Here are 5 numbers 2 5 7 8 9 one of the numbers is removed meaing the avarge of the remainnig four numbers is 6 which card removed numbers

To write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.

Step 1: Write the percentage as a fraction by dividing it by 100.For example, let's say we want to write 25% as a fraction in its simplest form.

25% is equivalent to 25/100 or 0.25 as a decimal.

Step 2: Simplify the fraction by finding a common factor between the numerator and denominator.

For example, let's simplify 25/100.

Both the numerator and denominator can be divided by 25, giving us 1/4.

Therefore, 25% as a fraction in its simplest form is 1/4.

Another example: let's write 60% as a fraction in its simplest form.

60% is equivalent to 60/100 or 0.6 as a decimal.

The numerator and denominator can both be divided by 20, giving us 3/5.

Therefore, 60% as a fraction in its simplest form is 3/5.

In summary, to write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.

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The domain and range of a function can be determined by analyzing its graph and also algebraically.

MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function

.(a) f(x)

= 3x - 2

Domain: All real numbers Range:

All real numbers(b) g(x)

= x² - 5

Domain: All real numbers Range

: y ≥ -5(c) h(x)

= √(x + 4)

Domain: x ≥ -4

Range: y ≥ 0(d) k(x)

= 4

Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.

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The greatest possible value for n(AUB) can be determined by finding the union of sets A and B, considering the maximum number of elements that can be in the union.

The notation n(A) represents the number of elements in set A. Given that n(U) = 16, it indicates that the universal set U contains 16 elements. Set A has 7 elements, and set B has 12 elements. To find the greatest possible value for n(AUB), we consider the maximum number of elements that can be in the union. The union of two sets combines all the elements from both sets without duplicating any common elements.

In this case, the greatest value for n(AUB) occurs when all the elements from both sets A and B are combined without duplication. Therefore, the greatest value for n(AUB) is the total number of elements in both sets A and B, which is 7 + 12 = 19.

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You can carve out 150 cubes of side 0.1 m from the given block of wood.

To determine the number of cubes, we need to calculate the volume of the block and the volume of each cube.

The volume of the block is given by:

Volume = length × width × height

Volume = 75 cm × 50 cm × 40 cm

Converting the measurements to meters:

Volume = (75 cm / 100) m × (50 cm / 100) m × (40 cm / 100) m

Volume = 0.75 m × 0.5 m × 0.4 m

Volume = 0.15 m³

The volume of each cube is given by:

Volume of each cube = side³

Volume of each cube = (0.1 m)³

Volume of each cube = 0.001 m³

To find the number of cubes that can be carved out of the block, we divide the volume of the block by the volume of each cube:

Number of cubes = Volume of block / Volume of each cube

Number of cubes = 0.15 m³ / 0.001 m³

Number of cubes = 150

Therefore, you can carve out 150 cubes of side 0.1 m from the given block of wood.

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We need to consider the discount applied and the sales tax added. Discounted price = $45.50 - (30/100) * $45.50 Sales tax = (8/100) * (discounted price) Total cost = discounted price + sales tax

First, we calculate the discounted price by subtracting 30% of the original price from the original price:

Discounted price = $45.50 - (30/100) * $45.50Next, we calculate the amount of sales tax by adding 8% of the discounted price to the discounted price:

Sales tax = (8/100) * (discounted price)Finally, we calculate the total cost of the video game by adding the discounted price and the sales tax: Total cost = discounted price + sales tax

By substituting the given values into the formulas and performing the calculations, we can find the total cost of the video game.

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The 95% two-proportion z confidence interval (0.1181, 0.2057) in the given problem indicates that there is a 95% probability that the true difference in proportions between the two polls falls within the range of 0.1181 to 0.2057.

This means that the proportion of registered voters who favor candidate X in the first poll is estimated to be between 11.81% and 20.57% higher than the proportion in the second poll.

The confidence interval is a statistical tool that provides a range of values within which the true difference between the proportions is likely to lie. The interval is constructed based on the sample data and takes into account the variability in the estimates. In this case, it suggests that there is evidence to support the claim that candidate X was more favored by registered voters in the first poll compared to the second poll.

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Thus, the number of square inches enclosed by the shaded region is 72√6 square inches.

Given, two congruent squares overlap, as shown, so that vertex A of one square lies at the intersection of the diagonals of the other square.

The side of each square has length 12 inches.

To find: The number of square inches enclosed by the shaded region.

Solution: It is given that, two squares are congruent and side of each square is 12 inches.

