A band teacher ordered T-shirts for the marching band members. T-shirts cost $15 each, including tax, plus a one-time shipping fee of $10 for the order. The teacher paid a total of $370 for the T-shirts .How many T-shirts did the teacher order?


A. 15
B. 16
C. 24
D. 25

The accounting equation is a fundamental principle in accounting that states that assets equal liabilities plus equity. Using this equation, missing amounts can be determined in various situations.

The accounting equation is expressed as Assets = Liabilities + Equity. It serves as the foundation for double-entry bookkeeping and ensures that the financial statements are balanced. By rearranging the equation, missing amounts can be determined.

For example, if the assets and equity are given, the missing amount of liabilities can be calculated by subtracting equity from assets. Conversely, if the liabilities and equity are known, the missing amount of assets can be calculated by adding liabilities to equity.

Similarly, if the assets and liabilities are provided, the missing amount of equity can be calculated by subtracting liabilities from assets. Alternatively, if the assets and equity are known, the missing amount of liabilities can be calculated by subtracting equity from assets.

In each situation, the missing amount can be determined by applying the accounting equation and rearranging it to solve for the missing variable. This equation provides a framework for ensuring that all financial transactions are properly recorded and that the financial statements accurately reflect the financial position of a business.

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Answer:

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Hope this helps :)

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

6 yards = 18 feet = 216 inches

\(2 \frac{1}{4}\) feet = 27 inches

Greatest to least

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Using a system of equations, we have that:

1. The table is completed on the image given at the end of the answer.

2. The equation is: 35w + 25t = 1600.

A system of equations is a set of equations in the context of a problem, and solving these equations, the numeric value of each variable in the context of the problem is found.

The variables in this problem are defined as follows:

A jug of drinking water weighs 35 pounds and a case of paper towels weighs 25 pounds. The truck can carry 1,600 pounds of cargo altogether. Hence the equation is:

35w + 25t = 1600.

When w = 10, the numeric value of t is obtained as follows:

35(10) + 25t = 1600

t = (1600 - 350)/25

t = 50.

When w = 30, the numeric value of t is obtained as follows:

35(30) + 25t = 1600

t = (1600 - 1050)/25

t = 22.

When t = 8, the numeric value of w is obtained as follows:

35w + 25(8) = 1600

w = 1400/35

w = 40.

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To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.

The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.

Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.

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Side 1 + side 2 + side 3

E.g.

2 + 4 + 3 = 9

Have a luvely day!

If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

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The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

Answer:

B. 2w^2 + 2w + 36

Step-by-step explanation:

The equation to find the perimeter of anything is: Length + Length + Width + Width = Perimeter.

Applying this logic to this problem, the equation would be as follows:

\(w^{2} + 13 + w^{2} + 13 + w+5+w+5\)

Then, we simplify. The like terms go together, and you have your solution.

\(2w^{2} + 2w+36\)

The solution to the coupled differential equations dx/dt= 2.x1 +x2 is x1 = t^2 + 2t and x2 = t^2, We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

To solve this set of differential equations, we can use the method of separation of variables. This method involves separating the variables in each equation so that they can be solved independently. In this case, we can separate the variables as follows: dx/(2.x1 +x2) = dt

We can then integrate both sides of the equation to get the following: ln(2.x1 +x2) = t + c

where c is an arbitrary constant. We can then exponentiate both sides of the equation to get the following 2.x1 +x2 = e^t.e^c

We can then substitute the initial conditions into this equation to get the following 2.x1 +x2 = e^t.1

where x1(0) = 0 and x2(0) = 0. This gives us the following solution for x1 and x2 x1 = t^2 + 2t and x2 = t^2

Here are some additional explanations:

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The money factor that will be used to calculate Bob's payment is 0.00333 if the annual percentage rate is 8% option (c) is correct.

It is defined as the ratio of the annual percentage rate to 2400. Usually, it can be used to calculating the financing costs of a lease with monthly installments.

Bob is thinking about leasing a car, the lease comes with an interest rate of 8%.

