we want to estimate a population mean using a 99% confidence interval and a random sample of 35 individuals. what is the critical t-score?

So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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Answer:

1-There were about 483 principals in attendance.

2-The college will have about 640 students who prefer pie

3-histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44

4-The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 18, with an median of  16

Hope you get them all right :)

Answer:

it A or B

Step-by-step explanation:

the other two C and D dont make sense to what the question is asking

After 8 seconds, the total surface area of the disturbed water would be increasing at a rate of 14,347,056 cm².

After 8 seconds, we will have 8 concentric circles on the surface of the water. The radius of each circle will be equal to the product of the speed of the wave (20cm/sec) and the time it has traveled (in this case, 8 seconds). Therefore, the radius of the first circle will be 20cm/sec x 8 sec = 160cm.

To find the total surface area of the disturbed water, we need to calculate the area of each of these circles and add them up. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Using this formula, the area of the first circle would be A = π(160cm)² = 80,256 cm². The area of the second circle would be A = π(2 x 160cm)² = 321,024 cm², and so on for each of the 8 circles.

To find the total surface area, we simply add up the areas of all 8 circles:

A = 80,256 + 321,024 + 721,920 + 1,282,176 + 2,004,096 + 2,887,584 + 3,932,160 + 5,137,920

A = 14,347,056 cm²

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Complete Question:

To a pond of water in complete calm, a stone is thrown that causes the formation of concentric circular waves, each wave moves away from the center at a speed of 20cm / sec with what speed is increasing the total surface of the disturbed water after 8 sec?

In the given case, 36 square feet will need to be painted.

To calculate the surface area that needs to be painted, we need to determine the total surface area of both the square prism and the square pyramid, and then subtract the area of the base of the pyramid, as it will not be painted.

The surface area of a square prism with base dimensions of 8 ft by 8 ft and height of 9 ft is:

Top and bottom: 8 ft x 8 ft = 64 sq ft each (2 x 64 = 128 sq ft)

Four sides: 8 ft x 9 ft = 72 sq ft each (4 x 72 = 288 sq ft)

Total surface area of the prism: 2(64 sq ft) + 4(72 sq ft) = 256 sq ft

The surface area of a square pyramid with slant height of 5 ft can be calculated by finding the area of each face and adding them together. Each face is a triangle, and the area of a triangle can be calculated using the formula: (base x height) / 2.

Base: 8 ft x 8 ft = 64 sq ft

Each triangular face: (1/2)(8 ft)(5 ft) = 20 sq ft

Total surface area of the pyramid: 4(20 sq ft) + 64 sq ft = 144 sq ft

Therefore, the total surface area that needs to be painted is:

256 sq ft + 144 sq ft - 64 sq ft = 336 sq ft

So, 336 square feet will need to be painted.

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Answer:

5x+20

Step-by-step explanation:

you are given that y=2x-5 so you can substitue that for the y value.

-3x-4(2x-5) is your new equation. You can further simply it and you will get:

-3x+8x+20

5x+20

The cost of labour per hour is $45.

To find the cost of labour per hour, we need to first subtract the cost of the parts from the total cost to get the cost of the labour.

Total cost - cost of parts = cost of labour

$347.25 - $156 = $191.25

Now we can divide the cost of labour by the number of hours the technician worked on the computer to find the cost of labour per hour.

Cost of labour / Hours worked = Cost of labour per hour

$191.25 / 4.25 hours = $45 per hour

Therefore, the cost of labour per hour was $45.

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The equations that can be used to solve for y are options 2, 3, and 5, and the solution is y = 30.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

Let's assume that the length of the room is y feet. Then, according to the problem, the width of the room is y-5 feet.

The area of the rectangular room is given by the formula:

Area = length x width

We are given that the area is 750 square feet. So we can write:

750 = y(y-5)

Simplifying this equation, we get:

y² - 5y - 750 = 0

This is a quadratic equation that can be solved using the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

where a = 1, b = -5, and c = -750.

Now let's check which of the given options can be used to solve this equation.

