cot (x + y)=
cotx coty-1/cotx+coty

Answer:

Rounding down to a whole number, we get:

6,666 people

Step-by-step explanation:

First, we need to calculate the total area of the beach:

1000 ft x 200 ft = 200,000 sq ft

Next, we divide the total area by the desired area per person:

200,000 sq ft ÷ 30 sq ft per person = 6,666.67 people

The coordinates of the rotation are

Problem 5:

(4, 0), (0, -2), and (0, 0)  

Problem 6:

(0, -4), (-2, 0), and (0, 0)  

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

2. 90 degrees clockwise rotation about the origin

Problem 5: The transformation rule for 90 degrees clockwise rotation about the origin is

(x, y) becomes (y, -x)

preimage coordinates           image coordinates

(0, 4)                becomes        (4, 0)

(2, 0)                becomes        (0, -2)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Problem 6: The transformation rule for 180 degrees counterclockwise rotation about the origin is

(x, y) becomes (-x, -y)

preimage coordinates           image coordinates

(0, 4)                becomes        (0, -4)

(2, 0)                becomes        (-2, 0)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

This can be likened to the rotation as in problem 6, the polygon moves in the counterclockwise direction and this is according to the rule:

(x, y) becomes (-y, x)

2. 90 degrees clockwise rotation about the origin

This is similar to the rotation as in problem 5, the polygon moves in the clockwise direction and this is according to the rule:

(x, y) becomes (y, -x)

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Answer:
B) 46 degrees

In the given problem,  the skaters might collide at the point (7, 35) or (3, 51). This is derived by solving a system of created equations.

To find the points where the two skaters might collide, we need to solve the system of equations:

y = -4x + 63

y = -3x^2 + 26x

We can substitute the first equation into the second equation to eliminate y:

-4x + 63 = -3x^2 + 26x

Rearranging and simplifying, we get:

3x^2 - 30x + 63 = 0

Dividing both sides by 3, we get:

x^2 - 10x + 21 = 0

Factoring, we get:

(x - 7)(x - 3) = 0

So the possible values of x where the skaters might collide are x = 7 and x = 3.

To find the corresponding y-values, we can substitute these values of x into either equation. Using y = -4x + 63, we get:

When x = 7, y = -4(7) + 63 = 35

When x = 3, y = -4(3) + 63 = 51

Therefore, the skaters might collide at the point (7, 35) or (3, 51).

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The number "0.0505505550..." is an irrational number. The reason for it is that the number can't be expressed as the quotient of two integers. SInce it has the ellipsis (...) at the end, it indicates that the number isn't showing all its significant figures, therefore, can't be represented as the ratio of two integers. Thus, it is irrational.

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Answer:

No, it's not

Step-by-step explanation:

A rational number can be written in the form [tex]\sf{\dfrac{p}{q}}[/tex], where q ≠ 0.

While an irrational number cannot  be written in such a form.

Well, not only can't we express 0.0505505550... as [tex]\sf{\dfrac{p}{q}}[/tex], we also see three dots in the end that indicate that the number goes on forever.

It's impossible to express a number that goes on for ever, as a fraction.

Therefore the number is irrational.

The decay rate is r = -1.36 or 136%. This equation represents exponential decay with a decay rate of 136%.

An exponential function is a mathematical function of the form. [tex]f(x) = a^x[/tex], where "a" is a constant called the base of the function and "x" is the exponent. In other words, the base "a" is raised to the power of "x" to obtain the output value of the function. Exponential functions are characterized by their rapid increase or decrease as x increases or decreases. When the base "a" is greater than 1, the function grows rapidly as x increases, and when "a" is between 0 and 1, the function decays rapidly as x increases. The function [tex]f(x) = (2/7) ^ x[/tex] represents exponential decay because as x increases, the value of the function decreases rapidly towards zero.

