what is the summation notation for 8+4+2+1+1/2

Answer:

249 feet

Step-by-step explanation:

Hello!

Let the missing side be x.

We can use a trigonometric ratio to solve this question. The one we are going to use is Tangent.

There are 3 trigonometric ratios: Sin (Opposite/Hypotenuse), Cos (adjacent/hypotenuse), and Tan(Opposite/Adjacent).

We need to use the ratio that involves the 2 sides, 144 and x. That would be Tan, as x is opposite to 60°, and 144 is adjacent to 60°.

The missing side is 249 feet.

If the p-value obtained from the paired t-test is less than the predetermined level of significance (usually 0.05), then it can be concluded that there is a statistically significant difference between the two treatments, and that imitrex is more effective than excedrin at eliminating migraines.

To determine if Imitrex works better than Excedrin at eliminating migraines in your study, the most appropriate statistical test to use is the Paired Samples t-test.

This test is suitable because:
We have two related samples: the same 25 women are given both Excedrin and Imitrex, so their response times are paired.
We're comparing the mean response times between two treatments, which requires a t-test.

The data is assumed to be normally distributed.
To conduct the Paired Samples t-test, follow these steps:
Calculate the difference in response times for each woman (Imitrex time - Excedrin time).

Calculate the mean of these differences.

Calculate the standard deviation of the differences.

Determine the degrees of freedom (25 women - 1 = 24).

Using the mean, standard deviation, and degrees of freedom, calculate the t-statistic.
Compare the t-statistic to the critical value from the t-distribution table, using your chosen significance level (e.g., 0.05).
If the t-statistic is greater than the critical value, reject the null hypothesis, concluding that there's a significant difference between the effectiveness of Imitrex and Excedrin for migraine relief.

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To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."

We are comparing the efficacy of Imitrex and Excedrin for Migraine in the same group of 25 women, with each woman acting as her own control. You are measuring the time it takes for the headache to subside after administering each drug. To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."

Step-by-step explanation:

1. Record the time it takes for the headache to subside after administering Excedrin and Imitrex to each woman.
2. Calculate the difference in time for each woman between the two drugs.
3. Compute the mean and standard deviation of these differences.
4. Perform a paired t-test to compare the mean difference to 0 (no difference between the two drugs).
5. Assess the p-value obtained from the t-test. If the p-value is less than the significance level (usually 0.05), then you can conclude that there is a statistically significant difference between the two drugs, suggesting that Imitrex works better than Excedrin in eliminating migraines.

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Answer:

1.a

2.c

3.d

4.b

Step-by-step explanation:

The second term of the expression represent the total depreciation value of the laptop. Therefore, the answer is C.

Pamela purchased a new laptop for her schoolwork.  She plans to sell it sometime in the future; however, its value depreciates monthly.

The expression below shows the depreciated sales value of the laptop.

Therefore, the meaning of the second term in the expression can be calculated as follows:

Therefore,

856 = The amount she bought the laptop

The second term 17m is the total depreciation value of the laptop where m = number of months.

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This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is often used in mathematics, science, engineering, and art. Triangles can be classified into different types based on the length of their sides and the size of their angles. Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.

Here,

To use similarity theorems to show that CD is parallel to AB, we need to first establish that triangles AEB and CED are similar. If we can show that these triangles are similar, then we can use the corresponding angles theorem, which states that if two pairs of corresponding angles are congruent, then the lines containing the sides are parallel.

Let's compare the two triangles AEB and CED:

Angle AEB is congruent to angle CED (both are vertical angles).

Angle EAB is congruent to angle ECD (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).

Angle BAE is congruent to angle DCE (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).

Therefore, we have established that triangles AEB and CED are similar by the angle-angle-angle similarity theorem.

Now that we have shown that the triangles are similar, we can use the corresponding sides theorem, which states that the corresponding sides of similar triangles are in proportion, to find out if CD is parallel to AB.

The corresponding sides of AEB and CED are:

AE/CE = AB/CD

Substituting the given values, we have:

AC + CE / CE = AB / BD

4 + 12 / 12 = AB / (14/3)

16/12 = AB / (14/3)

AB = (16/12) x (14/3)

= 56/9

Now we can use the corresponding sides theorem to find the length of CD:

AE/CE = AB/CD

Substituting the values we have found, we get:

4/12 = (56/9)/CD

CD = (56/9) x (12/4)

= 14

Since we have found that AB = 56/9 and CD = 14, we can see that:

AB/CD = (56/9)/14

= 4/3

This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.

