The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker, summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follows (AAII website, February 7, 2012) Brokerage Speed Satisfaction Scottrade, Inc 3.6 3.7Charles Schwab 3.5 3.6Fidelity Brokerage Services 3.6 4.1TD Ameritrade 3.8 3.9E*Trade Financial 3.4 3.1Vanguard Brokerage Services 4 3USAA Brokerage Services 4 3.8Thinkorswim 2.8 2.8Wells Fargo Investments 2.9 2.5Interactive Brokers 4.2 4.2Zecco.com 2.7 2.7a. Develop a scatter diagram for these data with the speed of execution as the independent variable b. What does the scatter diagram developed in part (a) indicate about the relationship between the 2 variables? c. Develop the least squares estimated regression equation d. Provide an interpretation for the slope of the estimated regression equation e. Suppose Zecco.com developed new software to increase its speed of execution rating. If the new software is able to increase Zecco.com's speed of execution rating from the current value of 2.7 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

The vertex form of the function is y = (x + 2)² - 9

The vertex is (-2 , -9)

We have,

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

(h , k) are the coordinates of the vertex point

a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept

h = -b/2a

k is the value of y when x = h

∵ y = x² +4x-5

∵ y = ax² + bx + c

∴ a = 1 , b = 4 , c  = -5

∵ h = -b/2a

∴ h = -4/2

∴ h = -2

To find k substitute y by k and x by -2 in the equation above

∵ k is the value of y when x = h

∵ h = -2

∴ k = (-2)² + 4(-2) - 5 = -9

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -2 , k = -9

∴ y = (1)(x - (-2))² + (-9)

∴ y = (x + 2)² - 9

∵ (h , k) are the coordinates of the vertex point

∵ h = -2 and k = -9

∴ The vertex is (-2 , -9)

The vertex form of the function is  y = (x + 2)² - 9

The vertex is (-2 , -9)

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To find the probability that the sample mean will be less than $11.482, first calculate the z-score:

Z = (Sample Mean - Population Mean) / Standard Error

Z = ($11.482 - $11.32) / $0.0985 ≈ 1.6434 (rounded to four decimal places)

a. To calculate the standard error of the mean, use the following formula:

Standard Error = (Standard Deviation) / √(Sample Size)

In this case, the standard deviation is $0.54, and the sample size is 30.

Standard Error = ($0.54) / √(30) ≈ $0.0985 (rounded to four decimal places)

b. To find the probability that the sample mean will be less than $11.482, first calculate the z-score:

Z = (Sample Mean - Population Mean) / Standard Error

Z = ($11.482 - $11.32) / $0.0985 ≈ 1.6434 (rounded to four decimal places)

Now, use a standard normal distribution table to find the probability corresponding to the z-score:

P(Z < 1.6434) ≈ 0.9499 (rounded to four decimal places)

c. To find the probability that the sample mean will be less than $11.27, first calculate the z-score for this value:

Z = ($11.27 - $11.32) / $0.0985 ≈ -0.5063 (rounded to four decimal places)

Now, use a standard normal distribution table to find the probability corresponding to the z-score:

P(Z < -0.5063) ≈ 0.3064 (rounded to four decimal places)

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The slope intercept form of the equation for each line is y = -1/3 -x.

When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.

Here, m is slope and c is constant.

To find the slope intercept form of the equation,

(4, -2) and (-5, 3)

The slope intercept form of the equation is y = -(3/4)x + 3.

Therefore, the slope of the line is;

m = Δy/Δx

m = 5/-9

When we simplify it, then we get the;

3 - y= -5/9(-5-x)

y = -25/9-3 -x

y = -3/9 -x

y = -1/3 -x

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4a) The null hypothesis is that there is no difference in math performance between learning while listening to classical music and learning without music.
4b) The research/alternative hypothesis based on the researcher's hypothesis is that learning while listening to classical music improves math performance.
4c) The mean math performance when music played was 15.5, and when no music played was 17.9. The calculated t statistic was -4.60, and the p-value associated with the test statistic was < .001.
4d) The p-value associated with this result is less than .05.
4e) Based on the p-value, we reject the null hypothesis.
4f) The result is statistically significant.
4g) Based on this information alone, it is not safe to conclude that students perform better when listening to music while learning. Other factors could have influenced the results, such as individual differences in the students or other environmental factors. Further research would be necessary to make a definitive conclusion.
4a.) The null hypothesis states that there is no significant difference in math performance between the two conditions (learning with classical music and learning without music).

4b.) The research/alternative hypothesis states that learning while listening to classical music improves performance in math compared to learning without music.

4c.)
- Mean math performance when music played: 15.5
- Mean math performance when no music played: 17.9
- Calculated t statistic: -4.60
- P-value associated with the test statistic: < 0.001

4d.) The p-value associated with this result is less than 0.05.

4e.) Based on the p-value, we reject the null hypothesis.

4f.) The result is statistically significant.

4g.) While the result is statistically significant, it actually shows that students performed better when not listening to music while learning. This contradicts the researcher's initial hypothesis, so it is not safe to conclude that students perform better when listening to music while learning.

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The equation of the line is: y = x + 10.

We are given that;

The points= ( − 2 , 2 ) (−2,2) and ( − 8 , 8 ) (−8,8).

Now,

Let’s apply these steps to find the equation of the perpendicular bisector.

To find the midpoint of (-2, 2) and (-8, 8). Using the midpoint formula, we get: ( (-2 + -8) / 2, (2 + 8) / 2) ( -10 / 2, 10 / 2) ( -5, 5) The midpoint is (-5, 5).

To find the slope of (-2, 2) and (-8, 8). Using the slope formula, we get: (8 - 2) / (-8 - -2) 6 / -6 -1 The slope is -1.

To find the negative reciprocal of -1. To do this, we flip the fraction and change the sign. Since -1 is equivalent to -1/1, we get: -1/1 1/-1 1 The negative reciprocal is 1.

The equation of a line in slope-intercept form using the slope of 1 and the midpoint (-5, 5) as a point on the line. Substituting these values into y = mx + b, we get: y = 1x + b 5 = 1(-5) + b 5 = -5 + b 10 = b The y-intercept is 10.

This is the equation of the perpendicular bisector of the line segment whose endpoints are (-2, 2) and (-8, 8).

Therefore, by the equation the answer will be y = x + 10

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(1) The x-intercept is 3

(2) The x-intercept is -2/3

(3)  3x² - 12x factorized as 3x(x - 4)

(4) x² - 49 factorized as  (x + 7)(x - 7)

(5) x² + 9x + 18  factorized as (x + 3 )(x + 6)

The x-intercept of the function is calculated as follows;

0 = -3x + 9

3x = 9

x = 9/3

x = 3

0 = 6x + 4

-4 = 6x

x = -4/6

x = -2/3

The expressions are factorized as follows;

3x² - 12x

= 3x(x - 4).

x² - 49

apply difference of two squares;

x² - 49 = (x + 7)(x - 7).

x² + 9x + 18

= x² + 6x + 3x + 18

= x (x + 6) + 3 (x + 6)

= (x + 3 )(x + 6)

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The inequality that is not equivalent to others is D -x<3

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

A -x>-3

B x <3

C x+1 <4

D -x<3

When the expressions are solved, we have

A x < 3

B x <3

C x <3

D x > 3

Hence, the odd option is D -x<3

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The calculated value of the area of this figure is 30 sq units

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

The composite figure

The area is the sum of the individual areas

Using the above and the area formulas as a guide, we have the following:

Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 8) * 4

Evaluate

Area = 30

Hence, the area is 30 sq units

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The linear function in this problem is given as follows:

y = -1/4x + 5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

What differentiates a linear function from the other functions is the variable x has an exponent of 1.

2x + 7 = 12 is not a function, as it does not have the y variable, it is an equation.

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The price per ticket that maximizes profit is $3.50.

The appropriate range for the given situation is 1.28  ≤ t ≤ 5.72.

PART 1

For a quadratic equation of the form of at² + bt + c. The maximum value of t is given by:

t = -b/2a

We have the function that model the profit: P(t)= -60t² + 420t - 440.

The price per ticket that maximizes profit is:

t = -b/2a,

where the  In this case, a = -60 and b = 420

t = -420/(2*(-60)) = 3.5.

Thus, the price per ticket that maximizes profit is $3.50.

PART 2

To find the appropriate range for the given situation, we have to solve for the two values of t.

P(t)= -60t² + 420t - 44

t = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

t = [-420 ± √(420² - 4(-60)(-440))] / 2(-60)

t = (-420 ± √(70800)) / (-120)

t = (-420 ± 266.08) / (-120)

t = 1.28 or 5.72

Thus, the appropriate range for the given situation is 1.28  ≤ t ≤ 5.72.

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Your answer is correct, the function is not a quadratic function.

A quadratic is a polynomial function such that the degree of the polynomial (this is the maximum exponent of the polynomial) is 2.

In the given one we have:

f(x) = 4x³ - 5x + 2

You can see that the maximum exponent is 3, so this is not a quadratic function,. so your answer is correct.

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To solve this problem, we need to use the normal distribution formula and standard deviation. We know that the mean score is 530.4 and the standard deviation is 25.7.

First, we need to standardize the score by calculating the z-score:

z = (534 - 530.4) / 25.7 = 0.141

Next, we can use a standard normal distribution table or a calculator to find the probability that a randomly chosen student scores 534 or higher:

P(z > 0.141) = 1 - P(z < 0.141)

Using a standard normal distribution table, we can find that P(z < 0.141) = 0.5564

Therefore,

P(z > 0.141) = 1 - 0.5564 = 0.4436

So the probability that a single student is randomly chosen from all those taking the test scores 534 or higher is 0.4436 or 44.36%.

In summary, the standard deviation and normal distribution formula are used to determine the probability of a student scoring 534 or higher on the SAT. The answer is calculated by standardizing the score, finding the area under the normal curve using a table or calculator, and subtracting from one to get the probability of a score above 534.

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There are 4/7 groups of 7/4 in 1.

The quotient for 3 divided by 7/4 is 12/7

We have,

Groups = 7/4

Entity = 1

So, the number of groups is

Number =Entity/Groups

Number = 1/(7/4)

Number = 4/7

Hence, there are 4/7 groups of 7/4 in 1

2. 3 divided by 7/4

Divisor = 7/4

and, Dividend = 3

So, the quotient is

Quotient = Dividend/Divisor

Quotient =3/(7/4)

Quotient = 12/7

Hence, 3 divided by 7/4 is 12/7

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The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .

First, find the number of people who have the flu:

= 5. 2 % x 10, 000

= 520 people

Those who don't have it:

= 10, 000 - 520

= 9, 480 people

True positive :

= 92 % x 520

= 478 people

False negatives:

= 8 % x 520

= 42 people

False positives:

= 15 % x 9, 480

= 1, 422 people

The ratio of true positives to false positives is therefore:

478 : 1, 422

239 : 711

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P (1), P (2), P (3)..., P (k) are all true, where k is a specific large, positive integer. The steps for a proof by mathematical induction that P (n) is true for all positive integers n are:

1. Verify that P (1) is true.
2. Demonstrate that the conditional statement P (k) implies P(k+1) is true for all positive integers k.
3. Verify that P (1), P (2), P (3) ..., P(k) are all true, where k is a specific large, positive integer.

Therefore, the correct answer is: Verify that P (1) is true, demonstrate that the conditional statement P(k) implies P(k+1) is true for all positive integers k, and verify that P (1), P (2), P (3),..., P (k) are all true, where k is a specific large, positive integer. These two steps are essential for proving a statement by mathematical induction. The other options provided do not follow the correct process for a proof by induction.

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The forecasting method that considers a number of variables, together with the effects of each on the item of interest, is called the "Multiple Regression" method.

The forecasting method that considers a number of variables, together with the effects of each on the item of interest, is called multiple regression analysis. This method takes into account various independent variables that can affect the outcome of interest and use statistical techniques to estimate their impact on the forecasted variable.

By analyzing multiple variables, this method provides a more comprehensive and accurate prediction than other forecasting methods that rely on only a single variable. In this method, various independent variables are used to predict the value of a dependent variable (the item of interest). By analyzing the relationships between these variables, more accurate forecasts can be generated.

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The type of items on the list, and the amount of time between list presentation and recall.

The shape of the function relating the probability of an item's recall to the item's position on a list is typically described as the serial position curve. The curve is generally U-shaped, with a higher probability of recall for items at the beginning and end of the list and a lower probability of recall for items in the middle of the list. This pattern is known as the primacy and recency effect, respectively.

The primacy effect refers to the higher probability of recall for items at the beginning of the list, which is thought to be due to the greater opportunity for rehearsal and encoding of these items into long-term memory. The recency effect refers to the higher probability of recall for items at the end of the list, which is thought to be due to the items still being held in short-term memory and easily retrieved.

