Find the amount of money (Future Value) in an account where $5,100 is deposited (Present Value) at an interest rate of 8% per year compounded continuously and the money is left in the account for 13 years.
round to 2 decimal places.

There are approximately 205.33 gallons of water in the water cooler when it is completely full.

What is the volume of the cylinder?

The volume of a cylinder is given by the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height of the cylinder.

The volume of the cylindrical water cooler is:

V = πr^2h

where r is the radius and h is the height. Substituting the given values:

V = 3.14 x (3.5/2)^2 x 2

= 27.44 cubic feet

To convert cubic feet to gallons, we can multiply by 7.48 gallons/cubic foot:

V = 27.44 x 7.48

= 205.32 gallons

Rounding to the nearest hundredth, the answer is:

205.32 ≈ 205.33 gallons

Hence, there are approximately 205.33 gallons of water in the water cooler when it is completely full.

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Answer:

The correct answer is 143.86 gallons

Step-by-step explanation:

Answer: look at the image for the answer and the solution

Step-by-step explanation:

The graph of the quadratic function y = -6x² + 1 is given by the image presented at the end of the answer.

The parent quadratic function is given as follows:

y = x².

The transformed quadratic function is given as follows:

y = -6x² + 1.

The transformations are given as follows:

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Answer:

1.8 quintillion or 1,800,000,000,000,000,000

Step-by-step explanation:

The slope of the line that passes through (-8,-1) and (12,4) is 1/4.

The equation of the line in slope intercept form is y = x/4 - 31/4.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (4 + 1)/(12 + 8)

Slope, m = 5/20

Slope, m = 1/4.

At point (-8, -1), a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-8) = 1/4(x - (-1))

y + 8 = x/4 + 1/4

y = x/4 - 31/4.

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Hi there, here's your answer:

The question asked here is, "Which of the following is a line segment in the  drawing?"

Let's review all the options first.

a) HD

H and D being two points of a line AK form a line segment.

b) HA

H being a point on the line AK and A being an end point of a line make HA a ray.

c) GH

Again, H being a point on line GJ and G being an end point of a line make GH a ray.

d) DI

DI are two distinct points and do not join, thus they don't form a line segment.

Therefore, the correct option is (a) HD

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The length of line segment DL of the system of similar triangles is 4√3. The length of line segment BD of the system is √3.

Two triangles are similar if they have congruent angles and if their sides are not congruent though proportional. The statement of the problem can be described by following equations:

Proportion formula

AD / BD = DL / AD

DL = 4 · BD

Then, we find the formula for line segment DL:

AD / BD = 4 · BD / AD

AD² = 4 · BD²

BD = √(AD / 2)

If we know that AD = 6, then the length of line segment DL:

BD = √3

DL = 4√3

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The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are     y = (-4/3)x + 11 and y = (-4/3)x + 9.

First, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:

Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.

Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):

r = √((7-3)^2 + (9-4)^2) = √(85)

So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.

To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.

To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.

To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).

The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:

At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.

At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.

Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.

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The value of x in the diagrams are 14 and 99 respectively

Note the following points;

From the information given in the diagram

56 degrees and 4x degrees are corresponding

Then,

4x = 56

Make 'x' the subject

x = 14

From the second image

Add the angles and equate to 360 degrees, we have;

3x + 2 + 36 + x - 74 = 360

collect like terms

4x = 360 + 36

4x = 396

Make 'x' the subject

x = 99

Hence, the values are 14 and 99

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Answer: 180

Step-by-step explanation: Hope this helps :D

Answer:

180 Cows

Step-by-step explanation:

24 in 2 = 12/hr

12 cows x 15 hours = 180 cows

The percentage change in the price is 15.78% decrease.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

Now,

Initial price=4.1

Final price=3.5

Change=3.5-4.1= -0.6 , minus means decrease in price

final value + initial value=7.6

then

percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100

=0.6/3.8*100

=0.1578*100

=15.78%

hence,

         The percentage change in the price is 15.78% decrease.

