Please help me do this question I have a test soon!

The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

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The variance of the number of customers who will make a purchase is 2.4.

The variance of the number of customers who will make a purchase can be calculated using the formula:

Variance = n * p * (1 - p)

where n is the number of customers and p is the probability of a customer making a purchase.

In this case, n = 10 and p = 0.6. Substituting these values into the formula, we get:

Variance = 10 * 0.6 * (1 - 0.6)
Variance = 10 * 0.6 * 0.4
Variance = 2.4

Therefore, the variance of the number of customers who will make a purchase is 2.4.

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Answer:

A) 6Gn + 12 (or 6n+12, if that’s what you meant)

B) 4p²+9p

C) 5r²+20r

Step-by-step explanation:

A. If you meant 6(n+2)...

Multiply 6 by n and also 6 by 2:

6n + 12

B. Multiply p by 4p and also p by 9

4p²+9p

C. Multiply 5r by r and also 5r by 4

5r²+20r

Hope this helped!

Answer:

The perimeter is 4√81 = 4 × 9 = 36 meters.

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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The Fourier transform F(ω) can be derived using the complex Fourier series coefficients cₙ, and the inverse Fourier transform expression f(t) is given by the sum of cₙ multiplied by e^(jnω₀t).

Show that the Fourier transform F(ω) of a function f(t) can be derived using the complex Fourier series, we start with the expression for the complex Fourier series coefficients cₙ:

cₙ = (1/T) ∫[T/2][-T/2] f(t) e^(-jnω₀t) dt

where ω₀ = 2π/T is the fundamental frequency and T is the period of the function.

Now, let's express the Fourier series in terms of angular frequency ω:

cₙ = (1/T) ∫[T/2][-T/2] f(t) e^(-jn(2π/T)t) dt

Using Euler's formula e^(ix) = cos(x) + isin(x), we can rewrite the above equation as:

cₙ = (1/T) ∫[T/2][-T/2] f(t) [cos(n(2π/T)t) - jsin(n(2π/T)t)] dt

Next, let's express the complex Fourier series as a sum:

f(t) = ∑[n=-∞][∞] cₙ e^(jnω₀t)

Substituting the value of cₙ, we have:

f(t) = ∑[n=-∞][∞] (1/T) ∫[T/2][-T/2] f(τ) [cos(n(2π/T)τ) - jsin(n(2π/T)τ)] e^(jnω₀t) dτ

Now, using the fact that ω₀ = 2π/T, we can rewrite e^(jnω₀t) as e^(jnω₀τ) e^(jnω₀(t-τ)):

f(t) = ∑[n=-∞][∞] (1/T) ∫[T/2][-T/2] f(τ) [cos(nω₀τ) - jsin(nω₀τ)] e^(jnω₀(t-τ)) dτ

Expanding the exponential term using Euler's formula, we get:

f(t) = ∑[n=-∞][∞] (1/T) ∫[T/2][-T/2] f(τ) [cos(nω₀τ) - jsin(nω₀τ)] [cos(nω₀(t-τ)) + jsin(nω₀(t-τ))] dτ

Now, by rearranging terms and using trigonometric identities, we can simplify the expression:

f(t) = ∑[n=-∞][∞] (1/T) ∫[T/2][-T/2] f(τ) [cos(nω₀t)cos(nω₀τ) + sin(nω₀t)sin(nω₀τ)] dτ

Using the trigonometric identity cos(x - y) = cos(x)cos(y) + sin(x)sin(y), we have:

f(t) = ∑[n=-∞][∞] (1/T) ∫[T/2][-T/2] f(τ) cos(nω₀(t - τ)) dτ

Finally, recognizing that (1/T) ∫[T/2][-T/2] f(τ) cos(nω₀(t - τ)) dτ is the inverse Fourier transform expression, we conclude that:

f(t) = ∑[n=-∞][∞] cₙ e^(jnω₀t)

Therefore, we have shown that the Fourier transform F(ω) and the inverse Fourier transform expression f(t).

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Answer:

Step-by-step explanation:

24 boys to 18 girls, total students:

Ratio of boys to the total number of students:

Correct choice is B

Answer:

Solution given;

girl's=18

boys=24

total no of students=24+18=42

now

the ratio of boys to the total number of students in the class=\( \frac{24}{42} \)

=24:42is the required ratio.

