (1.645 * 2.8)

= 17.624 to 18.376

3) Since the CI for the new drug (24.584 to 25.416) lies above the CI for the placebo (17.624 to 18.376), there is evidence that the drug is working.

The other options are incorrect. The CI for the new drug does not lie below the placebo CI, so there is evidence the drug is working, not not working.

Thekey is to compare the CI ranges for the two groups. If the CI range for the new drug group lies above the CI range for the placebo group, that indicates the new drug is likely more effective in reducing blood sugar levels, providing evidence that the drug is working.

Does this help explain the steps? Let me know if you have any other questions!

The parent function which is represented by the given table as required in the task content is; Choice B. f(x) = |x|.

It follows from the task content that the parent function which is represented by the table is to be determined.

On this note, by observation of the function; the values of y represent the positive version of x.

Consequently, it follows that the table represents the absolute value function.

Therefore, Choice B; f(x) = |x| is correct.

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The expanded form of 2d with an exponent of -5 is 32d⁵

2d with an exponent of -5

[tex] {(2d)}^{ - 5} [/tex]

[tex] = \frac{1}{ {(2d)}^{5} } [/tex]

expand

[tex] = \frac{1}{2d \times2d \times2d \times2d \times2d } [/tex]

[tex] = {32d}^{5} [/tex]

Therefore, 2d with an exponent of -5 is 32d⁵

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Answer: question#7 is 7/12

question#8 is 1  3/8

question#5 is 1/2

question#6 is 12

question#9 is 1  1/6

question#10 is 31/40

question#11 is 3/4

Step-by-step explanation: give brainliest

Question #5: Option A, [tex]\frac{1}{2}[/tex]

Question #6: Option A, 12

Question #7: Option A, [tex]\frac{7}{12}[/tex]

Question #8: Option D, [tex]1\frac{3}{8}[/tex]

Question #9: Option D, [tex]1\frac{1}{6}[/tex]

Question #10: [tex]\frac{31}{40}[/tex]

Question #11: [tex]\frac{3}{4}[/tex]

Pls mark brainliest

Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

Answer:

p < -2

Step-by-step explanation:

Answer:

The answer is -2

Step-by-step explanation:

4/5-1/2p>9/5

C.L.T

-1/2p>9/5-4/5

-1/2p>5/5

-1/2p=1

-p/2>1

-p=2

p= -2

Answer:

We can calculate the difference between Lori's and Melissa's purse masses by subtracting Melissa's purse mass from Lori's purse mass:

Lori's purse mass = 16 ounces

Melissa's purse mass = 11 ounces

Difference = Lori's purse mass - Melissa's purse mass

Difference = 16 ounces - 11 ounces

Difference = 5 ounces

Therefore, the difference between Lori's and Melissa's purse masses is 5 ounces.

$682.50

Simple interest only builds on the initial deposit.

Interest Formula

Unlike compound interest, the change per time period is constant for simple interest. This means that simple interest can be calculated through the formula:

In this formula, I represents the amount of interest earned. P is the principle, which is the initial deposit. r is the rate of interest expressed as a decimal. t is the time in years.

Solving For Interest

Now, we can use the information we were given to solve for the amount of interest earned. The question states that the principle is $7,000. From the table, we can tell that the rate is 0.0325. Finally, t is 3 years because 36 months = 3 years. Then, plug these values into the formula.

This means that the account at Victory Bank would earn $682.50 over the course of 3 years.