James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include _______ in gross income on his tax return.
14000

The volume of the cylinder generated by rotating the region bounded by y = x³ , y = 8 , x = 0 and x = 9 be, 1608.25 cubic units.

Given, a cylinder generated by rotating the region bounded by the given curves about the specified axis

y = x³ , y = 8 , x = 0 and x = 9

we have to find the volume of the cylinder generated by the given region,

So, using the concept of integration, we get

Volume of the cylinder =  Integrating y from x³ to 8 then integrating x from 0 to 9.

Volume of the cylinder = ∫∫dy dx

Volume of the cylinder = ∫(x³ - 8) dx

Volume of the cylinder = x^4/4 - 8x

Volume of the cylinder = (9)^4/4 - 8(4)

Volume of the cylinder = 1640.25 - 32

Volume of the cylinder = 1608.25

So, the volume of the cylinder be 1608.25 cubic units.

Hence, volume of the cylinder be 1608.25 cubic units.

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The percent of her monthly pay that goes to rent will be 20%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this situation, Dimple gets paid $4,800 per month and then she pays $960 a month for rent.

The percent of her monthly pay that goes to rent will be:

= 960 / 4800 × 100

= 20%

The percentage is 20%.

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Generalization refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts.

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and conclusion of conclusions from quantitative data. Sample size determination is the act of choosing the number of compliances or replicates to include in a statistical sample.

Statistical conception involves statistically calculating the likely parameters of a population using data from an arbitrary sample of that population.

One of the primary operations for data conception is when you need to analyze data that you've collected, but also need to ensure the sequestration of the individualities who are included in that data.

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Answer:  The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC

The percent of error for the given measured value and the absolute error is equal to 0.392%

As given in the question,

Measurement value is equal to 12.8 inches

Absolute error in the measurement is equal to 0.05

True value is equal to ( Measurement value - absolute error )

= ( 12.8 + 0.05 )

= 12.75

Percent of error is given by

= |True value - Measured value |/ (true value) × 100

= [ | 12.75 - 12.8 |/ 12.75 ] × 100

= 0.392%

Therefore, the percent of error for the given measured value and the absolute error is equal to 0.392%

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

A measurement is taken to be 12.8 in. and the absolute error is 0.05 in. What is the percent of error? Round off your answer to 3 decimal places.

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With the Application of probability The expression is [ x^r] = C ( r - 1, r - 8 ).

What is probability?

There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event. It is possible to claim that probability is the likelihood that a specific event will occur as the two words are equivalent.

solution:

G(x) = ( x^1 + x^2 + x^3 .....)^8

G(x) =  (x( x^1 + x^2 + x^3 .....) )^8

Then using infinite geometric series,

       = x^8 ( 1 / ( 1 - x )) ^8

Then using negative binomial series:

So [ x^r] = 0 if r = 0, 1, 2, 3...7 and [ x^r] = C ( r - 1, r - 8 ) if r > 7

Therefore, The expression is [ x^r] = C ( r - 1, r - 8 )

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Answer: Part 1) Option A

Part 2) Option B

Part 3) Option C

Part 4) Option C

Part 5) Option D

Part 6) Option B

Part 10)  Option B

Part 11) Option A  

Part 13) Option A

Part 14) Option D

Part 15) Option D

Part 16) Option C

Part 17) Option D

Part 18) Option D

Part 19) Option D distribute the  to the  and ; distribute the  to the  and

Part 20) Option B  

Step-by-step explanation:

Part 1) we have

solve for x

Part 2) we have

solve for x

Part 3) we have

solve for x

Part 4) we have

solve for x

Part 5) we have

solve for x

Part 6) we have

solve for x

remember that

convert to mixed number

Part 7) The model is not included

Part 8) The model is not included

Part 9) The model is not included

Part 10) we have

solve for x

Part 11) we have

solve for x

Part 12) The model is not included

Part 13) we have

solve for r

Part 14) and  Part 15)

the answer is the option D

Look for parenthesis and apply the distributive property; combine like terms; move your variable terms to one side and constants to the other side of the equal sign; go in reverse PEMorDAorS to isolate the variable using inverse operations

Part 16)

Let

n------> the number

we know that

-----> algebraic expression that represent the situation

solve for n

Part 17) we have

solve for y

Part 18) we have

solve for x

Part 19) we have

 ------> distribute the  to the  and ; distribute the  to the  and

Part 20) we have

step 1

distribute the  to the  and ; distribute the  to the  and

step 2

Group terms that contain the same variable and move the constant to the other side

step 3

Combine like terms

step 4

Divide by  both sides

The equation is y =  45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃ when x₂ = x₃ = 0.

