A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay. excluding tax, for the shirt?

One diameter makes two parts of the circle. A diameter is a chord that passes through the center of a circle. When a circle is divided into two halves by the diameter, each half is called a semicircle.

When a line segment that passes through the center of a circle is drawn, it is referred to as a diameter. A circle has a diameter, its longest chord, and its endpoints lie on the circle itself. The midpoint of the diameter is the center of the circle. A diameter divides a circle into two equal parts, known as semicircles. A semicircle is the region enclosed by the arc and the diameter.

The semicircle's area is half the circle from which it was derived. The diameter is the longest chord that a circle has, and it passes through the center of the circle. The diameter divides the circle into two halves. Every chord's perpendicular bisector passes through the center of the circle. This property of the diameter is also applicable to chords. The perpendicular bisector of the chord passes through the circle's center, and the chord is divided into two equal parts.

Therefore, one diameter makes two parts of the circle. A diameter is a chord that passes through the center of a circle. When a circle is divided into two halves by the diameter, each half is called a semicircle.

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The probability of rolling at least one six when rolling two standard number cubes is 11/36.

To determine the probability, we first need to find the total number of possible outcomes when rolling two standard number cubes. Each cube has 6 faces, numbered from 1 to 6, so the total number of outcomes is 6 multiplied by 6, which equals 36.

Next, we need to calculate the number of favorable outcomes, which is the number of outcomes where at least one six is rolled. There are three possible scenarios:

Rolling a six on the first cube and any number on the second cube.

Rolling any number on the first cube and a six on the second cube.

Rolling a six on both the first and second cubes.

For each scenario, there is a 1/6 probability of rolling a six on a single cube. Therefore, the number of favorable outcomes is 1 + 1 + 1 = 3.

Finally, we divide the number of favorable outcomes (3) by the total number of possible outcomes (36) to calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 3 / 36

= 1 / 12

= 11 / 36

Therefore, the probability of rolling at least one six when rolling two standard number cubes is 11/36.

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The number line can be used to determine the sum of the location of point T and -1 1/2. By visually representing the positions of these points on the number line, we can determine their sum by adding their locations.

To determine the sum of the location of point T and -1 1/2, we can plot the point T on the number line and then locate -1 1/2 on the number line. We can then add the locations of these points on the number line to find their sum.

For example, if point T is located at 3 on the number line and -1 1/2 is located at -1.5, we can add 3 and -1.5 to find their sum, which would be 3 + (-1.5) = 1.5.

By using the number line, we can visually represent the locations of the points and perform addition to find their sum accurately.

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Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.

(a) Using the inclusion-exclusion principle, we define events W, G, and R for the white, green, and red balls not appearing, respectively. To calculate the probability that we did not see all three colors, we use the formula P(W U G U R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R). Each individual probability can be calculated by considering the number of ways each event can occur divided by the total number of possible outcomes. For example, P(W) = (3/4)^3, P(G) = (3/4)^3, P(R) = (1/2)^3, P(W ∩ G) = (2/4)^3, and so on.

(b) In the direct computation method, we calculate the probability of not seeing all three colors by subtracting the probability of seeing all three colors from 1. The probability of seeing all three colors is calculated by considering the number of ways to select one ball of each color divided by the total number of possible outcomes. There are 4 possible outcomes for each ball drawn, so the probability of seeing all three colors is 4/4 * 4/4 * 2/4 = 1/4. Therefore, the probability of not seeing all three colors is 1 - 1/4 = 3/4.

Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.


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To find the probability that we did not see all three colors when drawing 3 balls with replacement from an urn containing 1 white, 1 green, and 2 red balls, we can use the inclusion-exclusion principle or calculate directly by counting the number of ways.

To find the probability that we did not see all three colors, we can use two different calculations.

(a) Let W be the event that the white ball did not appear, G be the event that the green ball did not appear, and R be the event that the red ball did not appear. We can use the inclusion-exclusion principle to calculate the probability:

P(W ∪ G ∪ R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R)

(b) Alternatively, we can directly compute the probability by counting the number of ways that we did not see all three colors and dividing by the total number of possible outcomes.

