Matthew has an investment that is now worth $21 537.82. Find the original amount
he invested if he has had the money invested at 2.5% per month for 3 years.

Answer:

B

Step-by-step explanation:

The revenue for a company's product is the amount of money the company earns from selling the product. R(x) = 0.36x^3 + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.

R(x) = 0.36x^3 + 824x

The revenue for a company's product is the amount of money the company earns from selling the product. To find the revenue function for a company, we can use the demand and price functions given. The demand function tells us how much of the product customers are willing to buy at a certain cost, while the price function tells us how much the company can charge for the product. R(x) = 0.36x^3 + 824x + 824x. This is the equation that tells us how much the company will earn in revenue for the product at a certain cost.

At x = 10,

R(10) = 0.36(10^3) + 824(10) + 824

R(10) = 3600 + 8240 + 824

R(10) = 17,664

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Therefore , the solution of the given problem of slope comes out to be  y = 15x + 10.

A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).

Here,

A racer:

Due to the fact that the race begins at the beginning, the y-intercept

is 0.

We can select any two locations from the table and use the following formula to determine the slope:

=> Slope Equals (Distance Change) / (change in time)

As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:

=>  slope = (40 - 10) / (3 - 1) = 30 / 2 = 15

As a result, Racer A's calculation is:

=>  y = 15x

Runner B:

As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:

=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15

As a result, Racer B's calculation is:

=>  y = 15x + 20

Runner B

The race begins at a distance of 10 feet, so the y-intercept is 10.

We can select any two locations from the table and use the following formula to determine the slope:

Slope Equals (Distance Change) / (change in time)

As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:

=>  slope = (65 - 35) / (3 - 1) = 30 / 2 = 15

As a result, Racer C's equation is:

=> y = 15x + 10

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Part II: Value of x=0

Part III: the lengths of the sides of EFG as EF = G = 11 and EG = -11.

Part IV: the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.

Value can be used to find the solution to an equation or to compare two or more values.

Part II: To find the value of x, we need to use measures for AC and EG. We can use the equation AC = 2x + 4 to solve for x.

We can rearrange the equation to 2x = AC - 4, and then substitute in the value of AC, which is 2x + 4.

This gives us 2x = 2x + 4 - 4, or 0 = 0

x = 0.

Part III: To find the lengths of the sides of EFG, we can use the equation EF = G + 7x - 11.

Substituting in the value of x, which is 0, we get

EF = G + 7 * 0 - 11,

or EF = G - 11.

Since EG = 7x - 11, substituting in the value of x gives us

EG = 7 * 0 - 11,

or EG = -11.

So EF = G and EG = -11

Part IV: To find the lengths of the sides of ABC, we can use the equation AB = 5x - 9, substituting in the value of x as 0.

This gives us AB = 5 * 0 - 9,

or AB = -9.

Since GF = 3x - 1 and AC = 2x + 4, substituting in the value of x gives us GF = 3 * 0 - 1,

or GF = -1,

and AC = 2 * 0 + 4

or AC = 4.

So AB = -9, GF = -1, and AC = 4, giving us the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.

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Answer: 0.75

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

Answer: -0.75

Step-by-step explanation:

1/4th of the way to point 0,-3 from 0

-3/4=-0.75, therefore, the answer is C, -0.75.

Answer:

forgot how to do this

Step-by-step explanation:

150√374 283727273737272727272

The volume of the spherical boulder is approximately 71.21 cubic feet.

To find the volume of a spherical boulder, we can use the formula for the volume of a sphere:

V = (4/3)πr³

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

We are given that the diameter of the boulder is 10 feet, so the radius is half of that, or:

r = 10/2 = 5 feet

We are also given that the boulder weighs almost 6 tons. To convert this weight to pounds, we can multiply by 2000 (since 1 ton is equal to 2000 pounds):

6 tons * 2000 pounds/ton = 12,000 pounds

The weight of the boulder is related to its volume through its density. The density of a boulder will depend on its composition, but we can make an estimate based on common rock types. For example, granite has a density of about 2.7 grams per cubic centimeter, or 2.7 metric tons per cubic meter (since 1 metric ton is equal to 1000 kilograms). A boulder made of granite would therefore weigh about 2.7 times its volume in cubic meters.

