Park city, Utah, gets 43. 8 inches of rain per year. Usually 45% of that amount falls in November through February. How much rain falls in those months?

Jorge, Martin, and Andres bought a big piece of cheese in an offer, and they divided it equally.

Jorge gave his sister half of the cheese he got, so what part of the whole cheese did Jorge's sister receive?

To begin with, let us find out how many people shared the big piece of cheese. Three people divided the cheese into equal parts.Then they shared it. We are not sure how much cheese there was in the first place,

so let us call the total amount of cheese T.Since it was divided equally among three people, each person got T/3 cheese.Then Jorge gave his sister half of the cheese he got.So, his sister received 1/2 of T/6 or T/12 cheese.

Therefore, the sister of Jorge received T/12 of the entire cheese.

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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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none of the provided approximations for the probabilities are accurate.To determine which statement is true, we need to calculate the probabilities of selecting each color marker.

Total number of markers = 20 green + 44 orange + 30 blue = 94 markers.

P(blue) = Number of blue markers / Total number of markers = 30 / 94 ≈ 0.319.

P(green) = Number of green markers / Total number of markers = 20 / 94 ≈ 0.213.

P(orange) = Number of orange markers / Total number of markers = 44 / 94 ≈ 0.468.

Based on the calculations, none of the given statements are true. The actual probabilities are approximately:

P(blue) ≈ 0.319,
P(green) ≈ 0.213,
P(orange) ≈ 0.468.

Therefore, none of the provided approximations for the probabilities are accurate.

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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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According to given information, option C is the correct answer.

Given that Darrel divided 8,675 by 87.

His work is shown below.

Step 1: Set up the problem with the dividend under the division symbol and the divisor outside.

Step 2: Estimate a reasonable quotient and place it above the dividend. Then multiply and subtract. Bring down the next digit of the dividend.

Step 3: Repeat step 2 until the dividend has been brought down completely.

The given picture shows the steps done:

Option C: Darrel forgot to place a zero in the quotient.

Thus option C is the correct answer.

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The values of a = 16 and b = 5 the exponential function in the form y = ab²x that passes through the given points is y = 16 × 5²x

An exponential function in the form y = ab²x that passes through the points (0, 16) and (2, 400), to determine the values of a and b.

Using the point (0, 16),  substitute x = 0 and y = 16 into the exponential function:

16 = ab²0

16 = a ×1

a = 16

The value of a, which is 16.

Using the point (2, 400), substitute x = 2, y = 400, and a = 16 into the exponential function:

400 = 16b²

To solve for b, divide both sides of the equation by 16:

400/16 = b²

25 = b²

Taking the square root of both sides,

b = ±√25

Since are looking for a positive base,  the positive square root:

b = 5

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1/6 is the fraction of Marjorie's ribbons that are green. Marjorie has a total of 6 ribbons and spools of thread for art, consisting of 3 pink ribbons, 1 green ribbon, and 2 blue spools of thread.

1. To determine the fraction of Marjorie's ribbons that are green, we divide the number of green ribbons by the total number of ribbons.

2. To find the fraction of Marjorie's ribbons that are green, we need to calculate the ratio of green ribbons to the total number of ribbons. The total number of ribbons is the sum of all the ribbons and spools of thread, which is 3 pink ribbons + 1 green ribbon + 2 blue spools of thread, equaling 6 ribbons in total.

3. Since Marjorie has only 1 green ribbon, we can say that the fraction of her ribbons that are green is 1 out of the total 6 ribbons. This can be expressed as 1/6. Therefore, 1/6 is the fraction of Marjorie's ribbons that are green.

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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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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

The sum or difference of expression(-7x²- 3) + (11x² + 8) is 4x² + 5.

To find the sum or difference of the given expressions, (-7x²- 3) + (11x² + 8)

Simply by combine like terms.

(-7x²- 3) + (11x² + 8) can be rewritten as:

-7x² + 11xx² + (-3 + 8)

Simplifying further, we have:

4x² + 5

So, the sum or difference of (-7x²- 3) + (11x² + 8) is 4x² + 5.

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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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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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The area or amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).

Given that the boom of a sailboat is 26 feet long and the sail is an equilateral triangle. We have to determine the amount of cloth that will be required to make the sail of the boat.

The formula to calculate the area of an equilateral triangle is:

A = (√(3)/4)*a²,

where

A represents the area of the equilateral triangle

a represents the side of the equilateral triangle.

Here, the sail is an equilateral triangle.

