Central Limit Theorem forms the foundation for the ___ branch of statistics

The statement that correctly compares the two functions on the interval [-1, 2] is A. Both functions are increasing, but function g increases at a faster average rate.

For function f, as x increases from -2 to 2, we can see that the corresponding values of f(x) also increase, but at a decreasing rate. This is because the function is exponential and approaching a horizontal asymptote as x goes to infinity. Therefore, f(x) is increasing, but at a decreasing rate.

For function g, we don't have enough information to determine if it's increasing or not, since only its equation is given. The correct option is A.

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The calculated height of the trapezoid is 5 ft.

The formula for the area of a trapezoid is:

A = (b1 + b2)h/2

where A is the area, b1 and b2 are the lengths of the parallel sides, and h is the height.

We are given that the area of the trapezoid is 25.5 ft^2, and the lengths of the parallel sides are 3.2 ft and 7 ft.

Substituting the given values into the formula, we get:

25.5 = (3.2 + 7)h/2

Simplifying the expression on the right side, we get:

25.5 = 5.1h

Dividing both sides by 5.1, we get:

h = 25.5/5.1

h = 5

Therefore, the height of the trapezoid is 5 ft.

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An expression that represents the amount of money Henry would have saved in w weeks is $95 + ($5 x w)

Henry already has $95, and he can save an additional $5 per week. So after one week of saving, Henry would have a total of $100 ($95 + $5). After two weeks, he would have $105 ($100 + $5), and so on.

To find out how much total money Henry would have after 10 weeks of saving, we can use the same method. After 10 weeks, Henry would have saved a total of $145 ($95 + ($5 x 10)). So, Henry would have a total of $145 after 10 weeks of saving.

Now, let's talk about an expression that represents the amount of money Henry would have saved in w weeks. We can use the formula:

Total amount saved = $95 + ($5 x w)

This formula takes into account the $95 that Henry already has, and the additional $5 he can save each week. The "w" in the formula represents the number of weeks Henry has been saving for. By plugging in different values of "w", we can determine how much money Henry would have saved at different points in time.

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The function rule that could model this situation is f(x)=sin(x)+3. The correct answer is (c).

The sine function is a mathematical function that describes a periodic oscillation. It is one of the basic trigonometric functions, along with cosine, tangent, cotangent, secant, and cosecant.

Let us relate this to our given question.

The midline of a sine function is the horizontal line that the graph oscillates around.

In this case, the midline is y=3, which means that the sine function oscillates between y=3+1=4 and y=3-1=2.

The function rule that could model this situation is c. f(x)=sin(x)+3, because adding 3 to the sine function shifts the midline up to y=3, and the sine function oscillates between y=4 and y=2.

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Given statement "3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors." is true. Because the rise and run of a gable roof allows you to calculate the slope factor, which can then be used to calculate the rake length and area of the roof.

If you know the rise and run of a gable roof, you can calculate the rake length and area using slope factors. The slope factor is a ratio that relates the length of the roof to the height of the roof.

The slope factor is calculated by dividing the rise of the roof by the run of the roof. Once you have the slope factor, you can use it to calculate the rake length and area of the roof.

The rake length is the length of the diagonal edge of the roof, and it can be calculated by multiplying the slope factor by the run of the roof.

For example, if the run of the roof is 10 feet and the slope factor is 0.5 (which corresponds to a 6:12 pitch), then the rake length would be 5 feet (0.5 x 10).

The area of the roof can be calculated by multiplying the rake length by the width of the roof.

For example, if the width of the roof is 20 feet and the rake length is 5 feet, then the area of the roof would be 100 square feet.

Statment is true.

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Therefore , the solution of the given problem of volume comes out to be ceramic mug has a 5 inch height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.

Here,

The following formula determines a cylinder's volume:

=> V = π * r² * h

where r is the cylinder's radius and h is its height, and is roughly equivalent to 3.14.

For the mug made of stainless steel:

1.5 inches is the radius (r).

Height in inches (h) is 8.5

With these values entered into the formula, we obtain:

=> V = 3.14 * (1.5)² * 8.5

=> V ≈ 3.14 * 2.25 * 8.5

=> V ≈ 60.14

The stainless steel mug has a 60 cubic inch volume, rounded to the nearest whole number.

Regarding the mug:

Radius (r) equals two inches

Given that it has the same volume as the stainless steel mug, its volume (V) is equal to 60 cubic inches.

=> 60 = 3.14 * (2)²* h

=> h = 60 / (3.14 * 4)

=> h ≈ 4.77

The ceramic mug has a 5 inch height.

