Steven has a small business that provides computer application training and data entry support services. He earns $25 per hour for training and $15 per hour for data entry support. Steven can work no more than 40 hours a week. He wants to use linear programming techniques to optimize his income.

Answer:

Step-by-step explanation:

y + 3 = 7(x - 1)

y + 3 = 7x - 7

y = 7x - 10

Answer:

i believe it is b :) not that hard

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Step-by-step explanation:

Find the sides and perimeter:

Perimeter:

Find the area using shoelace formula:

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

The value of p when q is 2 is 1

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means that has x increases y will decrease and vice versa.

If p is inversely proportional to q , then p = kq

when p = 2, q = 4

2 = k4

k = 2/4

k = 1/2

When q = 2

p = 1/2 × 2

p = 1

Therefore the value of p is 1

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Answer:

Yes

Step-by-step explanation:

8 + y = 4x is a linear equation in two variables ( x and y) .

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer: 25

Step-by-step explanation:

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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The surface area of the cube is 1536 ft².

We have,

The cube can be seen as 6 square areas in the net.

So,

The surface area of the cube.

= 6 x area of one square surface.

Now,

Side = 16 ft

Area of one square surface.

= side²

= 16²

= 256 ft²

Now,

The surface area of the cube.

= 6 x area of one square surface.

= 6 x 256

= 1536 ft²

Thus,

The surface area of the cube is 1536 ft².

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Answer:

15.6%

Step-by-step explanation:

Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...

94% / 100 = 0.94

\(0.94^{30}\) = 0.156

Now we can turn this decimal into a percentage by multiplying by 100

0.156 * 100 = 15.6%

Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%

Using the binomial distribution, it is found that there is a 0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

For each day, there are only two possible outcomes, either Lisa smiles at him, or she does not. The probability that she smiles at him on day is independent of any other day, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that Milhouse goes longer than a month without a smile from Lisa is the probability of no smiles during 30 days, that is, P(X = 0), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{30,0}.(0.06)^{0}.(0.94)^{30} = 0.1563\)

0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

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The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.

The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.

There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.

The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.

A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.

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"The spread of the data distribution for Lake Mockingbird is 5 inches bigger than the spread of the data distribution for Lake Warbler," is the answer to question 2.

The graphs do not support this statement since the difference in spread between the two lakes is not represented as 5 inches. The right answer to question 1 is B: "The spread of the data distribution for Lake Mockingbird is approximately 40% higher than the spread for Lake Warbler." This is due to the fact that the data distribution of the Lake Mockingbird is around 60 inches (from 5 to 65), whereas the data distribution of the Lake Warbler is approximately 43 inches (from 2 to 45). The difference between the two ranges is approximately 60 - 43 = 17. inches. From 43 to 60, the percentage rise is around 39.5%, which is close to 40%. The correct answer to question 3 is B: "The distribution of Lake Mockingbird reveals a center that is 3 inches greater than the distribution of Lake Warbler." This assertion is false since the graphs do not show the center of each distribution and cannot be established with the information supplied. Based on the data in the graphs, the other claims are correct.

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Answer:

4 months

Step-by-step explanation:

Leslie's equation: y = 15x + 20

Rashad's equation: y = 10x + 40

you can put them both in a table or substitute each answer option for x in both equations and see when they're equal

if you substitute 4 for x, both equation equal 80

Answer:

4

Step-by-step explanation:

If there are 5 times as many the. terriers would make the 6th part.

So, 24÷6= 4

There are 4 terriers and 20 labs

Answer:

c

Step-by-step explanation:

I think it's right but i am not sure

By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

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30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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Answer:

C

Step-by-step explanation:

This is because C is the only answer that equals 2 2/3

Option C (2 2/3 = 1 + 1 +1/3 + 1/3) is the correct equation.

A) 2 + 2 + 3 = 7

B) 1 + 1 + 2 + 3 = 7

C) 1 + 1 + 1/3 + 1/3 = 2 2/3

D) 1 + 1 + 1/3 = 2 1/3

I attached a picture to make it simpler!

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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Answer:

36.575

Step-by-step explanation:

you need to find line ab you can do \(A^{2} +B^{2} =C^{2}\)  for the triangle and get the line you also need to get the squar root of it as it is still squared then devide by 2 to get the rades then times that by pi and there you go you have the area also sorry for spelling I love math not English

Part A: Yes, there is a correlation between the number of hours students spent studying and the score on the music test because  As we increase the hours of studying by 0.5 hours, then the music score increases by 2.

Part B: A function that best fits the data is; y = 60 + 4x

Part C: The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.

We have given the table below showing the data:

Number of hours spent studying (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score on music test (y) 60 62 64 66 68 70 72 74 76

A) As we increase the hours of studying by 0.5 hours, then the music score increases by 2.

B) The function which best fits the data for the correlation from the above is; y = 60 + 4x

C) The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.

The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.

The y-intercept gives the music score when the number of hours spent on studying is zero.

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Answer:

Yes it is equivalent

Step-by-step explanation:

Simply 5(x+2)+10 and you will get 5x+12

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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