Let's find the shaded area.

By Pythagorean theorem, in ΔABO, we have:

OB² = AO² + AB²

We know that, side of square is 12 inches.

So, AO = BO = 6√2 inches

AB = 12 inches

Therefore,

OB² = (6√2)² + 12²

OB² = 72 + 144

OB² = 216

OB = 6√6 inches

Area of ΔABO = 1/2 × base × height= 1/2 × AB × OB= 1/2 × 12 × 6√6= 36√6 sq. inches

Area of shaded region = 2 × Area of ΔABO= 2 × 36√6= 72√6 sq. inches

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Rolando is making buttons that are shaped like circles. Each button has an area of 36 square centimeters. This article explains the measurement that shows the circumference of each of the buttons in centimeters.

The area of a circle is given by the formula: A = πr²where A is the area and r is the radius of the circle.The problem statement says that each button has an area of 36 square centimeters. So,36 = πr²Or,r² = 36/πSolving for r, we get:r = √(36/π)Thus, the radius of each button is given by:r = 3 √π square centimeters Circumference is given by the formula:C = 2πr.

So, substituting the value of r we get:C = 2π * 3 √π= 6 π √π cm Therefore, the measurement that shows the circumference of each of the buttons in centimeters is 6 π √π cm which is approximately equal to 10.85 cm.

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Congruent arcs determine equidistant chords in the same circle or in congruent circles.

This means that if two arcs in a circle are congruent, then any chords associated with those arcs will also be equidistant from the center of the circle. In other words, the distance from the center of the circle to any point on the chord will be the same for both chords.

So, the correct choice is "Equidistant".Let's break down the concept of congruent arcs and equidistant chords in more detail.

In a circle, an arc is a curved section of the circumference. When two arcs in the same circle or in congruent circles are congruent, it means they have the same measure or length. In other words, they span the same angle or distance along the circumference.

Now, when we talk about chords, we are referring to line segments that connect two points on the circle. A chord is formed by selecting any two points on the circle and joining them with a straight line.

When we say that congruent arcs determine equidistant chords, it means that if two arcs in a circle are congruent, then any chords associated with those arcs will have the same distance from the center of the circle.

In simpler terms, imagine you have two congruent arcs in a circle. Now, draw a chord for each of those arcs. The key point is that the distance from the center of the circle to any point on one chord will be equal to the distance from the center to any point on the other chord.

This property holds true because congruent arcs subtend the same angle at the center of the circle. Since the distances from the center to the chords are equal, the chords themselves are said to be equidistant.

To summarize, when two arcs in a circle are congruent, the chords associated with those arcs will be equidistant from the center of the circle. This is a fundamental property of circles and is true for any pair of congruent arcs in the same circle or in congruent circles.

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The cost of riding to Vominator for 47 minutes, to the nearest penny, is £6.56.

It costs £6.56 to ride to Vominator for 47 minutes.

Given, the cost of riding to Vominator for 23 minutes is £3.20.

Hence, the cost of riding for 1 minute is;`1 min = £3.20/23 = £0.13913...`

To the nearest penny, the cost of riding for 1 minute is £0.14.

To find the cost of riding to Vominator for 47 minutes, we multiply the cost of riding for one minute by 47.`

Cost for 47 minutes = 47 × £0.14 = £6.58`

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The correct answer is B (31,50), which shows the location of the new point Mr. Fisher must plot.

To determine the location of the new point Mr. Fisher must plot, let's analyze the given information:

The extra student scored 25 points higher than the student who was absent for 6 days.

This extra student was absent for 5 fewer days than the student who scored 55.

Let's assign variables to the relevant values:

Let "A" represent the number of days the absent student was absent for.

Let "S" represent the score of the student who scored 55.

From the given information, we can determine the following relationships:

The extra student's score = S + 25.

The extra student's number of absent days = A - 5.

Now, let's analyze the answer choices:

A (3,80): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

C (80,3): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

B (31,50): This point satisfies the given conditions: the extra student was absent for 5 fewer days than the student who scored 55, and the extra student's score is 25 points higher.

D (90,3): This point does not match the given information, as it does not fulfill the conditions related to the absent days and scores.

The correct option is b.

The complete question is:

Mr. Fisher remembered that he had one more exam to grade. The extra student scored 25 points, higher than the student who was absent for 6 days. This extra student was absent for 5 fewer days than the student who scored 55. Which shows the location of the new point Mr. Fisher must plot?

