During the course of your examination of the financial statements of Trojan Corporation for the year ended December 31, 2021, you come across several items needing further consideration. Currently, net income is $100,000. An insurance policy covering 12 months was purchased on October 1, 2021, for $24,000. The entire amount was debited to Prepaid Insurance and no adjusting entry was made for this item in 2021. During 2021, the company received a $4,000 cash advance from a customer for services to be performed in 2022. The $4,000 was incorrectly credited to Service Revenue. There were no supplies listed in the balance sheet under assets. However, you discover that supplies costing $2,750 were on hand at December 31, 2021. Trojan borrowed $70,000 from a local bank on September 1, 2021. Principal and interest at 9% will be paid on August 31, 2022. No accrual was made for interest in 2021.

The system of linear equations is solved by finding x = 2 and y = -4, making the solution (2, -4).

To find the solution to the system of linear equations,

find the values of x and y that satisfy both equations simultaneously.

The equations are,

y = -3x + 2

y = x - 6

To find the solution,  set the right-hand sides of both equations equal to each other:

-3x + 2 = x - 6

Now, let's solve for x:

-3x - x = -6 - 2

-4x = -8

x = -8 / -4

x = 2

Now that  the value of x, we can find y by substituting x back into one of the equations.

Let's use the second equation:

y = 2 - 6

y = -4

Therefore, the solution to the system of linear equations is equal to option A. (2, -4).

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The length of CG is approximately 5.4 units.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the property of similar triangles to solve this problem.

First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.

Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.

Therefore, we can set up the proportion:

AB/FB = HG/GB

Plugging in the given values, we get:

10/63 = (x + 57)/57

Solving for x, we get:

x = 5.4

Therefore, the length of CG is approximately 5.4 units.

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The linear equation that has no solutions with y = (5/4)x - 7 is

2y = (5/2)x - 14

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

y = (5/4)x - 7

We can create a linear equation that has no solutions with y = (5/4)x - 7.

Step 1:

y = (5/4)x - 7

Multiply 2 on both sides.

2y = (5/2)x - 14

Thus,

2y = (5/2)x - 14 is the linear equation that has no solutions with the given equation.

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Answer:

The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.

18x+30

Step-by-step explanation:

O think That's the answer...

Answer: To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the given time period

P = the principal (starting amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, the principal is $6500, the annual interest rate is 2.8% (or 0.028 as a decimal), and the interest is compounded monthly (so n = 12). We want to find the amount after 2 years, so t = 2.

Plugging these values into the formula, we get:

A = 6500(1 + 0.028/12)^(12*2)

A ≈ $7,107.08

Therefore, the amount of money after 2 years is approximately $7,107.08.

Step-by-step explanation:

Based on given question, average rate of change or slope is-0.004 and

the predicted price for 7500 shirts is $47.

The ordered pairs for the historical data are:

(12000, 29) and (18000, 5)

To find the slope (average rate of change) between these two data points, we can use the formula:

slope = (change in y) / (change in x)

slope = (5 - 29) / (18000 - 12000)

slope = -24 / 6000

slope = -0.004

Rounding to three decimal places, the slope is -0.004.

To find the linear equation, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Using the point (12000, 29) and the slope we just calculated, we get:

p - 29 = -0.004(x - 12000)

Simplifying and solving for p, we get:

p(x) = -0.004x + 77

Therefore, the equation for the price p they can charge for x shirts is p(x) = -0.004x + 77.

To predict the price they can charge for 7500 shirts, we can substitute x = 7500 into the equation:

p(7500) = -0.004(7500) + 77

p(7500) = 47

Therefore, the predicted price for 7500 shirts is $47.

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Answer:

14

Step-by-step explanation:

To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.

So, (f-g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f-g)(x) = (3x^2 + 1) - (1-x)

(f-g)(x) = 3x^2 + x

Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:

(f-g)(2) = 3(2)^2 + 2

(f-g)(2) = 3(4) + 2

(f-g)(2) = 12 + 2

(f-g)(2) = 14

Therefore, the value of (f-g)(2) is [14.]

Answer:

x = -1, y = 1

Step-by-step explanation:

2x - 3y = -5

3x + y = -2

2x - 3y = -5

9x + 3y = -6

11x = -11

x = -1

-3 + y = -2

y = 1

x = -1, y = 1

The measure of the largest exterior angle of the polygon in discuss is; 100°.

