A tee shirt company charges $240 for 12 tee shirts. They charge the same amount of money for each shirt.

Which table represents the relationship between the number of tee shirts the company sells and the amount of money they charge?

Number of shirts Amount charged (dollars)
2 $24
4 $48
6 $72
8 $96

Number of shirts Amount charged (dollars)
5 $100
10 $200
15 $300
20 $400

Number of shirts Amount charged (dollars)
10 $240
11 $240
12 $240
13 $240

Number of shirts Amount charged (dollars)
12 $240
14 $264
16 $288
18 $312

Answer:

x < 13

Step-by-step explanation:

- 2x > - 26

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x < 13

Answer:

x < 13

Step-by-step explanation:

\(-2x > -26\\\rule{150}{0.5}\\-2x>-26\\\\\frac{-2x>-26}{-2}\\\\\boxed{x <13}\)

Hope this helps.

The value of the function f(x) when x = 0 is not defined as the logarithm function is not defined for x ≤ 0.What is the

value of the function f(x) when x = 0?The value of the function f(x) when x = 0 is undefined as the logarithm function is not defined for x ≤ 0. Therefore, x = 0 is not in the range of the function f(x) = log(x).A natural logarithm function

defined only for values of x greater than zero (x > 0), so x = 0 is outside of the domain of the function f(x) = log(x). Therefore, x = 0 is not in the range of the function f(x) = log(x).In summary,x = 0 is not in the range of the function f(x) = log(x).The value of the function f(x) when x = 0 is undefined.

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The computed mean is 58.8 degrees based on frequency distribution.

To find the mean of the data summarized in the frequency distribution, we first need to find the midpoint of each class interval.

Midpoint of 40-44 = (40 + 44) / 2 = 42
Midpoint of 45-49 = (45 + 49) / 2 = 47
Midpoint of 50-54 = (50 + 54) / 2 = 52
Midpoint of 55-59 = (55 + 59) / 2 = 57
Midpoint of 60-64 = (60 + 64) / 2 = 62

Next, we multiply each midpoint by its corresponding frequency and add up the results.

(2 x 42) + (6 x 47) + (12 x 52) + (7 x 57) + (3 x 62) = 1764

Finally, we divide this sum by the total number of values (which is the sum of the frequencies).

2 + 6 + 12 + 7 + 3 = 30

1764 / 30 = 58.8

The computed mean is 58.8 degrees.

When we compare this to the actual mean of 57.8 degrees, we see that the computed mean is slightly higher. This may be due to the fact that there are more values in the higher end of the distribution (i.e. 50-54 and 55-59) compared to the lower end (i.e. 40-44 and 45-49).

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The area of the sphere is 8π.To find the area of the sphere, we need to determine its radius first. The tetrahedron's edge length (√2) represents the radius of the sphere.

The formula to find the area of a sphere is A = \(4\pi r^2\), where A is the area and r is the radius.

Plugging in the radius (√2) into the formula, we get:

A =\(4\pi(\sqrt{2} )^2\)
 = \(4\pi *2\)
 = \(8\pi\)

Therefore, the area of the sphere is 8π.

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The fraction of the cookies do they still need to made after Cameron and Lindsey made 80 cookies is 1/2.

Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be the entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin.

The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form. A piece or sector of any quantity is another name for the fraction.

Total cookies to be made is 160

Out of which Cameron made 2/5 of the cookies so,

2/5 x 160 = 64 cookies are made by Cameron

Lindsey made 16 cookies

So total cookies that still need to be made is,

= 160 - (64 + 16) = 80

The fraction of cookies still need to made is 80/160 = 1/2 .

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The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.

The given function is  F(x,y) = \(x^{2}\) + \(y^{2}\) - \(2x\)   → 1

D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).

Differentiate 1 partially with respect to x:

df/dx =  \(x^{2}\) + \(y^{2}\) - \(2x\)

\(f^{'}\)(x) = 2x - 2

Differentiate 1 partially with respect to y:

df/dy = \(x^{2}\) + \(y^{2}\) - \(2x\)

\(f^{'}\)(y)  = 2y

Consider \(f^{'}\)(x) = 0 and \(f^{'}\)(y) = 0 to find the critical points.

\(f^{'}\)(x) ⇒ 2x -2 =0

x = 1

\(f^{'}\)(y) ⇒ 2y

y = 0

Thus, the critical point is (x,y) = (1,0).

Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).

At (x,y) = (0,0)

f(0,0) ⇒ 0 + 0 - 0 = 0

At (x,y) = (0,2)

f(0,2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (0,-2)

f(0,-2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (1,0)

f(1,0) ⇒ 1 + 0 - 2 = -1

Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.

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Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

What is set ?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines,etc.

a) The set c = {north america, south america, europe, asia, australia, africa, antarctica} can be written in set-builder notation as:

c = {x | x is a continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}

b) The set-builder notation can be read as "the set c, such that x is a continent and x is an element of the set {north america, south america, europe, asia, australia, africa, antarctica}".

Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

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Answer:

Let's start by using a proportion to find the total number of questions on the test. We know that Charles answered 23 questions correctly and received a grade of 92%, which means he missed 8% of the questions.

Let x be the total number of questions on the test. Then 8% of the questions that Charles missed can be expressed as 0.08x.

The number of questions that Charles answered correctly plus the number of questions he missed must add up to the total number of questions on the test:

23 + 0.08x = x

Simplifying and solving for x, we get:

0.92x = 23

x = 23 / 0.92

x ≈ 25

Therefore, the total number of questions on the test was approximately 25.

Answer: -18x² + 3x +14y - 6

10y - 14x² + 3x - 4x² + 4y - 6

- 14x²- 4x² + 3x + 10y + 4y -6

-18x² + 3x +14y - 6

1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

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The answer is 33degree.

The solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2.

To solve this equation, we first need to square both sides:
sin^2x = 1 - cosx
Next, we can use the identity sin^2x + cos^2x = 1 to substitute sin^2x with 1 - cos^2x:
1 - cos^2x = 1 - cosx
Now we can simplify by moving all the terms to one side:
cos^2x - cosx = 0
Factorizing, we get:
cosx(cosx - 1) = 0
So the solutions are when cosx = 0 or cosx = 1. In the interval [0, 2π), the solutions for cosx = 0 are x = π/2 and 3π/2. The solution for cosx = 1 is x = 0. Therefore, the solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2. We express these solutions in radians in terms of π.

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Answer:

X=7

Step-by-step explanation:

yup

Answer:

Step-by-step explanation:

3(x+1)=10+2x

3x+3=10+2x

3x-2x=10-3

x=7

If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Answer:

?= 180-(75+39)=66

Step-by-step explanation:

......

Answer:

66

Step-by-step explanation:

A triangle's angles always add up to 180.

So to find the missing angle, subtract the angles we already have by 180.

180-(75+39) = ?

180-114 = 66

I hope this helps!

Answer:

m<1 = 175 degrees

Step-by-step explanation:

3x + 10 = 2x + 15

-2x - 10 = -2x - 10

x = 5

180 - 5 = 175 degrees

The percentage of the data set within the range of 10 to 22 is 68.26%.

To find the percentage of the data set for a normally distributed variable with a mean of 16 and a standard deviation of 6, we can use the concept of z-scores and the standard normal distribution.

First, we need to convert the values to z-scores, which measure the number of standard deviations a particular value is from the mean. The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the percentage of the data set within a certain range. Let's say we want to find the percentage of the data set between 10 and 22. We can calculate the z-scores for these values:

\(z1 = (10 - 16) / 6 = -1.0\)

\(z2 = (22 - 16) / 6 = 1.0\)

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. The area between -1.0 and 1.0 represents the percentage of the data set within the range of 10 to 22.

Looking up the z-scores in the standard normal distribution table, we find that the area between -1.0 and 1.0 is approximately 0.6826. This means that approximately 68.26% of the data set falls within the range of 10 to 22.

Therefore, the percentage of the data set within the range of 10 to 22 is 68.26%.

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Let m be a fixed number in n. Then the function f(x) = xm is defined on all of r. To show that f(x) is continuous on r, we need to show that it is continuous at every point a in r.

Consider a fixed point a in r, and let ε > 0 be given. We want to find a δ > 0 such that if |x - a| < δ, then |f(x) - f(a)| < ε.

Since f(x) = xm, we have

f(x) - f(a)| = |xm - ma| = |m||x-a||x^(m-1) + am^(m-1)|.

Now, since m^(m-1) is a constant, we have that |x-a| < δ implies

|m||x-a||x^(m-1) + am^(m-1)| ≤ |m|(|x-a|)δ^(m-1) + |am^(m-1)|.

Therefore, if we choose δ such that

δ < ε / (|m|(δ^(m-1)) + |am^(m-1)|),

then we have

|f(x) - f(a)| < ε,

and hence f(x) is continuous at a. Since a was arbitrary, we conclude that f(x) is continuous on r.

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Answer:

249.88

Step-by-step explanation:

415-82.13-9.74-31.75-41.50

Answer:

1. y = 3x + 2   2. y = -2x - 4

Step-by-step explanation:

Answer:

Exact Form:  2 √ 11

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:  2 √ 11

Decimal Form:  6.63324958 …

Whole Number: 7

Answer:

2 square root of 11

Step-by-step explanation:

Answer:

Procedure:

1) Form a system of 3 linear equations based on the two zeroes and a point.

2) Solve the resulting system by analytical methods.

3) Substitute all coefficients.

Step-by-step explanation:

A quadratic function is a polynomial of the form:

\(y = a\cdot x^{2}+b\cdot x + c\) (1)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(a\), \(b\), \(c\) - Coefficients.

A value of \(x\) is a zero of the quadratic function if and only if \(y = 0\). By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: \(A(x,y) = (r_{1}, 0)\), \(B(x,y) = (r_{2},0)\) and \(C(x,y) = (x,y)\)

Based on such information, we form the following system of linear equations:

\(a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0\) (2)

\(a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0\) (3)

\(a\cdot x^{2} + b\cdot x + c = y\) (4)

There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:

\(a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }\)

\(a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}\)

\(a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}\)

\(b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }\)

\(b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}\)

\(c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }\)

\(c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}\)

And finally we obtain the equation of the quadratic function given two zeroes and a point.

Answer:

The slope of the dotted line is -1. The slope of the solid line is 4.

The dimension the  a box with a square end the largest possible volume is 10 ×10 × 23.3

First, we will need to complete the question.

Let us assume that its dimensions are h by h by w and its girth is 2h + 2w.

Volume = h²w

Where h is the length

w is the girth

From the information given, we have;

Length + girth = 90

w+(2h+2w) = 90

2h + 3w = 90

Make 'w' the subject

w = 90- 2h/3

w = 30 - 2h/3

Substitute the values

Volume = h²(30 - 2h/3)

expand the bracket

Volume = 30h² - 2h³/3

Find the differential value

Volume = 60h - 6h²

h = 10

Substitute the values

w =  30 - 2h/3

w = 30 - 2(10)/3

w = 30 - 20/3

w = 23.3 in

The dimensions are 10 ×10 × 23.3

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The written index form of the given number as a product of prime factors is; 3¹².

Since the given number in discuss is; 81³.

Recall; 81 = 3⁴.

Therefore, we have that; 81³ = ( 3⁴ )³

= 3¹²

Hence ,the index form of number as required as a product of prime factors is; 3¹².

This is due to the fact that 3 is a prime number.

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The probability that a randomly selected land will be profitable, given that it is in a rural location, is 61/125 or 0.488.

The probability that a randomly selected land is going to be profitable, given that it is in a rural location, can be found using the following steps:

1. Identify the number of profitable lands in rural locations,

There are 61 profitable lands in rural locations.
2. Identify the total number of lands in rural locations,

There are 125 lands in rural locations.
3. Calculate the probability,

Divide the number of profitable lands in rural locations by the total number of lands in rural locations.

Probability = (Number of profitable lands in rural locations) / (Total number of lands in rural locations)

Probability = 61 / 125

So, the probability that a randomly selected land will be profitable, given that it is in a rural location, is 61/125 or 0.488.

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Answer:

19:22

Step-by-step explanation:

you put red first since it came first

Answer: $ 27.50

Step-by-step explanation:

We know that $24.75 is (100%-10%) = 90% of the original price.

24.75/90 = 0.275 (to find one percent)

0.275 x 100 = 27.5 (100%, the original price)