Louis drives a taxi cab. He records the total number of miles he travels each week for 15 weeks.

The mean and mean absolute deviation of the data are shown.


Mean: 3,642

Mean absolute deviation: 1,755

Problem


Select all the possible numbers of miles for day 16 that are within the mean absolute deviation.

The subjectively determined maximum amount a customer would pay for a product is its reservation price. The main answer is reservation.

An individual's reservation price is the highest price they are prepared to pay for a product or service. The maximum amount that an individual is willing to pay for a product or service is referred to as the reservation price, which is determined subjectively based on the individual's perception of the product's or service's worth.

To put it another way, the maximum amount a buyer will pay for an item is determined by his or her perception of the item's worth, which is influenced by the buyer's individual tastes and preferences.For example, if a person is willing to pay $50 for a pizza, that is their reservation price for a pizza. If the price of the pizza is higher than their reservation price, they are likely to leave without making a purchase. A reservation price is influenced by factors such as product quality, perceived benefits, personal income, and budget constraints.

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The expression that represents the total amount Marissa spent is (x * 19.99 + y * 14.99) + (3 * 19.99 + 4 * 14.99).

In summary, the expression (x * 19.99 + y * 14.99) represents the cost of the initial purchase, where x is the number of shirts and y is the number of shorts. The expression (3 * 19.99 + 4 * 14.99) represents the cost of the additional purchase the next day, where 3 is the number of shirts and 4 is the number of shorts. By adding both expressions together, we get the total amount Marissa spent.

The first part of the expression, x * 19.99, calculates the cost of the x shirts at $19.99 each. Similarly, the second part, y * 14.99, calculates the cost of the y pairs of shorts at $14.99 each. These two terms represent the initial purchase.

The next part of the expression, 3 * 19.99, calculates the cost of the 3 additional shirts bought the next day. Similarly, 4 * 14.99 calculates the cost of the 4 additional pairs of shorts. These two terms represent the additional purchase.

By adding the cost of the initial purchase and the additional purchase, we obtain the total amount Marissa spent on shirts and shorts.

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Answer: 15

Step-by-step explanation:

Period=distance between 2 top points.

15

The length of the side /CD/ is 6√3 square units. Option A

The trigonometric function known as the sine of an angle describes the ratio between the lengths of the hypotenuse and the side opposite the angle in a right triangle. The sine function, sometimes known as "sin", is described as follows:

Sin = opp/adj

The sine function can be used to determine how a right triangle's angles and sides match up.

Let the altitude /CD/ be x

Using the sine of an angle;

Sin 60 = √3/2

√3/2 = x/12

x = √3/2 * 12

x = 6√3 square units

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The given numbers can be classified into two categories: small values and very small values (closer to zero). All the given numbers have values that are either small or very small, with some being closer to zero than others based on the number of places the decimal point is moved to the left.

In scientific notation, numbers are expressed as a product of a decimal number between 1 and 10, and a power of 10. The power of 10 indicates the number of places the decimal point is moved to the right (if the exponent is positive) or to the left (if the exponent is negative).

Based on the given numbers:

1. 2 × 10^(-6): This number is very small, as the exponent is negative and indicates that the decimal point is moved 6 places to the left.

2. 1 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.

3. 1 × 10^(-2): Similar to the previous number, this is also a small value, with the exponent indicating a movement of 2 places to the left.

4. 2 × 10^(-5): This number is very small, with the exponent indicating a movement of 5 places to the left.

5. 5 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.

6. 8 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.

7. 2 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.

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A field project superintendent earns an annual salary of $72,800. This is a piece of information about the annual salary of a field project superintendent.

A field project superintendent is a person responsible for overseeing and managing construction projects. This position is responsible for ensuring that the construction project is completed on time, within budget, and in accordance with safety and quality standards. This person must have a thorough understanding of construction principles and techniques, as well as the ability to read and interpret blueprints and specifications.