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The midpoint of the line segment connecting two points can be found by averaging their corresponding coordinates. Therefore, to obtain the midpoint of line BC, we add the coordinates of B and C and divide by 2.

Midpoint of line BC is given by:

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]

The length of line AD is found by using the distance formula, which is given as:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]

Thus, we need to find the coordinates of point D and A to determine the length of AD. The coordinates of D are the average of the coordinates of B and C.

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]The coordinates of A are (1,2,-1).

The distance between A and D is found by substituting these values into the distance formula:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\] \[d=\sqrt{(1-(-2))^2+(2-0)^2+(-1-1)^2}\] \[d=\sqrt{(3)^2+(2)^2+(-2)^2}\] \[d=\sqrt{9+4+4}\] \[d=\sqrt{17}\]

Thus, the distance between points A and D is sqrt(17).Therefore, the midpoint of line BC is (-2,0,1) and the distance between points A and D is sqrt(17).

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The algebraic property that could be used to rewrite 4x + 2y as 2y + 4x is option C: Commutative Property of Addition.

From the question. if   a, b and c are any numbers,

Based on Associative Property of Addition, it state that:

a + ( b + c ) = ( a + b ) + c

Based on Associative Property of Multiplication, it state that:

a(bc) = (ab)c

Based on Commutative Property of Addition it state that:

a + b = b + a

Based on Commutative Property of Multiplication it state that:

ab = ba

Note that , 4x + 2y = 2y + 4x

So, Commutative Property of Addition is used in the expression.

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See text below

Which algebraic property could be used to rewrite 4x + 2y as 2y + 4x? A. Associative Property of Addition

B. Associative Property of Multiplication

C. Commutative Property of Addition

D. Commutative Property of Multiplication

Given that Aaron ate half as much pizza as David and Aaron ate 1/4 of a pie, we can determine the fraction of the pie David ate by setting up an equation and solving for it.

Let's assume that David ate x amount of pizza, which represents the fraction of the pie he consumed. Since Aaron ate half as much pizza as David, we can express Aaron's portion as (1/2)x. We are also given that Aaron ate 1/4 of a pie, so we can set up the equation:

(1/2)x = 1/4

To solve for x, we can multiply both sides of the equation by 2 to eliminate the fraction:

2 * (1/2)x = 2 * (1/4)

x = 1/2

Therefore, David ate 1/2 of the pie. This means that Aaron ate half as much pizza as David, while David consumed the remaining half of the pie.

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Ali has hired Mark and Alexis to work for his shipping company, and Mark can load a truck with packages in 120 minutes, while Alexis can load the same number of packages in 240 minutes.

To find out how long they will take to load a truck together, we'll use the formula below:T = (T₁ × T₂) ÷ (T₁ + T₂)Where T is the time it takes for Mark and Alexis to load a truck together, T₁ is the time it takes for Mark to load a truck alone, and T₂ is the time it takes for Alexis to load a truck alone.

We can plug in the given values: T = (120 × 240) ÷ (120 + 240) = 28,800 ÷ 360 = 80Therefore, it would take Mark and Alexis 80 minutes to load a truck together.

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The best measure of variability for the data is the range because the distribution is scattered.What is the range?The range of data is defined as the difference between the maximum value and the minimum value

. The list of weights is given below:8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7The minimum value in the list is 3, and the maximum value in the list is 81. So, the drange is calculate as follows:Range = Maximum value – Minimum value= 81 – 3= 78The distribution is scattered because the range is relatively large.    

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The expression "x - 12" can be modeled in a real world situation where you are trying to find the difference between a number x and 12. Here is an example:Suppose you have a jar containing x marbles.

You give away 12 marbles to your friend. The number of marbles you have left in the jar can be modeled by the expression "x - 12". In this situation, x represents the original number of marbles in the jar, and 12 represents the number of marbles given away to your friend. The expression "x - 12" calculates the number of marbles you have left after giving away 12.

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Lisa made $841.30 last week after working 35.8 hours and payingpaying $25 for health insurance.