Assuming the boulder is made of granite, we can find its volume by setting its weight equal to its volume times its density:

12,000 pounds = V * 2.7 metric tons/m³

To convert pounds to metric tons, we can divide by 2204.62 (since 1 metric ton is equal to 2204.62 pounds):

12,000 pounds / 2204.62 pounds/metric ton = 5.44 metric tons

Substituting this into the equation above, we get:

5.44 metric tons = V * 2.7 metric tons/m³

Dividing both sides by 2.7, we get:

V = 5.44 metric tons / 2.7 metric tons/m³ = 2.0148 m³

To convert this volume to cubic feet, we can use the conversion factor 1 cubic meter = 35.3147 cubic feet:

V = 2.0148 m³ * 35.3147 ft³/m³ = 71.21 ft³

Therefore, the volume of the spherical boulder is approximately 71.21 cubic feet.

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Therefore , the solution of the given problem of amount comes out to be 30000 is the new amount.

aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess

Here,

The straightforward interest formula can be used to determine the total amount owing on $20,000 that has been invested for five years at 10% annual interest:

=> Sum total = Principal + Interest

where Principal represents the amount invested initially and Interest represents the interest collected over the course of five years.

Since the interest gained annually is 10% of the principal, the total interest earned over the course of five years is as follows:

=> Interest is calculated as follows:

=> Interest = P*R*T

=> Interest = 20000 * 0.10 * 5

=> Interest = 10000

Total amount = 20000 +10000 = 30000

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a. The probability of getting exactly 1 girl in 8 births is given as follows: 0.0313 = 3.13%.

b. The probability of getting 1 or fewer girls in 8 births is given as follows: 0.0352 = 3.52%.

c. The relevant probability for significantly low is given as follows: B. Since the probability of getting more than 1 girl is the complement of the result from part (b), this is the relevant probability.

d. The correct option regarding whether the probability is significantly low is: D. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The relevant probabilities for this problem are given as follows:

Hence the probability of 1 or fewer, used to verify if the event is significantly low, is:

P(X <= 1) = P(X = 0) + P(X = 1)

P(X <= 1) = 0.0352.

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The value of x as per the similarity of triangles is = 7.1.

If two triangles' sides have the same ratio or proportion and their angles are the same (corresponding angles), then the triangles will resemble one another (corresponding sides).

Similar triangles may have varied side lengths when compared individually, but they must all have the same ratio of their side lengths and equal angles.

Now in the figure, the triangles are similar.

So, sides of the triangles will be proportional to each other.

Now, 9/15 = 4.3/x

⇒ x = (4.3 × 15)/ 9

⇒ x = 7.1

Therefore, the value of x as per the similarity of triangles is = 7.1.

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Answer:

Below

Step-by-step explanation:

See image attached

Step-by-step explanation:

We can solve for x-y by isolating the term on one side of the equation and simplifying:

5(x-y) + 4 = 7

5(x-y) = 7 - 4

5(x-y) = 3

Next, we can divide both sides by 5:

x - y = 3/5

Therefore, the value of x-y is 3/5.

Answer:

40000

Step-by-step explanation:

To find 4 percent of a number, multiply the number by 0.04. In this instance, 0.04 x 1000000 = 40000. Therefore, 4 percent of 1000000 is equal to 40000.

The prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.

Prοbability is a measure οf the likelihοοd οf an event οccurring, expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, and a prοbability οf 1 means the event is certain.

Out οf the tοtal number οf teams that wοn their first game, 12 are frοm the AFC and 6 are frοm the NFC. Out οf the tοtal number οf teams that lοst their first game, 4 are frοm the AFC and 10 are frοm the NFC.

Therefοre, the tοtal number οf AFC teams is 12 + 4 = 16, and the tοtal number οf NFC teams is 6 + 10 = 16.

If we randοmly select a team that wοn their first game, the prοbability that the team is frοm the AFC is:

P(AFC) = number οf AFC teams / tοtal number οf teams

= 16 / (16 + 16)

= 1/2

The prοbability that the team selected wοn their first game and is frοm the AFC is:

P(wοn first game AND AFC) = number οf AFC teams that wοn first game / tοtal number οf teams that wοn first game

= 12 / (12 + 6)

= 12/18

= 2/3

Therefοre, the prοbability that a team selected wοn their first game, given the team is frοm the AFC, is 2/3 οr apprοximately 0.67.

