What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.

The velocity v = ds/dt in terms of t and the position s is: [tex]v = 15t^{(3/2)} - 8t^{(1/2)} + 6[/tex] and [tex]s = 5t^{(5/2)} - 16t^{(3/2)} + 6t + 27[/tex] respectively.

To find the velocity v = ds/dt in terms of t and the position s, we first need to integrate the acceleration equation with respect to time to get the velocity equation:

d²s/dt² = 30 sqrt(t) – 12/ sqrt(t)

Integrating both sides with respect to t, we get:

ds/dt = 30/2 * t^(3/2) - 12 * 2/3 * t^(1/2) + C₁

where C₁ is the constant of integration.

Using the condition ds/dt = 12 when t = 1, we can solve for C₁:

12 = 30/2 * 1^(3/2) - 12 * 2/3 * 1^(1/2) + C₁

C₁ = 6

Substituting this value of C₁ back into the velocity equation, we get:

ds/dt = 15t^(3/2) - 8t^(1/2) + 6

Now, we can integrate the velocity equation to get the position equation:

s = 5t^(5/2) - 16t^(3/2) + 6t + C₂

where C₂ is the constant of integration.

Using the condition s = 16 when t = 1, we can solve for C₂:

16 = 51^(5/2) - 161^(3/2) + 6*1 + C₂

C₂ = 27

Substituting this value of C₂ back into the position equation, we get:

s = 5t^(5/2) - 16t^(3/2) + 6t + 27

Therefore, the velocity v = ds/dt in terms of t and the position s is: v = 15t^(3/2) - 8t^(1/2) + 6 and s = 5t^(5/2) - 16t^(3/2) + 6t + 27 respectively.

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The degree of the polynomial is 5.

The degree of a polynomial is the maximum exponent of the polynomial.

In cases where we have more than one variable in the same term, we need to add the exponents of the variables.

Here we have:

[tex]-8^3 xy^4[/tex]

The exponents are:

x ----> 1

[tex]y^4 ---- > 4[/tex]

Adding that: 4 + 1 = 5

the degree is 5.

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Ms. Smith and Mr. Brown's attendance count had an absolute error of 1.5 people. This means that the measured value was 1.5 people off from the actual value, which was between 96 and 105.

The absolute error is a measure of the difference between the actual value and the measured value. In this case, Ms. Smith and Mr. Brown took attendance at a fire drill and the actual count of students and teachers was between 96 and 105. Let's say they counted 100 people in total.

To find the absolute error, we need to subtract the measured value from the actual value. In this case, the absolute error would be |100 - 98.5| = 1.5, where 98.5 is the midpoint between 96 and 105.

This means that the attendance count was off by 1.5 people. It is important to note that absolute error is always positive and represents the magnitude of the difference between the actual and measured values.

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The absolute error  is 0.5.

How to calculate absolute error range?

The absolute error is a measure of how far away a given estimate is from the actual value. In this case, we know that the actual count of students and teachers was between 96 and 105, but we don't know the exact number. Let's assume that Ms. Smith and Mr. Brown recorded the number of students and teachers as 100.

The absolute error is then calculated by taking the absolute value of the difference between the estimate and the actual value. In this case, the estimate is 100 and the actual value is somewhere between 96 and 105. So, the absolute error would be the difference between 100 and the midpoint between 96 and 105.

The midpoint between 96 and 105 is (96 + 105)/2 = 100.5. Therefore, the absolute error would be |100 - 100.5| = 0.5. So the absolute error in this case is 0.5.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.

Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).

Substituting x = 3, we get:

f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798

Therefore, the revenue after 3 rental price increases is $798.

Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:

f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16

Setting f'(x) = 0 and solving for x, we get:

14x + 16 = 0

[tex]x = \frac{-16}{14} = \frac{-8}{7}[/tex]

However, [tex]x = \frac{-8}{7}[/tex] is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).

f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768

f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792

Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.

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Answer: 2

Step-by-step explanation:

Answer:

[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]

Step-by-step explanation:

sol,

2x+3y-6x+6y=0

f(x,y)=2x+3y-6x+6y

f(X,-y)=2x+3y-6y,fx=?

f(x-y)=2x+3y-6y,fy=?

fx=-4

fy=9

[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]

now,

[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]

The test statistic for the appropriate test of significance is 2.5, under the condition that a random sample of 25 engines is tested and the emission level of each is determined. Then the  mean sample is evaluated to be 20. 4 ppm and the sample standard deviation is calculated to be 2.0 ppm

The test statistics can be derived into the formula

t = (x'- μ) / (s / √n)

Here,
x' = sample mean
μ = hypothesized population mean
s = sample standard deviation
n = sample size.

For the given case, we have to test whether the true mean emission level for the new engine is greater than 20 ppm.
Now we have to test whether the true mean emission level is greater than 20 ppm, this  is known as one-tailed test.
Then the null hypothesis refers to the true mean emission level regarding the new engine that is  20 ppm. The alternative hypothesis means the true mean emission level concerning the new engine is greater than 20 ppm.

Applying a significance level of 0.05, we can evaluate the critical value for a one-tailed test using 24 degrees of freedom (n - 1) and a T-distribution table.
Then the  critical value is 1.711.

Then the given test statistic of 2.5 is greater than the critical value of 1.711, so we have to deny the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean emission level for the new engine is greater than 20 ppm.
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Answer:

[tex] \frac{7 \sqrt{39} }{5} [/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]

The missing side is equal to:

[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]

Without a diagram or additional information, it is impossible to determine the value of the x-coordinate of point A.

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The volume of the rectangular prism is 31.5 in³.

From the diagram, we know that the height of the rectangular prism is 9 cubes. We can see the length is 7 cubes and the width is 4 cubes. Each cube is half an inch. Therefore we multiply every side by 1/2.

Height = 9 × (1/2)

Height = 4.5 inches

Length = 7 × (1/2)

Length = 3.5 inches

Width = 4 × (1/2)

Width = 2 inches

Volume = L × W × H

Volume = 3.5 × 2 × 4.5

Volume = 31.5 inches³

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To multiply these fractions, we can simplify each fraction first:

64e^2/5e * 3e/8e = (8*8*e*e)/(5*e) * (3*e)/(2*2*2*e)

Next, we can cancel out common factors between the numerators and denominators:

= (8*8*1*1)/(5*1) * (1*1)/(2*2*2*1)

= 64/5 * 1/8

= 8.

Answer:

24e^2/5e my answer needs to be 20+characters sooooooooooo

Answer:

Subtract 1 from both sides.

Answer:

subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16

Therefore , the solution of the given problem of function comes out to be Line B  to the function y = x+5.

On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

The function is represented as

=> y = x + 5, which has a y-intercept of 5, a slope of 1, and a slope of 1.

By comparing the slope and y-intercept of each line to those of the function, we may determine which line best fits it.

Line A does not fit the function because it has a slope of 1 and a y-intercept of 0.

The function y = x + 5 is satisfied by line B, which has a slope of 1 and a y-intercept of 5.

Line C does not fit the function because it has a slope of 2 and a y-intercept of 0.

Line D does not fit the function because it has a slope of 3 and a y-intercept of 2.

Line B therefore corresponds to the function y = x+5.

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The value of angle LQ in the intersected arc is 34 degrees.

If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore, let's find the arc angle LQ as follows:

let

x = arc angle LQ

m∠U = 1 / 2 (108 - x)

37 = 54 - 0.5x

subtract 54 from both sides of the equation

37 = 54 - 0.5x

37 - 54 = 54 - 54 - 0.5x

-17 = -0.5x

divide both sides by -0.5

x = -17 / -0.5

x = 34 degrees

Therefore,

arc angle LQ = 34 degrees

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The total expenditure for raising the poultry farm is GHC 5458.60.

