Paul has 2/3 as many postcards as Shawn. The number of postcards Shawn has is 3/5 of the number of postcards Tim has. If the three boys have 280 postcards altogether, how many more postcards does Tim have than Paul

This is an improper. Perhaps you can fix it, so that I can assist you with it? I apologise.

Answer:

Q(x) = [tex](x+3)^{2}+5[/tex] is the final equation.

Step-by-step explanation:

By translation of the graph 3 units upward direction, it means that the y-value of the function is increased by 3 unit at each value of x.

Given , P(x) = [tex](x+3)^{2}+2[/tex]

We can actually translate the graph in any direction, and for that we have to make the necessary changes. If we translate the graph in the positive x direction, then we have to substitute (x - 3) instead of x in the equation.

Since we are translating the graph upwards ,

Q(x) = [tex](x+3)^{2}+2[/tex] + 3

Q(x) = [tex](x+3)^{2}+5[/tex]

This is the final equation of the graph after translation.

Answer:

0.140625

Step-by-step explanation:

Total numbers of possible combinations for a coin = 2^n

If the coin is tossed 10 times, we have 2^10 = 1024

If the coin is tossed once, we have 2^1 = 2 outcomes.

The possible outcomes are H, T.

We have 2 outcomes with no two consecutive head.

If the coin is tossed twice, we have 2^2 = 4 outcomes.

The possible outcomes are HH, HT, TH, TT

We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.

If the coin is tossed thrice, we have 2^3 = 8 outcomes.

The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT

We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.

Comparing the results from the outcomes of the coin,we have 2,3,5,......

This looks like a financial sequence. For the next 10 tosses, we have

2,3,5,8,13,21,34,55,89,144

We have 144 outcomes without two consecutive heads if the coin is tossed 10 times

Pr(number of two consecutive Heads in 10 tosses) = 144/1024

= 0.140625

The probability that two heads do not occur consecutively in 10 coin tosses is 45/512 or approximately 0.0879.

In order to calculate the probability that two heads do not occur consecutively in 10 coin tosses, we can use the concept of permutations with restrictions. Let's consider the possibilities:

When choosing a head, there are 10 possibilities for the first head (H) and 9 possibilities for the second head.

This gives us a total of 10 * 9 = 90 possibilities.

When choosing tails (T), there are 2 possibilities for each toss, giving us a total of 2^10 = 1024 possibilities.

Therefore, the probability that two heads do not occur consecutively is 90/1024, which simplifies to 45/512 or approximately 0.0879.

Answer:

Marks answer is more representative

Step-by-step explanation:

The number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Kevin and Mark took a random sample of 100 pieces of trail mix to determine the number of peanuts, raisins, and almonds in a container. If each container of trail mix is known to have 40% peanuts, 40% almonds, and 20% raisins.

The number will be calculated as,

40% peanut = 100 x 40 / 100 = 40

40% almonds =  100 x 40 / 100 = 40

20 % raisins = 100 x 20 /100 = 20

Therefore, the number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.

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Answer:

  B)  0.11

Step-by-step explanation:

Use the conditional probability formula.

  P(transfer | never graduated) = P(transfer & never graduated) / P(never graduated)

__

Denominator

But the P(never graduated) is made of two parts:

  P(never graduated) = P(transfer & never graduated) + P(freshman & never graduated)

  = (1 -0.80)×(1 -0.85) + (0.80)×(1 -0.70)

  = (0.20)(0.15) + (0.80)(0.30)

  = 0.0300 +0.2400 = 0.2700

__

Numerator

The numerator of our fraction is one of the components we just calculated:

 P(transfer & never graduated) = (1 -0.80)×(1 -0.85) = 0.0300

__

Conditional Probability

So ...

  P(transfer | never graduated) = 0.0300/0.2700 = 1/9 ≈ 0.11

A linear relation is described by an equation of the form y = mx + b, where m is the slope and b is the y-intercept. None of the options provided describe a linear relation.

A linear relation is described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept. Option A, "Double x and subtract five to get y," does not fit this form. Options B, C, and D do not fit this form either. Therefore, none of the given options describe a linear relation. The correct answer is none of the above.

Answer:B

Step-by-step explanation:

17, 300+ 1.25% You can take the decimal and move it to the other side then start doing the math

Answer:

C; 21625

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will separate our trips as "slow" and "fast".  Filling in a motion table:

              d        =        r        x        t

slow

fast

We know that the slow rate is 40 mph and the time is, in hours (because the time has to match the rate.  We can't say "40 mph" and then state the time in minutes), 1 hour.

We know that the fast rate is 70 mph and the time in hours is .5 hours.

If distance = rate times time, then the distance traveled at the slow speed is 40 * 1 = 40 miles

The distance traveled at the fast speed is 70 * .5 = 35 miles.

The trip was 40 + 35 = 75 miles total, and the time it took was 1 + .5 = 1.5 hours.

Answer:

The probability is [tex]\frac{16}{43}[/tex]

Step-by-step explanation:

The psychology class has 9 freshman male, 15 freshman females, 8 sophomore male and 12 sophomore female.

Total population constitution of the class=

17 males and 27 females and 44 students in total.

If on selecting on the first attempt, a male has been picked up then the number of males for the picking up in the second attempt has to decrease by one.

Also, the total number of students from which it has to be selected also decreases by 1, because one child has already been selected.

Therefore for Second Attempt, Total 43 students and 16 males.

Probability=[tex]\frac{No.OfFavorableOutcomes}{TotalNo.OfOutcomes}[/tex]

Probability=[tex]\frac{16}{43}[/tex]

Final answer:

The probability that the second student will also be a male, given that the first student is a male, is 16/43.

Explanation:

To find the probability that the second student will also be a male, given that the first student is a male, we need to determine the number of males left in the sample space after choosing the first male student. In the class, there are 9 freshman males and 8 sophomore males, making a total of 17 males. However, since we are choosing 2 students, the total sample space decreases by 1 after choosing the first male student.

Therefore, the probability of choosing a male as the second student, given that the first student is a male, is:
P(second student is male | first student is male) = (number of males left in sample space after choosing first male) / (total sample space after choosing first male)

P(second student is male | first student is male) = 16/43

Answer:

The probability of making at least one of these errors is 0.0025

Step-by-step explanation:

Consider the provided information.

Let P represents the error in processing.

Let F represents the error in filling.

Let R represents the error in retrieving.

The probability of an error in processing is 0.0010: P(P) = 0.0010

The probability of an in filing is 0.0009: P(F) = 0.0009

The probability of an error in retrieving is 0.0012: P(R) = 0.0012,

The probability of an error in processing as well as filing is 0.0002:

P(P∩F) = 0.0002

The probability of an error in processing as well as retrieving is 0.0003,

P(P∩R) = 0.0003

The probability of an error in processing and filing as well as retrieving is 0.0001.

P(P∩F∩R)=0.0001

P(R∩F)=0.0002

The probability of at least one is:

P(P∪F∪R)=P(P)+P(R)+P(F)-P(P∩F)-P(P∩R)-P(R∩F)+P(P∩F∩R)

P(P∪F∪R)=0.0010+0.0009+0.0012-0.0002-0.0002-0.0003+0.0001

P(P∪F∪R)=0.0025

Hence, the probability of making at least one of these errors is 0.0025

The required diagram is shown below.

Answer:

Step-by-step explanation:

The formula we need here is

[tex]6(6+x)=5(5+x+3)[/tex]

which simplifies to

[tex]6(6+x)=5(8+x)[/tex]

which simplifies to

36 + 6x = 40 + 5x and

x = 4

So DG = 5 + 4 + 3 which is 12

Answer:

The correct answer is C. 12

Step-by-step explanation:

I just took the test

Answer:

The 99% confidence interval is given by (8.4;12.6)  

A. (8.4,12.6)

Step-by-step explanation:

1) Notation and definitions  

n=100 represent the sample size  

[tex]\bar X= 10.5[/tex] represent the sample mean  

[tex]\sigma=8[/tex] represent the population standard deviation  assumed

m represent the margin of error  

Confidence =99% or 0.99

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

2) Calculate the critical value zc  

On this case we can to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. The degrees of freedom are given by:  

We can find the critical values in excel using the following formulas:  

"=NORM.INV(0.005,0,1)" for [tex]z_{\alpha/2}=-2.58[/tex]  

"=NORM.INV(1-0.005,0,1)" for [tex]z_{1-\alpha/2}=2.58[/tex]  

The critical value [tex]zc=\pm 2.74[/tex]  

3) Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

[tex]m=z_c \frac{\sigma}{\sqrt{n}}[/tex]  

[tex]m=2.58 \frac{8}{\sqrt{100}}=2.064[/tex]  

4) Calculate the confidence interval  

The interval for the mean is given by this formula:  

[tex]\bar X \pm z_{c} \frac{\sigma}{\sqrt{n}}[/tex]  

And calculating the limits we got:  

[tex]10.5 - 2.58 \frac{8}{\sqrt{100}}=8.4[/tex]  

[tex]10.5 + 2.58 \frac{8}{\sqrt{100}}=12.6[/tex]  

The 99% confidence interval is given by (8.4;12.6)  

A. (8.4,12.6)

Answer:

We conclude that the steel has an average hardness index of at least 64.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 64

Sample mean, [tex]\bar{x}[/tex] = 62

Sample size, n = 50

Alpha, α = 0.051

Sample standard deviation, s = 8

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 64\\H_A: \mu < 64[/tex]

We use one-tailed(left) z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{62 - 64}{\frac{8}{\sqrt{50}} } = -1.767[/tex]

Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -2.33[/tex]

Since,  

[tex]z_{stat} > z_{critical}[/tex]

We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that the steel has an average hardness index of at least 64.

This means that there is not enough evidence to support the claim that the average hardness index is less than 64.

To test the manufacturer's claim, we can conduct a one-sample z-test. The null hypothesis  is that the average hardness index is 64, and the alternative hypothesis  is that the average hardness index is less than 64.

 Given:

First, we calculate the standard error (SE) of the mean:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{8}{\sqrt{50}} \approx 1.1314 \][/tex]

 Next, we calculate the test statistic (z):

[tex]\[ z = \frac{\bar{x} - \mu_0}{SE} = \frac{62 - 64}{1.1314} \approx -1.7679 \][/tex]

 Now, we need to find the critical z-value for a one-tailed test at the 1% significance level.

From the standard normal distribution table, the critical z-value for the 99th percentile is approximately 2.326.

 Since the calculated z-value (-1.7679) is greater than the critical z-value (-2.326), we fail to reject the null hypothesis.

This means that there is not enough evidence to support the claim that the average hardness index is less than 64.

Answer:

  multiply the left side of the constant vector by the inverse matrix

Step-by-step explanation:

The matrix equation ...

  AX = B

is solved by left-multiplying by the inverse of A:

  A⁻¹AX = A⁻¹B

  IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix

  X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix

[tex]\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right][/tex]

Answer:

I used the above answer and got it wrong. Hope this helps! (Sorry it looks a little weird... just look at whta is in the boxes)

Step-by-step explanation:

The number 31 is a prime number and has exactly one factor pair which is 1 and the number itself, so the correct answer is option B.

The value 31 is considered a prime number.

A prime number is a number that only two distinct positive divisors: 1 and itself. Therefore, every prime number has exactly one factor pair, which is 1 and the number itself.

So, option B-31 is a prime because it has 1 factor pair is the correct answer. This means that the factors of 31 are simply 1 and 31.

so the correct answer is option B.

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Final answer:

The number 31 is a prime number because it is only divisible by 1 and itself, hence it has one factor pair, which is (1, 31). The correct answer to the question is B - 31 is a prime because it has 1 factor pair.

Explanation:

The question is asking whether the number 31 is a prime number or a composite number and to identify the number of factor pairs it has. A prime number is a number that has only two factors, 1 and the number itself. In contrast, a composite number is a number that has more than two factors.

For the number 31, we can confirm that it is not divisible by any integers other than 1 and 31 without a remainder. Therefore, 31 is a prime number, and it has only one factor pair, which is (1, 31). There are no other pairs of numbers that multiply together to give the product of 31. Thus, the correct choice is B - 31 is a prime because it has 1 factor pair.

Answer:

10:55

Step-by-step explanation:

Hour hand is at the 10,  minute hand at the 11 (which means 11 * 5 = 55)

Final answer:

The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. The function that models this relationship is f = 1800/d.

Explanation:

The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. In this case, the force required to move the rock varies inversely with the distance. Let's denote the force as f and the distance as d. The inverse variation function is given by f = k/d, where k is a constant.

To find the value of k, we can use the given information. When a force of 50 pounds is applied 36 inches from the pivot point, the rock is moved. Plugging these values into the inverse variation equation, we have 50 = k/36. Solving for k, we get k = 50 x 36 = 1800.

Therefore, the function that models the relationship between the force applied to the lever (f) and the distance of the applied force from the pivot point (d) is f = 1800/d.

The function that models the relationship between the force (f) applied and the distance (d) from the pivot point is:

[tex]f(d) = \frac{1800}{d}[/tex]

To model the relationship between the force (f) applied to the lever and the distance (d) from the pivot point, we need to understand that the force varies inversely with the distance. This means that as the distance increases, the force required decreases, and vice versa.

The mathematical model for such a relationship is given by the equation:

[tex]f = \frac{k}{d}[/tex]

Here, k is a constant that we need to determine using the given information. We know that a force of 50 pounds is applied to the lever 36 inches from the pivot point. Plug these values into the equation to find the value of k:

[tex]50 = \frac{k}{36}[/tex]

To solve for k, multiply both sides by 36:

[tex]k = 50 \times 36[/tex]

[tex]k = 1800[/tex]

Now, we substitute the value of k back into the equation to get the final model:

[tex]f = \frac{1800}{d}[/tex]

Answer:

The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]  

Step-by-step explanation:

Given:

Let the Number of CDs Monique has be represented as 'x'

Now Given:

Patricia has 6 less than three times the number of CDs in her collection than Monique has.

It means Number of CDs Patricia has is equal to 3 multiplied by number of   CDs Monique has and then Subtracting by 6.

Framing in equation form we get;

Number of CD' Patricia has  = [tex]3x-6[/tex]

Hence The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]  

Answer:

  [tex]h_2(t)=-16t^2+269[/tex]

Step-by-step explanation:

Put the initial height of ball 2 into the given formula. The problem statement tells you "h" stands for the initial height, and that height is 269 feet.

  [tex]h_2(t)=-16t^2+269[/tex]

Answer:

A. [tex]\displaystyle (x - 5)^2[/tex]

Step-by-step explanation:

Find two quantities that when added to −10, they are also multiplied to 25, and that number is a double −5.

I am joyous to assist you anytime.

Final answer:

The expression x^2-10x+25 can be factored as (x - 5)(x - 5).

Explanation:

The expression x^2-10x+25 can be factored as (x - 5)(x - 5). To factor the expression x^2-10x+25, we need to find two numbers that when multiplied together give us 25 (the constant term), and when added together give us -10 (the coefficient of the x term). In this case, the two numbers are -5 and -5. Therefore, the factored form of the expression is (x - 5)(x - 5), which is the same as option A.

Answer:B. 2x^2 + 4x - 1 - 9/4x + 1

Step-by-step explanation:

f(x) = 8x^3 + 18x^2 − 10

g(x) = 4x + 1

We want to determine f(x)/g(x). We would apply the long division method. The steps are shown in the attached photo.

The correct answer is

2x^2 + 4x - 1 - 9/4x + 1

Answer:

[tex]\text{B. }2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]

Step-by-step explanation:

One way is to use long division.

          2x² +  4x           -   1            

4x + 1) 8x³ + 18x²         - 10

          8x³  +  2x²                    

                    16x²

                    16x² + 4x              

                              -4x - 10

                              -4x -   1

                                    -   9

[tex]\dfrac{8x^{3} + 18x^{2} - 10} {4x+1} = 2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]

Answer:

n = 61 costumers

Step-by-step explanation:

For calculating the number of costumers he should sample we use the next equation:

[tex]n = \frac{z_{1-\alpha/2}^{2}p(1-p)}{E^{2} }[/tex]

                          Where E is the error that we are prepared to accept, in this  case E = 0.15

How we don't know the value of p, we can estimate it like p = 0.5

∝ = 1-0.98 = 0.02

1-∝/2 = 0.99

[tex]z_{0.99} = 2.33[/tex]

[tex]n = \frac{(2.33^{2})(0.5)(1-0.5)}{0.15^{2} }[/tex]

n = 60.32 costumers

n ≈ 61 costumers

Final answer:

To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula: n = (Z^2 * p' * (1-p')) / E^2. The manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98.