This is because the base of the exponential function, 2/7, is less than 1. The function [tex]y = 4e^(1/2x)[/tex] represents exponential growth because as x increases, the value of the function increases rapidly towards infinity. This is because the base of the exponential function,[tex]e^(1/2x)[/tex], is greater than 1. Additionally, the coefficient 4 indicates that the initial value of the function is 4, and as x increases,

The function grows exponentially from that initial value. Rewrite the equation in the form. [tex]y = a * (1 + r) ^ t[/tex]or[tex]y = a * (1 - r) ^ t[/tex]. Then state the growth or decay rate. 3. [tex]y = a * (2.36) ^ t[/tex]the equation [tex]y = a * (2.36) ^ t[/tex]can be rewritten in the form of [tex]y = a * (1 + r) ^ t[/tex] by dividing both sides by a and using the fact that 2.36 = 1 + r, where r is the growth rate: [tex]y/a = (1 + r) ^ t[/tex] Here, the growth rate is r = 2.36 - 1 = 1.36 or 136%.

This equation represents exponential growth with a growth rate of 136%.Alternatively, if we want to rewrite the equation in the form of [tex]y = a * (1 - r) ^ t[/tex], we can use the fact that 2.36 = 1 - (-1.36), where -1.36 is the decay rate: [tex]y/a = (1 - (-1.36)) ^ t[/tex] Here, the decay rate is r = -1.36 or 136%. This equation represents exponential decay with a decay rate of 136%

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The Probability for the given event will be  55/87.

What exactly is probability?

Probability is a measure of the possibility of an event to be occurred. In mathematics, it is defined as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

For example, if you flip a fair coin, the probability of getting heads is 0.5, since there are two equally likely outcomes (heads or tails) and only one of them is heads. Similarly, the probability of rolling a 6 on a fair six-sided die is 1/6, since there are six equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6) and 6 comes only once.

Now,

Given number of

Total males = 32

Total females = 55

Total =87

then probability of selecting a female will be =55/87

Hence,

             The Probability for the given event will be  55/87.

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Answer:

Step-by-step explanation:

Fraction that are egg and club sandwiches

    [tex]\frac{1}{3} +\frac{1}{2} =\frac{2}{6} +\frac{3}{6}=\frac{5}{6}[/tex]

The rest are peanut butter:

      [tex]1-\frac{5}{6} =\frac{6}{6} -\frac{5}{6} =\frac{1}{6}[/tex]

Solution: [tex]\frac{1}{6}[/tex] of the sandwiches are peanut butter.

The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

Answer:

Step-by-step explanation:

10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone

9x=9y-18 divide by 9

x=y-2

x-y=-2

x+y=10

add above two equations

2x=8 divide by 2

x=4

y=10-4=6

numbers are 46 and 64

64=46+18 4+6=10

Using square root property,

Square root of 4 is 2 and -2.

Both 2 and -2 are square roots of 4 as:

2 × 2 = 4

also,

-2 × -2 =4

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.

It follows that a × a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number.

In the given question,

Square root of 4 is 2 and -2.

Both 2 and -2 are square roots of 4 as:

2 × 2 = 4

also,

-2 × -2 =4

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We need to deposit $4,494.08 now into the account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily.

What is compound interest?

Compound interest is a type of interest where the interest earned on an investment is added to the principal amount, and then the total amount (principal + interest) earns interest again in the subsequent period.

To find out how much money needs to be deposited now into an account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily, we can use the formula for compound interest:

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

where:

FV is the future value we want to achieve, which is $6,400 in this case.

PV is the present value, or the amount of money we need to deposit now.

r is the interest rate per year, which is 6.5%.

n is the number of times the interest is compounded per year, which is 365.

t is the time period in years, which is 5 years.

Substituting these values into the formula, we get:

$6,400 = PV x [tex](1 + 0.065/365)^{(365*5)[/tex]

Simplifying the right-hand side of the equation, we get:

$6,400 = PV x [tex](1.00017808219)^{1825[/tex]

$6,400 = PV x 1.424663962

Dividing both sides of the equation by 1.424663962, we get:

PV = $4,494.08 (rounded to two decimal places)

Therefore, we need to deposit $4,494.08 now into the account to obtain $6,400 in 5 years if the interest rate is 6.5% per year compounded daily.

