The marginal cost function for a company is given by C'(q) = q^2 - 17q + 70 dollars/unit;
where q is the quantity produced. If C(0) = 650, find the total cost of producing 20 units. What is the fixed cost and what is the total variable cost for this quantity? Fixed cost = Variable Cost of producing 20 units =
Total cost of producing 20 units =

If velocity is negative,The body is moving backwards instead of forwards, so the displacement will be measured as a negative value.

An antiderivative of a velocity function can be used to find displacement of the body by integrating the velocity function over a given time interval. The result of this integration will give the total displacement of the body over that time interval.

If the velocity is negative, it means that the body is moving in the opposite direction to the positive direction of the coordinate system. This has an impact on the problem of finding displacement because the displacement will also be negative. In other words, the body is moving backwards instead of forwards, so the displacement will be measured as a negative value.

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Answer:

The rate is $7.50 per hour.

The unit rate is $7.50 per hour.

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Step-by-step explanation:

To find the rate, divide the total amount earned by the number of hours worked. In this case, you earned $45 for 6 hours.

Rate = Total amount earned / Number of hours worked

Rate = $45 / 6 hours

Rate = $7.50 per hour

The rate is $7.50 per hour.

The unit rate refers to the rate per unit of one. In this case, it would be the rate per hour.

Unit Rate = Rate / Number of units

Unit Rate = $7.50 / 1 hour

Unit Rate = $7.50 per hour

The unit rate is $7.50 per hour.

To write a function rule to represent this situation, let's use "x" to represent the number of hours worked and "y" to represent the amount earned:

y = Rate * x

Since the rate is $7.50 per hour, the function rule can be written as:

y = 7.50x

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Answer:

Step-by-step explanation:

7.5

Answer: 6,550.6666666666666666666666666667π

Step-by-step explanation:

Hope this helps! :)

Answer:

Explanation :

We are given with two shapes triangle and a rectangle.

From the above diagram

We can see that Breadth of the rectangle is 5 ft and length of 10 ft.

As we know that area of Rectangle is length × Breadth

Area(rectangle) = l × b

Area (rectangle) = 10 × 5

Area (rectangle) = 50 ft².

Now,

where

Area (triangle) = 4 × 6 ÷ 2

Area (triangle) = 24 ÷ 2

Area (triangle) = 12 ft².

Total area = Area of rectangle + Area of triangle

Total area = 50 + 12

Total area = 62 feet

Therefore, The area of the irregular shape is 62 feet.

Using area formula for rectangles, we can find the new area of the rectangle to be 7350m².

The new dimensions are:

Length = 105m

Breadth = 70m

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Each rectangle's two defining characteristics are its length and breadth. A rectangle's longer and shorter sides are its width and length, respectively.

Here in the question,

Dimensions of the rectangle are as follows:

Length, l = 42m.

Width, w = 28m.

Scale factor here is 1: 5/2

Now,

Let the new width be x.

The new width will be:

28/x = 1/ (5/2)

Cross multiplying:

⇒ 28 × 5/2 = x

⇒ x = 70m.

So, new width = 70m.

Now, let new length be x.

So,

42/x = 1/ (5/2)

Cross multiplying:

⇒ x = 42 × 5/2

⇒ x = 105m.

So, the new length = 105m.

Now new area will be:

70 × 105

= 7350m².

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The correct answer is option c i.e. the value of the function decreases as x approaches positive infinity.

The function g(x) = -4 log(x – 8) has the following features:

a. The domain is x > 8, because the expression x - 8 must be greater than 0 for the logarithm to be defined. Therefore, x must be greater than 8, so the domain is x > 8.

b. is incorrect because the range of the function is y < 0, not y > -8.

c. The value of the function decreases as x approaches positive infinity. As x gets larger and larger, the expression x - 8 gets larger and larger, so log(x - 8) gets larger and larger, approaching infinity. Multiplying by -4 makes the function more and more negative, so the value of the function decreases as x approaches positive infinity.

d. The value of the function does not increase as x approaches positive infinity, because as we just explained, the value of the function actually decreases as x approaches positive infinity. Therefore, option d is not correct.