Explanation:

To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula:

n = (Z^2 * p' * (1-p')) / E^2

Where:

n is the sample size

Z is the z-score corresponding to the desired confidence level

p' is the estimated proportion

E is the maximum error or margin of error

In this case, the manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98. Assuming p' is 0.5, we can calculate the required sample size.

Answer:

Explanation:

The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:

The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:

Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.

Answer:

128 servings

Step-by-step explanation:

16 cups in a gallon

16/1.25 = 12.8

12.8 * 10 = 128

128 servings

Answer:

Step-by-step explanation:

f(x) = sin(4x)f'    = 4 cos(4x)f''   = -16 sin(4x)f'''  = -64 cos(4x)f⁽⁴⁾ = 256 sin(4x)f⁽⁵⁾ = 1024 cos(4x)The 4-th order Taylor series expansion isf(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4!)f⁽⁴⁾(x) + ...The Maclaurin series is obtained by setting x = 0.Note that sin(0) = 0 and cos(0) = 1.The non zero terms aref(h) = 4h - (4h)³/3! + (4h)⁵/5! - (4h)⁷/7! + ...Answer: f(x) =4x- 4/3+4x/5+4x7

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Answer:

Small candies [tex]=9[/tex]

Extra large candies [tex]=12[/tex]

Step-by-step explanation:

Let small candies [tex]=x[/tex]

Extra large candies [tex]=y[/tex]

the number of candies is at least [tex]20[/tex].

[tex]x+y\geq20[/tex]

Cost of [tex]1[/tex] small candy [tex]=\$4[/tex]

Cost of [tex]1[/tex] extra large candy [tex]=\$12[/tex]

but she has only [tex]\$180[/tex] to spend

[tex]4x+12y\leq180[/tex]

Solve for

[tex]x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}[/tex]

Since number of candies should be integer.

let [tex]x=7,y=13[/tex]

total spend [tex]4\times7+12\times13=184 [/tex] which is more than [tex]\$180[/tex], so this combination is not possible.

[tex]let\ x=8,y=12\\8\times4+12\times12=176<180[/tex]

She has [tex]\$4[/tex] more so she can buy [tex]1[/tex] more small candy.

Hence  small candy [tex]=9[/tex]

extra large candy [tex]=12[/tex]

Answer:L(t) = 40 - 2t

Step-by-step explanation:

Total amount of money that Logan borrowed from his friend to buy the video game system is $40

Let x represent the constant amount that he agreed to pay the friend back each week.

After 7 weeks, he still owed his friend $26. This means that the amount that he paid in 7 weeks is 7×x = $7x

He still owed his friend $26.

This means that amount paid in 7 weeks would be 40 - 26 = $14

Therefore

7x = 14

x = 14/7 = 2

He pays $2 each week.

Let t represent the number of weeks, the equation for the function L(t),representing the amount Logan owes his friend after t weeks would be

L(t) = 40 - 2t

Answer:

It is (-4,-6)

Step-by-step explanation:

I just did it on E2020 ur welcome

To graph a system of linear equations, start at the y-intercept and use the slope to plot the next points. The solution to the system of equations is the point where the lines intersect, and can be found by setting the equations equal to each other and solving.

The problem involves graphing a system of linear equations, which are y = x + 5 and y = 2x + 2.

Each equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. For the first equation, the slope is 1 and the y-intercept is 5. For the second equation, the slope is 2 and the y-intercept is 2.

To graph these, you typically start at the y-intercept (where the line crosses the y-axis) and use the slope to determine the next points on the graph - you rise/run according to the slope.

The solution to the system of equations is the point where the two lines intersect. To find this point, you need to solve the system of equations either graphically or algebraically. This would involve setting the equations equal to each other and solving for x, and then substituting that value of x into either of the original equations to solve for y.

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Answer: $375,000

Step-by-step explanation:

Given : The subject property is a four-bedroom, two-bath, two-car-garage home in a new subdivision.

Comp A is a three-bedroom, two-bath home with a screened-in porch that sold for $365,500.

I.e. It has one less bedroom and one extra porch .

i.e. It requires to add one bedroom and remove screened-in porch .

Since ,The appraiser values the porch at $12,500 and estimates the bedroom adjustment at $22,000.

So , the A's adjusted sale price would become

Selling price of Comp A  + Value of bedroom - Value of  porch

= $365,500 + $22,000- $12,500

= $375,000

Hence, A's adjusted sale price= $375,000