To calculate Lisa's earnings, we need to multiply her hourly rate by the number of hours she worked. Lisa earns $23.50 per hour, and she worked for 35.8 hours. Multiplying these values, we get $23.50 * 35.8 = $841.30.
In addition to her earnings, we need to subtract the amount she paid for health insurance. Lisa pays $25 every week. So, to find her total earnings after deducting health insurance, we subtract $25 from $841.30: $841.30 - $25 = $816.30.
Therefore, Lisa made $816.30 last week after working 35.8 hours and paying $25 for health insurance.

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The temperature change per minute during the 20-minute cooling period at a steady rate was -3 degrees Celsius per minute.

To calculate the temperature change per minute, we need to determine the difference in temperature and divide it by the time in minutes. In this case, the initial temperature was +5 degrees Celsius, and the final temperature was -55 degrees Celsius. The temperature change is the difference between these two values: -55 - (+5) = -60 degrees Celsius.

Since the cooling period lasted for 20 minutes, we divide the temperature change by the time: -60 degrees Celsius / 20 minutes = -3 degrees Celsius per minute.

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Therefore, the probability of a randomly chosen boy having a height less than 66 inches is 15.87%.

The heights of the Lincoln High School boys have a normal distribution with a mean height of 70 inches and a standard deviation of 4 inches. The probability of a randomly chosen boy having a height less than 66 inches is asked. We can solve this problem by using the standard normal distribution or z-distribution. The standard normal distribution has a mean of zero and a standard deviation of one. It is a normal distribution that has been transformed to have a mean of 0 and a standard deviation of 1. Therefore, we must convert the given values into z-scores. The z-score formula is:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this problem, we want to find the probability that a boy's height is less than 66 inches, so x = 66. Using the formula above, we get:
z = (66 - 70) / 4 = -1
This means that a boy's height of 66 inches is one standard deviation below the mean. To find the probability of a boy having a height less than 66 inches, we look up the area to the left of the z-score of -1 in the standard normal distribution table. The table gives us the probability of a randomly chosen boy having a height less than 66 inches as 0.1587 or 15.87%.
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The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

Thus, this is the required answer.

Solution:

The given polynomial function is of degree 2 (quadratic function).f(x) = ax² + bx + c, Where a, b, and c are real numbers with a ≠ 0.

The quadratic function has the general form: f(x) = a(x - r)(x - s)where r and s are the x-intercepts.

The given x-intercepts are (-2,0) and (2,0) which means that:r = -2 and s = 2.

So, the quadratic function can be written as:

f(x) = a(x - (-2))(x - 2)f(x) = a(x + 2)(x - 2), where a is a non-zero constant.The y-intercept is (0,-4).

We know that the y-intercept occurs where x = 0.

Substituting x = 0 and y = -4 in the quadratic function:

f(x) = a(x + 2)(x - 2)

when x = 0,

y = -4.

-4 = a(0 + 2)(0 - 2)

=> -4 = -4a

=> a = 1

The quadratic function is:

f(x) = (x + 2)(x - 2)

The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

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The first five terms of the sequence defined by the explicit formula an = (-2)^(n-1) are 1, -2, 4, -8, 16.

To find the first five terms of the sequence defined by the explicit formula an = (-2)^(n-1), we can substitute the values of n from 1 to 5 into the formula and calculate the corresponding terms:

The explicit formula for the sequence is given by an = (-2)^(n-1).

When n = 1: a1 = (-2)^(1-1) = (-2)^0 = 1

When n = 2: a2 = (-2)^(2-1) = (-2)^1 = -2

When n = 3: a3 = (-2)^(3-1) = (-2)^2 = 4

When n = 4: a4 = (-2)^(4-1) = (-2)^3 = -8

When n = 5: a5 = (-2)^(5-1) = (-2)^4 = 16

Therefore, the first five terms of the sequence are:

1, -2, 4, -8, 16

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(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.

We have,

(a) To find the amount of fencing needed, we need to determine the perimeter of the yard in meters.

According to the scale, 2 cm on the drawing represents 3 m in reality. This means that 1 cm on the drawing represents 1.5 m in reality (since 3 m divided by 2 cm is 1.5 m/cm).