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Answer:

80,000 [tex]meters^{2}[/tex]

Step-by-step explanation:

200 x 400 = 80,000

Helping in the name of Jesus.

Answer:

A. rhombus

B. square

C. rhombus

D. parallelogram

The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .

To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.

The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):

[tex]R = px[/tex]

The profit (P) of a small business is the difference between its revenue and cost (C):

[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]

The profit will be positive when P > 0, which means that the revenue is greater than the cost:

[tex](p - 12)x > 3000[/tex]

[tex]x > 3000/(p - 12)[/tex]

This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]

Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.

Graph B: This graph shows a linear revenue function  [tex](R = 25x)[/tex] and a quadratic cost function  [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex]  is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .

We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]

This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.

Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function  [tex](C = 3000 + 20x).[/tex]The profit function  [tex](P = R - C)[/tex]  is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]

Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].

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(a) The value of  [h/g] function is h/g = (3x² - 4) / (-4x + 6).

(b) The domain of [h/g] is all real numbers except x = 3/2.

In mathematics, the domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable for which the function produces a valid output.

In the given question,

(a) To find h/g, we need to divide the function h(x) by the function g(x):

h/g = (3x² - 4) / (-4x + 6)

(b) To find the domain of [h/g], we need to determine which values of x would make the denominator equal to zero, since division by zero is undefined.

-4x + 6 = 0

-4x = -6

x = 6/4 = 3/2

So the only value that could make the denominator zero is x = 3/2. Therefore, the domain of [h/g] is all real numbers except x = 3/2.

[h/g] = (3x² - 4) / (-4x + 6), x ≠ 3/2.

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Answer:

1. To estimate the number of products sold after 48 months, we can assume that the sales follow a linear pattern over time. We can use the data given to find the rate of change (slope) of the line and then use that to predict the sales after 48 months.

Using the points (12, 4), (18, 7), and (36, 15), we can find the slope of the line that represents the sales:

slope = (15 - 7) / (36 - 18) = 8 / 18 = 4/9

Now we can use the point-slope form of a line to find the equation of the line:

y - 4 = (4/9)(x - 12)

where x is the number of months and y is the number of products sold.

To find the estimated number of products sold after 48 months, we can substitute x = 48 into the equation and solve for y:

y - 4 = (4/9)(48 - 12)

y - 4 = 16

y = 20

Therefore, we can estimate that the company will sell 20 thousand products after 48 months.

2. Yes, the number of products sold is a function of the amount of months. It is a linear function because the sales appear to follow a straight line over time, as we assumed in our calculation above. This means that for every increase of 1 month, the number of products sold increases by a constant rate of 4/9 thousand.

Step-by-step explanation:

the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their probabilities

In the given question,

We are given that the population mean per capita daily water consumption is 83 liters and the standard deviation is 11.9 liters. We are also given that random samples of size 50 are drawn from this population and the mean of each sample is determined.

We can use the central limit theorem to approximate the distribution of the sample means. According to the central limit theorem, the distribution of the sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 50, the standard deviation of the sample mean is:

standard deviation of sample mean = 11.9 / √(50) = 1.68

To find the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person, we need to find the z-scores corresponding to these values and use the standard normal distribution table or calculator to find the probability.

The z-score for 80 liters per person is:

z = (80 - 83) / 1.68 = -1.79

The z-score for 82 liters per person is:

z = (82 - 83) / 1.68 = -0.60

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score between -1.79 and -0.60 is 0.1271.

Therefore, the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%

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0.1728 proportion of suburban park users bike on the park trail .the answer is option O 0.1728.

what you mean by proportion?

Proportion refers to the relationship between a part and the whole. In statistics, a proportion is a measure that describes the size of a subset relative to the size of the entire set. It is usually expressed as a fraction or a percentage.

In the given question,

To find the proportion of suburban park users who bike on the park trail, we need to divide the number of suburban park users who bike by the total number of suburban park users.

From the table, we can see that the number of suburban park users who bike is 42 and the total number of suburban park users is 243.

So, the proportion of suburban park users who bike on the park trail is:

42/243 = 0.1728

Therefore, the answer is option O 0.1728.

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27 cubic inches make up the volume of a cube.

Part A: The side length is 3 inches

Part B: The total surface area of the cube is 54 square inches

Part A:

The formula for the volume of a cube is V = s^3, where V is the volume and s is the side length.

We are given that the volume of the cube is 27 cubic inches, so we can plug this into the formula and solve for s:

27 = [tex]s^3[/tex]

By taking the cube root of both sides, we arrive at:

s = 3

Therefore, the side length of the cube is 3 inches.

Part B:

The formula for the surface area of a cube is A = 6[tex]s^2[/tex], where A is the surface area and s is the side length.

Plugging in the value we found for s in Part A, we get:

A = 6([tex]3^2[/tex])

A = 6(9)

A = 54

Therefore, the total surface area of the cube is 54 square inches.

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The differentiation of the trigonometric function gives:

dy/dx = sin(x) - cos(x)

Here we want to find dy/dx for:

y = sec⁻¹(x) + csc⁻¹(x)

Remember that these two are the inverses of the sine and cosine function, then we can write that just as:

y = cos(x) + sin(x)

Now the differentiation is part by part, we know that:

d(cos(x))/dx = -sin(x)

d(sin(x))/dx = cos(x)

Then:

dy/dx = sin(x) - cos(x)

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The answer of the given question based on the triangle is the value of angle G or x  is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Trigonometric functions can be used to solve problems involving angles and sides of right triangles, as well as to model periodic phenomena such as waves and oscillations.

To find angle G, we need to use the trigonometric function tangent since we know the opposite and adjacent sides of angle G in the right triangle EFG.

Recall that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, i.e.,

tan(G) = opposite/adjacent = FG/EF

Substituting the given values, we get:

tan(G) = 3.4/2.6 = 1.3076

Using a calculator, we can find the inverse tangent of 1.3076, which gives us:

G ≈ [tex]tan^{-1}[/tex](1.3077) ≈ 52.6° degrees

Therefore, the value of angle G is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

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The volume of the hemisphere is given by:

V_hemisphere = (2/3)πr^3

The volume of water in the bowl is two-fifths of the volume of the hemisphere:

V_water = (2/5)(2/3)πr^3 = (4/15)πr^3

So the remaining volume in the bowl is:

V_bowl = V_hemisphere - V_water = (1/3)πr^3

We are told that this remaining volume is poured into a hollow cone with depth 12 cm. Let's call the radius of the surface of the water in the cone "R". We can set up an equation for the volume of the cone in terms of R and solve for R:

V_cone = (1/3)πR^2(12)

Setting V_cone equal to V_bowl, we have:

(1/3)πR^2(12) = (1/3)πr^3

Simplifying:

R^2 = (r^3)/(4312) = r^3/144

Taking the cube root of both sides:

R = (r^3/144)^(1/3) = r/3

Substituting the given radius of the hemisphere, r = 6 cm, we get:

R = (6 cm)/3 = 2 cm

Therefore, the radius of the surface of the water in the cone is 2 cm.

the area of the triangle is approximately 71.82 square units.

HOW TO SOLVE THE PROBLEM?

Using the Pythagorean theorem, we can find the length of the base of the right triangle:

Base² = Hypotenuse²- Perpendicular²

Base²= 18²- 15²

Base² = 324 - 225

Base² = 99

Taking the square root of both sides, we get:

Base = √99

Simplifying the square root of 99, we get:

Base = √(9 x 11)

Base = 3√11

Therefore, the length of the base of the right triangle is 3√11.

to find the area of the triangle 3√11-8=1.94

then we can find three side of triangles

which are 15,18,15.12

To find the area of a triangle when the lengths of its three sides are known, we can use Heron's formula:

Area = √[s(s-a)(s-b)(s-c)]

where s is the semiperimeter of the triangle, and a, b, and c are the lengths of its sides.

The semiperimeter s is half the perimeter of the triangle:

s = (15 + 18 + 15.14) / 2 = 24.57

Using this value for s, and plugging in the lengths of the sides a = 15, b = 18, and c = 15.14, we get:

Area = √[24.57(24.57-15)(24.57-18)(24.57-15.14)]

= √[24.57(9.57)(6.57)(9.43)]

= √5153.5853

= 71.82 (approx)

Therefore, the area of the triangle is approximately 71.82 square units.