Option 1: y(y + 5) = 750

This equation is not equivalent to the quadratic equation we derived above. We cannot use it to solve for y.

Option 2: y² - 5y = 750

This is the same equation we derived above. It can be used to solve for y using the quadratic formula.

Option 3: 750 - y(y - 5) = 0

This equation is equivalent to the quadratic equation we derived above, but it is not in standard form. We can simplify it to y² - 5y - 750 = 0, which can be used to solve for y.

Option 4: y(y - 5) + 750 = 0

This equation is not equivalent to the quadratic equation we derived above. We cannot use it to solve for y.

Option 5: (y + 25)(y - 30) = 0

This is a factorization of the quadratic equation y² - 5y - 750 = 0. It can be used to find the roots of the equation, which are y = -25 and y = 30. However, since the length of the room cannot be negative, the only valid solution is y = 30.

Therefore, the equations that can be used to solve for y are options 2, 3, and 5, and the solution is y = 30.

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To determine the sample size needed to have a % confidence that our sample mean will be within hours of the true mean, we would need to use a formula. Specifically, we would use the formula: n = (Z^2 * s^2) / E^2

Where n is the sample size needed, Z is the z-score associated with the desired confidence level, s is the standard deviation of the population, and E is the margin of error (in this case, the specified difference of hours between the sample mean and true mean).

Assuming we have information about the population standard deviation (s), we can plug in the values for Z, s, and E to find the necessary sample size. For example, if we wanted to be 95% confident that our sample mean would be within 2 hours of the true mean, we would use a Z-score of 1.96 (which corresponds to a 95% confidence level). Let's say the population standard deviation is 5 hours. Plugging in these values, we would get:

n = (1.96^2 * 5^2) / 2^2
n = 96.04

So we would need a sample size of at least 97 in order to be 95% confident that our sample mean would be within 2 hours of the true mean.
To determine the sample size needed to be confident that our sample mean will be within a specific number of hours of the true mean, we need to know the confidence level, standard deviation, and margin of error (in hours). The formula for calculating the sample size is:

n = (Z^2 * σ^2) / E^2

where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation
E = margin of error (in hours)

Once you provide the confidence level, standard deviation, and margin of error (hours), we can plug in the values and calculate the required

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List orders the times from shortest to longest

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

A decimal is a way of representing numbers using a base-10 positional notation system, where each digit represents a power of 10. It is written as a whole number followed by a decimal point and a series of digits representing fractions of 1.

According to the given information:

To order the times from shortest to longest, we need to convert them into a common format, such as a decimal or a common denominator.

First, let's convert the times to a common denominator of 9:

5 1/3 seconds = 16/3 seconds = 48/9 seconds

5 5/9 seconds = 50/9 seconds

5 1/2 seconds = 9/2 seconds = 45/9 seconds

Now we can order the times from shortest to longest:

48/9 seconds = 5 1/3 seconds

45/9 seconds = 5 1/2 seconds

50/9 seconds = 5 5/9 seconds

Therefore, the correct list in order from shortest to longest is:

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

So Bernard's first attempt was the shortest, his third attempt was the second longest, and his second attempt was the longest.

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The given expression in the form ax + b will be (B) 1.8x + 4.1.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

So, we have the expression:

(3.6x-1.4) - (1.8x-5.5)

First, solve it in the form of ax + b as follows:

(3.6x-1.4) - (1.8x-5.5)

3.6x-1.4 - 1.8x+5.5

1.8x + 4.1

So, we have the expression: 1.8x + 4.1

Then, the coefficient and content will be (B) and the correct expression would be 1.8x + 4.1.

Therefore, the given expression in the form ax + b will be (B) 1.8x + 4.1.

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Answer:

$525

Step-by-step explanation:

Jackie starts with $500, and the interest rate is 5% per year.

This means that, after one year, Jackie will have accumulated 5% interest with the $500 she put into the savings account.

Now, we can find 5% of $500 by converting 5% to its fraction form, which is 5/100. 5% of a value means that you need to multiply the fraction (or decimal) by the said value. So, we have:

[tex]\frac{5}{100}[/tex] · 500 =

[tex]\frac{2500}{100}[/tex] =

25

Therefore, the amount of interest she has accumulated in one year is $25. Combined with the money in her savings account, she has $525, since $500 + $25 = $525.

The total distance travelled by the two tortoises is 4.7 yards or 14 feet or 168 inches.

Also the distance between tortoises is 0.5 yards or 1.5 feet or 18 inches

For total distance travelled,

First, let's convert the initial distance between the two tortoises from feet and inches to inches:

1 foot and 6 inches = 12*1 + 6 = 18 inches

Let's also convert the distance traveled by tortoise B from feet and inches to inches:

4 feet and 8 inches = 12*4 + 8 = 56 inches

Now we can use the information given to set up two equations:

distance traveled by tortoise A = 2 * distance traveled by tortoise B

distance traveled by tortoise A + 18 inches = distance traveled by tortoise B + 56 inches

Let's simplify the second equation by subtracting 18 inches from both sides:

distance traveled by tortoise A = distance traveled by tortoise B + 38 inches

Now we can substitute the second equation into the first equation to get:

distance traveled by tortoise B + 38 inches = 2 * distance traveled by tortoise B

Simplifying this equation, we get:

distance traveled by tortoise B = 38 inches

So, after 2 minutes, tortoise B has traveled 56 inches, or 4 feet and 8 inches, and tortoise A has traveled twice that distance, which is 112 inches, or 9 feet and 4 inches.

The total distance traveled by the two tortoises after 2 minutes is the sum of the distances they traveled:

total distance = distance traveled by tortoise A + distance traveled by tortoise B

total distance = 112 inches + 56 inches

total distance = 168 inches = 4.7 yard or 14 feet

For distance between the tortoises,

We can use the same approach as before to solve this problem.

After 2 minutes, we found that tortoise A traveled 9 feet and 4 inches, or 2.8 yards, and tortoise B traveled 4 feet and 8 inches, or 1.5 yards.

Since both tortoises are moving at a constant speed, we can assume that they will continue to travel at the same rate. Therefore, after 5 minutes, tortoise A will have traveled 2.8 yards * (5/2) = 7 yards and tortoise B will have traveled 1.5 yards * 5 = 7.5 yards.

The distance between the two tortoises after 5 minutes is the difference between the distances they traveled:

distance between tortoises = distance traveled by tortoise A - distance traveled by tortoise B

distance between tortoises = 7 yards - 7.5 yards

distance between tortoises = -0.5 yards

Since the distance is negative, we can conclude that after 5 minutes, tortoise B will be ahead of tortoise A by 0.5 yards.

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The correct statement about the graph is,

A graph of two solid lines that intersect at point (4, 0).

Given that;

This system of inequalities models the scenario.

4x + 2y ≤ 16

And, x + y ≥ 4

Now, We can draw the inequalities in graph, we get;

The intersection point of the inequality is, (4, 0)

Thus, The correct statement about the graph is,

A graph of two solid lines that intersect at point (4, 0).

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The Vieth-Müller Circle is an imaginary circle that passes between both retinae and the fixation point.

The Vieth-Müller Circle is an ophthalmology concept that depicts an imaginary circle that passes across the foveas (the primary points of the retinae that are responsible for acute, detailed vision) and the fixation point (the point at which the eyes are directed).

The Vieth-Müller Circle is significant because it helps to explain the phenomenon of binocular vision, which is the ability to perceive depth and three-dimensional space using both eyes together. The circle aids in the definition of the equivalent locations on the two retinae, which are sites that receive visual field information and are critical in combining the images from the two eyes into a single, three-dimensional perception.

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The imaginary circle that passes through both retinae and the fixation point is called the horopter. The horopter is important in visual perception as it represents the set of points in space that stimulate corresponding points on each retina, which is necessary for binocular vision and depth perception.

The Horopter is an imaginary circle that passes through both retinae and the fixation point. In this context:

1. "Imaginary" refers to the fact that the Horopter is a theoretical concept rather than a physical object.
2. "Retinae" are the light-sensitive layers at the back of both eyes, which play a crucial role in processing visual information.
3. "Fixation" is the point where both eyes are focused on a single object in the visual field.

In brief, the Horopter represents a collection of points in the 3D space that are perceived as having the same depth or distance as the fixation point. It helps in understanding binocular vision and depth perception, as points on the Horopter contribute to forming a single, fused image from both eyes.

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The horizontal distance traveled by the rubber band is 4.5 feet

To write and solve an equation to find the horizontal distance traveled by the rubber band if its height is 0.75 feet, substitute f(x) = 0.75 feet into the equation representing the rubber band and solve for x. That is:

f(x) = -x² + 4x + 3

0.75 = -x² + 4x + 3

x² - 4x - 3 + 0.75 = 0

x² - 4x - 2.25 = 0

(x - 9/2)(x + 1/2) = 0       (factorize)

x = 9/2 or x = -1/2

x = 4.5 or x = -0.5

Since distance cannot be negative.

Thus, x = 4.5 feet

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A drill-down report is a type of report that displays a greater level of detail as the user navigates through it.

A drill-down report is a type of report that allows the user to access a greater level of detail as they navigate through it. It is an interactive report that presents a summary of data initially and then allows the user to drill down to more detailed information.

The report provides a visual representation of data that can be explored at different levels of granularity, providing a deeper understanding of the underlying information. Drill-down reports are useful for decision-making because they provide insights into the root causes of issues or trends.

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Answer: the equation represents a circle centered at (-6, -6) with radius 2.

Step-by-step explanation:

x^2 + 12x + 36 + y^2 + 12y + 12 - 36 = 0

Simplifying, we get:

(x + 6)^2 + y^2 - 12 = 0

For the y terms, we add (12/2)^2 = 36 to both sides to get:

x^2 + 12x + 36 + y^2 + 12y + 36 - 24 = 0

Simplifying, we get:

(x + 6)^2 + (y + 6)^2 = 4

Therefore, the equation represents a circle centered at (-6, -6) with radius 2.

Answer: 0

Step-by-step explanation:

Answer:

  48

Step-by-step explanation:

You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.

The diameter of the can will be found from the volume formula:

  V = (π/4)d²h

  d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches

The cans are 4 inches in diameter.

The number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.

  Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high

  Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep

  Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long

A total of 2 × 2 × 12 = 48 cans will fit on the shelf.

__

Additional comment

There will be 2 inches of empty space in each direction.

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Thus, the given quadratic equation has two real roots x = 3 and x = -2.

A function or mathematical statement of degree two is a quadratic function. This indicates that two is the function's highest power. The roots of all quadratic functions are two.

Given equation:

x² - x - 6 = 0

Using the quadratic formula:

x = [-b ± √(b² - 4ac) ] / 2a

a = 1 , b = -1 and c = -6

x = [1 ± √((-1)² - 4*1*(-6) ] / 2*1

x = [1 ± √(1 + 24) ] / 2

x = [1 ± 5 ] / 2

Now,

x = (1 + 5)/2 = 3

x = (1 - 5)/ 2 = -2

Thus, the given quadratic equation has two real roots x = 3 and x = -2.

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complete question:

Check whether the given equation has, one solution, two solution ,many solution or no real solution.

x² - x - 6 = 0

The approximation of √300 to the nearest integer is 17

An integer is a whole number that can be positive or negative or zero. Examples of integers are 0, -5, 10, 15, 1000. e.t.c. Decimal numbers are not integers.

Since the value of √300 can not give a whole number because 300 is not a perfect square. This means that the answer given will not be an integer. Therefore saying that we should approximate to integer means approximation to whole number.

√ 300 = 17.32. Therefore the approximation of the value of √300 to the nearest integer = 17.

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The systems of equation solved by elimination is (2, -6).

From the question, we have the following parameters that can be used in our computation:

2x + y = -2

5x + 3y = -8

To eliminate y, we can multiply the first equation by -3 and add it to the second equation:

-6x - 3y = 6

5x + 3y = -8

So, we have

-x = -2

Therefore, x = 2. To find y, we can substitute x = 2 into either equation:

2x + y = -2

2(2) + y = -2

4 + y = -2

y = -6

So the solution to the system is (2, -6).