Let's assume the length of the yard in the drawing is L cm and the width is W cm.

Then, the length of the actual yard would be L x 1.5 m, and the width would be W * 1.5 m.

The perimeter of the yard is given by the formula:

Perimeter = 2 x (length + width)

Substituting the actual measurements, we have:

Perimeter = 2 x (L x 1.5 m + W x 1.5 m)

= 3 x (L + W) m

Therefore, the landscaper would need 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden can be determined by calculating 1/3 of the area of the actual yard.

Let's assume the area of the yard in the drawing is A square cm. Then, the area of the actual yard would be A x (1.5 m)², since each dimension is scaled by 1.5 m/cm.

To find the area of the garden, we calculate:

Area of garden = (1/3) x Area of yard

= (1/3) x (A x (1.5 m)^2)

= (1/3) x (A x 2.25) square meters

Therefore, the area of the garden would be one-third of the area of the yard, multiplied by 2.25.

Thus,

(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.

(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.

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To find the distance between two points in the coordinate plane, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2].So the correct answer is C. √113.

Let's apply this formula to the given points in the coordinate plane  (-3, -2) and (5, 5):

Distance = √[(5 - (-3))^2 + (5 - (-2))^2]

= √[(8)^2 + (7)^2]

= √[64 + 49]

= √113

Therefore, the distance between two points in the coordinate plane (-3, -2) and (5, 5) is √113. Others options A. √13  B. √15  D. 5 E. 15

So the correct answer is C. √113.

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2 liters per hour is equal to 555.6 millimeters per second.

To convert 2 liters per hour to millimeters per second, you need to follow these steps:

Step 1: Convert liters to milliliters

Since 1 liter = 1000 milliliters, multiply 2 by 1000 to get the number of milliliters per hour.

Therefore, 2 liters per hour is equal to 2000 milliliters per hour.

Step 2: Convert hours to seconds

Since 1 hour = 3600 seconds, divide the number of milliliters per hour by 3600 to get the number of milliliters per second.

Therefore, 2000 milliliters per hour is equal to 0.5556 milliliters per second.

Step 3: Convert milliliters to millimeters

Since 1 milliliter is equal to 1 cubic centimeter (cc) and 1 cc is equal to 1 cubic millimeter, 0.5556 milliliters per second is equal to 0.5556 cubic millimeters per second or 555.6 millimeters per second (since there are 1000 cubic millimeters in a milliliter).

Therefore, 2 liters per hour is equal to 555.6 millimeters per second.

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The algebraic expression for the number of points scored by a football team that makes t touchdowns, f field goals, and e extra points is: 6t + 3f + 1e. Therefore, the team would have scored 15 points in this case.

To calculate the total number of points scored by a football team, we can assign variables to the number of touchdowns, field goals, and extra points. Let's use t for touchdowns, f for field goals, and e for extra points.

The points awarded for each touchdown is 6, for each field goal is 3, and for each extra point is 1. To find the total number of points, we multiply the number of touchdowns by 6, the number of field goals by 3, and the number of extra points by 1, and then add them together.

Hence, the algebraic expression for the number of points scored is: 6t + 3f + 1e.

For example, if a team scores 2 touchdowns, 1 field goal, and 0 extra points, we can substitute the values into the expression:

6(2) + 3(1) + 1(0) = 12 + 3 + 0 = 15.

Therefore, the team would have scored 15 points in this case.

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The measure of segment QS can be determined by adding the lengths of QR and RS. In this case, since QR is 10 units long and RS is 7 units long, the measure of QS would be 17 units.

To find the measure of segment QS, we need to add the lengths of QR and RS. Given that QR is 10 units long and RS is 7 units long, we can calculate the measure of QS by adding these two lengths together. Therefore, QS = QR + RS = 10 + 7 = 17. Hence, the measure of segment QS is 17 units. By adding the lengths of the two segments that make up QS, we obtain the total length of the segment itself.

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To determine the percentage of shots that the goalie saved, we need the actual numbers of saves and goals scored against the goalie. Since the specific values are not provided in the question, it is not possible to calculate the exact percentage.

