The demand d for a company’s product at cost x is predicted by the function d(x) = 500 – 2x. The price p in dollars that the company can charge for the product is given by p(x) = x + 5. Use the formula Revenue = price × demand to find the revenue function for the product.

The expression to simplify is

We will simplify by combining like terms.

• There are FIVE x's and TWENTY-SIX more x's. We add.

5x + 26x = 31 x

• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.

•

• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.

The final expression is

Answer:

209.43951 round to the nearest tenth is 209.44

Step-by-step explanation:

A cone with a base radius of 5 units and a height of 8 units has a volume of 209.44 cubed units.

If a cone has a flat bottom, meaning the height and radius meet at right angles, then this formula can be used to find of volume ('V') of that cone (also know as a right circular cone):

V = 1/3(PI*r squared * h )

The volume of a cone can be calculated by taking one-third of the result of the radius squared, multiplied by the height, multiplied by the mathematical constant pi.

Here is a step-by-step case that illustrates how to find to volume of a cone with a radius of 2 feet and a height of 3 feet. Note that in order to save space (and because pi cannot be determine precisely) a limited number of decimal places are used, the symbol ~ denotes that this answer is an approximation.

V = 1/3(pi * r^2 * h)

= 1/3(pi * 2^2 * 3)

= 1/3(pi * 12)

= 1/3(37.7)

~ 12.6 cubic feet

Hope this helps!!

If the data collection contains the given following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87 , Here 1 and 87 represents the outlier.

The important characteristics of the Statistics that are given as follows:

Statistics have always been numerically expressed.

For instance, if the data collection contains the following numbers: 1, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 87

The display of all data and outliers

The numbers 1 and 87, which are at the extreme and are hence outliers in the number line above, may be seen to be at these extremes.

The group outliers are a part of it, but they are not always close to the other group members.

Outliers are a concern as they cause an imbalance in the data set, which is why they are typically eliminated. Furthermore, an error can sometimes cause an outlier to appear in a data collection.

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Answer:

Step-by-step explanation:

Answer:

a. 4

b. -7

c. -7y+3x+9

Step-by-step explanation:

A. Okay well 5x, 9, -2x, and -7y are the 4 terms.

B. The coefficient (meaning the number attached to the y) is -7

C. Simplified would be finding the common variables; 5x and -2x. Subtract and you get 3x. You can't combine any more of your terms so you are left with -7y+3x+9

Answer:

the aanswer is 1

Step-by-step explanation:

Answer:

5.0 m/s

Step-by-step explanation:

The average speed is 5.0 m/s.

The distance covered in a unit of time is known as speed.

Given that, Sarah ran 400 m in 80 s.

The formula for the speed is:

speed = distance/time

Substitute distance = 400 m and time = 80 s into the above equation:

speed = 400/80

speed = 5.0 m/s.

Hence, the average speed is 5.0 m/s.

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True . In this distribution, the mean salary is lower than the median salary because the few employees who earn a very high salary pull the mean towards the left.

In a left-skewed distribution, the tail of the distribution is longer on the left-hand side, which means that there are more values on the left side of the distribution that are lower than the mean. This pulls the mean towards the left, making it lower than the median. Therefore, the median tends to be higher than the mean in a left-skewed distribution.

When we talk about the shape of a distribution, we refer to the way in which the values are spread out across the range of the variable. A left-skewed distribution is one in which the tail of the distribution is longer on the left-hand side, which means that there are more values on the left side of the distribution that are lower than the mean. The mean is the sum of all values divided by the number of values, while the median is the middle value of the distribution. In a left-skewed distribution, the mean is pulled towards the left, making it lower than the median. This happens because the more extreme values on the left side of the distribution have a larger impact on the mean than they do on the median.

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The probability that a person who tested positive for HIV actually has the virus is approximately 13.2%.

To determine the likelihood that a person who tested positive for HIV actually has the virus, we can use Bayes' theorem:

P(HIV|+) = P(+|HIV) * P(HIV) / [P(+|HIV) * P(HIV) + P(+|not HIV) * P(not HIV)]

where:

P(HIV|+) is the probability of having HIV given a positive test result

P(+|HIV) is the probability of testing positive given that the person has HIV (95%)

P(HIV) is the prevalence of HIV in the population (0.008)

P(+|not HIV) is the probability of testing positive given that the person does not have HIV (5%)

P(not HIV) is the complement of the prevalence of HIV (1 - 0.008 = 0.992)

Plugging in the values, we get:

P(HIV|+) = 0.95 * 0.008 / [0.95 * 0.008 + 0.05 * 0.992] = 0.132

Therefore, the probability that a person who tested positive for HIV actually has the virus is approximately 13.2%. This means that there is an 86.8% chance that the person who tested positive does not have HIV. It is important to note that this calculation only provides an estimate of the probability and should not be used as a definitive diagnosis. Further testing and evaluation by a healthcare professional is necessary to confirm whether or not a person has HIV.

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Where a and b are determined by the value of D.

A parabola is a type of graph, or curve, that is represented by an equation of the form y = ax² + bx + c. The vertex of a parabola is the point where the curve reaches its maximum or minimum point, depending on the direction of the opening of the parabola. In this case, the vertex of the parabola is at (-4,-1).
To find the equation of the parabola, we need to know two more points on the graph. We are given that when the y-value is 0, the x-value is 10-D. We can use this information to find another point on the graph.
When the y-value is 0, we have:
0 = a(10-D)² + b(10-D) + c
Simplifying this equation gives:
0 = 100a - 20aD + aD² + 10b - bD + c
Since the vertex is at (-4,-1), we know that:
-1 = a(-4)² + b(-4) + c
Simplifying this equation gives:
-1 = 16a - 4b + c
We now have two equations with three unknowns (a,b,c). To solve for these variables, we need one more point on the graph. Let's use the point (0,-5) as our third point.
When x = 0, y = -5:
-5 = a(0)² + b(0) + c
Simplifying this equation gives:
-5 = c
We can now substitute this value for c into the other two equations to get:
0 = 100a - 20aD + aD² + 10b - bD - 5
-1 = 16a - 4b - 5
Simplifying these equations gives:
100a - 20aD + aD² + 10b - bD = 5
16a - 4b = 4
We now have two equations with two unknowns (a,b). We can solve for these variables by using substitution or elimination. For example, we can solve for b in the second equation and substitute it into the first equation:
16a - 4b = 4
b = 4a - 1
100a - 20aD + aD² + 10(4a-1) - D(4a-1) = 5
Simplifying this equation gives:
aD² - 20aD - 391a + 391 = 0
We can now use the quadratic formula to solve for D:

D = [20 ± sqrt(20² - 4(a)(391a-391))]/2a
D = [20 ± sqrt(400 - 1564a² + 1564a)]/2a
D = 10 ± sqrt(100 - 391a² + 391a)/a
There are two possible values for D, depending on the value of a. However, since we don't have any information about the sign of a, we cannot determine which value of D is correct. Therefore, the final equation of the parabola is:
y = ax² + bx - 5

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The confidence level used for the margin of error was 95%.

The margin of error (MOE) is calculated by dividing the critical value (z*) of the confidence level by the square root of the sample size (n). For a 95% confidence level, the critical value (z*) is 1.96. MOE = 1.96 / sqrt(350) = 4.382% Therefore, the confidence level used for the margin of error was 95%. To calculate the margin of error, we must first determine the confidence level. For a 95% confidence level, the critical value (z*) is 1.96. The margin of error (MOE) is then calculated by dividing the critical value (z*) by the square root of the sample size (n). In this case, the MOE is 1.96 / sqrt(350) = 4.382%. This means that the confidence level used for the margin of error was 95%.

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Given the vertices of a triangle as A(1, 0, -1), B(3, -2, 0), and C(1, 5, 5), we are asked to find the three angles of the triangle.

The angles are measured in radians and are given as follows: ∠CAB = 1.742 radians, ∠LABC = 1.058 radians, and ∠LBCA = 0.341 radians.

To find the angles of a triangle with given vertices, we can use the dot product and cross product of the sides of the triangle. The dot product formula allows us to find the angle between two vectors, while the cross product provides the area of the parallelogram formed by those vectors.

First, we find the vectors AB and AC by subtracting the coordinates of point A from points B and C, respectively. Then, we calculate the magnitudes of these vectors.

Next, we find the dot product of AB and AC, which is equal to the product of their magnitudes multiplied by the cosine of the angle between them. Using the dot product formula, we can solve for the cosine of each angle.

Finally, we use the inverse cosine function (or arc cosine) to find the angles. The angles are typically given in radians, so we round them to the nearest degree.

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Answer:

Step-by-step explanation:

the answer is 25x^2-40x+16

25x^2-40x+16 is equivalent to (5x - 4)^2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

(5x - 4)^2

we know,

(a-b)^2= a^2-2ab+b^2

by using this, we get,

(5x - 4)^2

=5x*5x-2*5x*4+4*4

=25x^2-40x+16.