The recurrence relation N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1) represents the number of ways to spend all the money when we have a certain amount of dollars and four options for spending it: milk, juice, coffee, and cookies.

Let's denote the number of ways of spending all the money as N(n), where n represents the amount of money we have. Our goal is to find the recurrence relation for N(n).

To start, let's consider the base cases. When n = 0, it means we have no money left. In this case, there is only one way to spend the money, and that is by not buying anything. Therefore, N(0) = 1.

Now, let's consider the cases when n > 0. We have four options for spending the money: milk, juice, coffee, and cookies. Let's analyze each option separately.

If we decide to buy milk, it costs $2. After buying milk, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).

Therefore, the number of ways of spending all the money when buying milk is equal to N(n - 2).

If we decide to buy juice, it also costs $2. After buying juice, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).

Therefore, the number of ways of spending all the money when buying juice is equal to N(n - 2).

If we decide to buy coffee, it costs $3. After buying coffee, we are left with n - 3 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 3). Therefore, the number of ways of spending all the money when buying coffee is equal to N(n - 3).

If we decide to buy cookies, it costs $1. After buying cookies, we are left with n - 1 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 1). Therefore, the number of ways of spending all the money when buying cookies is equal to N(n - 1).

Now, let's consider the total number of ways to spend all the money when considering all the options. Since each option is independent, we can add up the number of ways for each option. Therefore, the recurrence relation for N(n) can be expressed as:

N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1)

This recurrence relation allows us to compute the number of ways of spending all the money for any given amount of money. By using dynamic programming techniques, we can start with the base case N(0) = 1 and compute the values of N(n) iteratively until we reach the desired amount of money.

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Answer:

1/3 a cookie each.

If I were splitting it however, my friends would get none and I would get all! :D

Answer:

1/3

Step-by-step explanation:

1 divided by 3 is 1/3.

The indifference curve equation given is x2 = 20 - 4x^(1/2)*1, where x1 and x2 represent the quantities of two goods Ambrose is consuming.

The marginal rate of substitution (MRS) measures the rate at which Ambrose is willing to trade one good for the other while remaining on the same indifference curve. It is calculated as the negative ratio of the derivatives of the indifference curve with respect to x1 and x2, i.e., MRS = -dx1/dx2. Given that Ambrose is consuming the bundle (4,16), we can substitute these values into the indifference curve equation to find the corresponding MRS.  Plugging in x1 = 4 and x2 = 16, we have: 16 = 20 - 4(4)^(1/2)*1; 16 = 20 - 8; 8 = 8. This confirms that the bundle (4,16) lies on the indifference curve. Now, we are given that the MRS at this point is 25/4.

Therefore, we can set up the following equation: dx1/dx2 = 25/4. Simplifying, we have: dx1/dx2 = -25/4. This indicates that the rate at which Ambrose is willing to trade good x1 for good x2 at the bundle (4,16) is -25/4. The MRS represents the slope of the indifference curve at a given point and reflects the trade-off between the two goods. In this case, it indicates that Ambrose is willing to give up 25/4 units of good x1 in exchange for one additional unit of good x2 while maintaining the same level of satisfaction.

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Answer:

165and 75 is your answer

Answer:

Answer:

The statement is;

The polynomial function has 3 roots with 2 being real roots and 1 being a complex root

Step-by-step explanation:

Here, we want to state the description of the number and nature of all roots for this function.

The statements are;

1. The polynomial have three roots

2. There are 2 real roots and 1 complex root

Answer:

A

Step-by-step explanation:

on edg 2020!

the most appropriate sampling method for Laura to determine if the 7th grade class wants to go on a field trip to an art museum, a concert.

how to solve the method?

The sampling method that would likely provide a representative sample of the population would be to survey every fifth 7th grade student as Laura arrives at school because it gives each seventh-grade student an equal opportunity to be a part of the survey. This method is known as systematic sampling, and it ensures that each student has an equal chance of being selected for the survey.

By using this method, Laura can avoid biases that may arise if she only surveyed athletes or members of the art club. For example, if she surveyed only 7th grade athletes, she would not be able to get the opinions of students who are not interested in sports. Similarly, if she only surveyed members of the art club, she would not be able to get the opinions of students who are not interested in art.

Surveying every fifth 7th grade student would also allow Laura to obtain a sample size that is large enough to be representative of the entire population. This method would ensure that her sample is not too small or too large and that it is a manageable size for analysis.

In summary, the most appropriate sampling method for Laura to determine if the 7th grade class wants to go on a field trip to an art museum, a concert, or a sporting event would be to survey every fifth 7th grade student as she arrives at school because it gives each seventh-grade student an equal opportunity to be a part of the survey, ensures a manageable sample size, and minimizes bias.

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Using sine ratio in trigonometric ratio, the length of the ladder is 29.6 feet

Trigonometric ratios are ratios of the sides of a right triangle that are used to describe the angles of the triangle. They are used in many different branches of mathematics, including geometry, calculus, and trigonometry. The most common trigonometric ratios are sine, cosine, and tangent.

To solve this problem, we have to determine which of the ratio we need.

Data;

Since we have the opposite side and angle, we can find the hypothenuse using sine ratio

sinθ = opposite / hypothenuse

sin 71 = 28 / x

x = 28 / sin 71

x = 29.6 feet

The length of the ladder is 29.6 feet

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Answer:

29.61

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

GEMDAS

G - groupings

E - exponents

M - multiply

A - add

S - subtract

The values οf the basic trigοnοmetric functiοns fοr an angle in standard pοsitiοn passing thrοugh (6,8) are:

\(\sin \theta &= 0.8\\\) \(\cos \theta &= 0.6\), etc.

Trigοnοmetry is a branch οf mathematics that deals with the study οf triangles and the relatiοnships between their sides and angles.

We can begin by finding the length οf the hypοtenuse οf the right triangle fοrmed by the given pοint and the οrigin. This will give us the value οf the trigοnοmetric functiοns sine, cοsine, and tangent.

The hypotenuse can be found using the Pythagorean theorem:

\(c^2 &= a^2 + b^2\)

\(&= 6^2 + 8^2\)

\(&= 36 + 64\)

\(&= 100\)

\(c &= \sqrt{100}\)

\(c &= 10\)

Therefore, the point (6,8) is 10 units away from the origin.

The sine of the angle can be found by dividing the opposite side (8) by the hypotenuse (10):

\(\sin \theta &= \frac{8}{10}\)

\(&= 0.8\)

The cosine of the angle can be found by dividing the adjacent side (6) by the hypotenuse (10):

\(\cos \theta &= \frac{6}{10}\)

\(&= 0.6\)

The tangent of the angle can be found by dividing the opposite side (8) by the adjacent side (6):

\(\tan \theta &= \frac{8}{6}\)

\(&= \frac{4}{3}\)

Therefore, the values of the basic trigonometric functions for an angle in standard position passing through (6,8) are:

\(\sin \theta &= 0.8\)

\(\cos \theta &= 0.6\)

\(\tan \theta &= \frac{4}{3}\)

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The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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A) The odds of picking a black jellybean are 14/37.

Step-by-step explanation:

The jar contains fourteen black, eight red, eleven yellow, and four green jellybeans.

Therefore, the Total number of jellybeans in the jar = 14+8+11+4=37

Since the question asks for odds, which is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. Let us first find the number of favorable outcomes, i.e. the number of black jellybeans.

Therefore, the number of black jellybeans = 14

Now, the number of unfavorable outcomes is the number of jellybeans that are not black.

Therefore, the number of unfavorable outcomes = 37-14=23

Hence, the odds of picking a black jellybean are the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

Odds of picking a black jellybean = (number of favorable outcomes)/(number of unfavorable outcomes)=14/37

Answer: Odds of picking a black jellybean are 14/37.

B) The odds of picking a green jellybean are 5/35.

Step-by-step explanation:

The jar contains ten black, eight red, twelve yellow, and five green jellybeans.

Therefore, the Total number of jellybeans in the jar = 10+8+12+5=35

Since the question asks for odds, which is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. Let us first find the number of favorable outcomes, i.e. the number of green jellybeans.

Therefore, the number of green jellybeans = 5Now, the number of unfavorable outcomes is the number of jellybeans that are not green.

Therefore, the number of unfavorable outcomes = 35-5=30

Hence, the odds of picking a green jellybean are the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

Odds of picking a green jellybean = (number of favorable outcomes)/(number of unfavorable outcomes)=5/30

Reducing the ratio to the simplest form, we get the odds of picking a green jellybean = 1/6

Hence, the odds of picking a green jellybean are 5/35.

Answer: Odds of picking a green jellybean are 5/35.

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Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Answer: the full gallon

Step-by-step explanation:

Half gallon = $2.20

full gallon = $3.68

since a half gallon is $2.20, when you buy 2 (to make a full gallon), it costs $4.40

since just buying a full gallon only costs $3.68, it is a better buy*

* if you don’t want a full gallon, however, you would just buy a half gallon. But, I don’t believe that this question is about whether you want a half or full gallon. It’s math.

Answer:

\(\bold\purple{Quadratic \: \: eq {}^{n} = x {}^{2} - ( \alpha + \beta )x + \alpha \beta} \\ \)

Sum of roots ,

\(( \alpha + \beta ) = (3 + 9) = 12\)

Product of roots ,

\(( \alpha \beta ) = (3)(9) = 27\)

Substituting the values in the above equation ,

\(\bold{x {}^{2} - ( \alpha + \beta )x + \alpha \beta} \\\\ \bold{⇢ x {}^{2} - (12)x + 27} \\\\ \bold\blue{ ⇢x {}^{2} - 12x + 27}\)

hope helpful~

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

(Choice C)

Slope and a point that is not an intercept

The value x in quadrilateral is 25.71.

We are given that;

The adjacent angles= (4x-4) and (3x+2)

Now,

If a polygon is four sided (a quadrilateral), the sum of its angles is 360°

The two adjacent angles are supplementary, meaning that they add up to 180 degrees. This is because in a quadrilateral, the sum of any two adjacent angles is 180 degrees.

Write an equation using this property and the given expressions for the angles. The equation is: (4x−4)+(3x+2)=180

The equation by combining like terms and subtracting 2 from both sides. The equation becomes: 7x−2=178

Solve for x by adding 2 to both sides and dividing by 7. The equation becomes: x=7180​

Therefore, by quadrilateral the answer will be 25.71

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The complete question is;

The sum of the measures of the angles of a quadrilateral is 360

degree Two adjacent angles of quadrilateral are (4x-4) and (3x+2). find x

Answer:

$23,520

Step-by-step explanation:

Given the question :

Eddie is a plant manager at North Salem Construction Company. He has been employed there for 20 years and will be retiring at the end of this year. His pension is calculated on the average of his last four years' salaries. In those years, he earned $82,000, $96,000, $105,000, snf $109,000. His employer will give him 1.2% of that average for each year he worked. Calculate Eddie's pension

Pension is calculated on the average of his last four years salary :

Salary for last four years :

82,000 + 96,000 + 105,000 + 109,000 = $392,000

Average salary over the last four years :

392,000 / 4 = $98,000

Number of years worked = 20 years

1.2% of his average salary over the last four years :

0.012 × $98,000 = $1,176

$1,176 × number of years worked

$1,176 × 20 = $23,520

Using the mean concept, it is found that Eddie's pension is of $23,520.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem, there are 4 observations, which are $82,000, $96,000, $105,000, and $109,000, hence, the mean is:

\(M = \frac{82000 + 96000 + 105000 + 109000}{4} = 98000\)

1.2% of the average is given by:

\(0.012(98000) = 1176\)

He worked for 20 years, hence, the pension is of:

\(P = 1176(20) = 23520\)

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Answer: 1,080 (in) or 30 yards

Explanation:

1. Convert yards to inches (1800 inches)

2. Multiply the amount of string each person will get by how many people there are (24 x 30= 720)

3. Subtract the total amount of string by the amount of string that will be used. (1800 - 720 = 1080)

Therefore the answer is 1080 (in) or 30 yards

Hope this helps!

:)

Answer:

  P'(3, -12)

Step-by-step explanation:

Assuming we're dilating the figure by a factor of 3 using the origin as the center of dilation, the coordinates of P' will be 3 times those of P:

  P' = 3P

  P' = 3(1, -4)

  P' = (3, -12)