Therefore, the length of each side of the sailboat is given as:

Length of each side of the sailboat = 26 feet / 3

                                                          = 8.67 feet or 8 feet (approximately)

We can calculate the area of the sail using the below formula;

A = (√(3)/4)×a²,

where,

A represents the area of the equilateral triangle

a represents the length of each side of the sailboat.

By substituting the value of a = 8.67 in the above equation, we get the area of the sail as follows:

A = (√(3)/4)×a²

A = (√(3)/4)*(8.67)²

A = 50.5 square feet (approx.)

Hence, the amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).

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In the given scenario, a dilation has been performed on a shape with a vertex at (2, 6). The vertex after the dilation is located at (-8, -24). The dilation center can be determined as well as the dilation factor. To find the dilation center and the dilation factor, we compare the coordinates of the original vertex and its image after the dilation.

The dilation center is the point around which the shape is dilated or expanded. In this case, the dilation center can be determined by finding the midpoint between the original vertex and its image. Using the midpoint formula, we calculate:

x-coordinate of the midpoint = (2 + (-8)) / 2 = -6/2 = -3

y-coordinate of the midpoint = (6 + (-24)) / 2 = -18/2 = -9

Therefore, the dilation center is (-3, -9).

The dilation factor represents the scale factor or the ratio of the distances between corresponding points of the original shape and its image after the dilation. In this case, we can determine the dilation factor by calculating the ratio of the distances between the x-coordinates and y-coordinates of the original vertex and its image.

Original x-coordinate: 2

Image x-coordinate: -8

Dilation factor for x-coordinates = Image x-coordinate / Original x-coordinate = -8 / 2 = -4

Original y-coordinate: 6

Image y-coordinate: -24

Dilation factor for y-coordinates = Image y-coordinate / Original y-coordinate = -24 / 6 = -4

Since the dilation factor is the same for both x and y coordinates, we can conclude that the dilation factor is -4. In summary, in the given scenario where a dilation has been performed on a shape with a vertex at (2, 6) resulting in the vertex moving to (-8, -24), the dilation center is (-3, -9), and the dilation factor is -4.

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The third term of the sequence is 11.

The sequence given by the rule

f(1) = 5

and

f(n) = f(n-1) + 3, for n bigger than 1.

The third term of the sequence can be calculated using the given formula of the sequence.

We are given that

f(1) = 5, which means that the first term of the sequence is 5.

We can find the second term of the sequence using the formula.

f(n) = f(n-1) + 3

Now n = 2

    f(2)  = f(2-1) + 3

           = f(1) + 3

           = 5 + 3

            = 8

Therefore, the second term of the sequence is 8.

Using the same formula we can find the third term of the sequence

f(n) = f(n-1) + 3

Now n = 3

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

     = f(2) + 3

     = 8 + 3

      = 11

Therefore, the third term of the sequence is 11. Hence, the correct answer is 11.

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The equation is 38.25 = 4.25h and Tomás worked for 9 hours.

To find the number of hours it took Tomás to clean the garage, we can set up an equation using the given information.

Let's assume the number of hours Tomás worked is "h."

We know that Tomás was paid $4.25 per hour, so the total amount he earned can be calculated by multiplying the hourly rate by the number of hours worked:

Total earnings = Hourly rate * Number of hours

In this case, the total earnings are $38.25, and the hourly rate is $4.25:

$38.25 = $4.25 * h

To solve for "h," we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by $4.25:

$38.25 / $4.25 = h

Simplifying the right side:

9 = h

Therefore, it took Tomás 9 hours to clean the garage.

By setting up the equation and solving it, we determined that Tomás worked for 9 hours.

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The relationship between the distance (d) covered by Robyn for different lengths of time (t) can be represented by the equation d = ct, where c is a constant. Robyn ran for different lengths of time and measured the distance she covered each time.

To represent the relationship between d and t, we need to consider how d and t are related. This can be done by finding a pattern in the data. Robyn may have collected data for different values of t and d. We can represent this data in a table like this Time (t) (in minutes) Distance (d) (in meters)1 The table shows that as the value of t increases, the value of d also increases.

We can represent this relationship between d and t using a linear equation of the form y = mx + b, where y is the dependent variable (in this case, d), x is the independent variable (in this case, t), m is the slope of the line, and b is the y-intercept. To find the equation that represents the relationship between d and t, we need to find the values of m and b. We can do this by using two points from the table. For example, we can use the points (10, 50) and (20, 100).The slope (m) of the line passing through these points can be found using the slope formula: m = (y2 - y1)/(x2 - x1) = (100 - 50)/(20 - 10) = 5.The y-intercept (b) can be found by substituting the value of m and one of the points into the equation y = mx + b. Using the point (10, 50), we get:50 = 5(10) + b Solving for b, we get b = 0. Therefore, the equation that represents the relationship between d and t is d = mt + b = 5t + 0 = 5t. The equation that represents the relationship between t and d is d = ct, where c is a constant.