It follows from the task content that the measure of the largest exterior angle of the polygon be determined.

Since the sum of all exterior angles of a polygon is equal to 360°;

x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°

36x° = 360°

x = 10

Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.

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Answer:

Step-by-step explanation:

Let's simplify the given expression by combining like terms:

3x + 6 + x - 2 + 8(x - 3) - 4 - 4 + x + 1 - 2(x + 2) + 6 + 7x - 8x

First, let's simplify the expression inside the parentheses:

8(x - 3) = 8x - 24

Now we can combine like terms:

3x + x + x + 7x - 8x + 6 - 2 - 4 - 4 + 1 + 6 - 2( x + 2) + 8x - 24

Simplifying further:

6x - 2 - 4 - 4 + 8x - 2(x + 2) - 17

6x + 8x - 2x - 2(2) - 25

12x - 4 - 25

12x - 29

Therefore, the answer to the given expression is 12x - 29.

Answer:

hope this helps!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

175

The fractional equivalent of the repeating decimal is 15/99

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

n = 0.1515...-------(1)

multiply n by 100 =10²

The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.

100n=15.15......--------(2)

Subtract (1) from (2)

100n=15.15...

n = 0.1515....

___________

99n=15

=> n=15/99

The fractional equivalent of the repeating decimal is 15/99

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Joanna can assemble her bracelet in 30 ways.

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

here, we have,

to find the number of ways in which the bracelet can be assembled:

It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.

The rest 4 are of different colors.

Six beads can be arranged in a circle in 6!/6 ways.

This means that the six beads can be arranged in 5! ways.

Since this is a bracelet, it can be flipped around.

Therefore, it can be arranged in 5!/2 ways.

5!/2

= 5*4*3*2*1/2

= 60

Now, we know that two beads are of the same color. Therefore, we must divide this by two again.

Therefore, we get:

60/2 = 30

The six beads can be arranged in 30 ways to make the bracelet.

Therefore, we have found that Joanna can assemble her bracelet in 30 ways.

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Answer:

x=3

Step-by-step explanation:

the answer is 3 because 3*12=36 and 4*12=48

Answer:

Step-by-step explanation:

-15

The tables that show a valid probability density function, are tables 1 to 3

From the question, we have the following parameters that can be used in our computation:

Table of values

For a table to show a valid probability density function, the following must be true

Sum of P(X = x) = 1

Using the above as a guide, we have the following:

Table 1: Sum = 0.37  + 0.06 + 0.01 + 0.56 = 1

Table 2: Sum = 3/8 + 3/8 + 1/4 = 1

Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1

Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17

Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4

Hence, the tables are tables 1 to 3

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The number of positive results for all persons with TB will be D. 423

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true

Rate of incidence of TB is 450 per 100,000

Column Totals of "Has TB" = (450 / 100,000) * Grand Total = (450 / 100,000) * 100,000 = 450

If a person does have TB, then the DNA test will be positive 94% of the time.

Therefore, P = Number of positive results for all persons with TB:

= 0.94 * 450

= 423

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His estimated monthly income should be $480.

In the given right triangle the length of side a is approximately 9.92 units.

A right triangle is a variety of triangles with a 90-degree angle (a right angle). The junction of the triangle's two legs, or the sides that meet at a right angle, creates this angle. The hypotenuse, which is always located opposite the right angle, is the third side of a right triangle.

A key characteristic of right triangles is the Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.

We can use the trigonometric ratios of sine, cosine, and tangent to solve for the missing side of a right triangle. Since we are given the measure of one acute angle and the length of the side opposite that angle, we can use the tangent ratio:

tan A = opposite/adjacent

tan 51° = a/8

Multiplying both sides by 8:

a = 8 tan 51°

Using a calculator, we find that:

a ≈ 9.92

Therefore, the length of side a is approximately 9.92 units.

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Using the arithmetic operation the value for x in the equation (x – 7)2 = 36 is obtained as 25.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is (x – 7)2 = 36.

Use the arithmetic operation of multiplication -

2x - 14 = 36

Collect all the like terms -

2x = 36 + 14

Use the arithmetic operation of addition -

2x = 50

Use the arithmetic operation of division -

x = 50/2

x = 25

Therefore, the value is 25.

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Answer:

13x-16

Step-by-step explanation:

I am assuming that you mean 5*(2 + 2x − 3) − (2*2 − 3x + 7).