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The perimeter of the figure with vertices D(-4, 5), E(-4, -6) and F(3, -6) is given as follows:

31.04 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The vertices of the polygon in this problem are given as follows:

D(-4, 5), E(-4, -6) and F(3, -6).

Hence the side lengths are given as follows:

Hence the perimeter of the polygon is given as follows:

11 + 13.04 + 7 = 31.04 units.

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[tex](6x+5)/(x+7)\\[/tex] can be represented as in the form quotient [tex]+( remainder )/( divisor )[/tex] as [tex]6 + 47/(x+7)[/tex] using division.

The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):

So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:

(6x+5)/(x+7) = 6 + 47/(x+7)

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The following are the correct measures for the angles and arc length:

m∠DFA = 58°

m∠COB = 114°

m∠EOB = 122°

arc CE = 124°.

m∠CED = [360 - 2(124)]/2 {angles at a point}

m∠CED = 56°

m∠A = [360 - 2(114)]/2 {angles at a point}

m∠A = 66°

m∠F = 180 - (56 + 66) {sum of interior angles of a triangle}

m∠F = 58°

The lines touching the circle at point C, B, and E respectively are tangents, hence the radii are perpendicular to each lines so;

angles m∠OCA, m∠OBA, m∠OBF, and m∠OEF are all equal to 90°

m∠COB = 360° - (90 + 90 + 66)° {sum of interior angles of a quadrilateral}

m∠COB = 114°

m∠EOB = 360° - (90 + 90 + 58)° {sum of interior angles of a quadrilateral}

m∠EOB = 122°

m∠CDE = 180° - arcCE

56° = 180° - arcCE

arcCE = 180° - 56°

arc CE = 124°.

Therefore, the correct measures of the angles and arc length are:

m∠DFA = 58°

m∠COB = 114°

m∠EOB = 122°

arc CE = 124°

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Cannot be determined

The population of Matteson can be calculated using the given formula: m(t) = 11410 + 220t. However, the current population of Matteson is not given in the question, so it cannot be calculated using the given formula. Therefore, the population of Matteson now cannot be determined based on the given information.

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The true statement about the function is (a) It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values

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

The table of values

In this table, each y-value is obtained by multiplying the previous y-value by 4.

This means that the function has a constant ratio or factor between each x- and y-value.

Such a pattern is typical of exponential functions, where equal intervals of x-values produce increasing or decreasing ratios of y-values.

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Step-by-step explanation:

Use the distance formula  ( a modified Pyhtagorean theorem)

d^2 = (x1-x2)^2 + ( y1-y2)^2

d^2 = ( -6 - -9)^2 + ( -1 - -6)^2

d^2 = ( 3^2)  + ( 5^2)

d^2 = 34

d = sqrt (34 ) =~ 5.8 units  

Answer: (16)➕6✖(25)➖(9)

Answer:294

Step-by-step explanation:

Answer:

[tex]294m^2[/tex]

Step-by-step explanation:

Volume of a cube is side x side x side or [tex]s^3[/tex]

now we find the value of one side

[tex]s^3 = 343m^3\\s = \sqrt[3]{343m^3} \\s = 7m\\[/tex]

Now we have a side value we can find the surface area of this cube which is

Surface area = [tex]6 * s^2[/tex]

= [tex]6 * (7m)^2[/tex]

= [tex]6 * 49m^2[/tex]

= [tex]294 m^2[/tex]

Hope this helps!

Brainliest and a like is much appreciated!

Answer:

Please Mark as Brainliest

Step-by-step explanation:

Based on the information provided, the three true statements about Josiah's solution are:

"300 = x." - This statement is true because Josiah predicted that there were 300 rock songs on his MP3 player.

"He did not multiply the numerator and denominator by the correct number to equal 1,500." - This statement is true because in his proportion, Josiah multiplied the numerator and denominator by 30, which is not a multiple of 1,500.

"He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500." - This statement is true because to set up a proportion with 1,500 as the denominator, Josiah should have multiplied the numerator and denominator by a multiple of 1,500. In this case, 75 is a multiple of 1,500, so multiplying by 75 would have been the correct approach.

The values of a and b  are -10 and 29, respectively of the curve.

What do you mean by turning point of a quadratic curve ?