What is meant by equation?

In math, equation refers a mathematical statement that is made up of two expressions connected by an equal sign.

Here we have given that,  x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme.

and we need to find the correct equation when the value of x₂ = x₃ = 0.

Here while we looking into the given question we have identified that the value of x₂ =0 and x₃ = 0.

Then the given equation will be remain same withouth any changes.

Therefore, the resulting equation of the given condition is written as,

=> y =  45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃

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The maximum number of pairs of super-fit jeans the factory can produce in a day is 949.the profit on each pair of super-hug is $9.50.

Given the information provided, the maximum daily profit the factory can make is $201,248.50. The maximum number of pairs of super-fit jeans the factory can produce in a day is 949, since it takes 20 minutes to cut each pair and there are only 18,999 minutes available for cutting each day. The maximum number of pairs of super-hug jeans the factory can produce in a day is 824, since it takes 55 minutes to sew and finish each pair and there are only 40,999 minutes available for sewing and finishing each day.

Maximum daily profit = (949 x $6.50) + (824 x $9.50)

= $201,248.50

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When two system of linear equations solved by Sara represents the lines parallel to each other then the equations have no solution.

Step by Step explanation:

Given system of two linear equations :

Let us consider system of two linear equation with Sara has :

y =  3x + 7

y = 3x + 9

Here both the lines have same slope = 3

Lines are parallel to each other.

Solve the equation by elimination method :

y =  3x + 7

y = 3x + 9

0 = 0x - 2

⇒ -2 = 0 which is not possible and has no solution.

Therefore, when the system of linear equations with Sara has no solution it represents lines are parallel to each other.

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Answer: See below

Step-by-step explanation:

C=20t+100

t= number of months

C= total cost over t number of months

Table of values

t                C

1                 120

2                140

3                160

4                 180

5                 200

It can be any distribution from the exponential family is true about the distribution of the response variable in a logistic regression model.

Logistic regression is a popular method for solving prediction and classification issues. Among these use cases are: Fraud detection: Logistic regression methods can assist teams in identifying data abnormalities that suggest fraud. The logistic model is a statistical model that represents the chance of an event occurring by making the event's log-odds a linear combination of one or more independent variables. Logistic regression is used in regression analysis to estimate the parameters of a logistic model.

Here,

The distribution of the response variable in a logistic regression model can be any distribution from the exponential family.

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Answer:

One real-world problem that can be represented by the algebraic equation 6x + 5 = 77 is determining the number of items that must be sold at a certain price in order to reach a target profit. For example, suppose a business owner wants to make a profit of $77 by selling items for $6 each. The algebraic equation 6x + 5 = 77 can be used to determine the number of items that must be sold in order to reach this profit. In this case, x represents the number of items that must be sold, and the solution to the equation (x = 11) indicates that the business owner must sell 11 items in order to make a profit of $77.

Answer:

You can't solve this unless its is the form of an equation!

The measure of ∠CDE is 54°

What is measure ?

When attributes of an item or event are quantified, they can be compared to other objects or events and utilized as a basis for comparison. Determining how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind is the process of measurement, in other words.

A measure is a piece of mathematics that expresses the size of sets in numerical terms. A different method of determining how large a set is is embodied by each unique measure. Initially, it could seem as though a set's cardinality is the only natural way to determine its size.

<CDE = far arc - near arc / 2

i.e

<CDE = arcCBE - arcCE / 2

arcCE = 126°

arcCBE = 360° - 126° = 234°

<CDE = (234° - 126°)/ 2

<CDE = 108 / 2

<CDE = 54°

Therefore the measure of < CDE is 54°

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The probability that an account in state 4 will be in bad debt be 0.3

Given, accounts receivable have been grouped into the following states:

State 1: Paid

State 2: Bad debt

State 3: 0–30 days old

State 4: 31–60 days old

Sixty percent of all new bills are paid before they are 30 days old.

The remainder go to state 4.

Seventy percent of all 30-day-old bills are paid before they become 60 days old.

If not paid, they are permanently classified as bad debts.