That equals 10x-5+3x-11=13x-16

Answer:

(a) Pour trouver le nombre d'étudiants qui suivent les trois matières, on peut utiliser la formule suivante:

Answer:

The width of the patio is 15 feet

Step-by-step explanation:

We can start by using the formula for the area of a rectangle:

Area = length x width

In this case, we know that the area of the patio is given by:

16x^2 + 20x square feet

And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:

16x^2 + 20x = (x + 5) x width

Simplifying the right-hand side by multiplying x + 5 by width, we get:

16x^2 + 20x = width x^2 + 5x

To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:

width x^2 - 16x^2 + 20x - 5x = 0

Simplifying the left-hand side by combining like terms, we get:

width x^2 - 16x^2 + 15x = 0

Factoring out x, we get:

x (width x - 16x + 15) = 0

Now we can solve for the width by setting each factor equal to zero and solving for x:

x = 0 or width x - 16x + 15 = 0

Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:

width x - 16x + 15 = 0

We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:

(width x - 1)(x - 15) = 0

Setting each factor equal to zero and solving for x, we get:

width x - 1 = 0 or x - 15 = 0

width x = 1 or x = 15

Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:

width x = 1, x = 15, so we choose x = 15

width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet

Therefore, the width of the patio is 15 feet.

Answer: x = 41

For x in the equation

5/25=9/(x+4)

5(x+4) =9(25)

5x + 20 = 225

5x = 205

x = 41

Therefore, the value of x for the equation 5/25=9/(x+4) is x = 41

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The transformations that are needed to graph the given function is

Shrink the graph vertically by a factor of 3.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x²

g(x) = x² - 3

We see that,

f(x) → g(x)

There is a vertical shrink by a factor of 3.

Thus,

There is a shrinking vertically of f(x) by a factor of 3.

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The solution for x in the given equation (x-c)/2 = d is x = 2d + c.

What is the solution for x in the given equation?

Given the equation in the question;

(x-c)/2 = d

x = ?

To solve for x, cross multiply and simplify.

(x-c)/2 = d

x - c = d × 2

x - c = 2d

Add +c to both sides

x - c + c = 2d + c

x = 2d + c

Therefore, the solution for x in the given equation (x-c)/2 = d is x = 2d + c.

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Therefore , the solution of the given problem of expression comes out to be approximately x ≈ 1.6247.

Addition, multiplication, and division in mathematics are required. When combined, they produce the following: A mathematical operator, some data, and an expression A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

First, we can rewrite the equation as:

4x × 2ˣ = 2ˣ  + 4

Dividing both sides by 2ˣ , we get:

4x = 1 + 4/2ˣ

Now, let f(x) = 4x - 1 - 4/2ˣ . We want to find the root of f(x) = 0.

Next, we bisect the interval [1,2] by finding the midpoint:

c = (a + b) / 2 = (1 + 2) / 2 = 1.5

Then, we evaluate f(c):

f(c) = 4c - 1 - 4/2ᶜ = 4(1.5) - 1 - 4/[tex]2^{1.5}[/tex] ≈ -0.6982

Since f(c) is negative, the root must be in the interval [c,b]. We repeat the process by setting a = c and finding the new midpoint:

c = (a + b) / 2 = (1.5 + 2) / 2 = 1.75

Then, we evaluate f(c):

f(c) = 4c - 1 - 4/2ᶜ = 4(1.75) - 1 - 4/[tex]2^{1.75}[/tex] ≈ 0.9026

Since f(c) is positive, the root must be in the interval [a, c]. We repeat the process by setting b = c and finding the new midpoint:

c = (a + b) / 2 = (1.5 + 1.75) / 2 = 1.625

Then, we evaluate f(c):

f(c) = 4c - 1 - 4/2ᶜ = 4(1.625) - 1 - 4/[tex]2^{1.625 }[/tex] ≈ 0.0879

Since f(c) is positive, the root must be in the interval [a, c]. We repeat the process by setting b = c and finding the new midpoint:

c = (a + b) / 2 = (1.5 + 1.625) / 2 = 1.5625

Then, we evaluate f(c):

f(c) = 4c - 1 - 4/2ᶜ = 4(1.5625) - 1 - 4/[tex]2^{1.5625}[/tex] ≈ -0.3081

Since f(c) is negative, the root must be in the interval [c, b]. We repeat the process until we reach a desired level of accuracy.

Continuing the process, we find that the solution is approximately

x ≈ 1.6247.

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The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

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