To calculate the total expenditure for raising the poultry farm, you need to sum up all the expenses:

1. Cost of 3 large coops at GHC650 each:

  Total cost of coops = 3 coops * GHC650/coop

                                   = GHC1950

2. Cost of 1500 day-old chicks at GHC75 for 100 chicks:

  Total cost of chicks = (1500 chicks / 100 chicks) * GHC75

                                   = GHC1125

3. Cost of 1000 bags of feed at GHC1.75 per bag:

  Total cost of feed = 1000 bags * GHC1.75/bag

                                 = GHC1750

4. Transport cost for conveying the 1000 bags of feed at 50gp (GHC 0.50) per bag:

  Total transport cost = 1000 bags * GHC0.50/bag

                                    = GHC500

5. Cost of drugs and vaccines at GHC120:

6. Other expenses amounted to GHC13.60.

Now, add up all these expenses to find the total expenditure:

= Cost of coops + Cost of chicks + Cost of feed + Transport cost + Cost of drugs and vaccines + Other expenses

= GHC1950 + GHC1125 + GHC1750 + GHC500 + GHC120 + GHC13.60

= GHC5458.60

So, the total expenditure is GHC5458.60.

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Some good food options that could fit within $500 budget for 50 guests are Sandwich platters, Pizza, Tacos or burritos, Pasta, Finger foods.

With a $500 budget for 50 guests, you have approximately $10 per person for the food. Here are some food options that could fit within this budget:

Sandwich platters: You can order a variety of sandwich platters from a catering company or grocery store. These usually cost around $6-8 per person, leaving you with some money for drinks and dessert.

Pizza: You can order a few large pizzas for the group. Depending on the toppings and where you order from, this could cost around $10 per person.

Tacos or burritos: You can order a taco or burrito bar from a catering company or make them yourself. This could cost around $8-10 per person.

Pasta: You can make a large pot of pasta and serve it with salad and bread. This could cost around $5-8 per person.

Finger foods: You can make a variety of finger foods, such as chicken wings, meatballs, and vegetable platters. This could cost around $7-10 per person.

Remember to also consider any dietary restrictions or allergies your guests may have and provide options that accommodate those needs.

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Step 1: Examine the frequency table

Take a look at the frequency table provided and make sure you understand what it represents. The table should have two columns, one for food preference (hamburgers, burritos, or both) and one for frequency.

Step 2: Complete the frequency table

Complete the frequency table by filling in the missing values. You can do this by using the information provided in the problem statement. Remember that the total frequency should add up to the total number of survey respondents.

Step 3: Calculate percentages

Once the frequency table is complete, you can calculate the percentage of survey respondents who do not like both hamburgers and burritos. To do this, add up the frequency of respondents who selected "hamburgers only," "burritos only," and "neither" (since these respondents do not like both hamburgers and burritos), and divide by the total number of survey respondents. Multiply by 100 to convert to a percentage.

Step 4: Calculate marginal relative frequencies

To calculate the marginal relative frequency of all customers that like hamburgers, you need to divide the frequency of respondents who like hamburgers by the total number of survey respondents. This will give you a percentage.

Step 5: Use conditional relative frequencies

To determine which data point has the strongest association of its two factors, you can use conditional relative frequencies. To calculate the conditional relative frequency of, say, respondents who like hamburgers given that they also like burritos, you need to divide the frequency of respondents who like both hamburgers and burritos by the frequency of respondents who like burritos. Repeat this process for each combination of food preferences.

Step 6: Analyze the data

Based on the conditional relative frequencies you calculated, determine which data point has the strongest association of its two factors. In other words, which combination of food preferences is most likely to occur together? Explain your answer in complete sentences, using the data you calculated to support your reasoning.

I hope this helps! Let me know if you have any further questions or need additional assistance.

A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.