A salary is a fixed amount of compensation paid to an employee for their work. The amount of salary is typically determined by the employee's position, job duties, and level of experience. Salaries are usually paid on a monthly or bi-weekly basis.

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Three people share seven brownies. Each person should get 2 brownies since 2 is the closest value that is less than 2.33 since the answer should be a whole number.

Explanation: We can calculate the number of brownies each person should get by dividing the total number of brownies by the number of people that will share them. Since three people are to share 7 brownies, we divide 7 by 3.Thus, each person should get 2 and 1/3 of a brownie. This value, however, cannot be the answer since it should be a whole number. Therefore, we take the closest b number that is less than 2.33, which is 2. This implies that each person should get 2 brownies.

In essence, we will have shared 6 brownies since 2 x 3 is equal to 6. So, one brownie will be left. This means that the brownie should be shared among the three people. Each person will receive two brownies and the remaining one brownie should be shared equally among the three. So, each person should get two and one-third pieces of brownies.

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we can continue solving the equation correctly and find the accurate value for x. identify where Chelsea made a mistake, let's analyze the equation and her solution step by step:

Given equation: 4x - 5 = 23(x - 3)

Chelsea's solution:
Step 1: Distribute the 23 to the terms inside the parentheses:
4x - 5 = 23x - 69

Step 2: Simplify the equation by subtracting 23x from both sides:
4x - 23x - 5 = -69

Step 3: Combine like terms:
-19x - 5 = -69

Step 4: Add 5 to both sides to isolate the variable:
-19x = -64

Step 5: Divide both sides by -19 to solve for x:
x = -64 / -19
x ≈ 3.3684

Chelsea's mistake occurred in step 4. Instead of adding 5 to both sides, she subtracted it. The correct equation should be:

-19x + 5 = -69

By making this correction, we can continue solving the equation correctly and find the accurate value for x.

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The top of the ladder is approximately 44.1 feet from the ground.

To find out how high the top of the ladder is from the ground, we need to use trigonometry, specifically the tangent function since we have the angle of elevation and the length of the adjacent side. Here are the steps to solve the problem:

Step 1: Label the diagram and identify the angle of elevation and the adjacent side.

Label the base of the ladder as the adjacent side (a), the height of the ladder as the opposite side (o), and the length of the ladder as the hypotenuse (h).Identify the angle of elevation as the angle between the adjacent side and the hypotenuse.

In this case, the angle of elevation is 74°.

Step 2: Write out the formula and substitute the given values.Tanθ = o/aTan74° = o/a Solve for o: o = a * tan74°

Step 3: Substitute the value of a and use a calculator to find o.

Substitute the value of a, which is 14 feet, and use a calculator to find o. o = 14 * tan74°o ≈ 44.1 feet (rounded to the nearest tenth)Therefore, the top of the ladder is approximately 44.1 feet from the ground.

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This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!

If you're planning a dinner party with a budget of $50 and a menu that consists of 1 main dish, 2 side dishes, and 1 dessert, there are plenty of affordable options you can choose from. Here's a sample menu that should fit within your budget:Main Dish: Baked Chicken - $10Ingredients:4 chicken leg quarters - $6.004 tbsp olive oil - $0.501 tbsp salt - $0.101 tbsp pepper - $0.101 tbsp garlic powder - $0.101 tbsp paprika - $0.10Directions:Preheat oven to 400°F. Combine salt, pepper, garlic powder, and paprika in a small bowl.

Drizzle chicken with olive oil and rub spice mixture onto chicken. Place chicken in a baking dish and bake for 45-50 minutes until chicken is cooked through.

Side Dish 1: Garlic Roasted Potatoes - $4Ingredients:6 medium-sized potatoes - $1.501/4 cup olive oil - $0.751 tbsp salt - $0.101 tbsp pepper - $0.101 tb sp garlic powder - $0.10Directions:Preheat oven to 400°F. Wash potatoes and cut them into small cubes.

Combine potatoes with olive oil, salt, pepper, and garlic powder in a large mixing bowl. Spread the potatoes out in a single layer on a baking sheet and bake for 30-35 minutes until golden brown and crispy.