A (3,80)

C (80,3)

B (31,50)

D (90,3)

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When rounded to the nearest liter, 103.468 liters would be rounded to 103 liters.

When rounding a number to the nearest liter, we consider the decimal part of the number. In this case, the number is 103.468 liters. The decimal part is 0.468.

To determine whether to round up or down, we compare the decimal part to 0.5. If the decimal part is 0.5 or greater, we round up. If it is less than 0.5, we round down.

In this case, the decimal part 0.468 is less than 0.5. Therefore, we round down to the nearest whole number, which is 103. Thus, 103.468 liters rounded to the nearest liter is 103 liters.

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a. To find the number of units produced with 300 units of labor (x) and 200 units of capital (y), we substitute these values into the production function:

P = (60^0.75)(200^0.25) = 60^0.75 * 200^0.25 ≈ 31.62 * 5 ≈ 158.10

Therefore, approximately 158 burgers would be produced with 300 units of labor and 200 units of capital.

b. The marginal productivity of labor (MPL) is the partial derivative of the production function with respect to labor (x), while the marginal productivity of capital (MPK) is the partial derivative with respect to capital (y). Taking the partial derivatives, we have:

MPL = 0.75 * 60^0.75 * 200^0.25 / 60 ≈ 0.75 * 31.62 ≈ 23.72

MPK = 0.25 * 60^0.75 * 200^0.25 / 200 ≈ 0.25 * 31.62 ≈ 7.90

c. Evaluating the marginal productivities with x = 300 and y = 200:

MPL = 0.75 * 60^0.75 * 200^0.25 / 60 ≈ 0.75 * 31.62 ≈ 23.72

MPK = 0.25 * 60^0.75 * 200^0.25 / 200 ≈ 0.25 * 31.62 ≈ 7.90

d. The marginal productivity of labor (MPL) represents the additional output gained by increasing the amount of labor while keeping capital constant. In this case, for every additional unit of labor, approximately 23.72 burgers will be produced.

The marginal productivity of capital (MPK) represents the additional output gained by increasing the amount of capital while keeping labor constant. For every additional unit of capital, approximately 7.90 burgers will be produced.

e. If the constraint x + y = 500 is applied, we can use the Lagrange multiplier method to find the maximum production. By maximizing the production function subject to this constraint, we can determine the optimal combination of labor and capital that yields the maximum production.

f. The Lagrange multiplier (λ) represents the rate of change of the production function subject to the constraint x + y = 500. Its value indicates how the maximum production is affected by changes in the constraint. The interpretation of λ in this context is that it quantifies the trade-off between labor and capital to achieve the highest production level while satisfying the given constraint of limited labor and capital resources.

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Cara invested $6,000 at 8.5% interest and $3,000 at 10.75% interest.

Let's solve the problem step by step.

Let's assume that Cara invested x dollars at 8.5% interest and y dollars at 10.75% interest. According to the given information, the total interest income for one year was $1,880.

We know that interest is calculated as the product of the principal amount, the interest rate, and the time period. Using this formula, we can write the equation:

0.085x + 0.1075y = 1,880 (equation 1)

The second given information states that x is $4,000 less than twice the y amount. Mathematically, we can express this as:

x = 2y - 4,000 (equation 2)

Now we have a system of two equations (equation 1 and equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.

By substituting equation 2 into equation 1, we get:

0.085(2y - 4,000) + 0.1075y = 1,880

Simplifying the equation, we have:

0.17y - 340 + 0.1075y = 1,880

Combining like terms, we get:

0.2775y = 2,220

Dividing both sides by 0.2775, we find that y ≈ 8,000.

Substituting this value back into equation 2, we can solve for x:

x = 2(8,000) - 4,000

Simplifying, we get x ≈ 12,000.

Therefore, Cara invested $6,000 at 8.5% interest (x = $12,000 - $4,000) and $3,000 at 10.75% interest (y = $8,000).

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The height of the rectangle is 16 cm. Finally, substituting the height into the equation b = 32 / h, we find b = 32 / 16 = 2 cm. Hence, the longest side of the rectangle in the compound shape is 2 cm.

The longest side of the rectangle in the compound shape can be found by subtracting the area of the triangle from the total area of the shape, and then dividing it by the base of the rectangle. The resulting value will give the length of the longest side of the rectangle.

Let's denote the base of the rectangle as 'b' and the height as 'h'. The area of a triangle is given by the formula (1/2) * base * height. In this case, we are given that the area of the triangle is 20 square cm, so we have (1/2) * b * h = 20.