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Let's say that the store starts with a coupon value of x.  On the first day, the probability of  drawing the pink tag is 1/n, where n is the total number of tags in the box.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probabilities can be expressed as fractions, decimals, or percentages.

A Coupon refers to a discount or a voucher that can be redeemed for a specified value or product at a store or business.

If the tag is not drawn, the probability of drawing it on the second day is 1/(n-1), since there is one less tag in the box. If the tag is not drawn on the second day, the probability of drawing it on the third day is 1/(n-2), and so on.

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The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.

Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.

Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.

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The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:

  (a)  $1350.46

  (b)  $50.46

Step-by-step explanation:

You want to know the future value of a $1300 CD earning 1.27% compounded monthly for 3 years, along with the amount of interest earned.

The compound interest formula tells you the future value is ...

  FV = P(1 +r/12)^(12·t)

where r is the annual interest rate and t is the number of years.

Using the given values, we have ...

  FV = $1300(1 +0.0127/12)^(12·3) ≈ $1350.46

(a) The value after 3 years is $1350.46.

The interest earned is the difference between the final value and the amount of the original investment:

  Interest = $1350.46 - 1300.00 = $50.46

(b) The interest earned by the CD is $50.46.

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The probability that two of those selected will be from the manufacturing department and one will be from the accounting department is approximately 0.409.

To solve the problem, we first need to find the total number of ways to select 3 people out of the 12 people in the company, which is given by the combination formula:

C(12,3) = 12! / (3! * (12-3)!) = 220

Next, we need to find the number of ways to select 2 people from the manufacturing department and 1 person from the accounting department. We can do this by using the combination formula again:

C(6,2) * C(4,1) = (6! / (2! * (6-2)!)) * (4! / (1! * (4-1)!)) = 90

Finally, we can find the probability by dividing the number of desired outcomes by the total number of possible outcomes:

P(2 manufacturing, 1 accounting) = 90 / 220 ≈ 0.409

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It would take the bowling ball approximately 3.1 seconds to fall 150 feet.

What is distance?

Distance is the total movement of an object, regardless of direction. We can define distance as how much ground an object has covered, regardless of its starting or ending point.

Distance is defined as the size or amount of displacement between two positions. Note that the distance between two locations is not the same as the distance between them. The distance traveled is the total length of the path traveled between two positions.

Here given equation,

d = 16t², where t is the time in seconds and d is the distance in feet and distance is 150 feet.

We want to find the value of t.

Now,

[tex]d = 16 {t}^{2} \\ {t}^{2} = \frac{d}{16} \\ {t}^{2} = \frac{150}{16} \\ t = \sqrt{( \frac{150}{16}) } \\ t = \sqrt{9.375} \\ t = 3.0619[/tex]

So, t = 3.1 (rounded to one decimal place)

Therefore, it would take the bowling ball approximately 3.1 seconds to fall 150 feet.

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Correct question is "How long would it take the bowling ball to fall 150 feet where equation of distance is d = 16t² ?(Estimate your answer to one decimal place). "

The linear equation have the following results: f(- 2) = 0, f(0) = 2, f(1) = 3.

In this problem we find a linear equation that must be evaluated at x = - 2, x = 0 and x = 1. Linear equations are expressions of the form:

y = m · x + b

Where:

Now we proceed to evaluate the function, the results are described:

x = - 2

f(- 2) = - 2 + 2

f(- 2) = 0

x = 0

f(0) = 0 + 2

f(0) = 2

x = 1

f(1) = 1 + 2

f(1) = 3

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The two consecutive digits whose product is 132 are equals to 11 and 12.

Product of two consecutive digits = 132

Let us consider that the two consecutive digits are y and y+1.

Then we can write the expression as,

⇒y × ( y + 1 ) = 132

Expanding the left side of the expression, we get,

⇒ y² + y = 132

Rearranging the values and solving for y, we get,

⇒ y² + y - 132 = 0

Factorize this quadratic equation to get the value of y we have,

⇒ y² + 12y - 11y - 132 = 0

⇒ y( y + 12 ) -11 ( y + 12 ) = 0

⇒ ( y + 12)(y - 11) = 0

This implies,

The two possible values of y are -12 and 11.

However, choose the positive value of y .

Since we are dealing with digits.

Thus, y = 11, and the consecutive digits are 11 and 12.

Therefore, the two consecutive digits are 11 and 12, and their product is indeed 132.

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The given question is incomplete, I answer the question in general according to my knowledge:

The product of two consecutive digit is equal to 132 . What are the numbers?