Side Dish 2: Sauteed Green Beans - $3Ingredients:

1 lb green beans - $2.001/4 cup butter - $0.501 tbsp garlic - $0.101/2 tbsp salt - $0.051/2 tbsp pepper - $0.05Directions:Bring a pot of water to a boil and blanch green beans for 2-3 minutes. Drain and rinse under cold water.  Combine flour, rolled oats, brown sugar, butter, cinnamon, and nutmeg in a mixing bowl. Use your hands to mix the ingredients together until crumbly. Spread the topping over the apples and bake for 35-40 minutes until golden brown and crispy.

Total cost: $25This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!

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The radical form of[tex](-3x^3)^-^2/3 is 1 / (9x^2)[/tex].

To rewrite the expression[tex](-3x^3)^-^2/3[/tex] as a radical, we can use the fact that a negative exponent indicates that the base is in the denominator. Therefore, we can rewrite the expression as:

[tex]1 / (-3x^3)^(^2^/^3^)[/tex]

Using this concept, we can rewrite the exponent -2/3 as [tex]3\sqrt(1/-3^2)[/tex], where 3√ is the cube root. We also need to take the cube root of the absolute value of -3x^3 to ensure that the result is always positive.

To find the radical form, we can simplify the expression under the radical by raising it to the power of 3/2:

[tex](-3x^3)^(^2^/^3) = [(-3)^(^2^/^3^) * (x^3)^(^2^/^3^)]^3 = [(9 * x^2)^(^1^/^3^)]^3 = 9x^2[/tex]

Substituting this back into the original expression gives:

1 / (-3x^3)^(2/3) = 1 / (9x^2).

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Specify primary audio , secondary audio (sound effects/music), and background audio (ambient music) in the storyboard. Note scenes with surrounding noise, use an external microphone for recording, and plan additional music for editing.



In storyboarding for an ad firm, Eric needs to consider three types of audio: primary audio, secondary audio, and background audio. Primary audio refers to the main audio component that drives the narrative or delivers important information in the ad. This can include dialogue, voiceover, or any sound directly related to the main subject. Secondary audio supports the primary audio and adds depth to the storytelling. It can include sound effects, ambient noise, or music that complements the visuals. Background audio provides the overall atmosphere and mood of the ad. It can include ambient music or soundscapes that create the desired emotional tone.

Additionally, Eric should make notes of scenes where surrounding noise is required. This means capturing the environmental sounds that enhance the authenticity and realism of the ad, such as street noise, nature sounds, or crowd reactions. He should also consider using an external microphone to simultaneously record audio while filming the video. This ensures high-quality audio capture and reduces the reliance on the camera's built-in microphone, which may not provide optimal sound recording. Lastly, Eric can make a note of any additional music he intends to add during the editing process. This can involve selecting appropriate background tracks, jingles, or any other musical elements that enhance the overall impact of the ad. By carefully considering these audio aspects during storyboarding, Eric can create a compelling and immersive ad experience for the audience.

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Yes, the probability of drawing a heart and then a diamond from a standard deck of 52 cards is indeed (13/52) x (13/52).

To calculate the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of drawing a heart on the first card is 13 out of 52 because there are 13 hearts in a standard deck of 52 cards. The probability of drawing a diamond on the second card is also 13 out of 52 since there are 13 diamonds in the deck.

Therefore, the probability of drawing a heart and then a diamond is:

(13/52) x (13/52) = (169/2704) = 1/16 ≈ 0.0625 ≈ 6.25%

So, the probability of drawing a heart and then a diamond from a standard deck is 13/52 multiplied by 13/52.

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The dimensions of a rectangular prism can be matched with the volume of the rectangular prism as follows:

To match the dimensions of the rectangular prism to the volume we need to know the formula or the volume of a rectangular prism. That is;

length * breadth * height.

