=
For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per
unit that produces maximum profit; and c) the maximum profit, P.
C(q) = 70+ 15q; p=63-2q
a) The number, q, of units that produces maximum profit is q =
b) The price, p, per unit that produces maximum profit is p = $
c) The maximum profit is P = $

Answer: 57

It won't let me show the steps, since I've already edited my answer once...

The shaded area above the line y = -x + 3 and below the line -2x + y = -1 is the solution region of the system that is option A.

A graph is a visual representation of data or mathematical concepts. It is a diagram that shows how variables or quantities relate to each other, often using points, lines, bars, or other symbols. In mathematics, a graph can be used to represent a set of points or a function, where the x-axis represents the input values and the y-axis represents the output values. A graph can show the shape of a function, its range, its domain, and other important features.

Here,

To graph the system, we can first graph the boundary lines of the two inequalities.

For the first inequality, y > -x + 3, we can draw the line y = -x + 3 and shade the area above the line. This is because the inequality is y > -x + 3, which means that all points above the line satisfy the inequality.

Next, for the second inequality, -2x + y < -1, we can draw the line -2x + y = -1 and shade the area below the line. This is because the inequality is -2x + y < -1, which means that all points below the line satisfy the inequality.

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Answer:

One-third cup of water is equivalent to approximately 2.67 ounces (8 ounces divided by 3).

Here is a bar diagram to illustrate this:

|

|

|

|

|

|

|

|______

2.67 oz

In this diagram, the vertical line represents the total amount of water in the cup (8 ounces), and the shaded portion represents the 1/3 cup of water needed for the recipe, which is approximately 2.67 ounces.

Answer:

1/3 cup is approximately equal to 2.67 ounces

Explanation:

In cooking and baking, recipes often use measurements that are different from the standard units of measurement used in daily life. One such measurement is the cup, commonly used to measure liquids like water, milk, and oil. A cup of water typically equals 8 fluid ounces in the United States.

If a recipe calls for 1/3 cup of water, we need to convert this measurement into ounces to know how much water is needed. To do this, we can use the fact that 1 cup is equal to 8 ounces.

To convert 1/3 cup to ounces, we can multiply the number of cups by the number of ounces in one cup. That is:

1/3 cup * 8 ounces/cup = 8/3 ounces

However, 8/3 ounces is not a convenient number to work with, so we need to round it to a more practical value. One reasonable approximation for 8/3 is 2.67. Therefore, we can say that 1/3 cup equals approximately 2.67 ounces.

This approximation is reasonable because it is close to the exact value of 8/3 ounces. Using 2.67 ounces as an estimate for 1/3 cup of water in a recipe should provide a good approximation of the water needed.

Answer:

Step-by-step explanation:

The general equation for a sinusoidal function of the form y = a sin b(x + c) + d is:

a is the amplitude (the maximum displacement from the midline).

b determines the period (the distance between two consecutive peaks or troughs).

c is the horizontal shift (the amount by which the graph is shifted horizontally).

d is the vertical shift (the amount by which the graph is shifted vertically).

From the given information, we can see that:

The amplitude is not given.

b = 3, which means the period is 2π/3.

c = 6, which means the graph is shifted 6 units to the left.

d = 9, which means the graph is shifted 9 units up.

Since the amplitude is not given, we need to look at the graph to determine it. However, the graph is not provided, so we cannot determine the amplitude with the given information.

Answer:

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

The total cost is the cost for a can of gas plus rental cost per number of hours.

So the total cost is:

The length of line BC as shown in the diagram below is 5√3.

Length is the distance between two points.

To calculate the length of Line BC, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, BC is 5√3.

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Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.

What is meant by events?

In probability theory, an event is a set of outcomes or results that can occur when performing a random experiment. An event can consist of a single outcome or multiple outcomes, and it is defined as a subset of the sample space of the random experiment.

1.Rolling a dice and flipping a coin are two independent events. The probability of rolling any particular number on a dice is 1/6, and the probability of flipping heads on a coin is 1/2. Since the outcome of rolling a dice does not affect the outcome of flipping a coin and vice versa, these events are considered independent.

2.Spinning two spinners each round are independent events. The probability of each spinner landing on a particular section is fixed, and the outcome of one spinner does not affect the outcome of the other spinner. Therefore, these events are considered independent. The probability of the first spinner landing on a specific section and the second spinner landing on another specific section at the same time is the product of their individual probabilities.

3.Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. In the beginning, there are 12 S tiles and 9 M tiles in the bag. The probability of drawing an S tile is initially 12/21 or 4/7. If an S tile is drawn first, the number of S tiles in the bag decreases to 11, and the probability of drawing an M tile on the second draw becomes 9/20. Therefore, the probability of drawing an S tile and then an M tile is (4/7) x (9/20) = 18/70 = 9/35.

4.Pulling a candy, eating it, and then pulling another out of a bag are dependent events. Initially, there are a certain number of candies in the bag. After one candy is drawn and eaten, the number of candies in the bag decreases, affecting the probability of drawing a specific candy on the second draw. Therefore, these events are considered dependent.

Therefore, Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.

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Answer:

divide figure in many parts.

Then, find volume of each divided figure :- v= l*b*h

Then add volume of all divided figure

Answer: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8

Step-by-step explanation:

Answer:

p-(p*.2274)

Step-by-step explanation:

P is the original price

P multiplied by .2274 gives the discount that's taken off

So the answer is P minus the discounted sum

Two parallel lines have the same slope, so we need to find the slope of the first line y = (1/4)x - 2, and then use it to find the equation of the parallel line that passes through (4, -2).

The slope of the first line is 1/4, so the slope of the parallel line will also be 1/4.

Using the point-slope form of the equation, we can write the equation of the parallel line as:

y - (-2) = (1/4)(x - 4)

Simplifying this equation, we get:

y + 2 = (1/4)x - 1

Subtracting 2 from both sides, we get:

y = (1/4)x - 3

Therefore, the equation of the line that is parallel to y = (1/4)x - 2 and passes through (4, -2) is y = (1/4)x - 3, which is option D.

The company should use the following values: Price per unit = $1,445; Variable costs per unit = $552; Fixed costs = $4.715 million ; Quantity = 95,000 units.

In algebra, a symbol (typically a letter) is used to represent an undetermined quantitative score in an expression or algebraic expression. Simply put, a variable is a number that may be changed yet remains fixed. Categorical and numeric variables are the two main types of variables. Then, discrete or continuous categories are made for each category for numerical and categorical variables, respectively. An overview of various types is given in this section. a metric that has a wide range of possible values. Something that can change; a variable's sign; an element of a science experiment that could vary.

To perform a best-case and worst-case scenario analysis, we need to adjust the estimates for each variable based on the given percentage error of 15%.

Best-case scenario analysis:

Price per unit = $1,700 + (15% x $1,700) = $1,955

Variable costs per unit = $480 - (15% x $480) = $408

Fixed costs = $4.1 million - (15% x $4.1 million) = $3.485 million

Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)

Worst-case scenario analysis:

Price per unit = $1,700 - (15% x $1,700) = $1,445

Variable costs per unit = $480 + (15% x $480) = $552

Fixed costs = $4.1 million + (15% x $4.1 million) = $4.715 million

Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)

Therefore, for the best-case scenario, the company should use the following values:

Price per unit = $1,955

Variable costs per unit = $408

Fixed costs = $3.485 million

Quantity = 95,000 units

And for the worst-case scenario, the company should use the following values:

Price per unit = $1,445

Variable costs per unit = $552

Fixed costs = $4.715 million

Quantity = 95,000 units

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Answer:

see the attachment

Step-by-step explanation:

The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.

The absolute deviation is a measure that quantifies the average deviation of data points from a central point, which can be any point in the data set such as the mean, median, or mode.

Typically, the mean is used as the central point. The formula to calculate the mean absolute deviation (MAD) involves finding the average of the absolute deviation (distance) of each data point from the mean of the data set.  

Here we have

Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches

In this situation, the MAD of 2.4 inches means that on average, the stem length of each tomato plant deviated from the mean stem length of 8 inches by 2.4 inches.

Therefore,

The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.

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Using the length of the arc formula we get the arc's length to be 57.33rad.

The following formulas can be used to determine a circle's arc length: Arc Length = r, where r is the radius of the circle and is the central angle that the arc subtends.

When is expressed in radians, this formula is employed. Arc Length is equal to (/180) r, where r is the radius of the circle and is the central angle that the arc subtends.

In the question,

Radius of the circle = 11ft.

Angle created by the arc = 300°.

We need the length of the arc.

Length of the arc = S= 2πr×(θ/360) °

S = 2 × 3.14 × 11 × 300/360

= 57.33 rad

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Answer:

7 workers are required, so we need 7-3 or 4 more workers.  

Step-by-step explanation:

Answer:

X = 35°

Y = 72.5°

Step-by-step explanation:

x is vertically opposite to 35° so x = 35°

35 × 2 = 70

360 - 70 = 290

290 / 4 = 72.5

Y = 72.5°

Answer:

x = 35

y = 72.5

Step-by-step explanation:

At your level, it is assumed that those lines are straight. Keeping this in mind, we can find the answer to this problem.

First, we have to find x.

x = 35º because opposite angles are equal (xº is opposite to 35º).

Then, we have to calculate y.

You should know that angles in a straight line add up to 180º.

So: yº + yº + 35º = 180º

You know have to solve this equation (solve for y).

y + y + 35 = 180

y + y = 180 - 35

y + y = 145

2y = 145

y = 145 / 2

y = 72.5

Check: 72.5 + 72.5 + 35 = 180

Answer:

√17 good luck

Step-by-step explanation:

The function c(x) = √x is a continuous and increasing function over the interval [0, ∞), which means that its minimum and maximum values on the given domain interval [1/121, 17] will occur at its endpoints.

At x = 1/121, we have c(1/121) = √(1/121) = 1/11.

At x = 17, we have c(17) = √17.

Therefore, the minimum value of c(x) on the given domain interval is 1/11, and the maximum value is √17.

Setting x = 0, we get the y-intercept: y = 31/5. So, the equation of the line is y = 6/5x + 31/5.

In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.

by the question.

To find different y-intercepts using the given slopes, we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. To find the y-intercept, we can set x = 0 and solve for y.

For slope 1/5, let's choose the point (2, 3) on the line. Using the point-slope form, we get:

y - 3 = 1/5(x - 2)

y - 3 = 1/5x - 2/5

y = 1/5x + 13/5

Setting x = 0, we get the y-intercept: y = 13/5. So, the equation of the line is y = 1/5x + 13/5.

For slope 3/5, let's choose the point (4, 2) on the line. Using the point-slope form, we get:

y - 2 = 3/5(x - 4)

y - 2 = 3/5x - 12/5

y = 3/5x + 8/5

Setting x = 0, we get the y-intercept: y = 8/5. So, the equation of the line is y = 3/5x + 8/5.

For slope 6/5, let's choose the point (-1, 5) on the line. Using the point-slope form, we get:

y - 5 = 6/5(x + 1)

y - 5 = 6/5x + 6/5

y = 6/5x + 31/5

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Noah is consistently adding 0.5 gallons of water every minute to a tank. 2 minutes are spent filling a gallon.

The rate of filling is the amount of water that is filled per unit of time. In this instance, Noah is consistently adding 0.5 gallons of water each minute to the tank.

To determine the rate of filling in minutes per gallon, we can simply take the reciprocal of the rate of filling in gallons per minute.

That is:

Rate of filling in minutes per gallon = 1 / Rate of filling in gallons per minute

So, the rate of filling in minutes per gallon is:

1 / 0.5 gallons per minute = 2 minutes per gallon

Therefore, Noah is filling the tank at a rate of 2 minutes per gallon.

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Answer:

240°

Step-by-step explanation:

A full rotation is 360°

2/3 x 360 = 240

Helping in the name of Jesus.

Option A : The lines that best approximate the directrices of the ellipse are x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

The directrices of an ellipse are lines that are equidistant from the two foci. In this case, the foci of the ellipse are located at (-5,0) and (5,0). The distance between the foci is 2c, where c is the distance from the center to a focus, and can be found using the equation [tex]c^2 = a^2 - b^2[/tex], where a and b are the lengths of the major and minor axes, respectively.

From the given diagram, we can see that the length of the major axis is 10 and the length of the minor axis is 8. Therefore, a = 5 and b = 4. The value of c can be found as follows:

[tex]c^2 = a^2 - b^2[/tex]

[tex]c^2 = 5^2 - 4^2[/tex]

[tex]c^2 = 9[/tex]

c = 3

Therefore, the directrices are the vertical lines that pass through (-5,-3) and (5,-3) and are equidistant from the foci. These lines are given by x = -5 and x = 5.

Therefore, the lines that best approximate the directrices of the ellipse are A. x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.

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Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.

A. x= -4.6 and x = 4.6

B. x = -3.5 and x = 3.5

C. y=-4.6 and y = 4.6

D. y = -3.5 and y = 3.5

Answer:

hope this helps

Step-by-step explanation:

Answer:

b-4/5×2 =g

Step-by-step explanation:

if u wrote down the equation correctly

The simple interest on a deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016 is given as follows:

$7.4.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

The interest accrued is modeled as follows:

I(t) = Prt.

The parameter values for this problem are given as follows:

Then the interest accrued is given as follows:

I = 365 x 0.1 x 74/365

I = $7.4.

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We can use the proportion of people carrying bags from the sample of 50 people to estimate the number of visitors who purchased something out of the total 4,800 visitors to the mall.

The proportion of people carrying bags in the sample is:

37/50 = 0.74

This means that 74% of the sample of 50 people were carrying bags.

To estimate the number of visitors who purchased something out of the total 4,800 visitors, we can multiply the proportion by the total number of visitors:

0.74 x 4,800 = 3,552

Therefore, we can predict that approximately 3,552 visitors out of the total 4,800 visitors purchased something on that day.

The answer of the given question is (a)  95% of the sample means will fall within the interval from 0.9448 to 0.9512. (b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35.  (c)  We used the central limit theorem to answer part (b).

The central limit theorem is a fundamental concept in statistics that states that for a sufficiently large sample size, the distribution of the sample mean will be approximately normal, regardless of the distribution of the population from which the sample is drawn. This means that if we take repeated random samples from a population, the distribution of the means of those samples will approach a normal distribution, even if the population itself is not normally distributed.

(a) We can use the formula for the confidence interval of a mean:

σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.

Substituting the given values, we get:

CI = 0.9480 ± 1.96*(0.0060/√35)

CI = (0.9448, 0.9512)

Therefore, 95% of the sample means will fall within the interval from 0.9448 to 0.9512.

(b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. This is because the central limit theorem states that for a sufficiently large sample size (n[tex]\geq[/tex]30), the sampling distribution of the sample mean will be approximately normal, regardless of the distribution of the population.

(c) We used the central limit theorem to answer part (b).

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Answer:

The total number of gallons of milk sold is equal to the total number of gallons of orange juice sold. This is because there are 2 quarts in a half-gallon, so the 14 half-gallon containers of milk sold is equal to 28 quarts. Therefore, the total amount of milk sold is the same as the total amount of orange juice sold, which is 28 gallons.

The slope of the line on this graph with points (2, 5) and (4, 4) is equal to: D. =1/2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - 4)/(2 - 4)

Slope (m) = -1/2

In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to -0.5 or -1/2.

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