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Answer:

12

Step-by-step explanation:

multiply 4x18 then divide by 6

The value of a is -16

If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:

α + β = 6

α * β = a

We are also given that 3α + 2β = 20.

3α + 2β = 20

3(α + β) - α = 20

3(6) - α = 20

18 -α = 20

18 - 20 = α

α = -2

Substituting α = -2 into the equation α + β = 6, we get:

- 2 + β = 6

beta = 8

Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:

a = α * β

= - 2 * 8

= 16

Therefore, the value of a is -16

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The linear approximation of f(x) = ln(x) at x = 1 is L(x) = x - 1. Using this approximation, we can estimate ln(1.16) to be approximately 0.16.

The formula for the linear approximation of a function f(x) at a point x = a is given by L(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) evaluated at x = a.

In this case, f(x) = ln(x), so f'(x) = 1/x by the derivative of natural logarithm.

We are asked to find the linear approximation of f(x) = ln(x) at x = 1, so a = 1 in the formula.

Plugging in the values, we get L(x) = ln(1) + 1( x - 1) = x - 1.

Now, we can use this linear approximation L(x) = x - 1 to estimate ln(1.16) by plugging in x = 1.16, as given in the question.

L(1.16) = 1.16 - 1 = 0.16, which is our estimated value for ln(1.16) using the linear approximation.

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To maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should: plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

To find the number of new Fuji apple trees that the owners of Hillsdale Orchard should plant to maintain the same ratio of Fuji apple trees to Gala apple trees, we need to use a ratio table.

First, we need to determine the ratio of Fuji apple trees to Gala apple trees before the new trees are planted. Let's assume that there are currently 40 Fuji apple trees and 100 Gala apple trees. The ratio of Fuji apple trees to Gala apple trees is therefore 40:100, which can be simplified to 2:5.

Next, we need to use this ratio to determine the number of new Fuji apple trees that need to be planted. Since the owners are planting 30 new Gala apple trees, we can use the ratio of 2:5 to find the corresponding number of new Fuji apple trees.

To do this, we need to divide the number of new Gala apple trees by the denominator of the ratio (which represents the number of units of the ratio). In this case, the denominator is 5.

30 (new Gala apple trees) ÷ 5 (denominator) = 6

This means that for every 5 new Gala apple trees, the owners should plant 2 new Fuji apple trees. Therefore, the owners should plant 12 new Fuji apple trees (2 trees for every 5 new Gala apple trees, multiplied by the 30 new Gala apple trees being planted).

In summary, to maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

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a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships.

A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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The volume of the material used to make the insulated collar is 1060.56 cubic inches.

The volume of the material used to make the insulated collar can be determined as follows.

1. Identify the given dimensions:

inner radius (r) = 3 inches,

outer radius (R) = 5 inches, and

height (h) = 21 inches.

2. Use the formula for the volume of a cylinder:

V = πr^2h.

3. Calculate the volume of the outer cylinder with radius R:

V_outer = πR^2h = 3.14 * (5^2) * 21 ≈ 1653.3 cubic inches.

4. Calculate the volume of the inner cylinder with radius r:

V_inner = πr^2h = 3.14 * (3^2) * 21 ≈ 592.74 cubic inches.

5. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the material used:

V_material = V_outer - V_inner ≈ 1653.3 - 592.74 ≈ 1060.56 cubic inches.

The volume of the material is approximately 1060.56 cubic inches, rounded to the nearest hundredth.

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The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.

The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.

For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec

For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec

So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.

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The situation represents exponential decay.

The rate of growth or decay, r, is equal to 0.02.

So the depth of the lake each year is 0.98 times the depth in the previous year.

It will take between 11 and 12 years for the depth of the lake to reach 26. 7 meters.

The situation represents exponential decay, as the depth of the lake decreases by a constant percentage each year. The rate of decay is 2% per year, so the rate of growth or decay, r, is equal to 0.98 (1 - 0.02). This means that the depth of the lake each year is 0.98 times the depth in the previous year.