Hence, 25x^2-40x+16 is equivalent to (5x - 4)^2.

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In a skewed distribution, the median can be precisely located on the graph without doing any calculations.

So, the correct answer is E.

The median represents the middle value in the data set, separating the distribution into two equal parts. Unlike the mean, it is not affected by extreme values, making it a more accurate representation of central tendency for skewed distributions. The mode, which indicates the most frequent value, can also be identified on the graph.

However, variance and standard deviation, both measures of dispersion, require calculations to be determined and cannot be precisely located on the graph without additional information.

Hence, the answer of the question is E.

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The set that we must describe is composed of those which are at least 6.5. At least means that these values are either 6.5 or greater. Then if n is any element of this set it meets the following condition:

Then the answer is the first option.

Answer:

A

Step-by-step explanation:

The terms in the function are increasing by 8, so that's the slope. If that's true, then you would have to subtract 8 from 10 to find the y-intercept. That would be -18.

Hope this helps :)

Answer:

You convert the fractions to a decimal, nut the rest is still the same

Step-by-step explanation:

The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length

Based on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.

The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.

Using the Pythagorean theorem, we can calculate the length of this diagonal as:

sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches

So Yeidalis needs a board that is at least 15 inches long to create her artwork.

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The first year in which the taxpayer could receive a qualified distribution from the Roth IRA would be 2022.

To determine this, we need to look at the five-year rule for Roth IRA distributions. This rule states that a taxpayer must wait five years from the year of their first contribution to a Roth IRA before they can take a qualified distribution (i.e., a tax-free distribution of earnings and contributions).

Since the taxpayer made their first contribution for the 2018 tax year, the five-year clock starts on January 1, 2018. Therefore, the earliest year in which they could receive a qualified distribution is 2022.

It is important to note that there are other rules and exceptions that could affect when a taxpayer can take distributions from a Roth IRA,

such as age and disability, and that tax implications should also be considered when making decisions about Roth IRA contributions and distributions.

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Answer:

y = 7/5x + -1

Step-by-step explanation:

First let's find the slope. To do that you find the difference between the given coordinate points. The slope I got was 7/5.

Then plug in the x and y values in the formula y = mx + b

6 = 7/5(5) + b

6 = 7 + b

-1 = b

If the y-intercept (b) is -1 we can complete the equation now.

y = 7/5x + -1

Hope that helps and have a great day!

Therefore, the cost of 3 pencils is approximately $1.80.

To find the cost of 3 pencils, we can set up a proportion based on the given information:

7 pencils cost $4.20

Let's assign the cost of 3 pencils as x dollars.

The proportion can be set up as: 7 pencils / $4.20 = 3 pencils / x

To solve for x, we can cross-multiply: 7 * x = 3 * $4.20

7x = $12.60

Dividing both sides of the equation by 7:

x = $12.60 / 7

x ≈ $1.80

Therefore, the cost of 3 pencils is approximately $1.80.

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Answer:  \(y < -\frac{1}{2}x+3\)

This is the same as writing y < (-1/2)x+3

==============================================================

Explanation:

The dashed boundary line goes through (0,3) and (4,1)

Apply the slope formula for those two points

m = (y2-y1)/(x2-x1)

m = (1-3)/(4-0)

m = -2/4

m = -1/2

The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing \(y = -\frac{1}{2}x+3\)

We shade below the dashed line to represent the inequality \(y < -\frac{1}{2}x+3\). Points in the shaded region are solutions to the inequality. One example point is (0,0).

Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.

Following the 5-step FDR (Function Design Recipe), here is the implementation of the area_cylinder function in MATLAB:

% Step 1: Problem Analysis

% The problem is to calculate the of a cylinder given its radius and height.

% Step 2: Specification

function area = area_cylinder(radius, height)

% area_cylinder calculates the area of a cylinder

%   Inputs:

%       - radius: the radius of the cylinder base

%       - height: the height of the cylinder

%   Output:

%       - area: the area of the cylinder

% Step 3: Examples

% Example 1: area_cylinder(6, 7) should return 376.9911

% Example 2: area_cylinder(3, 4) should return 131.9469

% Step 4: Algorithm

% The formula to calculate the area of a cylinder is: A = 2*pi*r^2 + 2*pi*r*h,

% where r is the radius of the base and h is the height of the cylinder.

% We can use this formula to calculate the area.

% Step 5: Implementation

% Calculate the area using the formula

area = 2 * pi * radius^2 + 2 * pi * radius * height;

end

You can now call the area_cylinder function with the radius and height values to calculate the area of the cylinder. For example:

area = area_cylinder(6, 7);

disp(['The area of the cylinder is: ', num2str(area)]);

This will output: "The area of the cylinder is: 376.9911" for the given radius of 6 and height of 7.

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7. The probability that both leaders are juniors is 0.1333.

8. The probability that neither leader is a senior is 0.3696.

9. The probability that one leader is a freshman and the other is a sophomore is 0.2000.

10. The probability that at least one leader is a sophomore is 0.5333.

7. To find the probability that both leaders are juniors, we need to consider the number of ways to choose 2 juniors out of the total number of clarinet players. There are 6 juniors in total, so the probability is:

Number of ways to choose 2 juniors / Total number of possible outcomes

= C(6, 2) / C(20, 2) = 15 / 190 ≈ 0.1333

8. To find the probability that neither leader is a senior, we consider the number of ways to choose 2 players who are not seniors out of the total number of clarinet players. There are 20 - 3 = 17 players who are not seniors, so the probability is:

Number of ways to choose 2 non-seniors / Total number of possible outcomes

= C(17, 2) / C(20, 2) = 136 / 190 ≈ 0.3696

9. To find the probability that one leader is a freshman and the other is a sophomore, we need to consider the number of ways to choose 1 freshman out of 4 and 1 sophomore out of 7, divided by the total number of possible outcomes:

Number of ways to choose 1 freshman * Number of ways to choose 1 sophomore / Total number of possible outcomes

= C(4, 1) * C(7, 1) / C(20, 2) = 4 * 7 / 190 = 28 / 190 = 0.2000

10. To find the probability that at least one leader is a sophomore, we can find the complement of the event "neither leader is a sophomore" and subtract it from 1:

1 - P(neither leader is a sophomore) = 1 - (C(13, 2) / C(20, 2)) = 1 - (78 / 190) ≈ 0.5333

The complete question must be:

There are 4 freshmen, 7 sophomores, 6junior and 3 senior clarinet players in the marching band. If two are chosen at random to lead the practice. Find each probability. COMBINATIONS 7. Both are juniors. 8. Neither is a senior  9. One is a freshman and the other is a sophomore 10. At least one is a sophomore.

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The following, find 2 solutions and 2 non solutions is \(x=\frac{30-5 y}{2}\)

What is non solutions?

Ideal solutions are those that follow Raoult's law throughout the whole concentration range. A solution is said to as a non-ideal solution if it violates Raoult's law.

\($$2 x+5 y=30$$\)

\(Move $5 y$ to the right side\)

\($$2 x=30-5 y$$\)

\(Divide both sides by 2\)

\($$\frac{2 x}{2}=\frac{30}{2}-\frac{5 y}{2}$$Simplify$$x=\frac{30-5 y}{2}$$\)

Non solutions, in the plural, refer to anything that falls short of offering a fix for a problem. These batteries also lose their charge, rendering them useless for solving the more significant issue of storing and utilizing renewable energy.

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Answer:

B

Step-by-step explanation:

60+40+x=180(angles in a triangle)

x= 180-100

x=80°

80+z=180(angles on a str line)

z= 100°

100+15+y=180(angles in a triangle)

y=180-115

y=65°

Answer:

c: x = 80, y = 65, z = 100

Step-by-step explanation:

The sum of all angles in a triangle is 180

so 40 + 60 + x = 180 and 15 + y + z = 180

40 + 60 + x = 180

100 + x = 80

x = 80

supplementary angles are equal to 180

x and z are supplementary

80 + z = 180

z = 100

15 + 100 + y = 180

115 + y = 180

y = 65

In 33 weeks, they will have sold 150 units.

What is sales of products?

Selling a good or service in exchange for cash, a benefit, or some other kind of payment is known as product sales. When a customer purchases a good or service that will meet their needs, the transaction is known as a product sale. The quantity of goods sold during a specific time period aids in calculating product sales.

Step by Step Explaination:

Equation that models the sales of the product

The equation that models the sales of the product after an initial release exists:

s = 12√4 + 10

where s denotes the total sales (in thousands)

t denotes the time in weeks

you want to replace the s with 150 in the equation and then just solve

for t.

150 = 12√4t + 10

Subtract 10 from both sides

150 - 10 = 12√4t + 10

140 = 12√4t

Divide both sides by 12      

11.66= √4t  

Taking square root on both sides of the equation.    

135.95 = 4t      

Now divide both sides by 4

33.98 = t (approximately).

so in 33 weeks, they will have sold 150 units.

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