Quintin raked his customer’s lawn for 1.2 hours. If Quintin charges $20 per hour, how much money did he make?

The formula for continuously compounded interest is:

A = P * e^(rt)

where:

A is the final amount

P is the initial amount (the principal)

r is the annual interest rate (in decimal form)

t is the number of years the interest is compounded

Substituting in the given values, we get:

A = $28,000 * e^(0.0525 * 4) = $28,000 * e^0.21 = $28,000 * 1.23 = $28000*1.23 = 34,540

Therefore, there will be $34,540 in the account after 4 years.

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The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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20 beacuse you need hiking boots to hike

Answer:

25

Step-by-step explanation:

let x = # of participants on the hike

(.80)x = 20

x = 20/0.80 = 25

Answer:

[tex]\displaystyle x=\frac{1}{5}y^2[/tex]

Step-by-step explanation:

[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]

To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.

What is the unit cost?

The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.

Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

The unitary method is used to find the unit cost of an object.

To find the cost of a unit object, multiply a by unit cost.

Given that, the unit cost of a unit pound of tomatoes.

The cost of 10 pounds of tomatoes is 10 ×  unit price of tomatoes.

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Answer:

844.5 calories.

Step-by-step explanation:

If a physically active adult weighing 170 pounds needs to consume about 2815 calories per day in order to maintain his or her weight, and a nutritionist recommends that no more than 30% of those calories should come from simple sugars, the maximum number of calories per day that should come from simple sugars is:

2815 calories * 30% = <<281530.01=844.5>>844.5 calories

So, the maximum number of calories per day that should come from simple sugars is 844.5 calories.

Answer

844.5

Step-by-step explanation:

80+100=180

180÷100=1.80

1.80×2815=844.5

Using simple unitary method process in the given problem with the provided values, The answer is £42 .

The unitary method is a method of solving mathematical problems in which the relationship between a quantity and its unit of measurement is used to find an unknown quantity. It involves expressing the given quantity in terms of a unit, then solving for the unknown quantity in terms of the same unit.

Arithmetic operators are used to perform basic mathematical operations, such as addition (+), subtraction (-), multiplication (*), division (/), and modulus (%). They take numerical values (either literals or variables) as their operands and return a single numerical value. These are widely used in mathematical computations, like in programming languages, spreadsheets and calculator apps.

4 glasses cost £24.

1 glass cost £24/4 = £6

7 glasses cost = £6 * 7 = £42

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The length of UV in the circle is given as follows:

13.2.

We are given two secant segments in the circle for this problem.

For two secants, the product of the lengths of one secant segment and it's external segment equals the product of the lengths of the other secant segment and it's external segment.

Hence, from the circle given by the image presented at the end of the answer, the relation for this problem is given as follows:

(22 + 17) x 17 = (20 + UV) x 20

Hence we must simply solve the expression to obtain the length of UV, as follows:

39 x 17 = 400 + 20UV

663 = 400 + 20 UV

20 UV = 263

UV = 263/20

UV = 13.2.

The circles are given by the image presented at the end of the answer.

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Answer: nine

Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9

Answer:

9

Step-by-step explanation:

1 first split  36 by 4 because  25% is 1/4

2 once when divided you should get 9 because 9x4 is 36  

Answer:

The cost of a manicure set in Nina's store is $12.30.

Step-by-step explanation:

To find the cost of the manicure set in Nina's store, you can use the following formula:

Selling price = Cost + Cost * Markup percentage

Substituting the given values into this formula, you get:

Selling price = $8.36 + $8.36 * 47%

To find the value of the markup percentage, you can convert 47% to a decimal by dividing it by 100: 47/100 = 0.47

Then you can use this value in the formula to find the selling price:

Selling price = $8.36 + $8.36 * 0.47

280 AND 245 RS  the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs

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Answer: The sum of the digits of 99 × n is 27 - 10 = 17.

Step-by-step explanation:

To find the sum of the digits of 99 × n, we can use the fact that 99 × n = 100 × n - n. The sum of the digits of 100 × n is simply n, since the hundreds digit is zero. Therefore, the sum of the digits of 99 × n is equal to the sum of the digits of n - n, which is simply zero.

For example, if n = 37, then 99 × n = 99 × 37 = 3,699. The sum of the digits of 3,699 is 3 + 6 + 9 + 9 = 27. The sum of the digits of 37 is 3 + 7 = 10. Therefore, the sum of the digits of 99 × n is 27 - 10 = 17.

Answer:

[tex]2 \frac{23}{27} [/tex]

I wish you luck in your assignments.

The conditions of the line to be intersecting, parallel, and coincident are explained below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The types of lines are as follows:

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Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

The required solution for the inequality a + 5 > -7 is (-12, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

a + 5 > -7

To find the solution for the inequality,

Simplify the inequality,

a + 5 > - 7

a > - 7 - 5

a > -12

The value of a is greater than -12, implies that,

The solution for the value of the given inequality is (-12, ∞).

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Answer:

From left to right picture,

Scale factor = 2/3

x = 24

y = 12

z = 21

Step-by-step explanation:

Look at the two figures and identify the sides where both lengths are known.

That is the top right-hand side.

Scale factor is hence 18/27 = 2/3

Next, find x, y and z:

Bottom left-hand side:   16/x = 2/3

                                            x = 3/2 x 16

                                             x = 24

Bottom right-hand side:    y/18 = 2/3

                                            y = 18 x 2/3

                                             y = 12

Top left-hand side:       14/z = 2/3

                                           z = 3/2 x 14

                                            z = 21

Heather spend $33.1 on school supplies.

Two or more expressions with an Equal sign is called as Equation.

