What are the coordinates of the point on the directed line segment from ( − 7 , 9 ) (−7,9) to ( 3 , − 1 ) (3,−1) that partitions the segment into a ratio of 2 to 3?

(a) 58 = 2(w + 5 + w)

(b)  I. The width of the rectangle is 12 cm.

II. The length of the rectangle is 17 cm.

III. The area of the rectangle is 204 cm².

Let's solve the problem step by step:

(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:

Perimeter = 2(length + width)

Substituting the values, we have:

58 = 2(w + 5 + w)

Simplifying the equation, we get:

58 = 2(2w + 5)

(b) Now let's solve for the width and length of the rectangle:

I. To find the width, we solve the equation:

58 = 2(2w + 5)

Dividing both sides by 2, we get:

29 = 2w + 5

Subtracting 5 from both sides, we have:

24 = 2w

Dividing both sides by 2, we find:

w = 12 cm

Therefore, the width of the rectangle is 12 cm.

II. To find the length, we substitute the value of the width into the equation:

Length = w + 5 = 12 + 5 = 17 cm

Therefore, the length of the rectangle is 17 cm.

III. The area of the rectangle can be calculated using the formula:

Area = length × width

Substituting the values, we have:

Area = 17 cm × 12 cm = 204 cm²

Therefore, the area of the rectangle is 204 cm².

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Answer: Logarithmic function

Step-by-step explanation:  y=logax and it's a reflection of an exponential curve that curves up and a logarithmic function curves down.

The mode of the given observations 2, 5, 3, 2, 4, 6, 2, 4 is 2, so the correct answer is 1) 2.

To find the mode of a set of observations, we need to identify the value that appears most frequently.

Let's analyze the given observations: 2, 5, 3, 2, 4, 6, 2, 4.

Looking at the observations, we can see that the number 2 appears three times, while the numbers 5, 3, 4, and 6 appear only once each.

Since the number 2 appears more frequently than any other number in the set, the mode of these observations is 2.

Therefore, the correct answer is 1) 2.

The mode is a measure of central tendency that represents the most commonly occurring value in a data set.

It can be useful in identifying the most frequent value or category in a dataset.

In this case, the mode of the given observations is 2 because it appears more frequently than any other number.

It's important to note that a dataset can have multiple modes if there are two or more values that occur with the same highest frequency. However, in this specific case, the number 2 is the only value that appears more than once, making it the mode.

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We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Answer:

  B.  linear

Step-by-step explanation:

You want to know the type of function represented by the table of values ...

When the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.

Here, the "first differences" are ...

They are constant with a value of 4.

The fact that first differences are constant means the function is a first-degree (linear) function.

The table represents a linear function.

__

Additional comment

The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.

The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.

If differences are not constant, but have a constant ratio, the function is exponential.

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Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model

Answer:

Step-by-step explanation:

no

they would be on different sides on the y axis

Withdrawal: If Henry decides to withdraw money from his bank account, the opposite quantity would be the amount he withdraws.

Transfer: If Henry transfers money from his account to another account, the opposite quantity would be the amount of the transfer.

Debit/Credit: If there are debit or credit transactions on Henry's account, the opposite quantity would depend on whether it is a debit (negative) or credit (positive) entry.

To determine the opposite quantity that makes Henry's balance, we need to know the specific transaction or action that affects the balance. Without further information, it is not possible to provide an exact answer.

However, I can explain a few scenarios based on common banking transactions that could result in an opposite quantity affecting Henry's balance:

1. Withdrawal: If Henry decides to withdraw money from his bank account, the opposite quantity would be the amount he withdraws. For example, if Henry withdraws $50 from his account, the opposite quantity would be -$50.

2. Transfer: If Henry transfers money from his account to another account, the opposite quantity would be the amount of the transfer. For instance, if Henry transfers $100 to another account, the opposite quantity would be -$100.

3. Debit/Credit: If there are debit or credit transactions on Henry's account, the opposite quantity would depend on whether it is a debit (negative) or credit (positive) entry.

It's important to note that these scenarios are examples, and the opposite quantity would vary depending on the specific transaction or action affecting Henry's balance. To accurately determine the opposite quantity, we would need more information about the specific transaction or action taken by Henry that impacts his account balance.

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To find an ordered pair that satisfies the given system of inequalities, we need to find a point that lies below the line y = -x - 3 and above the line y = 2x - 4.

One such point that satisfies both inequalities is (-1, 0).