The total area of the compound shape is given as 52 square cm, which consists of the triangle and the rectangle. Therefore, the area of the rectangle can be obtained by subtracting the area of the triangle from the total area: 52 - 20 = 32 square cm.

Now, we can find the length of the longest side of the rectangle by dividing the area of the rectangle by its base. Since the area of the rectangle is equal to the product of its base and height (32 = b * h), we can rearrange the equation to solve for the base: b = 32 / h.

Substituting this value of b into the equation (1/2) * b * h = 20, we get (1/2) * (32 / h) * h = 20. Simplifying the equation further, we have 16 = h. Therefore, the height of the rectangle is 16 cm.

Finally, substituting the height into the equation b = 32 / h, we find b = 32 / 16 = 2 cm. Hence, the longest side of the rectangle in the compound shape is 2 cm.

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The statement that is NOT true about the relationship between a function and its inverse is option B: "The domain of a function is the range of the inverse of the function."

In general, the domain of a function consists of all possible input values, while the range represents the set of all possible output values. When finding the inverse of a function, the roles of the domain and range are interchanged. Therefore, the range of the original function becomes the domain of its inverse, and vice versa.

The other options are true:

A. The graph of the inverse of a function is indeed the reflection across the line y = x of the graph of the function. This means that if you plot the function and its inverse on a coordinate plane, they will be symmetric with respect to the line y = x.

C. The range of a function does correspond to the domain of its inverse. The outputs of the original function become the inputs of its inverse.

D. The inverse of a function is not always a function. For a function to have an inverse, it must be one-to-one, meaning that each input value maps to a unique output value and vice versa. If a function fails to satisfy this criterion, it does not have an inverse. Here, option B is the statement that is not true. Therefore, Option B is correct.

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The final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.

The final volume of the gas in milliliters, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is unknown ml.

To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is:

P1 * V1 = P2 * V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Given that P1 = 0.428 atm, V1 = 240 ml, and P2 = 0.72338 atm, we can plug these values into the equation and solve for V2:

(0.428 atm) * (240 ml) = (0.72338 atm) * V2

103.2 atm * ml = 0.72338 atm * V2

V2 = (103.2 atm * ml) / 0.72338 atm

V2 ≈ 142.55 ml

Therefore, the final volume of the gas, when the pressure is increased from 0.428 atm to 0.72338 atm with an initial volume of 240 ml, is approximately 142.55 ml.

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If your commission is $1480, your total sales amount would be $22,500.

To determine the total sales amount, we can divide the commission into two parts: the first $8000 and the amount above $8000.

Let's calculate the commission earned on the first $8000:

Commission on the first $8000 = 8% of $8000

Commission on the first $8000 = 0.08 * $8000

Commission on the first $8000 = $640

Now, let's calculate the commission earned on the amount above $8000:

Commission on sales above $8000 = $1480 - Commission on the first $8000

Commission on sales above $8000 = $1480 - $640

Commission on sales above $8000 = $840

To find the sales amount corresponding to the commission on sales above $8000, we can use the formula:

Sales amount above $8000 = Commission on sales above $8000 / Commission rate

Sales amount above $8000 = $840 / 0.12 (since the commission rate is 12%)

Sales amount above $8000 = $7000

Now, to find the total sales amount, we add the sales amount above $8000 to the initial $8000:

Total sales amount = $8000 + Sales amount above $8000

Total sales amount = $8000 + $7000

Total sales amount = $15,000

However, we must note that this calculation assumes the commission is calculated based on the total sales amount, including the initial $8000. Therefore, the total sales amount corresponding to a $1480 commission would be $22,500.

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The correct function for Adrianne's purpose, where the growth is calculated every 3 months instead of every year, is f(x) = 467(5^(x/4)).

To calculate the growth every 3 months instead of every year, we need to modify the original function by adjusting the exponent of 5.

Step 1: The original function is f(x) = 467(5)^x, where x represents the number of years.

Step 2: To calculate the growth every 3 months, we divide x by 4, as there are 12 three-month periods in a year.

Step 3: Adjust the exponent of 5 to (x/4), representing the growth over each three-month period.

Step 4: The modified function becomes f(x) = 467(5^(x/4)), which calculates the growth every 3 months.

Therefore, the correct function for Adrianne's purpose is f(x) = 467(5^(x/4)).

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Based on the information provided by the box-and-whisker plot, the range of the given data (2, 5, 12, 13) is 5.

To determine the range of the data from the given box-and-whisker plot, we need to consider the highest and lowest values represented in the plot.

