Select the correct answer.
What is the justification for step 2 in the solution process?

12y − 40 − 4y = 6y − 18
Step 1: 8y − 40 = 6y − 18
Step 2: 2y − 40 = -18
A.
the subtraction property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the multiplication property of equality

To find the weight of the bowl, we need to first find its volume and then multiply it by the density of steel.

The region bounded by y = x and y = \(x^2\) in the first quadrant is shown below:

When this region is spun about the y-axis, it forms a bowl with a circular cross-section. The radius of each cross-section is given by y, and the height of each cross-section is given by the difference between the curves y = x and y = \(x^2\), which is:

y = x -\(x^2.\\\)

The volume of each cross-section is given by:

V(y) = π\(r^2h\) = πy^2\((x-x^2),\)

where r is the radius, h is the height, and y is the distance from the y-axis.

To find the total volume of the bowl, we integrate V(y) with respect to y from y = 0 to y = 1, since the bowl extends from y = 0 to y = 1:

V = ∫(0,1) π\(y^2(x-x^2)\) dx dy

Integrating with respect to x first, we get:

V = ∫(0,1) π\(y^2(x-x^2)\) dx dy

= ∫(0,1) π\(y^2x\) - π\(y^2x^2\) dx dy

= π/6

So the total volume of the bowl is π/6 cubic meters.

To find the weight of the bowl, we multiply the volume by the density of steel:

Weight = Density * Volume

= 8050 * π/6

≈ 13335.4 kg

Therefore, the weight of the bowl is approximately 13335.4 kg.

To find the weight of a 1mm slice of the bowl taken at y = 0.5m parallel to the x-z plane, we need to find the volume of this slice and then multiply it by the density of steel.

The slice is a disk with radius r = 0.5 m and thickness t = 0.001 m. The volume of the slice is:

V =\(r^2t\) = π\((0.5)^2(0.001)\) = \(0.0007854 m^3.\)

The weight of the slice is:

Weight = Density * Volume

= 8050 * 0.0007854

≈ 6.318 kg

Therefore, the weight of a 1mm slice of the bowl taken at y = 0.5m parallel to the x-z plane is approximately 6.318 kg.

The weight of the bowl made out of steel can be calculated by finding its volume and multiplying it by the density of the steel.

The weight of a 1mm slice of the bowl taken at y = 0.5m can be determined by finding the area of the slice and multiplying it by the thickness and the density of steel. To calculate the weight of the bowl made out of steel, we need to determine its volume.

The bowl is formed by rotating the region bounded by y = x and y = \(x^2\) about the y-axis. We can find the volume by integrating the cross-sectional area of the region with respect to y. The limits of integration will be from y = 0 to y = 1 (since y = x and y = \(x^2\) intersect at y = 1).

The cross-sectional area at each value of y is given by A = π\(y^2\)- π\(y^4\). Integrating this expression will give us the volume of the bowl. Once we have the volume of the bowl, we can calculate its weight by multiplying it by the density of the steel.

The density of steel is given as 8050 kg/\(m^3\). Therefore, the weight of the bowl can be calculated as weight = volume * density. To find the weight of a 1mm slice of the bowl taken at y = 0.5m parallel to the x-z plane, we need to calculate the area of the slice.

Since the slice is parallel to the x-z plane, its area will be the same as the cross-sectional area at y = 0.5m. We can use the same formula for the cross-sectional area, A = π\(y^2\) - π\(y^4\), and substitute y = 0.5 to calculate the area.

We then multiply the area by the thickness (1mm, or 0.001m) and the density of steel to obtain the weight of the slice. In conclusion, to find the weight of the bowl made out of steel, we calculate its volume using integration and multiply it by the density of steel.

To find the weight of a 1mm slice of the bowl taken at y = 0.5m, we calculate the area of the slice and multiply it by the thickness and the density of steel.

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Answer:

\(12c⁹+27c⁷\)

Step-by-step explanation:

3c⁶(9c+4c³)

=(3c⁶)(9c+4c³)

=(3c⁶)(9c)+(3c⁶)(4c³)

=27c⁷+12c⁹

=12c⁹+27c⁷

Answer:

x= \(\sqrt10\) - \(\sqrt10\)

Step-by-step explanation:

Answer:

x= -4 or x= 4

Step-by-step explanation:

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be: D. .95.

A confidence interval is also referred to as level of confidence and it can be defined as a range of estimated values that defines the probability that a population parameter would fall or lie within it.

For instance, the confidence interval at 95% is given by p - E < p < p + E

Since the confidence interval for the mean of a population is at 95%, the confidence coefficient would be calculated by simply dividing the confidence interval by 100:

Confidence coefficient = 95/100

Confidence coefficient = 0.95

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The fraction of the circumference of the circle is the length of arc AB is 1/6

Point A and B lie on a circle with radius 1 , and arc AB has a length of π/3

The circumference of a circle is given by the formula 2πr

We need to find the fraction of the circumference of the circle is the length of arc AB

Fraction of the circumference = Length of arc AB/ circumference

= (π/3)/2.π.r. =

(π/3)/2.π.1

= 1/6 or 1 : 6.

Therefore, The fraction of the circumference of the circle is the length of arc AB is 1/6

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We need to compare the cash flows of machines A and B using the concept of Capital Cost (CC) analysis and a minimum acceptable rate of return (MARR) of 10%.

For machine A, the CC is not provided in the question. To determine the CC for machine A, we need additional information such as the initial investment cost and the expected cash inflows and outflows over the machine's useful life. Similarly, for machine B, the CC is not provided in the question.

We need additional information about the initial investment cost and the expected cash inflows and outflows over the machine's useful life to calculate the CC for machine B. Without the CC values, we cannot determine which machine to select based on CC analysis. To make a decision, we need more information.

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Answer:

87.5°

Step-by-step explanation:

So we know that the arc CD is 175°. This is the same thing as saying that the measure of the central angle, ∠CAD, is 175°. By the Inscribed angle theorem, we know that the measure of the inscribed angle, ∠DBC, is half of the measure of the central angle, ∠CAD. So:

m∠DBC = m∠CAD × 1/2

m∠DBC = 175/2

m∠DBC = 87.5

So the measure of ∠DBC would be 87.5°. Answer choice 2 would be correct.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

1,830 sq. ft.

Step-by-step explanation:

12 x 15= _180_

1,650 + 180=_1,830__

Answer:

7cm to square centimeters is  2.6458 centimeters

Step-by-step explanation:

The potential energy of the King Air 200 aircraft is approximately 420,014,400,000 Nm.

To find the potential energy of the King Air 200 aircraft, we need to use the formula:

Potential Energy = Weight * Altitude

Given that the weight of the aircraft is 12,500 lb and the altitude is 25,000 ft, we can calculate the potential energy as follows:

Potential Energy = 12,500 lb * 25,000 ft

Now, let's convert the units to a more suitable form. Since the potential energy is usually measured in joules or foot-pounds, we'll convert the units accordingly.

1 lb = 4.448 N (approximately) 1 ft = 0.3048 m (approximately)

Using these conversion factors, we can convert the units:

Potential Energy = (12,500 lb * 4.448 N/lb) * (25,000 ft * 0.3048 m/ft) Potential Energy ≈ 55,120,000 N * 7,620 m

Finally, we can calculate the potential energy:

Potential Energy ≈ 420,014,400,000 Nm

Therefore, the potential energy of the King Air 200 aircraft is approximately 420,014,400,000 Nm.

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Answer:

8 days

Step-by-step explanation:

Let us represent the number of days as x

For Tina

Tina currently has $60 and is earning $4 a day dog walking.

= $60 + $4 × x

= 60 + 4x

For Tony

Tony has $68 and is spending 3$ a day on candy!

= $68 + $3 × x

= 68 + 3x

To calculate the number of days that they will both have the same amount of candy we equate both equations to each other

60 + 4x = 68 + 3x

Collect like terms

4x - 3x = 68 - 60

x = 8 days

Therefore, they will both have the same amount of candy in 8 days

Answer:

a

Step-by-step explanation:

d

Answer:

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·3 = 18.85(*)

In terms of diameter:

Circumference = π·d = 3.14·6 = 18.84(*)

In terms of area:

Circumference C = √4·π·A = √4·π·28.27 =18.85

Step-by-step explanation:

radius= 3in.

the circumference of the circle.

formula C=2πr

=2·π·3

≈18.84956in

nearest hundredth= 18.85in

The inverse of a function can be found by swapping the numbers in each ordered pair of the function.

When you have a function with ordered pairs, the inverse of that function can be found by reversing the order of the numbers within each pair. In other words, if you have a function f(x) with ordered pairs (a, b), the inverse function, f^ (-1) (x), will have ordered pairs (b, a). This process essentially switches the input and output values of the original function.

To find the inverse of a function, simply swap the numbers in each ordered pair, resulting in the ordered pairs for the inverse function.

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Answer:

a=3

Step-by-step explanation:

3a=9

/3   /3

a=3

hope this helps!

According to the angle of incidence, the angle of reflection will also be 36°

Angle of incidence:

In math it means the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.

Given,

Here we need to find the If light strikes a plate mirror at a 36° angle of incidence, then what would you expect the resulting angle of reflection to be.

Here we know that, the incident ray, the reflected ray and the normal ray at the point of incidence all lies in the same plane.

Then the angle of incidence is equal to the angle of reflection

And it can be written as,

=> Angle of incidence = angle of reflection

As per the 2nd law given above, we say that if a light ray incident at 45°, then the reflected angle will also be 45°

Here we know that the value of,

=> Angle of incidence = 36°

Therefore, the Angle of reflection = 36°

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1) the null and alterative hypotheses are  - H_o: p=0.20 H_1:p<0.26 (option C)

2)

1) The null hypothesis is that the population proportion of yellow peas is equal to 20%. The alternative hypothesis is that the population proportion of yellow peas is less than 20%.

hence,  H_o: p=0.20 H_1:p<0.26

2) The test statistic is calculated as follows  -

z = (pa   - p₀) / √(p₀(1-p₀)/ n)

Where  -

pa is the sample proportion of yellow peas (0.25)

p₀ is the hypothesized proportion of yellow peas (0.20)

n is the sample size (537)

The test statistic is -2.17

p- value =P(Z < -2.17)

The p -value is   0.0306.

Since the p-value is less than the significance level of 0.05,we reject the null hypothesis and    conclude that there is sufficient evidence to suggest that the population proportion of yellow peas is less than 20%.

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He will have to mix 3 pounds of cashews and 7 pounds of peanuts .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let c be denoted as cashew and p be denoted as peanuts

c + p = 10  ⇒ (1)

5.6c + 2.3p = 3.29*10 ⇒ (2)

Multiply eq(1) by 560

Multiply eq(2) by 100

560c + 560p = 5600

560c + 230p = 3290

Subtract and solve for "p":

330p = 2310

p = 7  (amt. of peanuts needed)

substitute  the value of p in eq(1)

c + 7 = 10

c = 3  (amt. of cashews needed)

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To find the cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we need to solve the system of linear equations formed by substituting the values into the general cubic function f(x) = ax^3 + bx^2 + cx + d. Once the values of a, b, and c are determined, the formula for f(x) can be expressed as f(x) = ax^3 + bx^2 + cx.

To find a formula for a cubic function f(x) given the conditions f(5) = 100, f(-5) = f(0) = f(6) = 0, we can start by assuming that the cubic function takes the form f(x) = ax^3 + bx^2 + cx + d.

Using the given conditions, we can create a system of equations to solve for the coefficients a, b, c, and d:

1. f(5) = 100: 100 = a(5)^3 + b(5)^2 + c(5) + d

2. f(-5) = 0: 0 = a(-5)^3 + b(-5)^2 + c(-5) + d

3. f(0) = 0: 0 = a(0)^3 + b(0)^2 + c(0) + d

4. f(6) = 0: 0 = a(6)^3 + b(6)^2 + c(6) + d

Simplifying these equations, we get:

1. 100 = 125a + 25b + 5c + d

2. 0 = -125a + 25b - 5c + d

3. 0 = d

4. 0 = 216a + 36b + 6c + d

From equation 3, we find that d = 0. Substituting this value into equations 1, 2, and 4, we have:

1. 100 = 125a + 25b + 5c

2. 0 = -125a + 25b - 5c

4. 0 = 216a + 36b + 6c

We can solve this system of linear equations to find the values of a, b, and c. Once we have those values, we can express the formula for f(x) as f(x) = ax^3 + bx^2 + cx + d, where d is already determined to be 0.

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Step-by-step explanation:

Remember a secant line is composed of two points and their slopes.

Meaning that to find a secant line , just find the slope between the two points and use one of the points in point slope form.

Slope is

\( \frac{10}{10} = 1\)

So our equation of the secant line

\(y =(x + 4) - 10\)

\(y = x - 6\)

The LCM of 6, 8, and 45 is 360

Given numbers are 6, 8, 45. We have to find the LCM of given numbers.

The LCM of two or more numbers is the smallest number that is evenly divisible by each of the given numbers without leaving a remainder.

2 |    6 8 45

_______________

2 |    3 4 45

_______________

2 |    3 2 45

_______________

3 |    3 1 45

_______________

3 |    1 1 15

_______________

5 |    1 1 5

_______________

1 1 1

LCM(6, 8, 45) = 2 × 2 × 2 × 3 × 3 × 5

= 360

Therefore, the LCM of 6, 8, and 45 is 360

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Answer:

C

Step-by-step explanation:

-2^4-5(5)+2(-2-3)^2

16-25+2(25)

16-25+50

41

Answer:

To prepare the adjusting entries, we need to consider the additional data given:

Fees earned but unbilled on June 30 were $10,710. This is revenue that has been earned but not yet billed to customers, so we need to recognize it by making the following adjusting entry:

Accounts receivable 10,710

Fees earned 10,710

Supplies on hand on June 30 were $8,740. This represents the cost of supplies that have been used up during the year, so we need to recognize the expense by making the following adjusting entry:

Supplies expense 14,930

Supplies 8,740

The Supplies expense is calculated as follows:

Supplies expense = Beginning supplies + Purchases - Ending supplies

= 23,670 + Purchases - 8,740

= 14,930 (Purchases are not given in the information provided.)

Depreciation of equipment was estimated to be $14,700 for the year. Depreciation is the process of allocating the cost of a long-term asset over its useful life. We need to recognize the expense by making the following adjusting entry:

Depreciation expense 14,700

Accumulated depreciation 14,700

The balance in unearned fees represented the June 1 receipt advance for services to be provided. During June, $20,560 of the services were provided. This means that $5,470 (26,030 - 20,560) of the advance has not yet been earned, so we need to recognize this liability by making the following adjusting entry:

Unearned fees 5,470

Fees earned 5,470

Unpaid wages accrued on June 30 were $1,890. This represents the wages that have been earned by employees but not yet paid, so we need to recognize the liability by making the following adjusting entry:

Wages expense 1,890

Wages payable 1,890

After making these adjusting entries, we can prepare the adjusted trial balance:

Milbank Repairs & Service Adjusted Trial Balance June 30, Debit Credit Balances Balances Cash 14,790 Accounts Receivable 109,930 Supplies 14,930 Equipment 554,610 Accumulated Depreciation 14,700 Accounts Payable 23,080 Unearned Fees 20,560 Wages Payable 1,890 Nancy Townes, Capital 399,000 Nancy Townes, Drawing19,530 Fees Earned607,850 Wages Expense139,160 Rent Expense 104,730 Utilities Expense 75,140 Supplies Expense 14,930 Depreciation Expense 14,700 Miscellaneous Expense 11,830 1,039,790 1,039,790

The adjusted trial balance confirms that the total debits equal the total credits, which means that the accounting equation is in balance.

Step-by-step explanation:

The eigenvalues of the matrix A are λ₁ = 1, λ₂ = 2, and λ₃ = 12. For each eigenvalue, the rank of the matrix A - λI is 2, 2, and 3, respectively. The matrix A is diagonalizable.

a. To find the eigenvalues of the matrix A = [ [4 0 1][ 2 3 2][ 1 0 4]], we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.

The characteristic equation is:

det([ [4 0 1][ 2 3 2][ 1 0 4]] - λ[ [1 0 0][ 0 1 0][ 0 0 1]]) = 0

Simplifying, we get:

det([ [4 - λ 0 1][ 2 3 - λ 2][ 1 0 4 - λ]]) = 0

Expanding the determinant, we get:

(4 - λ) * (3 - λ) * (4 - λ) - 2 * (4 - λ) - 2 * (3 - λ) + 2 * (1 - λ) = 0

Simplifying, we get:

-λ^3 + 11λ^2 - 32λ + 24 = 0

Factoring, we get:

-(λ - 1) * (λ - 2) * (λ - 12) = 0

Therefore, the eigenvalues of the matrix A are λ₁ = 1, λ₂ = 2, and λ₃ = 12.

b. For each eigenvalue, we need to find the rank of the matrix A - λI, where I is the identity matrix and λ is the eigenvalue.

For λ₁ = 1, we have:

A - λ₁I = [ [3 0 1][ 2 2 2][ 1 0 3]]

The rank of A - λ₁I is 2.

For λ₂ = 2, we have:

A - λ₂I = [ [2 0 1][ 2 1 2][ 1 0 2]]

The rank of A - λ₂I is 2.

For λ₃ = 12, we have:

A - λ₃I = [ [-8 0 1][ 2 -9 2][ 1 0 -8]]

The rank of A - λ₃I is 3.

c. To determine if matrix A is diagonalizable, we need to check if it has n linearly independent eigenvectors, where n is the size of the matrix.

Since matrix A is a 3x3 matrix, we need to find three linearly independent eigenvectors. We can find the eigenvectors by solving the system of equations (A - λI)x = 0 for each eigenvalue.

For λ₁ = 1, we have:

(A - λ₁I)x = [ [3 0 1][ 2 2 2][ 1 0 3]]x = 0

Solving the system of equations, we get:

x1 = -1/3 * x3

x2 = 1/2 * x3

Therefore, the eigenvector corresponding to λ₁ is [x1, x2, x3] = [-1, 3, 6].

For λ₂ = 2, we have:

(A - λ₂I)x = [ [2 0 1][ 2 1 2][ 1 0 2]]x = 0

Solving the system of equations, we get:

x1 = -1/2 * x3

x2 = x3

Therefore, the eigenvector corresponding to λ₂ is [x1, x2, x3] = [-1, 1, 2].

For λ₃ = 12, we have:

(A - λ₃I)x = [ [-8 0 1][ 2 -9 2][ 1 0 -8]]x = 0

Solving the system of equations, we get:

x1 = -1/8 * x3

x2 = -2/9 * x3

Therefore, the eigenvector corresponding to λ₃ is [x1, x2, x3] = [-1, -16/9, 8].

Since we have found three linearly independent eigenvectors, the matrix A is diagonalizable.

Therefore, the eigenvalues of the matrix A are λ₁ = 1, λ₂ = 2, and λ₃ = 12. For each eigenvalue, the rank of the matrix A - λI is 2, 2, and 3, respectively. The matrix A is diagonalizable.

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The probability of a. guessing all five questions is 0.00098. b. at least one question correctly is 0.76270.

According to the multiplication rule, which is part of probability theory, the likelihood that two or more independent events will occur together depends on the sum of their respective probabilities. The Bayes theorem, conditional probabilities, and issues involving independent occurrences are only a few areas of probability theory and statistics where the multiplication rule is applied.

Given that, probability of correctly guessing one question is 1/4.

The probability of guessing 5 questions correct is:

P(all correct) = (1/4) = 0.00097656

Hence, the probability of correctly guessing all five questions is 0.00098.

b. The probability of not guessing any question correctly is (3/4)^5.

Then, P of atleast one correct is:

P(at least one correct) = 1 - P(none correct) = 1 - (3/4)^5 = 0.76269531.

Hence, the probability of guessing at least one question correctly is 0.76270.

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a and b are relatively prime to n.

What is the relatively prime?

According to number theory, two integers a and b are coprime, substantially prime, or mutually prime if only one positive integer, 1, can divide them equally. As a result, every prime integer that divides a does not divide b, and the opposite is also true. This translates to having a greatest common divisor of 1 for them.

Here, we have

Given: Suppose a,b,n ∈ Z with n>0. Suppose that ab ≡ 1(modn).

We have to prove that both a and b are relatively prime to n.

Let a, b ∈ Z and n ∈ Z⁺

Given ab ≡ 1(modn)

= n|ab - 1

∴k∈ Z ⇒ ab - 1 = nk

∴ ab - nk = 1

Let gcd(a,n) = d

⇒d|a and d|n

∴ For b, k ∈ Z ⇒ d | ab - nk

∴ d | 1⇒ d = 1

∴ gcd(a,n) = 1

Similarly, suppose gcd(b,n) = m

⇒m|b and m|n

∴ For a, k ∈ Z ⇒ m | ab - nk

∴ m | 1⇒ m = 1

∴ gcd(b,n) = 1

Hence, a and b are relatively prime to n.

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Answer:

1\(\frac{7}{8}\)cups

Step-by-step explanation:

2 dozen muffins = \(\frac{3}{4}\)cups

5 dozen muffins = \(\frac{5}{2}\) × \(\frac{3}{4}\)cups

                           = \(\frac{15}{8}\)cups

                           = 1\(\frac{7}{8}\)cups