P(State 1 and State 3) = 0.6

P(State 4) = 0.40

We have to find the P(State 4 and State 2)

P(State 4 and State 2) = P(State 4) + P(State 2) - P(State 4 or State 2)

P(State 4 and State 2) = 0.4 + 0.6 - 0.7

P(State 4 and State 2) = 0.3

So, the required probability be, 0.3

Hence, the required probability be, 0.3

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Answer:

7

Step-by-step explanation:

If  a customer buys 2 cantaloupes and p pounds of potatoes on friday from the local farmers' market, the total cost equation would be A. C = 0.63p + 7.

Equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation also often contain an algebra. Algebra is used in maths when you do not know the exact number in a calculation.

Based from the question above, we don't know the exact number of potato that the customer bought. We only know that the customer buys p pounds of potatoes.

Potato price = $0.90

on Friday, the potato price is (30% discount)

= 0.90 - (0.90 * 30%)

= $0.63

Since the customer buys for p pounds of potatoes, therefore the total cost of potatoes

= $0.63 * p

= 0.63p

From the question above, we know that the customer buys 2 cantaloupes.

cantaloupes price = $3.50 each

The total cost for cantaloupes

= 2 * $3.50

= $7

Now, let's put it into the total cost equation to find the answer from the multiple choice.

Total cost (c) = 0.63p + 7

Therefore, the answer is A.

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The length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm² respectively.

A rectangle is a polygon in two dimension with four sides with opposide sides are equal and all the angles are right angles.

Given smaller rectangle is 1/2 scale drawing of the original figure. So the dimensions of the smaller rectangle will be half of the dimensions of the bigger rectangle.

For bigger rectangle,

Length = 36 cm

Width = 28 cm

Area = 1,008 cm²

So for smaller rectangle,

Length = 36/2 = 18 cm

Width = 28/2 = 14 cm

Area = 18 × 14 = 252 cm²

Hence the length, width and area of the smaller rectangle are 18 cm, 14 cm and 252 cm².

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The rate at which the distance between the buses is changing when they are 13 miles apart is -85.25 mph.

Given, two buses are driving along parallel freeways that are 12 miles apart, one heading east and the other heading west.

Assuming that each bus drives a constant 58 mph.

Now, we have to find the rate at which the distance between the buses is changing when they are 13 miles apart and heading towards each other.

Considering distance as a function of time,

D = f(t) = √((12)² + (13 - 116t)²)

f'(t) = (13 - 116t)(-116)/√((12)² + (13 - 116t)²)

f'(0) = (13 - 116(0))(-116)/√((12)² + (13 - 116(0))²)

f'(0) = -1508/√(144 + 169)

f'(0) = -1508/√313

f'(0) = -85.25

So, the rate of distance is decreasing at the rate of 85.25

Hence, the rate of distance is decreasing at the rate of 85.25

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Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.

The flow of air is drawn toward the ball by the low pressure area that surrounds it. As a result, the fluid (air) jet flows across the ping pong ball's curved surface. The "Coandă effect" refers to this phenomena.

The airflow's propensity to stick to the ball's surface is the Coandă effect in this situation. This indicates that the streamlines are curved at the ball's surface, with a radius of curvature roughly equal to the ball's radius. This curvature produces a pressure gradient, much like it does in the theory of lift, which I assume to be constant over the surface:

The equilibrium point, when the net forces acting on the ball cancel, is indicated by this, which points radially inward. Gravity causes the ball to hang below this spot during practice.

The Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.

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2f(3,1)

To use the midpoint rule to estimate the value of the double integral of a function f(x,y) over the region R=[0,6]x[0,6], we need to divide the region R into a grid of subintervals, with m subintervals in the x-direction and n subintervals in the y-direction. In this case, m=n=3, so we divide each side of the region R into 3 subintervals of equal length.

The midpoint rule states that the approximation of the integral is given by the sum of the areas of the rectangles formed by the subintervals, where the height of each rectangle is given by the value of the function at the midpoint of the subinterval.

To implement the midpoint rule, we first need to determine the width and height of each subinterval. The width of the subintervals in the x-direction is given by (6-0)÷3 = 2, and the width of the subintervals in the y-direction is also given by 2. The height of each rectangle is given by the value of the function f at the midpoint of the subinterval.

We can then evaluate the double integral by summing the areas of the rectangles formed by the subintervals. For example, the first rectangle would have a height equal to the value of the function at (0+2)÷2=1 and a width of 2, so its area would be 2f(1,1). The second rectangle would have a height equal to the value of the function at (2+4)÷2=3 and a width of 2, so its area would be 2f(3,1)

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Answer:

The square's area will be larger

Step-by-step explanation:

Let's say that a square's side length is 10.