Overall, the shape of the function can be affected by various factors such as the length of the list, the type of items on the list, and the amount of time between list presentation and recall.

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The option that makes this approach a valid method in general for solving a system of equations is A. As long as addition is used on both sides or subtraction is used on both sides, a true equation will remain true.

Option A is a correct reflection of the cause and effect of using addition or subtraction on both sides in solving an equation. While accurate, as well, option B fails to provide an adequate explanation for Derrick's approach.

As seen in Option C, one step of Derrick's plan involves adding equations A and B with the intent of eliminating the y-term. Nevertheless, this specific action only partially speaks to the effectiveness of his overall system of equations method.

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C. If we assume that 56% of Americans says that GM foods are generally unsafe to eat, then there is an 8.5% chance that random sample results will show 61% or more who says that GM foods are generally unsafe to eat.

This interpretation correctly states that the p-value represents the probability of obtaining a sample result as extreme or more extreme than the observed result (61%) if the null hypothesis (that the percentage is equal to 56%) is true. It does not mean that there is an 8.5% chance that the true percentage is 56%.

C. If we assume that 56% of Americans says that GM foods are generally unsafe to eat, then there is an 8.5% chance that random sample results will show 61% or more who says that GM foods are generally unsafe to eat.

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To count the number of different 6-letter strings that can be formed using the letters c, i, r, c, l, and e, we can use the permutation formula. There are 6 choices for the first letter, 5 choices for the second letter (since we can't use the same letter twice), and so on, giving us:

6 x 5 x 4 x 3 x 2 x 1 = 720

However, not all of these strings meet the condition that the two occurrences of the letter c are separated by at least one other letter. To count the number of strings that do meet this condition, we can use the complementary counting method.

First, let's count the number of strings in which the two c's are adjacent. There are 5 positions where the two c's could be (the first two, second and third, third and fourth, fourth and fifth, or last two positions), and once we place the c's, we have 4 letters left to fill in the remaining 4 positions. This gives us:

5 x 4 x 3 x 2 x 1 = 120

Now, let's count the total number of 6-letter strings that have at least one pair of adjacents c's. We can use the same method as above, but this time we can place the two c's anywhere in the string, giving us:

6 x 5 x 4 x 3 x 2 x 1 - 5 x 4 x 3 x 2 x 1 = 720 - 120 = 600

Finally, we can subtract this from the total number of 6-letter strings to get the number of strings in which the two c's are separated by at least one other letter:

720 - 600 = 120

Therefore, there are 120 different 6-letter strings that can be formed using the letters c, i, r, c, l, and e in which the two occurrences of the letter c are separated by at least one other letter.

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This implementation uses recursion to find the area of a triangle with a given width. The method continues to call itself with smaller width values until it reaches the base case, then combines the results to calculate the total area.

It looks like your question is related to recursion and finding the area of a triangle using the `getArea()` method in a Triangle class. Based on the given information, here's a step-by-step explanation of the recursive approach:

1. Define a Triangle class with a property `width`.
2. Implement a method `getArea()` within the Triangle class.
3. In the `getArea()` method, use a base case to terminate the recursion. For example, when the width is 1 or 0, return the current width value as the area.
4. For the recursive case, reduce the width by 1 and call the `getArea()` method recursively.
5. Add the current width value to the result of the recursive call and return it.

Here's a possible implementation of the `getArea()` method:

```java
public int getArea() {
 if (width == 0 || width == 1) {
   return width;
 } else {
   Triangle smallerTriangle = new Triangle(width - 1);
   int smallerArea = smallerTriangle.getArea();
   return width + smallerArea;
 }
}
```

This implementation uses recursion to find the area of a triangle with a given width. The method continues to call itself with smaller width values until it reaches the base case, then combines the results to calculate the total area.

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The total area under the standard normal curve to the left of t and to the right of z is the sum of these two areas, which is 0.1664 + 0.1664 = 0.3328. Rounded to four decimal places, the answer is 0.3328.

To find the total area under the standard normal curve to the left of t, we need to look up the z-score corresponding to t = -1.88 in a standard normal distribution table. This gives us a z-score of -0.9693. The area to the left of this z-score can be found in the table or using a calculator, and it is 0.1664.