The given quadratic equations by solving using inverse operations gives,

(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.

Given are some quadratic equations.

We have to solve this using the inverse operations.

Inverse operations are operations which undo the operation which is done to the equation.

(a) 1/2 x² - 4 = 0

Adding both sides by 4,

1/2 x² = 4

Multiplying both sides by 2,

x² = 8

Taking the square root on both sides,

x = ±√8 = ±2√2

(b) (x - 5)² = 18

Taking the square root on both sides,

x - 5 = ±√18

x - 5 = ±3√2

Adding 5 on both sides,

x = ±3√2 + 5

(c) 2x² + 7 = 71

Subtracting by 7 on both sides,

2x² = 64

Dividing by 2 on both sides,

x² = 32

Taking the square root on both sides,

x = ±4√2

(d) 5 (x + 2)² + 37 = 487

Subtracting by 37 on both sides,

5 (x + 2)² = 450

Dividing by 5 on both sides,

(x + 2)² = 90

Taking the square root on both sides,

x + 2 = ±√90

Subtracting by 2 on both sides,

x = ±√90 - 2

(e) (x - 4)² /3 + 8 = 17

Subtracting by 8 on both sides,

(x - 4)² /3 = 9

Multiplying both sides by 3,

(x - 4)² = 27

Taking the square root on both sides,

x - 4 = ±3√3

Adding both sides by 4,

x = 4 ±3√3

Hence the values are found.

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The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

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Answer:

£78.75

Step-by-step explanation:

An easy way step but longer way to do this is

10% of 75 is 7.5 ((75/10= 7.5))

divide by 2 on both sides

5% = 3.75

then just add it, its increasing 75 by 5%

so 75 + 3.75 = 78.75

The equation represents the total number of stars is y = 35x

The equation that represents the total number of stars earned, y, for passing x levels would be:

y = 35x

where y represents the total number of stars earned, and x represents the number of levels passed.

For example, if Marcellus and Anika passed 10 levels, they would earn:

y = 35(10) = 350 stars

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Answer:

Both 2B and 2A are not similar.

Step-by-step explanation:

----------------------------------------

Let me be helpful!

Let's start with 2B. It is easier to understand the subject that way.

->for a triangle to be similar, it's angles and sides must be the same.

-2B's triangle shows that line TW got scaled by x2.2 (22/10)

-Line ZW got scaled by 1.18

-2b are not similar.

Now on it 2A!

- line JK got scaled by 0.75

- Line JL got scaled by 0.5

-they are not similar

Let me know if I am incorrect!

-A friendly 8th grader :)

The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).

To use the CDF, we need to standardize the diameter values using the z-score formula:

z = (x - μ) / σ

where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.

For tomatoes with a diameter of at most 15 mm, we have:

z = (15 - 22) / 2.5 = -2.8

For tomatoes with a diameter of at least 30 mm, we have:

z = (30 - 22) / 2.5 = 3.2

Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.

Finally, we add these two areas together to get the total proportion of rejected tomatoes:

proportion = 0.0026 + (1 - 0.9993) = 0.0033

Hence the correct option is (a).

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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The regular triangle, regular hexagon, and regular dodecagon have special triangles formed by their radius and apothem, which are congruent right triangles with legs equal to half the length of one side and hypotenuse equal to the radius or apothem, and are 30-60-90 triangles.

Regular polygons with three special triangles formed by their radius and apothem are,

Regular triangle

The radius and apothem of an equilateral triangle are equal. Therefore, the special triangles formed by the radius and apothem are congruent right triangles with legs equal to half the length of one side of the equilateral triangle and hypotenuse equal to the radius or apothem. In other words, the special triangles are 30-60-90 triangles.

Regular hexagon

The radius of a regular hexagon is equal to the length of one side, and the apothem is equal to the height of an equilateral triangle with side length equal to the length of one side of the hexagon.

Regular dodecagon

The radius of a regular dodecagon is equal to the length of one side multiplied by the square root of 2 plus the square root of 2 times the square root of 3. The apothem is equal to the height of an isosceles triangle with base equal to one side of the dodecagon and legs equal to the radius of the dodecagon.

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For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

The three regular polygons that have special triangles formed by their radius and apothem are the triangle, square, and hexagon.

For the triangle, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the shorter leg.

For the square, the special triangle formed by its radius and apothem is a 45-45-90 right triangle, where the radius is the hypotenuse and the apothem is one of the legs.

For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.

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The absolute maximum value of f(x)=2x³ +3x² +1 on the closed interval [-3, 1] is 6, which occurs at x=1.