To find the perimeter of a square, we add up all of the sides.

10 + 10 + 10 + 10 = 40

The perimeter of the square would be 40.

Now let's figure out the area of this square.

To find the area, we multiply the length by the width.

10 × 10 = 100

The area of the square is 100.

Now let's move on to the rectangle.

The rectangle has a side length of 12, and 8.

Let's figure out the perimeter of this rectangle.

12 + 12 + 8 + 8 = 40

The perimeter of the rectangle is 40, which means that the perimeters are the same.

Now let's figure out the area.

If you remember, to find the area we multiply the side length by the width.

12 × 8 = 96

The area of the rectangle is 96.

If the area of the square is 100, and the area of the rectangle is 96, then we can conclude that the area of a square is larger.

If a rectangle and a square have the same perimeter then Square will have a larger area.

Suppose length of rectangle is 6 cm and breadth is 2 cm.

So, Area of a rectangle = length ×  breadth

                                  =(6×2) cm²

                                  = 12 cm²

Given that,

Perimeter of rectangle = Perimeter of square

2× (length + breadth)   =  4×side

Side = [tex]\frac{2 ( length + breadth)}{4}[/tex]

Side =  [tex]\frac{2 (6+2)}{4}[/tex]

Therefore, side = 4 unit.

Now,  Area of Square = (side)²

                                    = ( 4 )²

                                      16 unit²

Hence, Area of square (16) is more than area of rectangle (12).

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Answer:

$15,510.00

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] x [tex]\frac{41360}{1}[/tex] = [tex]\frac{124080}{8}[/tex]= 15510

The correct conclusion is A. Since the p-value is greater than the significance level, there is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.

For the null hypothesis, 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if the proportion is still of 0.87, so:

H₀: p = 0.87

For the alternative hypothesis, less than 87% of the graduates find full-time employment in their field within the first year of graduation. It is tested if it has decreased, so:

H₁: p < 0.87

Since the p-value is greater than the significance level (p-value is greater than 0.0), we do not reject the null hypothesis, and thus, the correct conclusion is A.

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An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

What is the explicit description of a null space matrix?

To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.

The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.

To find a spanning set for Nul A, we can use the following steps:

Row reduces the matrix A to a reduced row-echelon form using elementary row operations.

Identify the free variables in the row-reduced matrix.

For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.

The set of vectors created in step 3 form a spanning set for Nul A.

For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:

[1, 2, 3, 0] -> [1, 2, 3, 0]

[0, 0, 1, 0] -> [0, 0, 1, 0]

The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:

x3 = [0, 0, 1, 0]

x4 = [0, 0, 0, 1]

These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.

Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

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A Maclaurin polynomial can only be created for functions that are infinitely differentiable, and the given function is not infinitely differentiable.

Maclaurin polynomial is an important type of Taylor series, developed by the Scottish mathematician Colin Maclaurin in the 18th century. It is a special case of the Taylor series, which is used to approximate a function near a given point. Maclaurin polynomials are polynomials that are used to approximate a function near the origin. They are derived from the Taylor series expansion of a function around the zeroth order derivative. The general form of a Maclaurin polynomial is given by ⌊f(x)=∑n=0∞a_nx^n⌋, where a_n is the nth derivative at x=0. Maclaurin polynomials are used to approximate a variety of functions, from simple polynomials to more complicated ones such as trigonometric, exponential, and logarithmic functions. They can also be used to approximate certain integrals and derivatives. Maclaurin polynomials are widely used in mathematics, physics, engineering, and other sciences.

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Hence the minimum value of x is 18 cm

a minimal requirement of coverage that is applicable to employment-based health plans. You cannot receive a premium tax credit if you purchase a Marketplace insurance plan if your employer's plan satisfies this criterion and is deemed "affordable."

given,

Within 10 cm of the A, a laser beam will pierce the water.

Snell's law permits us to state:

[tex]n_{1}sin\alpha ^{2} = n_{2}sin\beta^{2}[/tex]

Where,

is equal to 1, which is air's refractive index.

a measure of water's refractive index is [tex]n_{2}[/tex] = 1.33

At the interface, we can formulate a formula using Sell's law.

θ[tex]_{2}[/tex] = 38.7°

x= 18 cm

hence the minimum value of x is 18 cm.

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