Therefore, the correct answer is option c

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Answer:

$432.18

Step-by-step explanation:

First year

$1800

-  540

$1260

Second year

$1260

-   378

$882

Third year

$882

- 264.60

$617.40

Fourth year

$617.40

-185.22

$432.18

The total distance that a round trip will cover is 5,600 miles, under the condition that The trip to California from Missouri was 2,800 miles one way.

After considering all the given data induced by the question we come to the state that here we have to apply the principles of multiplication, to evaluate the distance cover when a round trip is taken from California to Missouri.
Then the calculation is

Round trip distance = 2 × one way distance
Round trip distance = 2 × 2,800 miles
Round trip distance = 5,600 miles
Then the distance covered in the couse of making a round trip from California to Missouri is 5,600 miles.
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Answer:

Option B.

Step-by-step explanation:

Angle SOB and Angle VOK are vertical angles, and thus congruent because all vertical angles are congruent.

Lines SB and KV are parallel, cut by the transversal SV, and Angle S and Angle V are Alternate Interior Angles.  So, Angle S and Angle V are congruent by Alternate Interior Angle congruence.

Therefore, Triangle SOB and Triangle VOK are similar by Angle Angle similarity postulate.

It would be more efficient to take the new road from Crimson to Sunshine to get home.

To determine the shortest route home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two sides are the distances you traveled west (6 miles) and south (8 miles).

Using the Pythagorean theorem, we have:

Hypotenuse² = 6² + 8²
Hypotenuse² = 36 + 64
Hypotenuse² = 100
Hypotenuse = √100 = 10 miles

So, the shortest route home (the new road) is 10 miles. If you go back the way you came, you would travel 6 miles west and then 8 miles north, for a total of 14 miles. The longer route (14 miles) is 4 miles longer than the shorter route (10 miles). Therefore, you should take the new road to get home more quickly.

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Emilia make an error in step 3 she didn't use an x and y from the same coordinate pair.

In step 1 : point 1 : (5, 2.15)  point 2 : (12, 3.06)

In step 2 : m = [tex]\frac{12-5}{3.06-2.15}[/tex]

m = 7/0.91

m = 7.69

In Step 3 : y = mx + b

m = slope

Point used by Emilia (2.15 , 5)

But the point should be used be Emilia is (5, 2.15)

2.15 = 5(7.69) + b

b = y intercept

b = -36.3

step 3 is wrong she didn't use right coordinates of x and y

In step 4 : y = mx +b

y = 7.69x -36.3

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The final cost of the basketball, including sales tax, is $15.84.

The problem states that a new basketball costs $22.00, but it is on sale for 40% off. This means that the customer can purchase the basketball at a discount of 40% from its original price of $22.00.

To calculate the amount of discount, we multiply the original price of the basketball by the discount rate as a decimal:

Discount = 0.40 x $22.00 = $8.80

So, the sale price of the basketball would be:

Sale price = $22.00 - $8.80 = $13.20

Next, the problem states that the sales tax is 5%. Sales tax is a percentage of the sale price of the item, and it is added to the sale price to calculate the final cost of the item.

To calculate the amount of sales tax, we multiply the sale price by the sales tax rate as a decimal:

Sales tax = 0.05 x $13.20 = $0.66

Finally, to calculate the final cost of the basketball, we add the sale price and the sales tax:

Final cost = $13.20 + $0.66 = $15.84

Therefore, the final cost of the basketball, including sales tax, is $15.84.

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The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.

Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.

Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).

Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51

Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.

Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)

Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310

So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.

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The tumor was approximately 1.47 grams six months before the first measurement. It would not have been detected by the instrument at that time.

Let M(t) be the mass of the tumor at time t (in months) since the first measurement. Since the rate of growth is proportional to the size of the tumor, we have the differential equation dM/dt = kM, where k is the proportionality constant. The general solution to this differential equation is M(t) = Me^(kt), where M is the initial mass of the tumor.

Using the given data, we have M(0) = 4.0 and M(4) = 6.76. Substituting these values into the equation M(t) = Me^(kt), we get the system of equations M = 4.0 and 6.76 = Me^(4k). Solving for M and k, we get M = 4.0 and k = ln(6.76/4.0)/4 ≈ 0.153. Thus, the equation for the mass of the tumor is M(t) = 4.0e^(0.153t).