Let's check if this point satisfies both inequalities:

For the first inequality, y < -x - 3:

0 < -(-1) - 3

0 < 1 - 3

0 < -2 (True)

For the second inequality, y > 2x - 4:

0 > 2(-1) - 4

0 > -2 - 4

0 > -6 (True)

Therefore, the ordered pair (-1, 0) satisfies the system of inequalities y < -x - 3 and y > 2x - 4.

Answer:

-4 is the coefficient or -4x whatever the answers are

Step-by-step explanation:

the coefficient in mathematics is basically whatever the number is infront of a variable in an expression, equation, etc.

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

Let's denote the total number of boxes the hawker bought as "x".

The cost of each box is R18, so the total cost of buying "x" boxes is 18x.

He sold all but 5 boxes, so he sold (x - 5) boxes at R25 per box. The revenue from selling these boxes is 25 * (x - 5).

The profit is calculated by subtracting the cost from the revenue, so we have:

Profit = Revenue - Cost

155 = 25 * (x - 5) - 18x

Simplifying the equation:

155 = 25x - 125 - 18x

155 + 125 = 25x - 18x

280 = 7x

Dividing both sides by 7:

x = 280 / 7

x = 40

Therefore, the hawker bought 40 boxes of tomatoes.

Answer:

∠ NPQ = 120°

Step-by-step explanation:

the central angle NPQ is twice the angle on the circle NRQ , subtended by the same arc NQ , then

∠ NPQ = 2 × 60° = 120°

The expression 3x² + 6x + 4x + 8 is factorized as (x + 2)(3x + 4).

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs based on their common factors:

(3x² + 6x) + (4x + 8)

Step 2: Factor out common factors

Factor out the greatest common factor from each group of terms:

3x(x + 2) + 4(x + 2)

Now, we have a common factor of (x + 2) in both terms.

Step 3: Combine the factored terms

Combine the factored terms using the common factor:

(x + 2)(3x + 4)

The expression 3x² + 6x + 4x + 8 is factorized as (x + 2)(3x + 4).

In this process, we grouped the terms with similar variables and then factored out the greatest common factor from each group. Finally, we combined the factored terms using the common factor to obtain the fully factorized expression.

It's important to note that factoring algebraic expressions requires practice and familiarity with common factoring techniques. In some cases, you may encounter expressions that require additional methods such as factoring by grouping, using special factoring formulas, or applying quadratic factoring techniques.

By following these three steps, you can factorize the given expression by identifying common factors and combining terms accordingly.

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Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

The correct answer is a. 4. Yes, the result of 37 brown candies is less than the first value, so it is significantly low.b. The probability of exactly 37 brown chocolate candies is 0.0306.c. The probability of 37 or fewer brown chocolate candies is 0.0611.

a. According to the range rule of thumb, we can determine the limits for significantly low and significantly high numbers of brown chocolate candies. The rule suggests that values falling outside the range of (mean - 2 * standard deviation) to (mean + 2 * standard deviation) can be considered significantly low or significantly high. In this case:

Let's assume that the sample consists of N chocolate candies.

Given:

Total number of chocolate candies in the bag = 355

Number of brown chocolate candies = 37

Percentage of brown chocolate candies claimed by the company = 13%

We can calculate the mean and standard deviation as follows:

Mean = N * 0.13

Standard Deviation = sqrt(N * 0.13 * 0.87)

Using the range rule of thumb, the limits separating significantly low and significantly high numbers of brown chocolate candies are:

Significantly low: Mean - 2 * Standard Deviation

Significantly high: Mean + 2 * Standard Deviation

b. To find the probability of exactly 37 brown chocolate candies, we can use the binomial probability formula:

P(X = x) = (nCk) * p^k * (1 - p)^(n - k)

In this case, n = N (total number of candies), k = 37 (number of brown candies), and p = 0.13 (probability of a candy being brown).

c. To find the probability of 37 or fewer brown chocolate candies, we need to calculate the cumulative probability from 0 to 37 using the binomial probability formula:

P(X ≤ x) = P(X = 0) + P(X = 1) + ... + P(X = 37)

Let me perform the calculations for you.

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To show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.

To show that triangles ABC and AXYZ are congruent by the Side-Angle-Side (SAS) criterion, we need to establish that two corresponding sides and the included angle are congruent.

Given AB ≅ XY and BC ≅ YZ, we already have two corresponding sides congruent.

To complete the congruence by the SAS criterion, we need to establish that the included angles are congruent. In this case, the included angle is angle BAC (or angle XYZ).