The annual percentage rate(APR) = 8%

We know the formula for finding the money factor is given by:

\(\rm Money \ factor = \frac{APR}{2400}\)

\(\rm Money \ factor = \frac{8}{2400}\)

Money factor = 0.00333

Thus, the money factor that will be used to calculate Bob's payment is 0.00333 if the annual percentage rate is 8% option (c) is correct.

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The quantity of water in the reservoir after 9 hours be, 2835 gallons.

Given, water flows into an empty reservoir at a rate of 2800 + 15t gal/hour.

we have to find the quantity of water in the reservoir after 9 hours.

at the rate of 2800 + 15t

put t = 9

So, the quantity of water in the reservoir after 9 hours be,

2800 + 15(9)

2800 + 135

= 2835

So, the quantity of water in the reservoir after 9 hours be, 2835 gallons.

Hence, the quantity of water in the reservoir after 9 hours be, 2835 gallons.

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a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

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The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

Answer:

-6

Step-by-step explanation:

x= 21/3

x=7

using this value,

22-4x= 22-4*7

=22-28

=-6

Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3

Answer: If you are solving for x, then thee is no solution

Step-by-step explanation:

To plot the direction field associated with the differential equation u^n + 192u = 0, we need to first rewrite the equation as: u' = -192u^(1-n) where u' denotes the derivative of u with respect to some independent variable, such as time. The direction field represents the slope of the solution curve u(x) at each point (x, u(x)) in the xy-plane. To find this slope, we evaluate the right-hand side of the equation at each point: dy/dx = -192y^(1-n)

We can then plot short line segments with this slope at each point in the plane. The resulting picture will show us how the solution curves behave over the entire domain of the equation.To plot the phase plot of the solution corresponding to the initial value problem (IVP), we need to find the specific solution that satisfies the given initial condition. In other words, we need to find u(x) such that u(0) = y0, where y0 is some given constant. The solution to this IVP is: u(x) = (y0^n) / ((y0^n - 192) * e^(192x)) To plot the phase plot, we need to graph this solution as a function of time (or whatever independent variable is relevant to the problem), with u(x) on the vertical axis and x on the horizontal axis. We can then mark the initial condition (0, y0) on this graph and sketch the solution curve that passes through this point.Overall, the direction field and phase plot provide us with a visual representation of how the solution to the differential equation behaves over time. By analyzing these plots, we can gain insight into the long-term behavior of the solution and make predictions about its future behavior.

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Step-by-step explanation:

hope it helps

have a great day!!

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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The number of plants needed is 200. The perimeter of the lot is 40 m and the distance between plants is 0.2 m.

The perimeter of the square lot is 4 times the length of one side, or 4 * 10 m = 40 m.

Each plant will be placed 20 cm apart, which is 0.2 m.

To find the number of plants needed, we divide the perimeter of the lot by the distance between each plant:

Number of plants = perimeter/distance between plants

Number of plants = 40 m / 0.2 m

Number of plants = 200

Therefore, 200 Santan plants must be planted in all.

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Answer: the answer is 24 CO3 0

Step-by-step explanation:

The value of N when t=4 is: N = 300 + 450 = 750.

To evaluate the solution at the specified value of the independent variable, we need to find the relationship between N and t. Given the information, we have two points: (0, 150) and (1, 300).

Step 1: Calculate the slope (m) between the two points.
m = (N2 - N1) / (t2 - t1) = (300 - 150) / (1 - 0) = 150

Step 2: Use one of the points (e.g., (0, 150)) and the slope to find the equation N = mt + b.
150 = 150 * 0 + b
b = 150

Step 3: Write the equation with the slope and intercept.
N = 150t + 150

Step 4: Evaluate the value of N when the specified value of the independent variable t = 4.
N = 150 * 4 + 150
N = 600 + 150
N = 750

The value of N when t = 4 is 750.

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The expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

Algebraic expressions are expressions that consists of terms, variables, coefficients, and constants.

They are also made up of arithmetic operations such as division, addition, multiplication, subtraction, etc

From the information given, we have that;

B is the number of blue bikes

And there are 9 red bikes

The expression for the sum of blue and red bikes is written as;

B + 9

Thus, the expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

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Answer:

Area of square A is x² + 6x + 9.

Area of square B is 4a² - 4a + 1.

Volume of the cube is (x - 2)³, or x³ - 6x² + 12x - 8.

Step-by-step explanation:

Area of square A = I²

I = side length

I = x + 3

(x + 3)² = x² + 6x + 9

Area of square B = I²

I = side length

I = 2a - 1

(2a - 1)² = 4a² - 4a + 1

V= a³

a = edge length

a = x - 2

(x - 2)³ = x³ - 6x² + 12x - 8

Answer:

x = 3

Step-by-step explanation:

2(4 + 3x) + 6 = 32 ( subtract 6 from both sides )

2(4 + 3x) = 26 ( divide both sides by 2 )

4 + 3x = 13 ( subtract 4 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check

substitute x = 3 into the left side of the equation and if value obtained is equal to the right side (32) then it is a solution to the equation.

2(4 + 3(3)) + 6

= 2(4 + 9) + 6

= 2(13) + 6

= 26 + 6

= 32

left side = right side

then x = 3 is the solution to the equation

Answer:

\( \sf \: x = 3\)

Step-by-step explanation:

\( \sf \rightarrow \: 2(4 + 3x) + 6 = 32\)

Apply the distributive property

\( \sf \rightarrow8 + 6x + 6 = 32\)

Combine like terms

\( \sf \rightarrow 14 + 6x = 32\)

Rearrange variables to the left side of the equation

\( \sf \rightarrow 6x = 32 - 14\)

Calculate

\( \sf \rightarrow 6x = 18\)

Divide both sides by the coefficient of 6

\( \sf \rightarrow \frac{6x}{6} = \frac{18}{6} \)

Calculate

\( \sf \rightarrow x = \frac{18}{6} \)

\( \sf \rightarrow \: x = 3\)

Answer:

(x+8)²-2=0

(x+8+√2)(x+8-√2)=0

x= - 8- √2 =  -9.41 lesser x

x= -8 + √2 = -6.59  greater x

Answer:

\(\mathrm{Decimal}:\quad x=-6.58578\ ,\:x=-9.41421\)

Step-by-step explanation:

\(\left(x+8\right)^2-2=0\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\\left(x+8\right)^2-2+2=0+2\\Simplify\\\left(x+8\right)^2=2\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+8=\sqrt{2}:\quad x=\sqrt{2}-8\\x+8=\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=\sqrt{2}-8\\\mathrm{Simplify}\\x=\sqrt{2}-8\)

\(\mathrm{Solve\:}\:x+8=-\sqrt{2}:\quad x=-\sqrt{2}-8\\x+8=-\sqrt{2}\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\x+8-8=-\sqrt{2}-8\\\mathrm{Simplify}\\x=-\sqrt{2}-8\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=\sqrt{2}-8,\:x=-\sqrt{2}-8\\\mathrm{Decimal}:\quad x=-6.58578 ,\:x=-9.41421\)

Answer:

The area is 200.96 in^2

Step-by-step explanation:

Answer:

200.96 in^2

Step-by-step explanation:

circle area formula is πr^2

radius = diameter / 2, radius is 8

8^2.π  = 64π  

π  = 3,14

final answer is 64 X 3.14= 200.96 in^2

Answer:

Step-by-step explanation:

Well all you really need to do is add 31 and 104 which is 135 then divide it by 3 and well you got the answer 45

The expression (31 + 104) / 3 is equal to 45.

The expression that represents the sum of 31 and 104, divided by 3, can be written as (31 + 104) / 3.

To calculate the value, we start by evaluating the sum of 31 and 104, which gives us 135. So, the expression becomes 135 / 3.

Dividing 135 by 3 yields a result of 45.

Therefore, (31 + 104) / 3 is equal to 45.

The expression simplifies the process of finding the sum of the two numbers (31 and 104) by first adding them together and then dividing the sum by 3. This calculation provides a concise representation of the desired arithmetic operation and its solution.

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It is B :)

Step-by-step explanation: