On January 1, 2019, Hackman Corporation issued $1 million face value 12% bonds dated January 1, 2019, for $1,023,000. The bonds pay interest semiannually on June 30 and December 31 and are due December 31, 2023. Hackman uses the straight-line amortization method

Answer:

\({ \tt{ \sqrt{ {x}^{2} } + 2x + 2}} \\ { \tt{ = x + 2x + 2}} \\ = { \tt{3x + 2}}\)

Step-by-step explanation:

x=√(141)

that is the answer

Answer:

x = \(\sqrt{141}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 22² = 25²

x² + 484 = 625 ( subtract 484 from both sides )

x² = 141 ( take square root of both sides )

x = \(\sqrt{141}\)

The two height functions are h₁(t) = −16t² + 121 is a vertical translation of h₂(t) = −16t² + 225. The y-intercept of h₁ is 104 ft less than that of h₂. The correct answer is option (c)

To understand why this is the correct answer, let's first understand what the given information represents. Two identical baseballs are dropped from different heights, and we are asked to find their respective height functions. The height function gives the height of the baseball at any given time during its descent.

We know that the height function of a ball dropped from a height h₀ is given by h(t) = −16t² + h₀, where t is the time in seconds since the ball was dropped.

Using this formula, we can find the height functions for the two baseballs:

For the first baseball dropped from a height of 121 feet, the height function is h₁(t) = −16t² + 121.

For the second baseball dropped from a height of 225 feet, the height function is h₂(t) = −16t² + 225.

Now, we are given that h₁(t) is a vertical translation of h₂(t) with a difference of 104 ft in the y-intercept. This means that h₁(t) can be obtained from h₂(t) by shifting the graph vertically downward by 104 ft.

Since both functions have the same leading coefficient (-16), they have the same shape but different y-intercepts. Therefore, the correct option is (c).

Comparing their graphs, we can see that h₂(t) starts at a higher point on the y-axis (225 ft) and drops faster than h₁(t) which starts at a lower point (121 ft) and drops at a slower rate. This is because the greater the initial height, the longer it takes for the ball to reach the ground.

The correct answer is option (c)

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The surface area of the larger solid is 8075 cm².

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

Volume ratio = 1 : 125

Take the cube root of both sides

So, we have

Length ratio = 1 : 5

Square both sides

So, we have

Area ratio = 1 : 25

We have

The surface area of the smaller solid is 323 cm².

This means that

323 : Large = 1 : 25

So, we have

Large/323 = 25/1

Evaluate

Large = 8075

Hence. the surface area of the larger solid is 8075 cm².

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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The gross earnings are $225, federal taxes are $40.50, state taxes are $9, social security deduction is $15.86, total deductions are $65.36, and the net pay is $159.64.

The gross earnings are determined by multiplying the pay rate by the number of hours worked.

Federal taxes, state taxes, and social security deductions are calculated by applying the respective tax rates to the gross earnings.

Total deductions are the sum of federal taxes, state taxes, and social security deductions.

Net pay is obtained by subtracting the total deductions from the gross earnings.

To calculate the gross earnings, we multiply the pay rate of $7.50 by the number of hours worked, which is 30.

Therefore, the gross earnings are $7.50 * 30 = $225.

Next, we can calculate the federal taxes by applying the tax rate of 18% to the gross earnings.

The federal taxes amount to 18% * $225 = $40.50.

Similarly, the state taxes can be calculated by applying the tax rate of 4% to the gross earnings.

The state taxes amount to 4% * $225 = $9.

To determine the social security deduction, we apply the tax rate of 7.05% to the gross earnings.

The social security deduction amounts to 7.05% * $225 = $15.86.

The total deductions are the sum of the federal taxes, state taxes, and social security deduction.

Thus, the total deductions are $40.50 + $9 + $15.86 = $65.36.

Finally, to calculate the net pay, we subtract the total deductions from the gross earnings.

Therefore, the net pay is $225 - $65.36 = $159.64.

In conclusion, the gross earnings are $225, federal taxes are $40.50, state taxes are $9, social security deduction is $15.86, total deductions are $65.36, and the net pay is $159.64.

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When the wheel weighs 19.5 pounds, this implies that each hub cover weighs approximately 11.08 pounds.

A mathematical equation is a statement that expresses the connection between two or more quantities using symbols like elements, numbers, and mathematical operations. It may also signify a requirement that must be met or an issue that must be resolved. There are numerous ways to express equations in writing, including the algebraic, geometric, logarithmic, and exponential formats. The expression y = mx + b, for instance, depicts a linear connection between variables x and y, with m denoting the line's slope and b its y-intercept. The sine function and the variable x are related in a trigonometric way by the solution sin(x) = 0.5, where sin(x) is the ratio of a right triangle's opposing side's length to its hypotenuse's length.

given

Let's suppose that each hubcap weighs x pounds.

Since there are 6 of the same hubcaps, their combined weight is 6.

The hubcaps and the tire together weigh 86 pounds, according to the issue. Thus, the following solution can be written:

6x + 19.5 = 86

We can begin by removing 19.5 from both sides to find x:

6x = 86 - 19.5

6x = 66.5

Finally, we can identify x by dividing both sides by 6:

x = 11.08

When the wheel weighs 19.5 pounds, this implies that each hub cover weighs approximately 11.08 pounds.

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The length of the other leg of the triangle is 11.7 inches

Now, According to the question:

We have the right triangle

The length of the right triangle is 24 inches

The length of the hypotenuse is 26.7 inches

To find the length of the other leg of the triangle

We know that the Pythagorean theorem.

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

Let the length of the other leg of the triangle be 'x'

According to the information:

\(24^2 + x^2 = 26.7^2\)

576 + \(x^{2}\) = 712.89

\(x^{2}\) = 712.89 - 576

\(x^{2}\) = 136.89

x = \(\sqrt{136.89}\)

x = 11.7

Hence, The length of the other leg of the triangle is 11.7 inches.

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Answer:

Answer is step 1

Step-by-step explanation:

don't click on links

Answer:

252 centimeters squared is the answer.

The area of the rectangle is 252 cm².

A rectangle is a plane shape that has pair of opposite sides and angles equal

To calculate the area of a rectangle, we use the formula below.

Formula:

Area of a rectangle(A) = Length(L)×Width(W).............. Equation 1

⇒ Let the length of the rectangle be x and the width of the rectangle be y.

If the length is decreased by 6 cm

And if the width is increased by 3 cm

Since the new length and the new width form a square,

Note: In a square, all sides are equal

Also, The area of the new square formed is smaller than the area of the rectangle by 27 cm²

Substitute these values of x in equation 2 into equation 3

Collect like terms

Substitute the value of y into equation 1 to get x

Hence, The area of the rectangle is 252 cm².

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There are approximately 2.471 acres in a hectare in Australia.

An acre and a hectare are both units of area measurement used in different parts of the world. In Australia, the metric system is used, which includes the use of hectares as a standard unit of measurement for land area.

One hectare is equal to 10,000 square meters or approximately 2.471 acres. This conversion factor may vary slightly in different regions of the world, depending on the specific definition of an acre and the rounding conventions used.

It is important to note that the use of hectares is becoming increasingly common in other parts of the world as well, especially in countries that have adopted the metric system.

However, in some countries, including the United States and the United Kingdom, the acre remains a commonly used unit of land area measurement.

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The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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The exponential smoothing forecast for period 5, assuming an alpha (α) value of 0.4, is determined by applying the exponential smoothing formula.

The exponential smoothing formula is given by:

Forecast for period t = α * Actual value for period t + (1 - α) * Forecast for period t-1

In this case, we need the forecast for period 5, so we will use the formula to calculate it based on the available data.

To calculate the exponential smoothing forecast for period 5, we use the given alpha (α) value of 0.4 and the available data for previous periods. The formula considers the actual value for period t and the forecast for the previous period (t-1).

Since we are calculating the forecast for period 5, we need the actual value for period 5 and the forecast for period 4. However, these values are not provided in the given information. Without the actual value for period 5 or the forecast for period 4, it is not possible to provide a specific numerical answer for the exponential smoothing forecast for period 5.

The exponential smoothing technique is commonly used for forecasting, where the alpha (α) value determines the weight given to the most recent observations. A higher alpha value places more weight on recent data, while a lower alpha value gives more weight to historical data. By adjusting the alpha value, the forecast can be adjusted to respond more quickly or more slowly to changes in the data.

To calculate the exponential smoothing forecast for period 5, it is essential to have the necessary data points. With the provided alpha (α) value of 0.4, the formula can be applied once the required data is available.

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Answer:

-4 and -2

Step-by-step explanation:

Sum = - 6

\( - 4 + ( - 2) \\ - 4 - 2 = - 6\)

The product = 8

\(( - 4) \times ( - 2) = 8\)

Remind that negative multiply negative equal positive.

Answer:

16

Step-by-step explanation:

20*80/100 use this formula to find it

Answer:

x = 292.2 pounds (£)

Step-by-step explanation:

Write and solve an equation of ratios:

 € 1        £0.72

--------- = ----------

€410         x

Cross-multiplying, we get:

x = 292.2 pounds (£)

Answer:  π = c/d

Step-by-step explanation: srry if its wrong im not well at math

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

The required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.

The slope of the line is a tangent angle made by line with horizontal. i.e. m = tax where x in degrees.

m = (y₂ - y₁) /  (x₂ - x₁)

The graph of lines A  has the slope of -2/3 and 2 as,

m = (y₂ - y₁) /  (x₂ - x₁)

Put points (0, 2) and (3, 0) in the above expression
m = 0-2/3-0
m = -2/3

And at x = 0 there y = 2

Thus, the required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.

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In summary the equivalence relation on the set of real numbers is:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

To show that the relation {(x, y) | x − y ∈ Q} is an equivalence relation on the set of real numbers, we need to verify three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any real number x, we have x - x = 0, which is a rational number (0 ∈ Q). Therefore, (x, x) ∈ {(x, y) | x − y ∈ Q} for all x, and the relation is reflexive.

2. Symmetry: If (x, y) ∈ {(x, y) | x − y ∈ Q}, then x - y is a rational number. Since the negation of a rational number is still a rational number, -(x - y) = y - x is also a rational number. Therefore, (y, x) ∈ {(x, y) | x − y ∈ Q}, and the relation is symmetric.

3. Transitivity: If (x, y) ∈ {(x, y) | x − y ∈ Q} and (y, z) ∈ {(x, y) | x − y ∈ Q}, then x - y and y - z are both rational numbers. The sum of two rational numbers is also a rational number, so (x - y) + (y - z) = x - z is a rational number. Therefore, (x, z) ∈ {(x, y) | x − y ∈ Q}, and the relation is transitive.

Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on the set of real numbers.

Now, let's determine the equivalence classes [1], [1/2], and [π].

The equivalence class [1] consists of all real numbers x such that x - 1 ∈ Q. In other words, [1] = {x ∈ R | x - 1 ∈ Q}. This means that any real number x in the form x = 1 + q, where q is a rational number, belongs to [1].

Similarly, the equivalence class [1/2] consists of all real numbers x such that x - 1/2 ∈ Q. Therefore, [1/2] = {x ∈ R | x - 1/2 ∈ Q}, which means that any real number x in the form x = 1/2 + q, where q is a rational number, belongs to [1/2].

Finally, the equivalence class [π] consists of all real numbers x such that x - π ∈ Q. Thus, [π] = {x ∈ R | x - π ∈ Q}. This means that any real number x in the form x = π + q, where q is a rational number, belongs to [π].

In summary:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

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first question: Number of student's ticket(s) = 400

And number of adult's ticket(d) = 100

Second question: The goal of $3050 fell by $710

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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Answer:

300 dollars

Step-by-step explanation:

Note that:

{Peter's revenue on Monday: 150 dollars

Peter's revenue on Tuesday: 100 dollars

Peter's revenue on Wednesday: 50 dollars}

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

In this problem, we need to find how much is Peter's revenue so far (total).

We need to use addition to determine how much Peter's revenue is in total.

So, add 150, 100, and 50.

We get 150 + 100 + 50 = 300

Finally, Peter's revenue in total is 300 dollars.

Answer:

$300

Step-by-step explanation:

add 150+100+50

=300

Answer:

30.48 cm. in a foot, 91.44 in a yard

Step-by-step explanation:

2.54 x 12 (12 inches in a foot) is 30.48. 30.48 × 3 (3 feet in a yard) is 91.44

Answer:

Step-by-step explanation:

This is a quadrilateral. A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

The interior angles of a simple quadrilateral ABCD add up to 360 degrees of arc.

Answer:

Angle x = 40°

Step-by-step explanation:

All angles of any quadrilateral sum up to 360°.

So here, already measure of 3 angles are given.

So if we add up all angles + Angle x then it sums up to 360°.

So, the following steps will lead you to the answer:

73° + 157° + 90° + Angle x = 360°

(Now add up the measure of the three given angles)

320° + Angle x = 360°

(Now, through transposition moves 320° to the RHS) (Remember when transposing the signs change)

Angle x = 360° - 320°

Finally,

Angle x = 40°

Hope it helps!!!

1. There are 24 different ways to arrange the letters in the word MATH.

2. there are 168 possible combinations of the shoe company's lady's shoes.

3. if there were 8 possible outcomes, it implies that 8 coins fell on the floor.

1. To determine the number of ways you can arrange the letters in the word MATH, we can use the concept of permutations. The word MATH has four letters.

The number of ways to arrange these four letters can be calculated as 4 factorial (4!).

4! = 4 × 3 × 2 × 1 = 24

Therefore, there are 24 different ways to arrange the letters in the word MATH.

2. To find the number of possible combinations for the shoe company's lady's shoes, we need to multiply the number of styles, colors, and sizes together.

Number of styles = 8

Number of colors = 7

Number of sizes = 3

Total combinations = Number of styles × Number of colors × Number of sizes

Total combinations = 8 × 7 × 3 = 168

Therefore, there are 168 possible combinations of the shoe company's lady's shoes.

3. If there were 8 possible outcomes when Daniel got coins from her pocket, we can assume that each coin has two possible outcomes: either it fell on the floor or it didn't. So, we can treat this situation as a binary outcome.

Since there are 8 possible outcomes, it means there are 8 coins in total. Each coin can either fall on the floor (1) or not (0).

Therefore, the number of coins that fell on the floor is equal to the sum of the outcomes, which is 8.

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Answer:

−4

Step-by-step explanation

Answer:

−4

Step-by-step explanation:

-6 x (1/3 + 1/3)

Since 1/3 and 1/3 have the same denominator, add them by adding their numerators.

-6 x (1+1/3)

Add 1 and 1 to get 2.

-6 x (2/3)

Express -6 x (2/3) as a single fraction.

-6 x 2/3

Multiply −6 and 2 to get −12.

-12/3

Divide −12 by 3 to get −4.

−4