So, for the dimensions given, we would simply multiply all the side lengths to arrive at the final volume of the rectangular prism. For the first one,

4 * 3 * 6 = 72 in³

6 * 3 * 2  = 36 in³

4 * 5 * 4  = 80 in³

2 * 9 * 3 = 54 in³

The results represent the final volumes of the rectangular prisms.

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the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

To find th positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees, and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees,

we can use the following formulas:For a positive coterminal angle, add 360 degrees repeatedly until we reach the desired range.For a negative coterminal angle, subtract 360 degrees repeatedly until we reach the desired range.

Let's start with the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees.

To find this angle, we need to add 360 degrees repeatedly until we reach a value between 500 degrees and 1000 degrees.

So, we can write:47 + 360 = 407 (not in range)

407 + 360 = 767 (not in range)

767 + 360 = 1127 (not in range)

1127 + 360 = 1487 (not in range)

1487 + 360 = 1847 (not in range)

1847 + 360 = 2207 (not in range)

2207 + 360 = 2567 (not in range)

2567 + 360 = 2927 (not in range)

2927 + 360 = 3287 (not in range)

3287 + 360 = 3647 (not in range)

3647 + 360 = 4007 (not in range)

4007 + 360 = 4367 (not in range

4367 + 360 = 4727 (not in range)

4727 + 360 = 5087 (not in range

5087 + 360 = 5447 (not in range

)5447 + 360 = 5807 (not in range)

5807 + 360 = 6167 (not in range)

6167 + 360 = 6527 (not in range)

6527 + 360 = 6887not in range)

6887 + 360 = 7247 (not in range

)7247 + 360 = 7607 (not in range)

7607 + 360 = 7967 (not in range)

7967 + 360 = 8327 (not in range)

8327 + 360 = 8687 (not in range)

8687 + 360 = 9047 (not in range)

9047 + 360 = 9407 (not in range)

9407 + 360 = 9767 (not in range

)9767 + 360 = 10127 (not in range)

10127 + 360 = 10487 (not in range)

10487 + 360 = 10847 (not in range)

10847 + 360 = 11207 (in range)

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 11207 - 10847 = 360 degrees.

To find the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees, we need to subtract 360 degrees repeatedly until we reach a value between -500 degrees and 0 degrees. So, we can write:

47 - 360 = -313 (not in range)

-313 - 360 = -673 (not in range)

-673 - 360 = -1033 (not in range)

-1033 - 360 = -1393 (not in range

-1393 - 360 = -1753 (not in range)

-1753 - 360 = -2113 (not in range)

-2113 - 360 = -2473 (not in range)

-2473 - 360 = -2833 (not in range

-2833 - 360 = -3193 (not in range

-3193 - 360 = -3553 (not in range)

-3553 - 360 = -3913 (not in range)

-3913 - 360 = -4273 (not in range)

-4273 - 360 = -4633 (not in range)

-4633 - 360 = -4993 (in range)

therefore, the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is -4993 - (-5183) = 190 degrees.

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

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The solution to the system of equations is (-4, 4).

The system of equations is: x + y = -8 and x - y = 0
Mr. Brown can find the solution to the system of equations by solving it using the elimination method as follows:
x + y = -8 (Equation 1)
x - y = 0 (Equation 2)
Add Equation 1 and Equation 2.
Doing so will eliminate y from the equations and solve for x.
x + y + x - y = -8 + 0
2x = -8 x = -4
Substitute x = -4 into any of the original equations to solve for y.
Let's use Equation 2: x - y = 0 -4 - y = 0
y = -(-4) y = 4

Therefore, the solution to the system of equations is (-4, 4).

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Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.

The given information states that the average length of the head and body of a western harvest mouse is 2.9 inches, while the average length of the tail is 2.8 inches. To estimate the total length of the mouse, we can add these two measurements together:

Estimated total length = Average length of head and body + Average length of tail

Estimated total length = 2.9 inches + 2.8 inches

Estimated total length = 5.7 inches

Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.

It's important to note that this estimate represents the average length and may not accurately reflect the actual total length of each individual mouse. There may be variations in the lengths of different mice within the population. Factors such as genetics, age, and environment can influence the actual total length of a mouse. Therefore, the estimate serves as a general approximation and the actual total length of each mouse may differ slightly from the estimate of 5.7 inches.

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Quadratic equations are equations of the form ax^2 + bx + c = 0, where a, b, and c are coefficients, and x represents the variable.

To solve quadratic equations, you can use several methods, including factoring, completing the square, or using the quadratic formula. The approach may vary depending on whether the coefficient 'a' is equal to 1 or not.

If 'a' is equal to 1:

Factor the equation if possible. Look for two binomials that multiply to give the quadratic expression. Set each binomial equal to zero and solve for x.

If factoring is not possible or doesn't yield rational solutions, you can use the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). Substitute the coefficients into the formula and simplify to find the values of x.

If 'a' does not equal 1:

Multiply the equation by a constant to make the coefficient of x^2 equal to 1. Divide all terms by 'a' to simplify the equation.

Apply the same methods as above to solve the simplified equation. Factor if possible or use the quadratic formula to find the solutions.

Remember to consider any extra factors introduced by multiplying by 'a' when determining the final solutions.

It's important to note that quadratic equations can have zero, one, or two real solutions, depending on the discriminant (b^2 - 4ac). If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions, but there may be complex solutions.

It's recommended to practice solving quadratic equations using these methods and to check your solutions by substituting them back into the original equation to ensure they satisfy it.

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Plot C serves as the control in the study, providing a baseline or reference point for comparison.

In scientific studies, a control group or condition is used to establish a baseline against which experimental results are compared. In the context of a plot, Plot C is likely subjected to the same conditions as the other plots but without any specific treatment or intervention.

This allows researchers to observe and measure the natural or expected outcome in the absence of the experimental variable. By comparing the results from the treated plots to the control plot, researchers can determine the effect of the intervention or treatment.

Plot C helps eliminate confounding factors and provides a basis for evaluating the effectiveness or impact of the experimental variables.

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The probability that a randomly chosen card from a standard deck of 52 cards is red is 1/2.

To determine the probability of picking a red card, we need to understand the composition of a standard deck of playing cards. A standard deck consists of 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades. The hearts and diamonds are considered red suits, while the clubs and spades are considered black suits.

Out of the 52 cards in the deck, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades). Since each card has an equal chance of being picked when chosen randomly, the probability of selecting a red card is the ratio of the number of red cards to the total number of cards in the deck.

Therefore, the probability of picking a red card is 26 (number of red cards) divided by 52 (total number of cards), which simplifies to 1/2.

In conclusion, when picking a card at random from a standard deck, the probability of selecting a red card is 1/2.

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The fabric used on a headband and wristband for each players are 19.97 inches and 9.68 inches respectively.

He uses 698.95 inches of fabrics on headbands for 32 players and 3 Coaches.

He also use 309.76 inches of fabrics on wristbands for just players.

The fabric that was used on a headband and wristband for each player can be calculated as follows;

The total fabrics used on headbands for 32 players and 3 coaches is 698.95 inches.

Therefore, the fabric for each individual will be as follows:

698.95 / 32 + 3

= 698.95 / 35

= 19.97 inches

So, The total fabrics used on wristband for just players is 309.76 inches. Therefore, the fabric used for each player is as follows:

309.76 / 32 = 9.68 inches

Therefore, the fabric used on a headband and wristband for each players are 19.97 inches and 9.68 inches respectively.

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Complete question is,

Joey is making accessories for the soccer team. He uses 698.95 inches of fabric on headbands for 32 players and 3 coaches. He also uses 309.76 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

Using algebraic equations, the value of the number assumed to be x is 13.

Let's assume that the number in question be "x". Thus, the expression can be written as:

2x + 9 = 5 (x - 6).

Let's solve this equation and find the value of x:

Distributing the 5 across the parentheses,

2x + 9 = 5x - 30  

Subtracting 2x from both sides,

we get, 3x = 39  

Dividing both sides by 3,

x = 13    

Thus, the number is 13.

Thus, we have found the number by forming and solving an equation.

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The expressions that have a value of 15 when x = 15 include the following:

A. x/3 + 10

C. (3,015 ÷ x) - 186

Based on the information provided, we would determine the output value of each of the given expression by substituting 15 for the value of x as follows;

Expression = x/3 + 10

Expression = 15/3 + 10

Expression = 5 + 10

Expression = 15 (True).

Expression = 15,521 ÷ x

Expression = 15,521 ÷ 15

Expression = 1034.73 (False).

Expression = (3,015 ÷ x) - 186

Expression = (3,015 ÷ 15) - 186

Expression = 201 - 186

Expression = 15 (True).

Expression = 20x² ÷ 30

Expression = 20(15)² ÷ 30

Expression = 4500 ÷ 30

Expression = 150 (False).

Expression = 20x²/5 - 25

Expression = 20(15)²/5 - 25

Expression = 900 - 25

Expression = 875 (False).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The call center made approximately 676 calls per hour. In 7 hours, operators at a call center make 4,732 telemarketing calls.

To represent the number of phone calls made per hour at the call center, we can use the equation:

Number of phone calls made per hour = Total number of phone calls / Number of hours

Given that in 7 hours, operators at the call center made 4,732 telemarketing calls, we can substitute the values into the equation to find the number of calls made per hour:

Number of phone calls made per hour = 4,732 / 7

Performing the division:

Number of phone calls made per hour = 676

Therefore, the call center made approximately 676 calls per hour.

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The correct total cost of the 5 tickets is $85.

The calculation that Maria is using to calculate the total cost of the tickets is incorrect. She is multiplying the number of tickets by $10 and $7 separately, instead of multiplying the number of tickets by the cost per ticket.

To correctly calculate the total cost of the tickets, Maria should multiply the number of tickets (5) by the cost per ticket ($17) as follows:

Total cost = 5 x $17 = $85

It seems that Maria made a mistake in her calculation by multiplying the number of tickets by two different values ($10 and $7) instead of using the actual cost per ticket. This mistake leads to an incorrect total cost of $50 + $35 = $85.

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The sapling tree is 30 inches tall when planted and it grows 2 inches each year. Let y be the height of the tree in inches and x be the age of the tree in years.

Since the tree grows 2 inches each year, the height y of the tree in x years can be represented as:y = 30 + 2xThe function that shows the relationship between the age of the tree in years (x) and the height (y) is y = 30 + 2x.The answer is y = 30 + 2x.

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The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]\(r\)[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .

To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of [tex]\(r + 2\)[/tex]cm, while the inner cylinder has a radius of [tex]r[/tex] cm. The length of both cylinders is [tex]9r[/tex] cm.

The volume of the outer cylinder can be calculated using the formula: [tex]\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3[/tex].

The volume of the inner cylinder can be calculated using the formula: [tex]\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3[/tex].

To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:

[tex]\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\][/tex]

Simplifying further:

[tex]\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\][/tex]

Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]r[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .

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Given, the volume of a cube is 407cm³.Let's assume that a is the length of a side of the cube. We know that the volume of a cube = a³So,

a³ = 407Take the cube root of both sides to find the value of a.

a = (407)^(1/3)≈ 7.96cm(rounded to 1 decimal place)

Hence, the length of the side of the cube rounded to 1 DP is 7.96 cm (more than 100 words).

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To write and evaluate an addition expression to determine Tressa's current score, we need to subtract the number of points she loses from her original score. The original score is 57.9 points and she loses 8.6 points.

So, Tressa's current score can be determined by adding the difference (which is -8.6) to her original score. Therefore, the addition expression to determine Tressa's current score can be written as:

57.9 + (-8.6)

To evaluate this expression, we simply need to add the numbers:

57.9 + (-8.6) = 49.3

Therefore, Tressa's current score is 49.3 points.

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