The turning point of a quadratic curve is the point at which the curve changes direction from going up to going down, or vice versa. It is also known as the vertex of the parabola. The x-coordinate of the turning point is given by -b/2a, and the y-coordinate is the value of the function at that point.

Finding the values of a and b :

Given that the turning point of the curve is (5,4), we can write the following equations:

[tex]4 = 5^2 + 5a + b[/tex] (since the turning point lies on the curve)

[tex]0 = 2(5) + a[/tex] (since the derivative of the curve at the turning point is 0)

Simplifying the second equation gives us:

[tex]a = -10[/tex]

Substituting this value of a in the first equation, we get:

[tex]4 = 5^2 - 50 + b[/tex]

[tex]b = 29[/tex]

Therefore, the values of a and b are -10 and 29, respectively.

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Answer:

Below

Step-by-step explanation:

You will need to multiply the exponents in the parens   by 2 and square 4 so it is 16

16 x^(2*2) y^(3*2)  =   16 x^4 y^6

The perimeter of the square garden is 100 feet.

To find the perimeter of the square garden, first we need to determine the length of one side of the square. The given

information states that the hose, which lies along one diagonal of the garden, has a length of 25√2 feet.

Recall that the diagonal of a square divides it into two congruent right triangles, with the diagonal being the

hypotenuse.

Use the Pythagorean theorem to find the side length of the square. Let 'a' represent the side length of the square.

Then, we have:

a² + a² = (25√2)²

Simplify the equation:

2a² = 625 × 2

Divide both sides by 2:

a² = 625

Find the square root of both sides:

a = 25

Now that we know the side length of the square garden is 25 feet, we can calculate the perimeter.

The perimeter of a square is given by the formula:

Perimeter = 4 × side length

Substitute the side length:

Perimeter = 4 × 25

Calculate the perimeter:

Perimeter = 100

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the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.

To find the scale factor of the dilation, we can compare the corresponding side lengths of the two squares. The distance between the points (-5,5) and (5,5) is 10 units, which is also the length of the side of the original square. The distance between the points (-10,10) and (10,10) is 20 units, which is the length of the side of the dilated square. Therefore, the scale factor is:

Scale factor = Length of dilated square side / Length of original square side = 20 / 10 = 2

This means that the dilated square is twice as large as the original square.

To find the perimeter of the original square, we can add up the length of each side. Each side of the square has a length of 10 units, so the perimeter is:

Perimeter of original square = 4 × length of one side = 4 × 10 = 40 units

To find the perimeter of the dilated square, we can use the same method. Each side of the dilated square has a length of 20 units, so the perimeter is:

Perimeter of dilated square = 4 × length of one side = 4 × 20 = 80 units

Therefore, the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.

Dilation is a transformation that changes the size of an object but leaves its shape unchanged. In this case, the dilation of the square resulted in a larger square that was similar to the original square, meaning that the corresponding angles in the two squares were equal. The scale factor of the dilation determined the ratio of the side lengths of the two squares, and the perimeter of each square was proportional to its side length. Dilations are used in geometry to create similar figures and to scale up or down an object in size.

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Answer:

A)  £20
B)  £180

Step-by-step explanation:

The original price is £200. The price was reduced by 10% so the sale price is 90% of the original price.

A)  Price Reduction = 200 * 0.1 = £20

B)  Sale Price = Original Price - Price Reduction = 200 - 20 = £180
                          Original Price * Percent Paid = 200 * 0.9 = £180

The probability of obtaining exactly four tails {( T,T,T,T)}, when flipping four coins is equals to the 1/16 = 0.0625.

Independent Events : If the result of one event does not influence the result of another event, then the events are referred to as independent. In other words, it can be said that both events can happen simultaneously without interference. Probability is defined as a chance of occurrence of an event. Let E be the event that exactly four tails when flipping four coins. As we know that, when One coin is flip, total outcomes = 2 = { H,T}

So, 4 coins flipped, total possible outcomes = 16

Probability of getting tail on flipping one coin = 1/2

That is exactly four tails when flipping four coins are independent events. Therefore, the probability of obtaining four tails in a row in 4 flips of a coin is the product of probability in 4 flips. Since each flipping of a coin is independent, so

the probability of obtaining exactly four tails when flipping four coins = P(X = 4)

=( 1/2)(1/2)(1/2)(1/2) = (1/2)⁴

= 0.0625

Hence, required probability is 0.0625.

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