The whiskers in the plot extend from 102 to 115. This means that the lowest value in the data is 102, and the highest value is 115.

The box in the plot ranges from 109 to 114. The lower boundary of the box represents the 25th percentile (Q1), which is the median of the lower half of the data. In this case, Q1 is 109. The upper boundary of the box represents the 75th percentile (Q3), which is the median of the upper half of the data. In this case, Q3 is 114.

The line dividing the box at 111 represents the median (Q2), which is the middle value when the data is sorted in ascending order. So, Q2 is 111.

Now, let's analyze the given data values: 2, 5, 12, and 13.

Based on the box-and-whisker plot, we can see that the data range from the lowest whisker (102) to the highest whisker (115). However, the given data values fall within the range of the box, which is from 109 to 114.

Therefore, the range of the given data is from the lowest value within the box (109) to the highest value within the box (114). The range can be calculated as:

Range = Highest value - Lowest value

Range = 114 - 109

Range = 5

So, the range of the given data is 5.

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The item that does not belong in the given list is "25 oz."

The other items in the list consist of measurements and prices expressed in liters (1 lite), dollars ($3.75, $3.65, $3.05), and milliliters (500 mil).

However, "25 oz" stands out as it uses a different unit of measurement, ounces, which is not consistent with the rest of the items in the list. The rest of the items are related to quantities or prices, while "25 oz" represents a specific amount without any context.

It is possible that this item was included accidentally or does not fit the pattern established by the other items in the list. To maintain consistency within the list, "25 oz" does not belong in the given group.

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Here's an example of possible measurements for Sharon's liquid ingredients:

Ingredient A: 8.53 L (liters) - This could represent a larger quantity of a liquid ingredient that needs to be added in liters, such as water or broth.

Ingredient B: 1.5 L (liters) - This measurement could represent another liquid ingredient that needs to be added in liters, like oil or a sauce.

Ingredient C: 3500 mL (milliliters) - This measurement represents a smaller quantity of a liquid ingredient that is measured in milliliters, such as a flavoring extract or a concentrated ingredient.

Ingredient D: 250 mL (milliliters) - This measurement could represent another liquid ingredient measured in milliliters, like a specific sauce or a liquid seasoning.

In this example, Sharon uses a combination of liter and milliliter measurements to accurately measure different volumes of liquid ingredients for her recipe. The liter measurements (Ingredient A and Ingredient B) are used for larger quantities, while the milliliter measurements (Ingredient C and Ingredient D) are used for smaller amounts. This combination allows for precise measurement and flexibility in handling both large and small quantities of liquid ingredients.

It's important to note that the specific measurements can vary depending on the recipe and the desired quantities of each ingredient.

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The person can rent the car for 5 days and drive a maximum of 1800 miles within the $450 budget.

To determine the number of days the person can rent the car, we divide the remaining budget of $450 by the daily rental cost of $45. This gives us 10, indicating that the person can rent the car for up to 10 days. However, the goal is to spend the entire budget, so renting the car for the maximum number of days would exceed the budget.

Next, we need to calculate the maximum distance the person can drive within the budget. Since the cost is $0.25 per mile, we divide the remaining budget by $0.25 to find the maximum number of miles. This results in 1800 miles.

Therefore, the person can rent the car for 5 days and drive a maximum of 1800 miles within the $450 budget. By renting the car for 5 days and driving within this mileage limit, the person will spend the entire budget without exceeding it.

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The surface area of the rectangular brick can be calculated by adding up the areas of all its faces. The surface area of the rectangular brick is 650 square centimeters.

The given dimensions of the brick are:

Length = 5 centimeters

Width = 9 centimeters

Height = 20 centimeters

To find the surface area, we need to calculate the areas of the six faces of the brick. The rectangular brick has three pairs of equal faces: top and bottom, front and back, and left and right sides.

The area of each face can be found by multiplying the length by the width.

The top and bottom faces have the same dimensions, so each face has an area of 5 cm * 9 cm = 45 square centimeters.

The front and back faces also have the same dimensions, so each face has an area of 5 cm * 20 cm = 100 square centimeters.

The left and right side faces also have the same dimensions, so each face has an area of 9 cm * 20 cm = 180 square centimeters.

To find the total surface area, we add up the areas of all the faces:

Total Surface Area = 2 * (45 + 100 + 180) = 2 * 325 = 650 square centimeters.

Therefore, the surface area of the rectangular brick is 650 square centimeters.


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The coordinates after applying a dilation with a scale factor of 1/5 and centered at the origin to the line segment MN with endpoints M(-2, -4) and N(1, 5) are as follows:

   M: (-2, -4) → (-2/5, -4/5)

   N: (1, 5) → (1/5, 1)

So, the matching coordinates for the points are:

M (-2, -4) → (-2/5, -4/5)

N (1, 5) → (1/5, 1)

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Ms. Watson paid a flat fee of $110 for the first year and $10 monthly for the membership. As we know, Ms. Watson has to pay for 12 months of membership. The total cost of membership for the year is $230. We can calculate the cost of membership for the year as follows:

Yearly cost = Flat fee + Monthly fee for 12 months

Yearly cost = $110 + ($10 x 12)

Yearly cost = $110 + $120

Yearly cost = $230

Therefore, Ms. Watson has to pay $230 for her membership for the year. Ms. Watson is planning to join Planet Fitness for the first time. She has to pay a flat fee for the first year and a monthly fee for the membership. The flat fee is $110, and the monthly fee is $10. Ms. Watson needs to know the total membership cost for the year. We can calculate the total cost of the membership by using simple arithmetic.

The membership for the first year is a flat fee of $110. This fee is payable only once for the first year. After that, Ms. Watson needs to pay a monthly fee of $10. The membership is valid for 12 months. Therefore, we need to calculate the total cost of 12 months of membership for Ms. Watson.

We can do this by multiplying the monthly fee of $10 by 12 months. Ms. Watson must pay a flat fee of $110 for the first year and a monthly fee of $10. She needs to pay this fee for 12 months of membership. Therefore, the total cost of membership for the year is $230.

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The standard deviation for the amount of food consumed by the dogs in the lab is approximately 4.69 oz, indicating the spread or dispersion of the data set.



To calculate the standard deviation, we need to follow these steps:

1. Calculate the variance: The variance is the average of the squared deviations from the mean. It is calculated by dividing the sum of squared deviations by the number of observations. In this case, the sum of squared deviations is 220, and the number of observations is 10. So, the variance is 220/10 = 22.

2. Take the square root of the variance: The standard deviation is the square root of the variance. Using the calculated variance of 22, we find that the standard deviation is the square root of 22, which is approximately 4.69 oz.

Therefore, the standard deviation for the amount of food consumed by the dogs in the lab is approximately 4.69 oz. The standard deviation measures the spread or dispersion of the data set, indicating how much the individual observations deviate from the mean value.

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Let's represent the two numbers as variables. Let the first number be x and the second number be y.

According to the given information, one number is 5 more than the other, so we can write the equation x = y + 5.

The second piece of information states that three times the first number plus twice the second number equals 30, which can be expressed as the equation 3x + 2y = 30.

To find the values of x and y, we can solve this system of equations simultaneously. By substituting the value of x from the first equation into the second equation, we have 3(y + 5) + 2y = 30.

Simplifying the equation, we get 3y + 15 + 2y = 30, which can be further simplified to 5y + 15 = 30.

By subtracting 15 from both sides of the equation, we have 5y = 15, and dividing both sides by 5, we get y = 3.

Substituting this value of y back into the first equation x = y + 5, we find x = 3 + 5, which gives x = 8.

Therefore, the two numbers are 8 and 3.

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Paul earned a total of $1,368 during his summer vacation. To calculate how much money Paul earned during his summer vacation, we need to determine his hourly rate and the total number of hours he worked.

Given that Paul earned $8.55 per hour and worked 20 hours per week for 8 weeks, we can calculate his total earnings.

First, let's find the total number of hours Paul worked:

20 hours/week * 8 weeks = 160 hours.

Next, we multiply the total number of hours by his hourly rate to find his total earnings:

160 hours * $8.55/hour = $1,368.

Therefore, Paul earned a total of $1,368 during his summer vacation.

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The discounted price of the suit is $168.

Explanation: To calculate the discounted price, we need to subtract the discount percentage from 100% and then multiply it by the original price. In this case, the original price of the suit is $280, and it was discounted by 40%.

First, we calculate the discount amount:

Discount amount = Original price * (Discount percentage / 100)

Discount amount = $280 * (40 / 100)

Discount amount = $280 * 0.4

Discount amount = $112

Next, we will subtract the discount amount from the original price to find the discount price:

Discounted price = Original price - Discount amount.

Discounted price = $280 - $112

Discounted price = $168

Therefore, the discounted price of the suit is $168 after applying a 40% discount to the original price of $280.

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