Assuming all parabolas are of the form y = ax² + bx + c, drag and drop the graphs to match the appropriate a-value (if necessary).
A -4
a = 4
a = -1​

For fau/cet filter:

For pitcher-filter:

Let's start with the fau/cet model:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $90 - $25

Contribution margin per unit = $65

Contribution margin ratio = contribution margin per unit / selling price

Contribution margin ratio = $65 / $90

Contribution margin ratio = 0.722

The sales mix is 2 faucet models for every 3 pitcher filters sold, so the contribution margin weighted average is:

= (2/5)($65) + (3/5)($90-$20)

= $42

Now we can calculate the break-even point in units for the faucet model:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $42

= 28,571 units

For pitcher filter:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $110 - $20

Contribution margin per unit = $90

Contribution margin ratio = contribution margin per unit / selling price

= $90 / $110

Contribution margin ratio = 0.818

Contribution margin weighted average:

= (2/5)($25) + (3/5)($90-$20)

= $54

Break-even point in units for pitc/her filter:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $54

= 22,222 units

Break-even point in dollars for fau/cet model:

= 28,571 units x $90 per unit

= $2,571,390

Break-even point in dollars for pitc/her-filter:

= 22,222 units x $110 per unit

= $2,444,420

Full question "Multiproduct CVP and decision making. Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcherfilter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcherfilter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.

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A sample size that would give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years is 1,227.

In Mathematics and Statistics, a sample size that would result in a standard deviation of 0.8 years can be calculated by using the mathematical equation (formula):

Sample size, n = (zσ/ME)²

Where:

By assuming a confidence level of 95% with a z-score of 1.96, we would substitute the given parameters into the formula for sample size as follows;

Sample size, n = (zσ/E)²

Sample size, n = (1.96 × 14.3/0.8)²

Sample size, n = (28.028/0.8)²

Sample size, n = (35.035)²

Sample size, n = 1,227.45 ≈ 1,227.

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Complete Question:

Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let [tex]\bar{x}[/tex] be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years?

Round the solution up to the nearest whole number, if necessary.

The best line that represents the relation between the lines that passes through the points (8, 2) and (3, 5) and the line (-3, -7) and (0, -12) is a perpendicular line.

What are perpendicular lines?

In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90 ∘). The term ‘perpendicular’ originated from the Latin word ‘perpendicularis,’ meaning a plumb line. If two lines AB and CD are perpendicular, then we can write them as AB ⊥ CD.

To determine the relationship between the two lines, we can first find the slope of each line using the two-point formula:

Slope of the line passing through (8, 2) and (3, 5):

m1 = (5 - 2) / (3 - 8) = -3/5

Slope of the line passing through (–3, –7) and (0, –12):

m2 = (-12 - (-7)) / (0 - (-3)) = -5/-3 = 5/3

If the two lines are parallel, their slopes will be equal. However, -3/5 is not equal to 5/3. If the two lines are perpendicular, their slopes will be negative reciprocals of each other. That is,

m1 x m2 = -1

But, (-3/5) x (5/3) = -1, which means that the two lines are perpendicular.

Therefore, the correct answer is C. perpendicular.

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We can easily say that the following about this question:

[tex]f(x)=x^2-x+1[/tex]  and  [tex]g(x)=2x+3[/tex]  can be combined as;

Answer:$163.68

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = final amount ($600,000)

P = initial amount (unknown)

r = interest rate (8%)

n = number of times interest is compounded per year (12 for monthly)

t = time in years (25)

Substituting in the values, we get:

$600,000 = P(1 + 0.08/12)^(12*25)

Simplifying:

$600,000 = P(1.00666666666667)^300

Dividing both sides by (1.00666666666667)^300:

P = $600,000 / (1.00666666666667)^300

Using a calculator, we get:

P = $163.68

Therefore, we would need to invest $163.68 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.

a)  The number of units that produces maximum profit is q = 12.

b) The price per unit that produces maximum profit is p = $39.

c)  The maximum profit is P = $386.

What is profit?

a) To find the number of units that produces maximum profit, we need to find the point where revenue equals cost. The revenue function is given by:

R(q) = pq = (63-2q)q = 63q - 2q²

The cost function is given by:

C(q) = 70 + 15q

The profit function is given by:

P(q) = R(q) - C(q) = (63q - 2q²) - (70 + 15q) = -2q² + 48q - 70

To find the number of units that produces maximum profit, we take the derivative of the profit function with respect to q, and set it equal to zero:

P'(q) = -4q + 48 = 0

Solving for q, we get:

q = 12

Therefore, the number of units that produces maximum profit is q = 12.

b) To find the price per unit that produces maximum profit, we substitute q = 12 into the price function:

p = 63 - 2q = 63 - 2(12) = 39

Therefore, the price per unit that produces maximum profit is p = $39.

c) To find the maximum profit, we substitute q = 12 and p = 39 into the profit function:

P = -2q² + 48q - 70 = -2(12)² + 48(12) - 70 = $386

Therefore, the maximum profit is P = $386.

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Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.

Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be 6x.

We then add our number to that, giving us .6x + x

We know the result is 160, so

.6x + x = 160

Since any number multiplied by 1 is itself, that x can be written as 1x.

.6x + 1x = 160

Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).

(.6 + 1)x = 160

1.6x = 160

We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with

x = 160/1.6

x=100

The deli needs to sell the tuna salad at a price of R2.33 per kg to achieve a profit of 40% of the selling price after 5kg spoilage.

A desired profit also known as target profit means expected amount of profit that the managers of a business expect to achieve by the end of a designated accounting period.

First, let's calculate the cost of the tuna salad the deli purchased:

= 45kg x R1.48/kg

= R66.60

How much tuna salad the deli has left after spoilage:

= 45kg - 5kg

= 40kg

To achieve a profit of 40% of the selling price, the selling price should be 140% of the cost price: which is:

= 140% of cost price

= 1.4 x R66.60

= R93.24

To find the price per kilogram, we divide the selling price by the remaining amount of tuna salad:

= Selling price / Remaining amount of tuna salad

= R93.24 / 40kg

= R2.33/kg

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Answer: 6 dolla per kg

Step-by-step explanation:

The maximum profit is $2492.08.

What is the selling price?

The cost a consumer pays to purchase a good or a commodity is known as the selling price. It is a price that is higher than the cost price and includes a profit margin. The cost of an item when acquired is referred to as its selling price (S.P.).

Here, we have

Given: A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation.

y = -3x² + 239x - 2268

At a maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 239

0 = -6x + 239

x = 239/6

x = 39.8

The maximum profit is gotten when the selling price of each widget is 39.8. Hence:

y = -3(39.8)² + 239(39.8) - 2268

y = 2492.08

Hence,  the maximum profit is $2492.08.

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Answer:

Step-by-step explanation:

You want the absolute extremes of f(x) = -x +cos(3πx) in the interval [0, π/6].

The attached graph shows the extremes to be ...

__

Additional comment

The x-value at the minimum is (π+arcsin(1/(3π)))/(3π) ≈ 0.344612473782. The corresponding y-value is about −1.33896758676.

Answer:

[tex]\frac{x^{7} }{y^{10} }[/tex]

The length of the arc that is drawn in a circle of radius 14 cm and angle of arc  135° is approximately 32.67 cm.

An arc is a portion of a curve that is part of a circle. It is defined as a continuous portion of the circumference of a circle. In other words, an arc is a segment of a circle's circumference.

To find the length of an arc of circle, you can use the formula:

arc length = (angle of arc / 360) x (2 x π x radius)

Where π (pi) is a mathematical constant approximately equal to 3.14.

In this problem, the radius of the circle is given as 14 cm and the angle of the arc is 135°. So, By substituting these values in the formula, we get:

arc length = (135/360) x (2 x π x 14)

arc length = (3/8) x (2 x 3.14 x 14)

arc length = (3/8) x (87.92)

arc length = 32.67 cm (rounded to two decimal places)

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Tim's score range would be between 20.2 - 56.25 and 20.2 + 56.25, or between -36.05 and 76.45. To find the percentage of games

a. To find the percentage of candy wrappers that would have between 3.4 and 3.6 ounces, we need to calculate the z-scores for each of the values:

[tex]z-score for 3.4 ounces = (3.4 - 3.5) / 0.16 = -0.625[/tex]

[tex]z-score for 3.6 ounces = (3.6 - 3.5) / 0.16 = 0.625[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers between these two values is approximately 47.70%.

b. To find the percentage of candy wrappers that would have less than 3.3 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.3 ounces = (3.3 - 3.5) / 0.16 = -1.25[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with less than 3.3 ounces is approximately 10.92%.

To find the percentage of candy wrappers with more than 3.62 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.62 ounces = (3.62 - 3.5) / 0.16 = 0.75[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with more than 3.62 ounces is approximately 22.77%.

c. To find how many of the 1358 packets made that day have between 3.35 and 3.65 ounces, we need to convert these values to z-scores:

[tex]z-score for 3.35 ounces = (3.35 - 3.5) / 0.16 = -0.9375[/tex]

[tex]z-score for 3.65 ounces = (3.65 - 3.5) / 0.16 = 0.9375[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of candy wrappers between these two values, which is approximately 62.97%. To find how many packets this represents, we can multiply this percentage by the total number of packets made:

[tex]0.6297 * 1358 = 856 packets[/tex]

Therefore, approximately 856 packets made that day have between 3.35 and 3.65 ounces.

d. To find how many games Tim would have scored 22 points or more if he plays 32 games, we first need to calculate the z-score for this value:

[tex]z-score for 22 points = (22 - 20.2) / 25 = 0.072[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of games with a z-score greater than or equal to 0.072, which is approximately 53.10%. To find how many games this represents, we can multiply this percentage by the total number of games:

[tex]0.5310 x 32 = 17 games[/tex]

Therefore, Tim would have scored 22 points or more in approximately 17 games out of 32.

e. To find how many games Tim would have scored within 2.25 standard deviations from his average if he plays 32 games, we first need to calculate 2.25 standard deviations:

[tex]2.25 x 25 = 56.25[/tex]

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According to the solving time will they take together to wax the same car 16 minutes

The minute is a unit of time usually equal to 160 (the first sexagesimal fraction) of an hour, or 60 seconds.

Let's assume that Andrea takes x minutes to wax the car. Then Mathew takes x/2 minutes to wax the same car since he waxes twice as fast as Andrea.

We know that Andrea takes 24 minutes to wax the car. So we can substitute this value in the equation and solve for x.

x = 24 * 2 = 48

So Andrea takes 48 minutes to wax the car alone.

Now we can use the formula:

1/x + 1/(x/2) = 1/t

where t is the time taken by both of them together to wax the same car.

Substituting x = 48, we get:

1/48 + 1/24 = 1/t

Solving for t, we get:

t = 16minutes

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Answer:

60.5

Step-by-step explanation:

Answer: 60.50

Step-by-step explanation:

.

After answering the provided question, we can conclude that So the total  equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x^2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call Sarah's reading time "r" in minutes.

We can deduce from the problem:

Sarah painted for 5 minutes.

Because she spent twice as much time reading as she did painting,[tex]r = 2*5 = 10.[/tex]

She hiked for 35 minutes longer than she read, so [tex]h = r + 35.[/tex]

To calculate Sarah's total time spent on these three activities, simply add the times:

Time spent painting + time spent reading + time spent hiking = total time

Time total =[tex]5 + 10 + (r + 35)[/tex]

Time total = [tex]50 + r[/tex]

So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.

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Answer: x = -1 and y = 9

Step-by-step explanation:

To solve this system of equations, we can use the substitution method.

First, solve the first equation for y:

y = -x + 8

Now, substitute this expression for y into the second equation and solve for x:

4x + y = 5

4x + (-x + 8) = 5 (substituting -x + 8 for y)

3x + 8 = 5

3x = -3

x = -1

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

y = -x + 8

y = -(-1) + 8

y = 9

Therefore, the solution to the system of equations is x = -1 and y = 9.

This transformation of figure 1  has been transformed to produce figure 2, can be described by (x' , y') = (x' -y')

Transformation describes how an item moves, particularly as they are shown on a coordinate plane.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or position. The four methods comprise

Pre-Image refers to the item's shape before transformation, whereas Image refers to the object's ultimate location and shape.

The linked image's preimage and image may be examined to determine that reflection is the involved translation.

The transformation rule for reflection over the y-axis is as follows:

(x, y) → (x, -y)

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Answer:

Step-by-step explanation:

P(x)=x³+6x²+3x-10=0

x³+2x²+4x²+8x-5x-10=0

x²(x+2)+x(x+2)-5(x+2)=0

(x+2)(x²+x-5)=0

either x+2=0,x=-2

or

x²+x-5=0

[tex]x=\frac{-1 \pm \sqrt{1^2-4 \times 1 \times(-5)} }{2 \times 1} \\=\frac{-1 \pm \sqrt{21} }{2} \\Hence ~x=\frac{-1+\sqrt{21} }{2} \\or\\x=\frac{-1 -\sqrt{21} }{2}[/tex]

Answer:

Thank you for the statement. Is there a question or additional information you would like me to respond to?

Step-by-step explanation:

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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Answer:

y = [tex]\frac{1}{3}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x - 10 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (9, - 2 ) into the partial equation

- 2 = [tex]\frac{1}{3}[/tex] (9) + c = 3 + c ( subtract 3 from both sides )

- 5 = c

y = [tex]\frac{1}{3}[/tex] x - 5 ← equation of perpendicular line

The nearest cent, the amount of money in the account after 13 years is $2,094.18.

The formula for continuous compound interest is:

V = Pe^(rt)

where V is the value of the account after t years, P is the principal (initial amount) invested, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time period in years.

In this case, P = $741, r = 0.058 (since the annual interest rate is 5.8%), and t = 13. Substituting these values into the formula, we get:

V = 741e^(0.058*13)

Using a calculator, we can evaluate e^(0.058*13) to be approximately 2.8302. Then, we can multiply this value by 741 to get:

V = 741*2.8302

V ≈ $2,094.18

Therefore, to the nearest cent, the amount of money in the account after 13 years is $2,094.18.

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Hypothesis Testing ,Sample data  , Categorical  ,one variable ,one sample and sample z test for a proportion are the  responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.

(a) The question type in this study is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(b) The study type is sample data, as a sample of adult Americans was surveyed to learn about the population of adults who self-identify as entrepreneurs.

(c) The data is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(d) There is one variable in this study, as the responses to the question about self-identification as an entrepreneur are the only data collected.

(e) There is one sample in this study, as only one group of adult Americans was surveyed.

(f) The appropriate method for analyzing the data in this study is the one-sample z test for a proportion. This method is used when we have one categorical variable and want to test whether the proportion of a certain response differs significantly from a hypothesized proportion. In this case, the hypothesized proportion would be the proportion of adult Americans who self-identify as entrepreneurs. We would use the z-test to determine if the proportion of respondents who self-identify as entrepreneurs is significantly different from the hypothesized proportion. If the difference is significant, we can conclude that there is a difference between the sample and population proportions, and if the difference is not significant, we cannot reject the null hypothesis that the sample proportion is the same as the population proportion.

Overall, this study is using categorical data to learn about the proportion of adult Americans who self-identify as entrepreneurs. The appropriate method for analyzing this type of data is the one-sample z test for a proportion, which allows us to test whether the sample proportion is significantly different from the hypothesized population proportion.

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Answer:

a) 30 × .5 = 15 days

b) .2 + .1 = .3

Answer:

Step-by-step explanation:

Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to express the result as a percentage.

The difference between the original price and the new price is:

990 - 765 = 225

Dividing the difference by the original price gives:

225 ÷ 990 ≈ 0.227

Multiplying by 100 gives:

0.227 x 100 ≈ 22.7

Therefore, the percentage decrease in the monthly price of the contract is approximately 22.7%.

Step-by-step explanation: