King raised $28, which is 35% of their goal.
What is the band's goal?

The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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Answer:

The answer is: 4y(2x+y)

Step-by-step explanation:

The trade this country will import is given by the option (C) 300 pair of shoes.

The number of shoes exported will be calculated by the formula -

Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.

The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.

Imports = 1300 - 1000

Performing subtraction on Right Hand Side of the equation

Imports = 300

Hence, the import is 300.

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The complete question is attached in figure.

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

8x + 28

Step-by-step explanation:

The domain of function f(x) is given as follows:

{x | 1 ≤ x < 5}.

The values of x of the function given at the end of the answer are as follows:

Hence the domain is given as follows:

{x | 1 ≤ x < 5}.

The function is given by the image presented at the end of the answer.

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Answer:

A - {x | 1 < x < 5}

Step-by-step explanation:

took the Quiz

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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Answer: what the hell the happened

Step-by-step explanation:

The value of X in the given system of matrix is,

\(X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right]\)

Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.

We have 2 by 2 matrix in the form,

\(\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\\)

After multiplication,

\(9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\\)

After solving the given system of equations

\(a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right]\)

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The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer: See attached.

Step-by-step explanation:

   We will input the given x-values and solve for y by substituting x for the values in the original function, h(x)=2x-2.

h(-5) = 2(-5)-2 = -12

h(-1) = 2(-1)-2 = -4

h(1) = 2(1)-2 = 0

h(2) = 2(2)-2 = 2

The additional gas it will take to fill the tank is 16 gallons

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

Capacity = 24 gallons

Current volume = 1/3 full

This means that

Remaning volume = 1 - 1/3

Evaluate

Remaning volume = 2/3

The additional gas it will take to fill the tank is

Additional = 2/3 * 24

Evaluate

Additional = 16

Hence, the additional gas it will take to fill the tank is 16 gallons

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Answer:

Step-by-step explanation:

The correct interpretation of the 95% confidence level is (D) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the mean size of farms in the United States.

In other words, if we repeatedly take random samples of size 30 from the population of farm sizes in the United States and construct 95% confidence intervals for the mean size in each sample, approximately 95% of those intervals will contain the true mean size of farms in the United States. The interval (367, 558) is just one of those intervals, and it is not a statement about the farm sizes in the sample or the farm sizes in the entire population.

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Based on the definition of the midpoint of a line segment, the length of QS is calculated as: 25 units.

When a point lies on a line segment in such a way that it bisects the line into two equal halves, that point is said to be the midpoint of that line segment.

In the image attached below, on line segment QS, R bisects QS into two equal halves because it is the midpoint of segment QS.

Given that segment QR = 12.5, this means that it is half of the line segment QS.

Therefore:

Length of QR = 12.5

Length of QR = 1/2(length of QS)

Thus:

12.5 = 1/2(length of QS)

Multiply 2 by both sides

2(12.5) = length of QS

25 = length of QS

Length of QS = 25 units.

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Answer:

\(12x^7\)

Step-by-step explanation:

\(3x^2 \times 4x^5\)

\(3 \times x^2 \times 4 \times x^5\)

\(3 \times 4 \times x^{2+5}\)

\(12 \times x^7\)

Answer:

± (1 ÷ 9)

Step-by-step explanation:

Data provided in the question

Since  3 is added to the absolute value and -9

The result is 4

Now this information should be transformed in a mathematical equation

Let us assume be x so the product of the number and -9 be -9x

Fo rthe absolute value we use the mode. Thus the required expression is:

3 + |-9x|

Given that the result is 4

So, it would be

3 + |-9x| = 4

Now Solving the above equation which is given below:

|-9x| = 4-3

|-9x| = 1

here we will remove the mode by introducing ± sign which is shown below:

-9x = ± 1

-9x = 1 or -9x = -1

x = -1/9

or

x = \(\frac{1}{9}\)

Therefore, the value of x is ± (1 ÷ 9).

Answer:

18.85

Step-by-step explanation:

The area of a circle is A= pi × r² (r being the radius)

The radius is half the diamter so the radius would be 6

Plug 6 into the equation for the radius

A = pi × 6²

A = pi ×36

A= 18.85

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

The number of times the spinner lands on a shaded section are 8 times.

What is the probability?

Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.

We have,

2 Shaded sections are on a spinner,

8 unshaded sections are on a spinner,

10 total sections are on a spinner,

Therefore,

The probability of the spinner to land on a shaded section:

P = 2 ÷ 10 = 1 ÷ 5

consider x, the number of times the spinner lands on a shaded section.

If the spinner were spun 40 times:

so,   \(\frac{x}{40} = \frac{1}{5}\)

By cross multiplying we get,

5x = 40

x = 8

Hence, the number of times the spinner lands on a shaded section are 8 times.

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Answer:

100 wizards in magic club

Step-by-step explanation:

20% of 120 is 20 so

120-20=100

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer: A,B,E,F

Step-by-step explanation:

Answer:

The answer is A, B, E, F

Step-by-step explanation:

The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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Answer:

$450.

Step-by-step explanation:

62% = 0.62.

Let yesterday's price be $x, then.

0.62x = 279

x = 279 / 0.62

= $450.

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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The expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

A simplified expression is an expression that is evaluated to its simplest form, that is, it cannot be simplified further.

Given:

(6x - 2) - (-x + 5)

Open the bracket by multiplying each of the terms in (-x + 5) by the negative sign (-):

6x - 2 + x - 5

Combine like terms

7x - 7

Thus, the expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

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The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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Answer:

Step-by-step explanation:

volume = 34cm³

volume = 4/3×π×radius³

34cm³ = 4/3 × 3.14 × radius³

34cm³ = 12.56/3 × radius³

radius³ = 34×3/12.56

radius³ = 8

radius = ³√8

radius = 2cm

diameter = 2×radius

= 2×2

= 4cm

FOLLOW ME PLEASE

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side