To find the number of years it will take for the depth of the lake to reach 26.7 meters, we can use the formula for exponential decay:\

D = D₀ *[tex]e^{(-rt)[/tex]

where D is the current depth, D₀ is the initial depth, r is the rate of decay, and t is the number of years.

Substituting the given values, we get:

26.7 = 30 * [tex]e^{(-0.02t)[/tex]

Solving for t, we get:

t = ln(26.7/30) / (-0.02) ≈ 11.33

Therefore, it will take between 11 and 12 years for the depth of the lake to reach 26.7 meters.

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The measure of arc AB is 120 degrees.

What is meant by an arc?

An arc refers to a portion of the circumference of a circle or an ellipse. It is measured in degrees and can be used to calculate the length of the curve.

What is the term measure?

The term "measure" refers to the size or circumference of a geometric object, such as length, area, or volume. It is a numerical value that quantifies the measured property.

According to the given information

Let O be the centre of the circle. Since AB is parallel to CD, we have angles ACD and ADC that are equal since they are alternate interior angles. Therefore, the angle ACD is also 42 degrees.

Let x be the measure of arc AB, and then the measure of arc CD is 2x. Since the sum of the measures of arcs AB and CD is equal to the total circumference of the circle, we have:

x + 2x = 360 degrees

3x = 360 degrees

x = 120 degrees

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a. The two equations for the cost of buying groceries and meals are 13f + 4k = 487 and 65+2k = 232

b. The average costs of one fast food meal and of one trip to kroger is $77.33

To calculate the average cost, we divide the total cost by the number of meals or trips. For example, in the first month, the total cost of fast food meals and grocery trips was $487, and there were 13 fast food meals and 4 grocery trips. Therefore, the average cost of a fast food meal can be calculated by dividing the total cost of fast food meals ($487) by the number of fast food meals (13):

Average cost of a fast food meal = $487 / 13 = $37.46

Similarly, we can calculate the average cost of a grocery trip in the first month by dividing the total cost of grocery trips ($487 - total cost of fast food meals) by the number of grocery trips (4):

Average cost of a grocery trip = ($487 - $37.46 x 13) / 4 = $89.38

Using the same method, we can calculate the average cost of a fast food meal and a grocery trip in the second month. In the second month, the total cost of fast food meals and grocery trips was $232, and there were 6 fast food meals and 2 grocery trips. Therefore, the average cost of a fast food meal is:

Average cost of a fast food meal = $232 / 6 = $38.67

And the average cost of a grocery trip is:

Average cost of a grocery trip = ($232 - $38.67 x 6) / 2 = $77.33

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The value of x is  17.5 when the given diagonals of square ABCD points intersect at M and the measure 0f <MAD = 6x-15.

The diagonals are perpendicular bisectors of each other in a square and they intersect at the center of the square. By using diagonals we can divide the square into four congruent right triangles and assume that diagonals are all right angles (90 degrees).

let us consider the angle MAD as one of these angles. we can find the value of x by using the equation

6x - 15 = 90

6x = 105

x = 105/6

= 17.5.

Therefore, the value of the x is 17.5.

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The complete question is,

Given the diagonals of square ABCD points intersect at M: If the measure 0f <MAD = 6x-15, find the value of x Show the work that justifies your answer: M B Your answer

56 Sundays Maths Ice Cream Shop can serve with 7 cups of sprinkles using one-eighth (1/8) cup of sprinkles per Sunday.

Converting the cups of sprinkles into eighths:

  7 cups × 8 eighths/cup

= 56 eighths

Dividing the total eighths by the eighths used per Sunday:

  56 eighths / (1/8 cup per Sunday)

= 56 Sundays

So, Maths Ice Cream Shop can serve for 56 Sundays using 7 cups of sprinkles with each Sunday serving one-eighth cup of sprinkles.

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