To find the total area under the standard normal curve to the right of z, we need to look up the z-score corresponding to z = 1.88 in the same table. This gives us a z-score of 0.9693. The area to the right of this z-score can also be found in the table or using a calculator, and it is 0.1664.

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Option B is correct, the value of x in the triangle is 13.

The given triangle is a right angle triangle

We have to find the value of x which is hypotenuse length in the triangle

By pythagoras theorem we find the value of x in triangle

12²+5²=x²

144+25=x²

169=x²

Take square root on both sides

x=13

Hence, option B is correct, the value of x in the triangle is 13.

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Answer: 568mm ²

Step-by-step explanation:

area of trapezoid = [h(b₁+b₂)]/2

b₁ and b₂ are the lengths of the top and bottom sides, h is the height; 16

The actual change in the politician's support is 17% (51% - 34%). The relative change can be calculated as (actual change/original value) x 100, which in this case is ((51% - 34%)/34%) x 100 = 50%. Therefore, the politician's support has increased by 50% relative to the original value of 34%.

To determine the actual and relative change in a politician's support that increases from 34% to 51%, we need to follow these steps:

Step 1: Calculate the actual change.
Actual Change = Final Percentage - Initial Percentage
Actual Change = 51% - 34%
Actual Change = 17%

Step 2: Calculate the relative change.
Relative Change = (Actual Change / Initial Percentage) * 100
Relative Change = (17% / 34%) * 100
Relative Change ≈ 50%

So, the actual change in the politician's support is 17%, and the relative change is approximately 50%.

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The number of vases painted in the second week is given as follows:

39 vases.

The number of vases painted in the second week is obtained applying the proportions in the context of the problem.

They painted 225% more vases than in the first week, hence the equivalent percentage is of 100 + 225 = 325%, which is 3.25 times more vases than in the first week.

They painted 12 vases in the first week, hence the number of vases painted in the second week is given as follows:

3.25 x 12 = 39 vases.

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The full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.  When converting 104 from base 10 to base 2 using repeated division by 2.

The quotient obtained from the third division is as follows:

1. 104 ÷ 2 = 52 (remainder: 0)
2. 52 ÷ 2 = 26 (remainder: 0)
3. 26 ÷ 2 = 13 (remainder: 0)

After the third division, the quotient is 13. The full answer for converting 104 to base 2 will require a few more divisions:

4. 13 ÷ 2 = 6 (remainder: 1)
5. 6 ÷ 2 = 3 (remainder: 0)
6. 3 ÷ 2 = 1 (remainder: 1)
7. 1 ÷ 2 = 0 (remainder: 1)

Reading the remainder from bottom to top, the full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.

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The probability that a laser fails before 5,800 hours is approximately 0.3505 or 35.05%.

The life in hours that 90% of the lasers exceed is approximately 21,713 hours.

a. To find the probability that a laser fails before 5,800 hours, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF of an exponential distribution with mean μ is given by F(x) = 1 - e^(-x/μ). Plugging in the values given, we get F(5,800) = 1 - e^(-5,800/7,000) ≈ 0.3505.

b. To find the life in hours that 90% of the lasers exceed, we need to find the 90th percentile of the exponential distribution. The 90th percentile, denoted by x_0.9, is the value such that P(X > x_0.9) = 0.1, where X is the random variable representing the life of the laser. Using the formula for the CDF of the exponential distribution, we can write this as e^(-x_0.9/7,000) = 0.1. Solving for x_0.9, we get x_0.9 = -7,000 ln(0.1) ≈ 21,713.

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The value of x. if the angle CBA is a right angle is -36

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

The measure of CBA is (0.25x +99)

Assuming the angle is a right angle

Then we have

0.25x +99 = 90

Subtract 99 from both sides

0.25x = -9

So, we have

x = -36

Hence the value of x is x = -36

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Answer:

The house will be worth $287,163 in 5 years.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (the value of the house in 5 years)

P = the initial amount (the value of the house when it was bought)

r = the annual interest rate (5%)

n = the number of times the interest is compounded in a year (we will assume it is compounded annually, so n = 1)

t = the number of years (5)

Plugging in the values, we get:

A = 225,000(1 + 0.05/1)^(1*5)

A = 225,000(1.05)^5

A = 225,000(1.27628)

A = $287,163.00

Therefore, the house will be worth approximately $287,163 in 5 years, rounded to the nearest dollar.

Answer:

$287.2 (After I round it)

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