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Whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram

is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.

It would be appropriate to display these data in a histogram without first plotting them in a time plot if you are looking

to analyze the distribution or frequency of herbicide usage across different amounts or categories.

A histogram can provide a clear visualization of the distribution and help identify any patterns or trends in the data.

However, if your goal is to analyze the trend of herbicide usage over time, then it would be more appropriate to use a

time plot.

A time plot will show changes in the usage of herbicides over a specific time period and help identify any seasonal

patterns or trends in the data.

In summary, whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram

is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.

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The quotient and the remainder of the rational function are x + 4 and - 4.

In this problem we find the case of a rational function of the form R(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials for the numerator and the denominator, respectively. The result of the rational function is represented by the following expression:

R(x) = S(x) + D(x) / Q(x)

Where:

If we know that P(x) = 2 · x² + 16 · x + 24 and Q(x) = 2 · x + 4, then the quotient and the remainder are, respectively:

R(x) = (2 · x² + 16 · x + 24) / (2 · x + 4)

R(x) = [2 · (x² + 8 · x + 12)] / [2 · (x + 4)]

R(x) = (x² + 8 · x + 12) / (x + 4)

R(x) = [(x² + 8 · x + 16) - 4] / (x + 4)

R(x) = [(x + 4)² - 4] / (x + 4)

R(x) = (x + 4) - 4 / (x + 4)

Quotient: (x + 4)

Remainder: - 4

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a) The inverse function is given as follows: [tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]

b) The radius of the cone with a volume of 4190 cubic inches is given as follows: r = 10 inches.

The function for this problem is defined as follows:

v(r) = 40/3πr²

We want to find the radius as a function of the volume for the inverse function, hence:

[tex]r^2 = \frac{3v}{40\pi}[/tex]

[tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]

Then the radius of the cone with a volume of 4190 cubic inches is given as follows:

[tex]r = \sqrt{\frac{3 \times 4190}{40\pi}}[/tex]

r = 10 inches.

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The length of chord XY is 5√2.

What is the length of the chord?

It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.

Here, we have

Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. ​If the measure of arc XY is 90 degrees.

We have to find the length of chord XY.

∠XOY = 90°

OX = OY = 5

We draw a perpendicular from the center to chord XY bisect XY at D.

Now, since OD bisects ∠XOY

∠XOD = ∠YOD = 90°/2 = 45°

Now, in ΔXOD

sin45° = XD/OX

1/√2 = XD/5

5/√2  = XD...(1)

In ΔYOD

sin45° = YD/OY

5/√2  = YD...(2)

Adding (1) and (2), we get

XD + YD = 5/√2 + 5/√2

XY = 5√2

Hence, the length of chord XY is 5√2.

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An equation of a line that is parallel to the line y=-5x-8 and passes through the point (7, -2) is y = -5x + 33.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y=-5x-8, the slope is equal to -5.

At data point (7, -2) and a slope of -5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = -5(x - 7)  

y + 2 = -5x + 35

y = -5x + 35 - 2

y = -5x + 33

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The equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.

To find an equation that is parallel to the line y = -5x - 8, we know that it must have the same slope. So the slope of the new line is -5.

Now we use the point-slope form of a linear equation to find the equation of the line passing through (7,-2) with slope -5:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting the values we get:

y - (-2) = -5(x - 7)

Simplifying and solving for y, we get:

y + 2 = -5x + 35

y = -5x + 33

Therefore, the equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.

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The total cost of mower is $10,228.48. The correct option from the following option given is D.

A down payment on a cottage is the money paid in advance by the buyer in a real estate transaction or other large purchase. Down payments are typically a portion of the sales price and can range from 3% to 20% for a primary residence.

The total cost of the mower will be the sum of the down payment and the total amount paid through the loan:

Down payment = $1,000

Total amount paid through the loan = (monthly payment) x (number of months) = $192.26 x 48 = $9,228.48

The total cost of the mower is:

Total cost = Down payment + Total amount paid through the loan

Total cost = $1,000 + $9,228.48

Total cost = $10,228.48

Therefore, the total cost of the mower is $10,228.48.

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The total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

The triangular prism can be observed to be a large rectangle and two identical triangles, so we shall calculate for the total surface area as follows:

area of one triangle = 1/2 × 8 cm × 12 cm

area of one triangle = 48 cm²

area of the two triangle faces = 2(48) = 96 cm²

area of the large rectangle face = (10 + 12 + 12) cm × 16 cm = 512 cm²

Total surface area of prism = 96 cm² + 512 cm² = 608 cm²

Therefore, the total surface area of the triangular prism is calculated to be equal to 608 square centimeters.

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Answer: 3

Step-by-step explanation:

The missing length is 7.5 cm.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Let the missing length be x cm.

The formula for the surface area of a rectangular prism is:

SA = 2lw + 2lh + 2wh

We are given that the height and width are both 9 cm, so we can substitute those values and simplify:

432 = 2(x)(9) + 2(x)(9) + 2(9)(9)

432 = 18x + 18x + 162

432 - 162 = 36x

270 = 36x

x = 270/36

x = 7.5

Hence, the missing length is 7.5 cm.

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The decimal which is less than 0. 8 and greater than 0. 02 is 0. 46 (option B).

To answer this question, we need to understand how decimals work. A decimal is a number that represents a value less than one, and it is denoted by a dot or a period. The digits that come after the dot represent the number of tenths, hundredths, thousandths, etc., depending on the place value of the digit.

Now, let's consider the given options: 0.81, 0.46, 0.86, and 0.6. We need to find the decimal that lies between 0.8 and 0.02.

We can eliminate option D, 0.6, as it is less than 0.8. Similarly, we can eliminate option A, 0.81, as it is greater than 0.8.

To choose between options B, 0.46, and C, 0.86, we need to compare them with the given values, 0.8 and 0.02. We can see that 0.46 is less than 0.8 but greater than 0.02.

Therefore, the answer is option B, 0.46.

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The slope-intercept equation of line is -1 and equation will be y = -x - 1.

What is the slope?

m = (y2 - y1) / (x2 - x1) is the formula for calculating slope from two points on a line, (x1, y1) and (x2, y2). Here,

m = the line's slope

x1 is equal to the initial point's x-coordinate.

y1 is the first point's y-coordinate.

x2 is equal to the second point's x-coordinate.

The second point's x-coordinate is equal to y2.

x1 = -3, y1 = 4; x2= -2, y2=3

m = (3-4)/(-2 - (-3))

= -1 / (-2+3)

= -1/1

m = -1

Substitute the value in given equation:

y = -x + (-1)

y = -x - 1

Hence, the slope-intercept equation of line is -1 and equation will be y = -x - 1.

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the value of the car decreases by 15 percent each year. This means that the value of the car decreases to 85% of its previous year's value every year.

what do you mean by term  decreases  ?

In this context, "decreases" means that the value of the car is getting smaller over time. The term "decrease" is often used in mathematics to describe a decrease in the numerical value of a quantity. In this case, the value of the car is decreasing by 15% each year, which means that its value is getting smaller by 15% of the previous year's value.

In the given question,

The given function for the value of the car is:

v(t) = P(0.85)ⁿ

Here, P is the initial purchase price of the car, and t is the time in years since the car was purchased.

To find the percent that the value of the car decreases by each year, we need to find the ratio of the decrease in value to the initial value, and express it as a percentage.

Let's consider the value of the car after one year, i.e., when t=1. The value of the car after one year is:

v(1) = P(0.85)¹ = 0.85P

The decrease in value from the initial value P is:

P - v(1) = P - 0.85P = 0.15P

Therefore, the ratio of the decrease in value to the initial value is:

(0.15P/P) = 0.15

To express this ratio as a percentage, we multiply by 100, which gives:

0.15 x 100% = 15%

Therefore, the value of the car decreases by 15% each year. This means that the value of the car decreases to 85% of its previous year's value every year.

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The Waffleskate campaign's claim that less than 34% of registered voters wish to see her defeated is not supported by the data, as the 98% confidence interval (0.236 to 0.336) for the proportion of voters who want her to lose does not include 0.34.

To determine if the 98% confidence interval supports the Waffleskate campaign's claim that no more than 34% of registered voters wish to see her defeated, we need to construct the confidence interval and see if 34% falls within the interval.

The sample proportion of registered voters who wished to see Waffleskate lose her next election is 133/464 ≈ 0.286. To construct the 98% confidence interval for the true proportion, we can use the formula p ± Z√(pq/n), where p is the sample proportion, q is the complement of p, n is the sample size, and Z is the standard normal value corresponding to the desired confidence level.

Plugging in the values, we get:

p ± Z√(pq/n) = 0.286 ± 2.33√((0.2860.714)/464) ≈ 0.236 to 0.336

Therefore, the 98% confidence interval for the proportion of registered voters who wish to see Waffleskate lose her next election is 0.236 to 0.336. Since this interval does not include 0.34, the Waffleskate campaign's claim that no more than 34% of registered voters wish to see her defeated is not supported by the 98% confidence interval for the proportion.

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The volume of the solid as shown in the diagram is 540 cm².

Volume is the space occupied by a solid shape.

To calculate the volume of the of the solid, we use the formula below

Formula:

Where:

From the diagram in question,

Given:

Substitute these values into equation 1

Hence, the volume is 540 cm³.

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Answer:

[tex]3(6+x)=24[/tex]

[tex]3x+18=24[/tex]

[tex]3x=6[/tex]

[tex]x=2[/tex]

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Therefore , the solution of the given problem of equation comes out to be 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).

Variable words are frequently used in complex algorithms to show consistency between two arguments that are opposed to one another. Academic expressions called equations are used to show the equality of various academic figures. Take into account the details in the z + 7 proposals.

Here,

The equation for the line passing between the points (6, -9) and (7, 1) must be found in the point-slope form.

Using the equation m = (y2 - y1) / (x2 - x1), find the slope (m) of the line, where (x1, y1) and (x2, y2) are the coordinates of the two points.

=> (x1, y1) = (6, -9)

=> (x2, y2) = (7, 1)

=> m = (1 - (-9)) / (7 - 6)

=> m = 10 / 1 m = 10

Consequently, the line's slope is 10.

=> y - y1 = m(x - x1)

=> m = 10 (x1, y1) = (6, -9)

=> y - (-9) = 10(x - 6)

=> y + 9 = 10x - 60

=> 10x - y = 51

Therefore, 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).

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The number 0.19 is a d. statistic, which represents a numerical summary of a sample. The z-score would be calculated by (0.19 - 0.23) / sqrt((0.23 * 0.77) / 300) and would indicate how many standard deviations the sample proportion is from the population proportion.

The p-value and significance level would be used in hypothesis testing to determine the likelihood of obtaining a sample proportion as extreme or more extreme than the observed proportion, assuming the null hypothesis is true.

The parameter is the true proportion of all undergraduate students at the local university who live on campus, which is estimated by the sample statistic.

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The value of arc PQ is 110°

The circumference of a circle is the length of the 360 degree arc of that circle. Therefore the sum of the arc on a circumference of a circle is 360°

Therefore ,

8x-10+ 6x + 10x+10 = 360

24x -10+10 = 360

24x = 360

divide both sides by 24

x = 360/24

x = 15

therefore the value of x is 15

Arc PQ = 8x -10

substitute 15 for x

ArcPQ = 8×15-10

= 120-10

= 110°

therefore the value of arc PQ is 110°

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The proportionality constant to find the amount to be paid based on the number of "cocadas" is the price per "cocada"

Proportionality constant is a mathematical term that refers to the constant value that relates two variables that are directly proportional to each other.

The proportionality constant to find the amount to be paid based on the number of "cocadas" will depend on the price per "cocada".

Let's say the price per "cocada" is represented by the variable "p" (in some currency), and the number of "cocadas" purchased is represented by the variable "n".

Then, the amount to be paid can be calculated using the formula

amount to be paid = p × n

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Buy-side order flow is the number of individual buy orders and the total number of shares that wish to buy. ​

This is a crucial metric that is used by traders, investors, and analysts to gauge the demand for a particular security or asset.

The buy-side order flow refers to the number of shares that market participants want to purchase at a given time, and it provides valuable insights into the sentiment of the market. If there are more buy orders than sell orders, then there is a higher demand for the security, which can lead to an increase in the price of the asset. On the other hand, if there are more sell orders than buy orders, then there is a higher supply of the security, which can lead to a decrease in the price of the asset.

Traders and investors use buy-side order flow data to help them make informed decisions about when to buy or sell a security. By analyzing the number of buy orders and the total number of shares that wish to buy, they can identify trends and patterns in the market, and adjust their strategies accordingly. Additionally, buy-side order flow data can be used to help identify potential support and resistance levels for a security, which can be useful in setting stop-loss orders and other risk management measures.

Overall, the buy-side order flow is an important metric that provides valuable insights into the sentiment of the market and helps traders and investors make informed decisions about their investments.

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The standard-form equation of the line using the coordinates of the labeled point is: B. 8x + 7y = 60.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (4, 4) and a slope of -8/7, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -8/7(x - 4)

By multiplying all through by 7, we have:

7(y - 4) = -8(x - 4)

7y - 28 = -8x + 32

7y + 8x = 32 + 28

8x + 7y = 60.