Therefore, to show that ABC ≅ AXYZ by SAS, we would need to establish that angle BAC ≅ angle XYZ.

None of the answer choices directly addresses the congruence of the angles. So, none of the given options (A, B, C, D) are sufficient to show the congruence of the triangles by SAS.

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Group A is performing most consistently in terms of quality and associate engagement compared to last month.

To determine which performance area the groups are performing most consistently compared to last month, we need to compare the scores of each performance area between the two months.

Let's analyze each performance area:

Quality:

For Group A, the quality score increased from 90 to 94, indicating an improvement in quality performance. However, for Group B, the quality score decreased from 74 to 70, indicating a decline in quality performance. Therefore, Group A is performing more consistently in terms of quality compared to last month.

Productivity:

For Group A, the productivity score decreased from 79 to 62, showing a significant decline in productivity performance. Similarly, for Group B, the productivity score decreased from 86 to 58, indicating a notable decline as well. Both groups experienced a decrease in productivity performance, but Group A had a larger decline. Therefore, neither group is performing consistently in terms of productivity compared to last month.

Associate Engagement:

For Group A, the engagement score increased from 68 to 70, suggesting a slight improvement in associate engagement. Conversely, for Group B, the engagement score increased from 76 to 72, indicating a slight decline. Both groups had minor changes in engagement scores, but Group A had a smaller change. Therefore, Group A is performing more consistently in terms of associate engagement compared to last month.

Based on the analysis, Group A is performing most consistently in terms of quality and associate engagement compared to last month. However, neither group is performing consistently in terms of productivity. It is important to address the productivity decline and identify areas for improvement to ensure consistent performance across all categories.

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Answer:

The system of linear inequalities represented by the graph is:

y > x - 2 and y < x + 1

This system of inequalities indicates that y is greater than x - 2, which represents the upper boundary of the shaded region in the graph. Additionally, y is less than x + 1, which represents the lower boundary of the shaded region. The intersection of these two conditions is the region between the lines, satisfying both inequalities.

Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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Answer:

Given that sin(θ) = 8/17 and tan(θ) < 0, we can use the trigonometric identity to find cos(θ).

Since sin(θ) = opposite/hypotenuse, we can assign a value of 8 to the opposite side and a value of 17 to the hypotenuse.

Let's assume that θ is an angle in the second quadrant, where sin(θ) is positive and tan(θ) is negative.

In the second quadrant, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is positive.

Using the Pythagorean theorem, we can find the length of the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2

adjacent^2 = 17^2 - 8^2

adjacent^2 = 289 - 64

adjacent^2 = 225

adjacent = √225

adjacent = 15

Therefore, the length of the adjacent side is 15.

Now we can calculate cos(θ) using the ratio of adjacent/hypotenuse:

cos(θ) = adjacent/hypotenuse

cos(θ) = 15/17

So, cos(θ) = 15/17.

Answer:

23 Heads or Legs

The function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies the specified conditions of decreasing at x = -5, having a local minimum at x = -3, and a local maximum at x = 3.

One possible function that satisfies the given properties is:

f(x) = -0.5(x + 5)³(x + 3)(x - 3)

Check as follows:

Decreasing at x = -5:

Taking the derivative of f(x) and evaluating it at x = -5, we have:

f'(x) = -1.5(x + 5)²(x + 3)(x - 3) - 0.5(x + 5)³

f'(-5) = -1.5(0)²(-2)(-8) - 0.5(0)³ = 0 - 0 = 0

The derivative is zero at x = -5, therefore the function has a critical point at that location. To check if it is a maximum or minimum, we can examine the second derivative.

Taking the second derivative:

f''(x) = -3(x + 5)(x + 3)(x - 3) - 3(x + 5)²(x - 3)

f''(-5) = -3(0)(-2)(-8) - 3(0)²(-8) = 0 - 0 = 0

The second derivative is also zero at x = -5. However, since the first derivative is negative for x < -5 and positive for x > -5, this means that f(x) is decreasing at x = -5.

Local minimum at x = -3:

To check if f(x) has a local minimum at x = -3, we can examine the first and second derivatives at that point.

Taking the first derivative:

f'(-3) = -1.5(2)²(0)(-6) - 0.5(2)³ = 0

The first derivative is zero at x = -3, indicating a critical point.

Taking the second derivative:

f''(-3) = -3(2)(0)(-6) - 3(2)²(-6) = 0 - 72 = -72

Since the second derivative is negative at x = -3, this confirms the presence of a local minimum.

Local maximum at x = 3:

To check if f(x) has a local maximum at x = 3, we can again examine the first and second derivatives at that point.

Taking the first derivative:

f'(3) = -1.5(8)²(6)(0) - 0.5(8)³ = 0

The first derivative is zero at x = 3, indicating a critical point.

Taking the second derivative:

f''(3) = -3(8)(6)(0) - 3(8)²(0) = 0 - 0 = 0

The second derivative is zero at x = 3, indicating that the test is inconclusive. However, since the first derivative is positive for x < 3 and negative for x > 3, this means that f(x) is decreasing at x = 3.

Therefore, the function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies all the given conditions.

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Answer:

x = 82

Step-by-step explanation:

x and 98 are same- side exterior angles. They are on the same side of the transversal and are outside the parallel lines.

same- side exterior angles sum to 180° , so

x + 98 = 180 ( subtract 98 from both sides )

x = 82

[tex]x[/tex] and [tex]98^{\circ}[/tex] are same side exterior angles which add up to [tex]180^{\circ}[/tex].

Therefore

[tex]x+98^{\circ}=180^{\circ}\\x=82^{\circ}[/tex]

The range for the graph provided is from -10 to 10, inclusive.

To determine the range of the graph, we look at the vertical values or the y-values. The lowest y-value on the graph is -10, which corresponds to the point (-6, -10). The highest y-value on the graph is 10, which corresponds to the point (6, 10).

Therefore, the range of the graph is from -10 to 10, which means that all the y-values on the graph fall within this range. This indicates that the graph spans a vertical distance of 20 units, starting from -10 and ending at 10.

It's important to note that the range includes the minimum and maximum values attained by the graph. In this case, the graph reaches its lowest point at -10 and its highest point at 10.

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Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

10.4°

Step-by-step explanation:

the angle of elevation is the angle from the horizontal , upward from one point on the horizontal to another point, not on the horizontal

in this case the angle of elevation is represented by ∠ A

using the sine ratio in the right triangle

sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{36}{200}[/tex] , then

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{36}{200}[/tex] ) ≈ 10.4° ( to the nearest tenth )

the angle of elevation to the kite is approximately 10.4°

Answer:

[tex] \frac{1}{4} [/tex]

Answer:

the probability that at least one of the cards drawn is a diamond is 5/32

Step-by-step explanation:

In a standard 52-card  deck, there are 13 diamond cards,

Now,

The probability of a card being a diamond is ,

P = 13/52

P = 1/4

Now, we have to find the probability that atleast one of the 4 cards is a diamond, we calculate the probabilities,

There is 1 diamond in the 4 cards,

Hence the other 3 are not diamonds i.e the porbability for not being a diamond is,

N = 1-1/4 = 3/4

So,

The total probability is,

T1 = (3/4)(3/4)(3/4)(1/4)

T1 = 27/256

There are 2 diamonds in the 4 cards,

And the other 2 are not diamonds, we get,

T2 = (1/4)(1/4)(3/4)(3/4)

T2=9/256

There are 3 diamonds in the 4 cards,

and 1 is not,

T3 = (1/4)(1/4)(1/4)(3/4)

T3 = 3/256

ALL FOUR are diamonds,

T4 = (1/4)(1/4)(1/4)(1/4)

T4 = 1/256

Hence, the probability that at least 1 is a diamond is,

T = T1 + T2 + T3 + T4

T = (27/256) + (9/256) + (3/256) + (1/256)

T = 40/256

T = 5/32

The amount of money there would be in 18 years is $82078.65.

The value of the bond increased over the 18 years period.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]A(18) = 20000(1 + \frac{0.08}{2})^{2 \times 18}\\\\A(18) = 20000(1.04)^{36}[/tex]

Future value, A(18) = $82078.65

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Answer:

  $82078.65

Step-by-step explanation:

You want the value of a $20,000 investment that pays 8% interest compounded semiannually for 18 years.

The value of the investment of principal amount P at interest rate r compounded n times per year for t years is given by the formula ...

  A = P(1 +r/n)^(nt)

Using the given values, we find the amount of money in 18 years will be ...

  A = $20,000(1 + 0.08/2)^(2·18) = $20,000(1.04^36) ≈ $82,078.65

In 18 years there will be $82,078.65.

__

Additional comment

Some calculators and all spreadsheets have built-in functions for evaluating financial formulas.

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