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The area of the region bounded by the curves y = 5/x and y = 5/x^2, and the vertical line x = 3 is approximately 7.385 square units.

To find the area of the region bounded by the curves, we need to first determine the points of intersection between them.

Setting the two given functions equal to each other, we have

5/x = 5/x^2

Multiplying both sides by x^2, we get

5x = 5

Solving for x, we get

x = 1

So the curves intersect at x = 1.

Next, we need to determine the limits of integration. The region is bounded by the vertical line x = 3, so we integrate from x = 1 to x = 3.

The area is given by

A = [tex]\int\limits^3_1[/tex] [(5/x) - (5/x^2)] dx

Using the power rule of integration, we get:

A = [5ln(3) + (5/3)] - [5ln(1) + (5/1)]

Simplifying, we get

A = 5ln(3) + (10/3)

A = 7.385 square units

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The dress was sold at a profit of 20%.

Profit percent is the percentage of profit earned on a product or investment, calculated as the profit divided by the cost price multiplied by 100%.

The profit or loss percent can be calculated using the following formula:

Profit/Loss percent = (Profit or Loss / Cost Price) x 100%

Here, the Cost Price (CP) of the dress is Rs. 2500, and the Selling Price (SP) is Rs. 3000.

Profit = SP - CP = Rs. 3000 - Rs. 2500 = Rs. 500

Therefore, the profit percent is

Profit percent = (Profit / CP) x 100%

Substitute the values in the equation

= (500 / 2500) x 100%

= 20%

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A dress was bought for Rs. 2500 and sold for Rs. 3000. Find the profit or loss percent

Therefore, Cindy and her friends raised $20.00 on the first day.

Let's assume that x represents the amount of money that Cindy and her friends raise on the first day.

According to the problem, they only raised a little money on the first day, which means the amount raised on the first day is less than the amount raised on the second day.

On the second day, they raised $56.75.

So, the total amount raised on the first two days is $76.75.

Therefore, we can use the equation:

x + $56.75 = $76.75

To solve for x, we can simplify the equation by subtracting $56.75 from both sides:

x = $76.75 - $56.75

x = $20.00

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Answer: 3 pieces

Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.

The given image is rotated by 180 degrees.

The term "rotation" describes how an object or a point rotates around a fixed axis or center. In mathematics, rotation is a transformation where an object is twisted or spun in one direction or another around a fixed point known as the centre of rotation.

The center, angle, and direction of a rotation can all be identified in terms of geometry. Either clockwise or anticlockwise rotation is possible. A 360-degree rotation is a full turn or full revolution, while a 90-degree anticlockwise rotation is also referred to as a quarter-turn.

For the given quadrilateral when the image is rotated along the axis of symmetry the other image is obtained at 180 degree rotation.

Thus, the given image is rotated by 180 degrees.

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The sum $a b c$ is 11760 if the ratio of the areas of two squares is  [tex]$\frac{32}{63}$[/tex].

Let the side length of the first square be x and the side length of the second square be y. Then we have:

[tex]\frac{Area of first square}{Area of second square} = \frac{x^2}{y^2} = \frac{32}{63}[/tex]

By cross multiplying, we get:

63 x² = 32 y²

And then by rearranging:

[tex]\frac{x}{y} = \frac{4\sqrt{7} }{9}[/tex]

Now, rationalizing the denominator, we get:

[tex]\frac{x}{y} = \frac{4\sqrt{7} }{9} . \frac{\sqrt{7} }{\sqrt{7} } = \frac{28\sqrt{7} }{63}[/tex]

Thus, a.b.c = 28.7.63 = 11760.

Therefore, the value of the sum $a b c$ is 11760.

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Answer:

$2655.40

Step-by-step explanation:

Answer:

$2655.4

Step-by-step explanation:

6%= 0.06

1870 x 0.06 = 112.2

7 x 112.2= 785.4

$785.4 + $1870= 2655.4

$2655.4 will be in the account after 7 years