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The significance level chosen for the tests with total number of test performed as 1000 for given p-value is equal to 0.87 or 87%.

Total number of test performed = 1000

p-value is equal to 0.00013

The Bonferroni correction involves ,

Adjusting the significance level for multiple comparisons by dividing it by the number of comparisons performed.

Here, 1000 tests were performed and the resulting p-value is 0.00013.

The significance level that was chosen for the tests,

Reverse the Bonferroni correction by multiplying the p-value by the number of comparisons,

adjusted p-value = p-value / number of comparisons

number of comparisons = 1000

adjusted p-value = 0.00013

p-value = adjusted p-value x number of comparisons

⇒p-value = 0.00013 x 1000

⇒p-value = 0.13

So the original p-value before the Bonferroni correction was 0.13.

The significance level, we subtract the p-value from 1,

significance level = 1 - p-value

⇒significance level = 1 - 0.13

⇒significance level = 0.87

Therefore, the significance level chosen for the tests was 0.87 or 87%

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If a factory machine bends wire at rate of 2 units of curvature per  second, then the time required to bend the "straight-wire" into a circle of radius of 4 is 12.56 seconds.

The "Circumference" of a circle is defined as the total length of the curve which makes up the circle's outer boundary,

The formula for "circumference" of a circle is ⇒ C = 2 × π × r,

where "C" = circumference, "π" ≈ 3.14159, and "r" = radius,

In this case, the radius of circle is = 4 units,

So, we substitute "r" = 4,

We get,

⇒ Circumference = 2 × π × 4,

⇒ Circumference = 8π

The machine bends wire at a rate of 2 units of curvature per second, we  use the circumference of circle to calculate how long it takes to bend the wire into a complete circle.

The machine bends 2 units of curvature per second, and the circumference of the circle is 8π units,

So, the time taken to bend wire into a complete circle is :

⇒ Time = (Circumference)/(Rate of bending),

⇒ Time = 8π/2,

⇒ Time = 4π ≈ 12.56 seconds.

Therefore, it would take approximately 12.56 seconds to bend a "straight-wire" into a circle.

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Answers:

(a)    $564,239.50

(b)    2026

(c)    $36,585.44

==========================================

Explanation:

Part (a)

One template for exponential equations would be

y = a*b^x

Another template is

y = a(1+r)^x

which is a bit more descriptive. I'll use the second template.

r is positive for exponential growth or appreciation.

The equation y = a(1+r)^x updates to y = 400000*(1+0.035)^x and then simplifies to y = 400000*(1.035)^x

From here we plug in x = 10 because the year 2015 is ten years after 2005.

So,

y = 400000*(1.035)^x

y = 400000*(1.035)^10

y = 564239.504248449

y = 564239.50

The house is worth about $564,239.50 in the year 2015.

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Part (b)

We work the process of part (a) in reverse.

This time we know what y is and we want to solve for x.

Use logarithms to isolate the exponent.

y = 400000*(1.035)^x

800000 = 400000(1.035)^x

800000/400000 = (1.035)^x

2 = (1.035)^x

Log(2) = Log( (1.035)^x )

Log(2) = x*Log( 1.035 )

x = Log(2)/Log(1.035)

x = 20.1487916840008

If x = 20, then,

y = 400000*(1.035)^x

y = 400000*(1.035)^20

y = 795,915.545386338

y = 795,915.55

We're short of the goal of $800,000.

If x = 21, then

y = 400000*(1.035)^x

y = 400000*(1.035)^21

y = 823,772.589474859

y = 823,772.59

We've gone over the goal.

Somewhere between x = 20 and x = 21 is when the house will be worth exactly $800,000.

It's better to side with x = 21 since x = 20 comes up short.

21 years after 2005 is 2005+21 = 2026

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Part (c)

Go back to the template: y = a(1+r)^x

This time we have

The r value is negative to indicate exponential decay or depreciation.

y = a(1+r)^x

y = 200000(1+(-0.02))^x

y = 200000(1-0.02)^x

y = 200000(0.98)^x

The 0.98 means the house keeps 98% of its value from year to year.

Plug in x = 10.

y = 200000(0.98)^x

y = 200000(0.98)^10

y = 163,414.56137751

y = 163,414.56

The house starts off at $200,000 and ten years later it's $163,414.56

Subtract the values to determine how much home value was lost.

200,000 - 163,414.56 = 36,585.44

The home value will have lost $36,585.44 over the 10 year period.