To find the mass of the tumor six months before the first measurement (i.e., when t = -6), we plug in t = -6 into the equation M(t) = 4.0e^(0.153t) to get M(-6) ≈ 1.47 grams.

Finally, we check whether the tumor would have been detected at that time. Since the mass of the tumor was less than 1 gram at that time, the instrument would not have detected it.

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To find the other possible vertices of the square, we need to determine the coordinates of the other three vertices. Since we know that the length of each side is 3 units, we can use this information to determine the distance between the given vertex (5, 4) and the other vertices.

First, we can determine the direction of the square by looking at the given vertex and knowing that the sides of a square are equal in length and perpendicular. Since we know that the side length is 3 units, we can move 3 units to the right to find one possible vertex. This gives us the point (8, 4).

Next, we can move 3 units up to find another possible vertex. This gives us the point (5, 7).

Finally, we can move 3 units to the left to find the last possible vertex. This gives us the point (2, 4).

Therefore, the letter that should be circled by all the ordered pairs that could be another vertex is D, which represents the point (2, 4).

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The rate of change between August and October is

Rate is how a quantity changes over a period of time.

Therefore rate = change in quantity/change in time.

For example acceleration is defined as the rate of change of velocity with time. This means that acceleration = change in velocity/time

change in quantity = 85-81 = 4

change in time = 2 months

therefore rate of change = 4/2 = $2 per month

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Answer:

20

Step-by-step explanation:

Answer:

23.50

Step-by-step explanation:

23.4571 rounded of to the nearest tenth 23.4+1

The probability of choosing a student whose name begins with "K" is 40%.

To find the probability of choosing a student whose name begins with "K," P(K name), we need to calculate the ratio of students with "K" names to the total number of students in the prom committee.
There are 10 students in the prom committee: 7 girls (Kelly, Karri, Michela, Raquel, Rara, Nadya, Neesa) and 3 boys (Rio, Elke, Kevin). Out of these, 4 students have names that start with "K": Kelly, Karri, Kevin, and Elke (note that Elke has been mistakenly included in the boys' list, but we'll consider it as a "K" name).

To find the probability, we'll use the formula:
P(K name) = (number of students with "K" names) / (total number of students)
P(K name) = 4 / 10 = 0.4 or 40%
So, the probability of choosing a student whose name begins with "K" is 40%.

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To do this, we first need to factor the denominator of the integrand into linear factors. In this case, the denominator is given as 24 + 16.02 = 40, which is already a factorization. Therefore, we can write:

∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = ∫ [(a/(24 + 16.02)) + (b/(22 + 16))] dx

where a, b are constants that we need to find. To do this, we can use the method of partial fractions, which involves equating the coefficients of like terms on both sides of the equation. Specifically, we can write:

6x3 + 10x2 + 64x + 96 = (a/(24 + 16.02))(22 + 16) + (b/(22 + 16))(24 + 16.02)

Multiplying both sides by the common denominator (24 + 16.02)(22 + 16), we get:

(6x3 + 10x2 + 64x + 96)(24 + 16.02)(22 + 16) = a(22 + 16) + b(24 + 16.02)(24 + 16)

Expanding both sides and collecting like terms, we get a system of two linear equations in two unknowns:

(24 + 16.02)(22 + 16)a + (24 + 16.02)(24 + 16)b = 6(24 + 16.02)(22 + 16) + 10(22 + 16)(24 + 16.02) + 64(24 + 16.02) + 96(22 + 16)

(22 + 16)a + (24 + 16.02)b = 6(22 + 16) + 10(24 + 16.02) + 64 + 96

Solving this system (which involves some algebraic manipulation) gives:

a = -6/5
b = 18/5

Therefore, we can write:

∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = (-6/5) ∫ (22 + 16)/(24 + 16.02) dx + (18/5) ∫ (24 + 16.02)/(22 + 16) dx

To evaluate these integrals, we can use the substitution u = 24 + 16.02 in the first integral and u = 22 + 16 in the second integral. This gives:

∫ (6x3 + 10x2 + 64x + 96)/(24 + 16.02) dx = (-6/5) ln|24 + 16.02| + (18/5) ln|22 + 16| + C

where C is the constant of integration. Finally, using the given expression for the integral, we can equate coefficients of like terms to obtain:

16x3 + 10x2 + 64x + 96 = (6/5)(24 + 16.02) ln|24 + 16.02| - (18/5)(22 + 16) ln|22 + 16| + C

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Both ratios provided by Heather and Allen are correct, they are just inverse.

Heather says that the ratio of bass and violins to cellos is 10 to 5. Allen says the ratio of cellos to bass and violins is 1 to 2. To determine who is correct, let's compare the ratios.

1: Simplify Heather's ratio.

Heather's ratio is 10:5, which can be simplified by dividing both sides by 5. This gives a simplified ratio of 2:1 (bass and violins to cellos).

2: Compare the simplified ratios.

Heather's simplified ratio is 2:1, which represents the ratio of bass and violins to cellos. Allen's ratio is 1:2, which represents the ratio of cellos to bass and violins.

3: Analyze the results.

Heather's ratio (2:1) and Allen's ratio (1:2) are inverses of each other. Both ratios are correct, but they represent different perspectives: Heather is expressing the ratio of bass and violins to cellos, while Allen is expressing the ratio of cellos to bass and violins.

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The simplified expression for p(z), the profit the company earns, in dollars is: p(z) = -3z² + 18z

The set X is known as the domain of the function, and the set Y is known as the codomain of the function. A function from a set X to a set Y assigns each element of X to exactly one element of Y. Originally, functions were an idealization of how one variable depends on another.

First, let's substitute the expressions for r(z) and c(z) in the expression for p(z):

p(z) = r(z) - c(z)

p(z) = 60z - (3z² + 42z)

p(z) = 60z - 3z² - 42z

p(z) = -3z² + 18z

Therefore, the simplified expression for p(z), the profit the company earns, in dollars is:

p(z) = -3z² + 18z

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If the school district surveyed 500 families to see if they were satisfied or not satisfied with the new district website. the maximum number of families who are satisfied with the new district website is approximately 130,771.

First, we need to calculate the confidence level, which is 1 minus the margin of error:

Confidence level = 1 - margin of error

Confidence level = 1 - 0.027

Confidence level = 0.973

Next, we can use the proportion of satisfied families in the sample to estimate the proportion in the population:

Proportion satisfied in population = Proportion satisfied in sample

Proportion satisfied in population = 480/500

Proportion satisfied in population = 0.96

Now we can use this proportion and the confidence level to calculate the maximum number of satisfied families in the population:

Maximum number of satisfied families = Proportion satisfied in population x Total number of families x Confidence level

Maximum number of satisfied families = 0.96 x 140,000 x 0.973

Maximum number of satisfied families ≈ 130,771

Therefore, the maximum number of families who are satisfied with the new district website is approximately 130,771.

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Horseshoe Falls has a flow rate of approximately 2.52 x 10⁷ cubic meters of water per hour, but the given options do not accurately represent this value.

Horseshoe Falls is one of the three waterfalls that make up Niagara Falls near Buffalo, New York. It has an average flow of 7 x 10³ cubic meters per second. To determine the amount of water that goes over Horseshoe Falls hourly, we need to convert the flow rate from cubic meters per second to cubic meters per hour.

There are 3600 seconds in an hour. To convert the flow rate to cubic meters per hour, we simply multiply the flow rate by the number of seconds in an hour:

(7 x 10³ cubic meters/second) x (3600 seconds/hour) = 25.2 x 10⁶ cubic meters/hour

The closest value to this among the given options is:

b. 4.20 x 10⁵ cubic meters per hour

However, there seems to be a typo or error in the provided options. The correct answer should be:

25.2 x 10⁶ cubic meters per hour (approximately 2.52 x 10⁷ cubic meters per hour)

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The value of measure of RU is,

⇒ 149°

We have to given that;

In circle,

m RS = 88 degree

m ST = 35 degree

Hence, We can formulate;

The value of measure of RU is,

⇒ 360° - ( 88° + 35° + 88°)

⇒ 360° - 211°

⇒ 149°

Thus, The value of measure of RU is,

⇒ 149°

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You need to pay $3,243.50 in property taxes.

The appraised value of the house after setting out the homestead exemption is $315,000 - $50,000 = $265,000.

To calculate the assets taxes, we need to multiply the appraised cost by means of the tax rate, which is 1.22% or 0.0122 as a decimal:

property taxes = $265,000 x zero.0122 = $3,243.50

Therefore, you have to pay $3,243.50 in property taxes.

It's far essential to factor in property taxes whilst thinking about the general price of purchasing a home and to recognize the method for applying for exemptions or appealing the appraised cost if necessary.

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37.5% of the students collected between 49 and 98 kilograms of newspapers for the recycling project. Percentage method can be used here.

To answer this question, we need to determine the number of students who collected between 49 and 98 kilograms of newspapers and then calculate what percentage of the total number of students that represents.

First, we need to gather the data and sort it into categories. We can create a frequency table with intervals of 10 kilograms:
Mass Range | Number of Students
   0-9 kg               3
   10-19 kg            5
  20-29 kg           7
  30-39 kg           4
  40-49 kg           6
  50-59 kg           8
  60-69 kg           5
  70-79 kg           2
  80-89 kg           1
  90-99 kg           2

To find the number of students who collected between 49 and 98 kilograms of newspapers, we need to add up the frequencies for the 50-59, 60-69, and 70-79 kg categories. That gives us a total of 15 students.
To calculate the percentage of students who collected between 49 and 98 kilograms of newspapers, we need to divide the number of students in that range by the total number of students and then multiply by 100. In this case, we have 15 students in the range and a total of 40 students overall, so:
15/40 * 100 = 37.5%.

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For function f(x,y) = x² e^{3xy} ,  fx = 2xe^{3xy} + 3x²y e^{3xy}, fy = 3x² e^{3xy}

The given function is f(x,y) = x² e^{3xy}.

To find the partial derivatives of f(x,y) with respect to x and y,

we differentiate the function with respect to each variable while treating the other variable as a constant.

To find fx, we differentiate the function f(x,y) with respect to x while treating y as a constant.

The derivative of x² is 2x, and the derivative of e^{3xy} is e^{3xy} times the derivative of 3xy with respect to x, which is 3y.

Therefore, we get:

fx = (d/dx)(x² e^{3xy}) = 2xe^{3xy} + 3x²y e^{3xy}

To find fy,

we differentiate the function f(x,y) with respect to y while treating x as a constant.

The derivative of e^{3xy} with respect to y is e^{3xy} times the derivative of 3xy with respect to y, which is 3x². Therefore, we get:

fy = (d/dy)(x² e^{3xy}) = 3x² e^{3xy}

Hence, the partial derivatives of f(x,y) are fx = 2xe^{3xy} + 3x^2y e^{3xy} and fy = 3x² e^{3xy}.

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The two letters in which the new point lie include the following: C. between G and H.

In Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

This ultimately implies that, all number lines would primarily increase in numerical value (number) towards the right from zero (0) and decrease in numerical value (number) towards the left from zero (0).

From the number line shown in the image attached below, we can logically deduce the following point:

|J - E| = 45% of x

|J - E| = 0.45x

|J - E| = GH

In conclusion, 45% is almost half way or 50% between E and J, which makes the distance between the two letters G and H, the new point.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Without this information, I cannot evaluate the repeated integral or determine the correct answer choice. Please provide additional information so I can assist you better.

 To evaluate the repeated integral, we must first understand the given question. It appears that some information is missing, making it difficult to provide a complete answer.

Please provide the complete problem statement, including the limits of integration for each variable (x, y, and z). This will allow me to accurately evaluate the repeated integral and provide you with the correct answer.

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The minimum and maximum measurements taken by Joshua is 44.5 inches and 45.5 inches, under the condition that Joshua is building a model airplane that measures 45 inches.

Now in order to find the scale factor necessary to find the minimum and maximum measurements of Joshua's model airplane, we have to apply the given information.
The given information include that the difference in measurements of the model vary by 0. 5 inches.
Therefore,
Minimum measurement = 45 - 0.5 = 44.5 inches
Maximum measurement = 45 + 0.5 = 45.5 inches

Hence, the minimum measurement is 44.5 inches and the maximum measurement is 45.5 inches.

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