To find the absolute maximum value of the function f(x) on the closed interval [-3, 1], we need to evaluate the function at the endpoints of the interval and at any critical points in the interior of the interval.

First, we evaluate the function at the endpoints of the interval

f(-3) = 2(-3)³ + 3(-3)² + 1 = -17

f(1) = 2(1)³ + 3(1)² + 1 = 6

Next, we find the critical points of the function f(x) by taking its derivative and setting it equal to zero

f'(x) = 6x² + 6x

6x(x+1) = 0

x = 0 or x = -1

Now we evaluate the function at these critical points

f(0) = 1

f(-1) = 2(-1)³ + 3(-1)² + 1 = 2

Therefore, the absolute maximum value of f(x) on the closed interval [-3, 1] is 6, which occurs at x=1.

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The given question is incomplete, the complete question is:

Let f be the function given by f(x)=2x³ +3x² +1. What is the absolute maximum value of f on the closed interval [-3,1] ?

a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².

ii) The pressure on the ground by European hare is 0.15 N/cm².

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.

a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.

i) For the snowshoe hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 14 N / 200 cm²

Pressure = 0.07 N/cm²

ii) For the European hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 38 N / 250 cm²

Pressure = 0.15 N/cm²

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.

Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.

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Given statement "3-6 You can determine the slope of a roof using a flat board, a bubble level and a ruler,or a sight card can be used." is true. Because flat board, a bubble level and a ruler,or a sight card methods are commonly used to determine the slope of a roof, and both are effective.

Determining the slope of a roof is an important task for many construction and roofing projects.

One method to determine the slope of a roof is to use a flat board, a bubble level, and a ruler.

First, place the flat board horizontally on the roof surface, and use the bubble level to make sure it is level.

Then, measure the distance between the bottom of the board and the roof surface at the point where the board intersects with the roof using the ruler. This distance is the rise.

Next, measure the distance from the point where the board intersects with the roof to the end of the board using the ruler. This distance is the run. Finally, divide the rise by the run to get the slope.

Another method to determine the slope of a roof is to use a sight card. A sight card is a specially designed tool that can help to measure the angle of a slope or pitch. The sight card is held at the bottom of the roof and lined up with a known vertical or horizontal line, such as the edge of a building.

Statement is true.

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Given statement: On a 1500 square foot gable roof, there will be approximately 11% waste.

The given statement is False.

The statement provides information on the amount of waste but does not provide sufficient information to determine the total area of roofing material required for the gable roof.

Therefore, it is impossible to determine whether the waste percentage is accurate or not.

The statement "On a 1500 square foot gable roof, there will be approximately 11% waste" can be either True or False depending on the specific roofing materials and project details.
However, it's not uncommon for roofing projects to have waste percentages in that range (around 10-15%), especially for complex designs or when using materials like shingles.

Keep in mind that waste factors may vary depending on the type of roof, materials used, and installation methods. Always consult with a professional to get accurate waste estimates for your specific project.

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The slope of the cathedral ceiling is 0.83.

To calculate the slope of the cathedral ceiling, we need to find the rise over the run. The rise is the difference in ceiling heights between the two points. The run is the horizontal distance between the two points.

From the problem statement, we know that the ceiling is 8 feet high at the west wall and 10.5 feet high three feet from the west wall. So the rise is:

rise = 10.5 - 8 = 2.5 feet

The run is the horizontal distance between the two points, which is:

run = 3 feet

Now we can calculate the slope:

slope = rise/run = 2.5/3 = 0.83

Therefore, the slope of the cathedral ceiling is 0.83.

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The number of heart cakes that were sold at the cake sale was 28

According to the question,

Cost of circular-shaped cake = $7

Cost of heart shaped cake = $5

Total sale = $238

Let the number of circular cakes shaped be x

Since the number of heart cakes was sold twice as many as the circular cake, the number of heart cakes will be 2x

Cost of x circular-shaped cake = $7 * x

Cost of 2x heart shaped cake = $5 * 2x

Total sale = Cost of x circular cake + Cost of 2x heart cake

Thus, we get the following equation,

238 = 7x + 10x

238 = 17x

x = 14

Thus, the number of heart cakes sold was 2x that is 28.

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The area of the figure is 160.6 unit²

Since the figure is composed of a parallelogram and one semicircle, the area will be:

Area of figure = area of parallelogram + area of semicircle

Area of figure = bh + 1/2πr²

where b = 10, h = 6 and r = 8

Area of figure = (10*6) + (1/2 * 22/7 * 8²)

Area of figure = 60 + 100.6

Area of figure = 160.6 unit²

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