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Answer:

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Step-by-step explanation:

Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:

The x-coordinates of f(x) and h(x) are the same, so x is unchanged.

The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.

The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.

Given the equation of f(x) = x^2, the equation of h(x) can be written as:

h(x) = -x^2 + 3

So the equation of the transformed function h(x) is h(x) = -x^2 + 3.

Using fitted curve, a similar new blockbuster would expect

A fitted curve is a curve that is created to model a set of data points, such that the curve passes as closely as possible to the points. The process of finding a fitted curve is called curve fitting or regression analysis.

Tracing the fitted curve, we have that

week 1 = 150 million

Week 2 = 75 million

Week 3 =  40 million

Week 4 =  25 million

Adding up the amounts

= 150 + 75 + 40 + 25

= 290 million

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Answer: number 2 is A

Step-by-step explanation:

On solving the provided question, we can say that  The following are the mean and standard deviation of the sample distribution of x: Average: 225 sec. 19 second standard deviation.

Standard deviation is a statistic that expresses the variability οr variance of a grοup of numbers. While a high standard deviation suggests that the values are mοre dispersed, a low standard deviation suggests that the values tend tο be closer to the established mean.

A measure of hοw dispersed the data are frοm the mean is the standard deviation (οr ). When the standard deviation is lοw, the data tend to be grouped around the mean, and when it is large, the data are mοre dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each scοre from the mean.

The median matches the median οf the population.

The pοpulation standard deviation is divided by the square root of the sample size tο produce the standard deviation.

The following are the criteria fοr this issue:

average population of 225 seconds.

60 second population standard deviatiοn.

10 second sample size.

Consequently, the following is the standard deviation fοr the sample distributiοn of x:

19 seconds are equal to 60/√(10).

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The table that represents a linear relationship that is also proportional is; Table 2

A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).

Table 1:

The proportions are;

-3/2, 0/3, 3/4

They are not equal and so not proportional

Table 2:

The proportions are;

-2/4 and -1/2

They are equal and so are proportional

Table 3:

The proportions are;

0/-2, 1/1 and 2/4

They are not equal and so not proportional.

Table 4:

The proportions are;

-4/0, 0/1 and 4/2

They are not equal and so not proportional.

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The values that make the inequality true are -5, -2, 0, 2, 2.9, 2.99 and 2.999.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Since the inequality is a < 3. Thus, any value that is less than 3 will make the inequality true.

Therefore, the values are -5, -2, 0, 2, 2.9, 2.99 and 2.999.

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The equation that shows the length of the table is  length = 11/5 × 22/5

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

Length = 2 1/5 × Width

Width = 4 2/5 feet

Turn into improper fractions

Width = 22/5 feet

Then, length = 11/5 × 22/5

Hence, the equation is 11/5 × 22/5

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Answer:

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

Definition:

Substitute for cos α:

The measures of all the angles D, C, E and F are 90 degrees

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

The circle

On the circle, we have the angles D, C, E and F to be angles in a semicircle

As a general rule:

Angles in a semicircle are right angle

This means that

Angle in a semicircle = 90 degrees

Using the above as a guide, we have the following:

D, C, E and F = 90 degrees

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Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

Step-by-step explanation:

The counterexample of the given conditional statement is "14 is even number and is divisible by 7."

Counterexamples are used in math to contradict a statement. Counterexamples are used to prove the limitations of possible theorems.

The given statement is "If a number is divisible by seven, then it is odd."

Number, 14, 28, 42, 56 are even numbers and they are divisible by seven.

Therefore, the counterexample of the given conditional statement is "14 is even number and is divisible by 7."

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Answer: the answer is 28

Step-by-step explanation: 28 is divisible by 7 and it is a even number

The value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a composite function is essentially applied to the output of another function.