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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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The three parts are: x = 24, y = 8, and z = 32. The first part is three times the second, and the third part is equal to the sum of the first and second.

Let's assume the three parts are x, y, and z.

According to the given conditions:

1) The first part is triple the second:

x = 3y

2) The third part is equal to the sum of the first and second:

z = x + y

We are also given that the sum of the three parts is 96:

x + y + z = 96

Now we can solve the equations simultaneously to find the values of x, y, and z.

Substituting the value of x from the first equation into the third equation:

(3y) + y + (3y + y) = 96

Simplifying the equation:

8y + 4y = 96

12y = 96

Dividing both sides by 12:

y = 96 / 12

y = 8

Now that we have the value of y, we can substitute it back into the first equation to find x:

x = 3y = 3(8) = 24

Lastly, substitute the values of x and y into the second equation to find z:

z = x + y = 24 + 8 = 32

Therefore, the three parts are:

x = 24

y = 8

z = 32

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Acceptance sampling is a statistical procedure that involves taking a sample of a product or a lot of products and determining if it meets the required standards or specifications.

One method of acceptance sampling involves randomly selecting a sample of items without replacement and accepting the entire batch only if every item in the sample is okay.The ABC Electronics Company has just manufactured 1200 write-rewrite CDs, out of which 90 are defective. The question is asking about the probability that the entire batch will be accepted if 3 of these CDs are randomly selected for testing.We know that out of 1200 CDs, 90 are defective.

Therefore, the number of good CDs is:1200 - 90 = 1110If 3 CDs are randomly selected, the probability of getting a good CD on the first try is:1110/1200 = 37/40The probability of getting a good CD on the second try is:1109/1199The probability of getting a good CD on the third try is:1108/1198The probability of getting all three CDs that are good is:37/40 * 1109/1199 * 1108/1198 = 0.7978Therefore, the probability that the entire batch will be accepted is 0.7978 or approximately 79.78%.

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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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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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Joshua spent an amount determined by the prices of mixed nuts, chocolate candies, and granola to make the trail mix.

The exact cost cannot be determined without the price per pound of each ingredient.

To calculate how much Joshua spent to make the trail mix, we need to know the price per pound of each ingredient: mixed nuts, chocolate candies, and granola. Without this information, we cannot provide an exact answer.

However, we can provide a general approach to calculate the cost if we have the price per pound for each ingredient. Let's assume the price per pound of mixed nuts is $x, the price per pound of chocolate candies is $y, and the price per pound of granola is $z.

To determine the cost of each ingredient, we multiply the weight in pounds by the respective price per pound. For mixed nuts, Joshua bought 1/5 pound, so the cost of mixed nuts would be (1/5) * x. For chocolate candies, he bought 1/2 pound, so the cost of chocolate candies would be (1/2) * y. Lastly, for granola, he bought 1 1/4 pounds, so the cost of granola would be (1 1/4) * z.

To find the total cost, we add the costs of all three ingredients: (1/5) * x + (1/2) * y + (1 1/4) * z.

Without the specific prices per pound, we cannot provide a numerical answer, but you can calculate the total cost using the given weights and the corresponding prices per pound.

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After reducing the price by 12%, the price of the car would be $2,376. To find the price of the car after a 12% reduction, we can calculate 12% of the original price and subtract it from the original price.  

To find the price of the car after the 12% reduction, we need to calculate 12% of $2,700 and subtract that amount from the original price. First, we find 12% of $2,700 by multiplying 0.12 (12% expressed as a decimal) by $2,700:

12% of $2,700 = 0.12 * $2,700 = $324

Next, we subtract $324 from the original price of $2,700:

$2,700 - $324 = $2,376

Therefore, after the 12% reduction, the price of the car would be $2,376. This reduction reflects a decrease in price from the original value, providing potential buyers with a discounted price for the car.

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The total number of miles driven to and from school in 6 days would be 30 miles.

Since the round-trip drive to school is 2 1/2 miles, we can consider this as a distance traveled in one day. To find the total distance driven in 6 days, we need to multiply the distance traveled per day by the number of days.