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The answer d because it is the only option that describes a circle with a center at (-7, 2) and a radius of 10. d (x − 7)² + (y + 2)² = 10

The standard form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) represents the coordinates of the center of the circle and r is the radius.

From this equation we can see that the x-coordinate of the center is equal to h and the y-coordinate is equal to k.

In answer d, the x-coordinate of the center is -7, and the y-coordinate is +2. This means that the center of the circle is located at (-7, 2).

The radius of the circle is given by the value of r, which is equal to 10.

Therefore, answer d is the correct answer because it is the only option that describes a circle with a center at (-7, 2) and a radius of 10.

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Answer:

8

Step-by-step explanation:

Therefore, 98.3% of households took two or more kids to the theme attraction.

An equation known as proportion shows that the two numbers provided are equal to one another. In other terms, the proportion declares that the two ratios or portions are identical.

The following is how the info can be displayed in a table:

Number of Children Number of Families

0                                            450

1                                            1720

2                                            2090

3                                            2320

4                                            1450

5                                            1200

6                                            770

Total                                    10000

To find the proportion of families that brought two or more children, we need to add the number of families with two or more children (2090+2320+1450+1200+770) and divide by the total number of families:

(2090+2320+1450+1200+770)/10000 = 0.983

So approximately 98.3% of families brought two or more children to the amusement park.

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The probability that a freshman is selected is 0.39. the probability that an art major is chosen is 0.36. the probability that a freshman math major or a sophomore biology major is chosen is 0.23.

(a) To find the probability that a freshman is selected, we need to add up the probabilities of selecting any of the three types of majors among the freshman group. Thus:

Probability of selecting a freshman = Probability of selecting a freshman math major + Probability of selecting a freshman art major + Probability of selecting a freshman biology major

Probability of selecting a freshman = 0.12 + 0.09 + 0.18

Probability of selecting a freshman = 0.39

(b) To find the probability that an art major is chosen, we need to add up the probabilities of selecting an art major from both the freshman and sophomore groups. Thus:

Probability of selecting an art major = Probability of selecting a freshman art major + Probability of selecting a sophomore art major

Probability of selecting an art major = 0.09 + 0.27

Probability of selecting an art major = 0.36

(c) To find the probability that a freshman math major or a sophomore biology major is chosen, we need to add up the probabilities of selecting a freshman math major and a sophomore biology major. Thus:

Probability of selecting a freshman math major or a sophomore biology major = Probability of selecting a freshman math major + Probability of selecting a sophomore biology major

Probability of selecting a freshman math major or a sophomore biology major = 0.12 + 0.11

Probability of selecting a freshman math major or a sophomore biology major = 0.23

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In linear equation, 1600 had he paid for the painting.

What's a linear equation in calculation?

A linear equation is an algebraic equation of the form y = mxb. involving only a constant and a first- order( linear) term, where m is the pitch and b is the y- intercept. sometimes, the below is called a" linear equation of two variables," where y and x are the variables.

Jose made 25% profit, so if he bought the painting for x, he sold it for:

                x + 0.25x = 1.25x = 2000

                x = 2000 ÷ 1.25

                   = 1600

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a. The periodic deposit should be $643.28 (rounded to the nearest cent).

b. $15,438.72 of the $27,000 comes from deposits, and $11,561.28 comes from interest.

a. To determine the periodic deposit, we can use the formula for the future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, FV = $27,000, r = 8% / 4 = 2%, n = 6 x 4 = 24 (since there are 4 quarters in a year and the time period is 6 years).

Substituting these values into the formula, we get:

$27,000 = Pmt x [(1 + 0.02)^24 - 1] / 0.02

Solving for Pmt, we get:

Pmt = $643.28

b. The total amount contributed by deposits is:

$643.28 x 24 = $15,438.72

To find the amount of interest earned, we subtract the total deposits from the financial goal:

$27,000 - $15,438.72 = $11,561.28

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