However, I can explain the general process for calculating the percentage of savings.

To find the percentage of saves, we need to divide the number of saves by the total number of shots and then multiply by 100. The formula for calculating the percentage is:

Percentage of saves = (Number of saves / Total number of shots) * 100

For example, if the goalie made 30 saves out of 40 total shots, the calculation would be:

Percentage of saves = (30 / 40) * 100 = 75%

In this case, the goalie saved 75% of the shots.

Without the specific values of saves and shots, it is not possible to determine the exact percentage.

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When a straight angle is split into two angles, the sum of those angles is 180 degrees because a straight angle measures 180 degrees.

Let's assume that the smaller angle is represented by x. Since the larger angle is twice as big as the smaller angle, it can be represented as 2x. Therefore, the sum of the two angles can be expressed as:

x + 2x = 180 degrees This simplifies to 3x = 180 degrees.

Dividing both sides by 3, we get: x = 60 degrees.

This means that the smaller angle is 60 degrees and the larger angle is twice as big, or 2(60) = 120 degrees.

Therefore, the two angles are 60 degrees and 120 degrees.

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The cost of one pack of streamers can be calculated by finding the difference in the total cost of the two purchases and dividing it by the difference in the number of packs of streamers. Therefore, one pack of streamers costs $2.75.

Let's denote the cost of one pack of streamers as "x". From the given information, we know that Randy bought 8 packs of streamers for $48.60, and later bought 3 packs of streamers for $34.85.

Using this information, we can set up the following equation to represent the total cost of the two purchases:

8x + 28 balloons = $48.60

3x + 28 balloons = $34.85

To find the cost of one pack of streamers, we need to subtract the second equation from the first equation to eliminate the balloons:

(8x + 28 balloons) - (3x + 28 balloons) = $48.60 - $34.85

Simplifying the equation gives:

5x = $13.75

Dividing both sides by 5, we find that:

x = $2.75

Therefore, one pack of streamers costs $2.75.

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The amount of lemonade left after the consumption of 280 ml of lemonade by 14 children is 4.08 liters. The given problem can be solved by using basic mathematical operations. In the problem, it is shown that there are 14 children at the birthday party, and each child drinks 280 ml of lemonade.

And, 8 liters of lemonade are also available. The solution of the problem is as follows:

1 litre of liquid = 1000 ml of liquid

8 liters of liquid = 8 × 1000

                   = 8000 ml of liquid

Now, we can calculate the total lemonade consumed by the 14 children as follows:

Total lemonade consumed = 14 × 280

                                          = 3920 ml of liquid

                                      = 3.92liters of liquid

Therefore, the amount of lemonade left after 14 children have consumed 280 ml of lemonade each is given by:

Amount of lemonade left = 8 − 3.92

                                = 4.08liters of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children. The problem is calculating the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. To solve the problem, we first need to calculate the total amount of lemonade consumed by the 14 children. We know that each child consumed 280 ml of lemonade.

Now, we can calculate the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. The amount of lemonade left is given by the difference between the total amount of lemonade available and the total lemonade consumed by the 14 children.

Therefore,

Amount of lemonade left = Total lemonade available − Total lemonade consumed

                                     = 8000 − 3920

                               = 4080 ml of liquid

                            = 4.08litres of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children.

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If angles 1 and 2 are vertical angles, then they are congruent. If angle 1 measures 62 degrees, then angle 2 will also measure 62 degrees.

Vertical angles are formed by the intersection of two lines. They are opposite each other and have equal measures. In this case, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees because they are vertical angles.

This property of vertical angles can be understood based on the concept of a straight line. When two lines intersect, they form two pairs of vertical angles. Since a straight line measures 180 degrees, each pair of vertical angles will have a total measure of 180 degrees, and thus, each angle within the pair will have the same measure. Therefore, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees.

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No, the diagonal of a parallelogram cannot be congruent to one of its side.

Given data,

Let the parallelogram be represented as ABCD

Now , the diagonal is AC and BD

The opposing sides of a parallelogram are parallel and congruent. This implies that the length of every pair of opposing sides is the same.