Given that the round-trip distance is 2 1/2 miles, we can convert this mixed fraction to an improper fraction: 2 1/2 = 5/2 miles.

Multiplying the distance per day (5/2 miles) by the number of days (6 days) gives us:

(5/2) * 6 = (5 * 6)/2 = 30/2 = 15 miles.

Therefore, the total distance driven to and from school in 6 days is 15 miles.

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Hence, the correct option is B) 11.1.

Given that Suzy had been working for 15 minutes when she finished problem 5 and she completed all 20 questions in 45 minutes.To find what fraction of the questions Suzy had finished when she finished problem 5; we need to subtract the time taken to finish problem 5 from total time and divide it by total time and the multiply it by 20. The answer can be rounded off to the nearest tenth if necessary.

Fraction of questions completed by Suzy = [(45-15)/45] × 20= 0.556 × 20= 11.12

As we see that Suzy had completed 11.12 questions when she finished the fifth problem.

Therefore, rounding it to the nearest tenth, the decimal form of the answer is 11.1.

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To calculate the amount Josef will pay for the shirt on sale, we need to consider the discount of 15% off the regular price. Several expressions can be used to calculate the final amount, including options (a), (b), (c), and (f).

These expressions involve manipulating the regular price of the shirt and the discount percentage to determine the final price after the discount is applied.

(a) The expression "5-0.855" is not a valid calculation for the amount Josef will pay. It seems to be a typographical error.

(b) The expression "s-0.15s" is a valid expression to calculate the amount Josef will pay. It represents the regular price (s) minus the discount of 15% of the regular price.

(c) The expression "0.855" is not a valid calculation for the amount Josef will pay. It seems to be the result of mistakenly subtracting 15% from 100%.

(d) The expression "1.155" is not a valid calculation for the amount Josef will pay. It seems to be the result of mistakenly adding 15% to 100%.

(e) The expression "(1+0.15)s" is not a valid calculation for the amount Josef will pay. It seems to mistakenly add 15% to the regular price.

(f) The expression "(1-0.15)s" is a valid expression to calculate the amount Josef will pay. It represents the regular price (s) multiplied by the factor of (1-0.15), which accounts for the 15% discount.

The expressions (b) "s-0.15s" and (f) "(1-0.15)s" can be used to calculate the amount Josef will pay for the shirt on sale, as they account for the 15% discount off the regular price.

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The expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:

The model for finding the total distanceNatalie went on a jog 3 nights in a row and jogged the same distance each night.

The model for finding the total distance that Natalie jogged during the 3 nights is shown below:

Model for finding the total distance where each column represents one mile, and the shaded parts of each column represent the fraction of a mile that Natalie jogged each night.

From the model, we can find the total distance in miles Natalie jogged by counting the number of shaded parts in each column and then adding them together.

The number of shaded parts in each column represents the fraction of a mile that Natalie jogged each night.

Therefore, the expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:

[tex]$$3 \cdot 1 + \frac{1}{2} + \frac{3}{4}$$ $$= 3 + \frac{2}{4} + \frac{3}{4}$$$$= 3 + \frac{5}{4}$$$$= \frac{12}{4} + \frac{5}{4}$$$$= \frac{17}{4}$$$$= \boxed{4\frac{1}{4}}\ miles$$[/tex]

Therefore, Natalie jogged a total distance of 4 and 1/4 miles over these three nights.

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Answer: To solve the linear system using determinants, we can write the system of equations in matrix form:

| 2 3 | | x | | 6 |

| -8 -3 | | y | = | 12 |

The determinant of the coefficient matrix is calculated as follows:

D = | 2 3 |

| -8 -3 |

The determinant of a 2x2 matrix is calculated by taking the product of the main diagonal elements and subtracting the product of the off-diagonal elements:

D = (2 * -3) - (3 * -8)

D = -6 + 24

D = 18

Now, we will find the determinant of the x matrix, which is obtained by replacing the x column in the coefficient matrix with the constants:

Dx = | 6 3 |

| 12 -3 |

Dx = (6 * -3) - (3 * 12)

Dx = -18 - 36

Dx = -54

Next, we find the determinant of the y matrix, which is obtained by replacing the y column in the coefficient matrix with the constants:

Dy = | 2 6 |

| -8 12 |

Dy = (2 * 12) - (6 * -8)

Dy = 24 + 48

Dy = 72

Finally, we can solve for x and y using the determinants:

x = Dx / D

x = -54 / 18

x = -3

y = Dy / D

y = 72 / 18

y = 4

Therefore, the solution to the given linear system is x = -3 and y = 4.

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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