Given that Melinda, Zachary, and heather went to the mall to shop for school supplies

Melinda spent $14.25 on her supplies.

Melinda=$14.25

Zachary spent $2.30 more than Melinda spent

Zachary=$14.25+$2.3

=$16.55

Heather spent 2 times as much money as Zachary spent

Heather=2×$16.55

=$33.1

Hence, Heather spend $33.1 on school supplies.

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The required graph of the function of h(x) is shown, where h(x) =  |x| + |x + 2|.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|

So,
h(x) = f + g

Now substitue the functions,

h(x) = |x| + |x + 2|

Thus, the required graph of the function of h(x) is shown.

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If a company has issued 8% debentures of INR 10 each at a 10% discount repayable after 10 years. then the cost of capital or pretax cost of debt is 8%.

A bond or other sort of financial instrument that is secured by collateral is referred to as a debenture. Debentures must rely on the issuer's trustworthiness and reputation for support because they lack a collateral backstop. Debentures are commonly issued by both businesses and governments to raise cash or money. The interest paid on these security can be termed as cost of Debt or pretax cost of Debt.

The pretax cost of debt is interest paid on debenture security without giving effect of corporate tax on the rate of interest to be yearly or as per terms and conditions attached to it.

When debt security issued on discount then the loss on issue of these debenture instrument shall also be form part of cost of security or cost of capital.

Thus the year one pretax cost of  Debt capital will be Rs. 1 per debenture and 8% cost of debt.  

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Using the concept of similar triangles, the value of m to the nearest tenth of a unit in the given figure is 6.71.

Triangles with the same geometry but different sizes are said to be similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two triangles that are similar have corresponding sides that are proportionate equal and corresponding angles that are similar.

From the concept of the similar triangle,

3/BD = BD/12

BD² = 12 × 3

BD² = 36

As triangle BDC is a right-angled triangle, use Pythagoras' theorem

m² = BD² + 3²

m² = 36 + 9

m² = 45

m = √45

m = 6.708

m ≈ 6.71

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Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)

The midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.

The formula of midpoint of a line is given as;

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.

The x - coordinate is calculated as;

-1 = (4 + x₁) / 2

-2  = 4 + x₁

x₁ = -2 - 4

x₁ = -6

The y - coordinates is calculated as;

8 = (-15 + y₁) / 2

16 = -15 + y₁

y₁ = 16 + 15

y₁ = 31

The coordinates of k is (-6, 31)

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An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. The variable is 28 square feet with x = 150 and A = (4)(7).

A variable is anything that can take on any one of a number of values, such as a quantity, a sign for a variable, or an element of a scientific experiment that is susceptible to change.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye colour, and vehicle type.

A variable is a value that can be altered depending on the mathematical issue. Numerous mathematical expressions and equations use the generic letters x, y, and z.

1)

[tex]$$\begin{aligned}& \frac{6}{100}=\frac{9}{x} \\& \frac{6 x}{6}=\frac{900}{6} \\& x=\frac{300}{2}\end{aligned}$$[/tex]=150.

2)

[tex]$A=(4)(7)$[/tex]

[tex]$A=28$[/tex] thirty feet

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Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.

Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.

In geometry, a shape's perimeter, or overall length, is referred to as its perimeter. The lengths of all a shape's sides and edges are added up to determine its perimeter.

Here,

Given :  length = 5 - 1(x) or

=> length = 5-x

Width is twice the length

thus,

=>Width = 2(5-x)

=>Width = 10-2x

So ,To find the perimeter

We use,

=> Perimeter = 2(length + width)

=> Perimeter = 2( 5-x + 10-2x )

=>  Perimeter = 2( 15 -3x)

=>   Perimeter = 30 -6x

Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.

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Answer:

Step-by-step explanation:

1. ( -2, 2), (-1, 5)

   (5 - 2)/(-1 + 2)= 3/1= 3

2. (-4, 2), (2, 0)

   (0 - 2)/(2 + 4) = -2/6 = -1/3

3. (0, 3), (5, 1)

(1 - 3)/(5 - 0)= -2/5

4. (0, 0), (1, 1)

  (1 - 0)/(1 - 0)= 1/1= 1

5. (3, 0), (3, 1)

(1 - 0)/(3 - 3) = 1/0 = undefined

6. (0, -1)  (1, -1)

   (-1 + 1)/(1 - 0)= 0/1 = 0

Answer:

chocolate chip 7

walnuts 3.5

Step-by-step explanation:

assume x=chocolate chips

 y=walnuts.

equation

4x + 8y=33

(2x+3y=13)×2

new eq

4x + 8y=33

4x + 6y=26

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

 2y=7

  y=7/2

4x+ 8y = 33

4x + 8(7/2)= 333

4x= 33-28

x=7.00

The amount (present value) of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15 years is $80,000.

The price of a bond is its present value.

The present value can be determined as the discounted cash inflows.

In this situation, we can determine the present value of the bond using an online finance calculator as follows:

N (# of periods) = 30 (15 years x 2)

I/Y (Interest per year) = 3%

PMT (Periodic Payment) = $1,200

FV (Future Value) = $80,000

Results:

Present Value (PV) = $80,000.00

Sum of all periodic payments = $36,000.00

Total Interest = $36,000.00

Thus, the amount of the bond is $80,000.

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The pre-image and picture will become congruent to one another by the following transformations: Reflection, Rotation and Translation

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms).

Any of the aforementioned modifications result in an exact replica of the pre-image in the picture. The only thing that has changed about the figure is that it has been moved, rotated, or somehow reflected. The figurine is still the same size and form as before. Isometries are the name for these transformations.

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