The parallelogram's opposite sides would be equal in length if one of its diagonals were congruent to one of its sides. However, unless it is a rectangle or a rhombus, this goes against the definition of a parallelogram, which calls for opposing sides to be parallel but not equal in length.

Therefore, a parallelogram's diagonal cannot be congruent to one of its sides by definition.

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The correct expression with the substituted values is −5±√(5^2 - 4(4)(-6)) / (2(4)).

The expression that shows the correct numbers substituted into the quadratic formula to solve the equation 4x^2 + 5x - 6 = 0 is:

−5±√(5^2 - 4(4)(-6)) / (2(4))

In the quadratic formula, the general form is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 4, b = 5, and c = -6.

Substituting these values into the quadratic formula, we have:

x = (-5 ± √(5^2 - 4(4)(-6))) / (2(4))

Simplifying further:

x = (-5 ± √(25 + 96)) / (8)

x = (-5 ± √121) / 8

x = (-5 ± 11) / 8

Therefore, the correct expression with the substituted values is:

−5±√(5^2 - 4(4)(-6)) / (2(4))

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To find the mean and standard deviation of the distribution of excess cleaning solution, we need to calculate the difference between the advertised amount of cleaning solution and the actual amount filled in the bottles.

1 fluid ounce (1 fl oz) is approximately equal to 30 milliliters (30 mL), so we can convert the measurements to milliliters for consistency.

Mean:

The mean of the distribution of excess cleaning solution can be calculated as the difference between the mean amount of filling (33 fl oz) and the advertised amount (32 fl oz), both converted to milliliters:

Mean = (33 - 32) fl oz * 30 mL/fl oz = 30 mL

Therefore, the mean of the distribution of excess cleaning solution is 30 milliliters.

Standard Deviation:

The standard deviation of the distribution can be found using the formula for the propagation of uncertainty. Since the standard deviation of the filling amount is given as 1.5 fl oz, we convert it to milliliters as well:

Standard Deviation = 1.5 fl oz * 30 mL/fl oz = 45 mL

Therefore, the standard deviation of the distribution of excess cleaning solution is 45 milliliters.

In summary, the mean of the distribution of excess cleaning solution is 30 milliliters and the standard deviation is 45 milliliters.

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The listing price for the residence is $158,400. This ensures that the seller will make a 20% profit on the original cost price of $132,000.

To calculate the listing price of the residence, we need to add the 20% profit to the cost price of $132,000.

To find the profit amount, we multiply the cost price by the profit percentage:

Profit = 20% of $132,000 = 0.20 * $132,000 = $26,400

The listing price is obtained by adding the profit to the cost price:

Listing Price = Cost Price + Profit = $132,000 + $26,400 = $158,400

Therefore, the listing price for the residence is $158,400. This ensures that the seller will make a 20% profit on the original cost price of $132,000.


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Dylan is at a position 10 feet from the meeting place after 5/6 seconds, while Ryan is not at a position 10 feet from the meeting place.

To find when each person is at a position 10 feet from the meeting place, we can use their velocities and the concept of relative motion.

For Dylan:

Dylan's velocity is 12 feet per second. Since Dylan is walking towards the meeting place, his velocity is positive. To find when Dylan is at a position 10 feet from the meeting place, we can set up the following equation:

Distance = Velocity × Time

10 = 12t

Solving for t, we divide both sides of the equation by 12:

t = 10/12

t = 5/6 seconds

Therefore, Dylan is at a position 10 feet from the meeting place after 5/6 seconds.

For Ryan:

Ryan's velocity is -10 feet per second. Since Ryan is walking in the opposite direction, his velocity is negative. To find when Ryan is at a position 10 feet from the meeting place, we can set up the following equation:

Distance = Velocity × Time

10 = (-10)t

Solving for t, we divide both sides of the equation by -10:

t = 10/(-10)

t = -1 second

Since time cannot be negative in this context, we can conclude that Ryan is not at a position 10 feet from the meeting place.

In summary, Dylan is at a position 10 feet from the meeting place after 5/6 seconds, while Ryan is not at a position 10 feet from the meeting place.

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