Given that,

s(x)=x²

t(x) = 4x³

The value of the composite functions is given as:

(t + s)(x) = t(x) + s(x) = 4x³ + x²

(t.s)(x) = (4x³)x² = [tex]4x^5[/tex]

(t - s)(x) = t(x) - s(x) = 4x³ - x²

Hence, the value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

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Answer:

The correct answer is D. 7 pounds.

Step-by-step explanation:

The weight of the baby when its born is 7 pounds.

The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.

Using this principle, we can calculate the range of possible distances between each of the following cities:

Minneapolis and San Francisco: The sum of the distances from Minneapolis to Chicago and from Chicago to San Francisco is 1584 + 355 = 1939. Therefore, the minimum distance between Minneapolis and San Francisco is 1939 - 1584 = 355. The maximum distance between Minneapolis and San Francisco is 1939.

Minneapolis and Houston: The sum of the distances from Minneapolis to Chicago and from Chicago to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Minneapolis and Houston is 2640 - 1584 = 1056. The maximum distance between Minneapolis and Houston is 2640.

Minneapolis and New York: The sum of the distances from Minneapolis to Chicago and from Chicago to New York is 1584 + 1018 = 2602. Therefore, the minimum distance between Minneapolis and New York is 2602 - 1584 = 1018. The maximum distance between Minneapolis and New York is 2602.

Chicago and Houston: The sum of the distances from Chicago to Minneapolis and from Minneapolis to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Chicago and Houston is 2640 - 1056 = 1584. The maximum distance between Chicago and Houston is 2640.

San Francisco and Chicago: The sum of the distances from San Francisco to Minneapolis and from Minneapolis to Chicago is 355 + 1584 = 1939. Therefore, the minimum distance between San Francisco and Chicago is 1939 - 355 = 1584. The maximum distance between San Francisco and Chicago is 1939.

New York and San Francisco: The sum of the distances from New York to Minneapolis and from Minneapolis to San Francisco is 1018 + 355 = 1373. Therefore, the minimum distance between New York and San Francisco is 1373 - 1018 = 355. The maximum distance between New York and San Francisco is 1373.

Houston and New York: The sum of the distances from Houston to Minneapolis and from Minneapolis to New York is 1056 + 1018 = 2074. Therefore, the minimum distance between Houston and New York is 2074 - 1056 = 1018. The maximum distance between Houston and New York is 2074.

Answer:

Step-by-step explanation:

The sum of the exterior angles of a triangle is equal to 360 degrees, while the sum of the interior angles of a triangle is equal to 180 degrees.

When you combine the sum of the exterior angles and the sum of the interior angles of a triangle, you get:

360 degrees + 180 degrees = 540 degrees

So, the sum of the exterior angles and the sum of the interior angles of a triangle is equal to 540 degrees.

Answer:

letter R rounded off to the nearest tenth is 40

15 is the answer because this is the nearest

Answer:

is not a solution to the system of equations.

Step-by-step explanation:

Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:

Substitute the x and y values into the first equation:

y = 1/2x + 6

3 = 1/2(-6) + 6

Simplify the right side of the equation:

3 = -3 + 6

Solve for the value of y:

3 = 3

The first equation is satisfied, so now let's substitute the x and y values into the second equation:

2y = -x - 3

2 * 3 = -(-6) - 3

6 = +6 - 3

Simplify the right side of the equation:

6 = -3

The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.

Answer: Let's call the number of hours it takes for Rayna and Desi to build the fence together as "h". During this time, Rayna will build 10h feet of fence line, and Desi will build 2h feet of fence line.

Together, they will build 10h + 2h = 12h feet of fence line in h hours.

To build 80 feet of fence line, they will need h hours such that:

12h = 80

So,

h = 80 / 12 = 6.67 hours

So it will take Rayna and Desi 6.67 hours to build 80 feet of fence line together.

Step-by-step explanation: