The length of a rectangle is five inches less than twice its width. If the rectangle has a perimeter of 80 inches, find
the length and width.

Given parameters:

Commission per sale  = 8.15%

Cost of house sold = $877,000

Unknown:

Amount of commission earned  = ?

Solution;

 The amount of commissioned earned;

          = Commission per sale x cost of house sold

          = [tex]\frac{8.15}{100}[/tex]  x 877,000

          = $71,475.5

The commission earned on this sale is  $71,475.5

Answer:18

Step-by-step explanation:

Check on a calculation

(a)image averaging is a very effective method of reducing noise in images. Image averaging reduces noise by adding multiple images of the same scene together and then dividing by the number of images added.The conditions that must be fulfilled for the image averaging method are as follows:-

(i) The background of the image must not move between each image capture.- The noise present in the image must be random.- The source of the noise must be consistent.

(ii)The mathematical expression that characterizes the noise in the resultant image when K images are averaged, as K becomes large is given by;sigma_n^2/K

Where;sigma_n^2 is the variance of the noise and K is the number of images that have been averaged.

Therefore, as K increases, the variance of the noise in the resultant image reduces, and thus, the noise reduces.When either method can be used for noise reduction, the temporal image averaging method would be the preferred method to select.

(iii)This is because it uses a sequence of images that are taken at different times, usually at high speeds, to produce a single image that is free of noise. This method is best when dealing with fast-moving objects, and it can be used in situations where the camera cannot be stabilized and is experiencing unwanted vibration or shaking.

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Answer:

a² + b² = 22

Step-by-step explanation:

(a + b)² = a² + 2ab + b² ← substitute a + b = 6 and ab = 7

6² = a² + 2(7) + b²

36 = a² + 14 + b² ( subtract 14 from both sides )

22 = a² + b²

Answer:

[tex]\frac{1}{2}, \frac{1}{4}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

9

Step-by-step explanation:

Answer:

I BELIEVE THIS IS THE FIRST ONE!!1 HOPE THIS HELPS

Step-by-step explanation:

Answer:

-1<=X<=9

Step-by-step explanation:

The inequality is given as the negative 1 < x < 9.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A number x is at least -1 and no more than 9. Then the inequality is given as

- 1 < x < 9

The inequality is given as the negative 1 < x < 9.

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Answer:

sure

Step-by-step explanation:

Answer:

sure, but there questions for me to answer

Step-by-step explanation:

Emma's luggage may be lost with probability p = 0.1. The luggage and its content are estimated to be worth 316.05. Emma's utility insures against the loss of the luggage. What is the maximum insurance premium I that Emma would be willing to pay?

Solution:To calculate Emma's maximum insurance premium, let's start by calculating her expected utility if she doesn't insure her luggage.U (no insurance) = 0.9 x U (316.05) + 0.1 x U (0)where U (316.05) is Emma's utility function for 316.05 value, and U (0) is Emma's utility function for a loss of the luggage. Emma has not insured her luggage, hence, if it gets lost, she will get 0 value for it.A sum of 316.05 is worth more than 0, Emma will still get a certain amount of utility, which will be larger than 0.

Therefore, Emma's utility function is likely to be positive, so let us assume that U (0) = 0.If we plug this information into the above equation, we will have:U (no insurance) = 0.9U (316.05) + 0.1 × 0 = 0.9U (316.05)Hence, Emma's expected utility, if she doesn't insure her luggage, will be 0.9U (316.05).However, if Emma chooses to insure her luggage, she will pay the insurance premium I. If the luggage gets lost, she will get reimbursed by the insurance company for 316.05. Her expected utility function, if she insures her luggage, will be:

U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)Where U (316.05 – I) is Emma's utility function for 316.05 – I value. Emma will get this amount if the luggage is not lost, but she has to pay the premium I.If we compare Emma's expected utility when she insures her luggage and when she doesn't insure her luggage, we will have the following inequality:

U (insurance) ≥ U (no insurance)0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)Let us solve this inequality:0.9U (316.05 – I) + 0.1U (316.05) ≥ 0.9U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Since U (316.05 – I) is a decreasing function, it will get smaller as I gets larger.

Hence, to maximize Emma's expected utility, we need to minimize the insurance premium I that she pays to the insurance company.If Emma doesn't insure her luggage, her expected utility will be 0.9U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage.U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05)0.9U (316.05 – I) ≥ 0.8U (316.05)U (316.05 – I) ≥ 0.89U (316.05)Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Hence,Emma's maximum insurance premium I that Emma would be willing to pay is $31.35.

If Emma chooses to insure her luggage, she will pay the insurance premium I. Her expected utility function, if she insures her luggage, will be U (insurance) = 0.9U (316.05 – I) + 0.1U (316.05). Emma will choose to insure her luggage if her expected utility is larger if she insures her luggage. Therefore, Emma's maximum insurance premium I that Emma would be willing to pay is $31.35. The utility function is considered decreasing as Emma has to pay more premium.

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Answer:

The angles that are congruent due to being vertical angles are:

m∠2 and m∠4

m∠1 and m∠3

m∠8 and m∠6

m∠5 and m∠7

Answer:

v >=18

Step-by-step explanation:

Really don't know how to explain it

a) a square has 4 right angles and all 4 sides are the same lengths

b) not sure, I'll edit later when and if I know

c) isosceles triangle

Experimental data and non-experimental data differ in their method of collection and the level of control over the variables involved.

Experimental data is obtained through controlled experiments where researchers manipulate independent variables to observe their effects on dependent variables. Non-experimental data, on the other hand, is collected without direct manipulation of variables, often through observation or existing records.

Experimental data involves conducting controlled experiments to gather information. In such cases, researchers actively manipulate variables to study their impact on the outcome. For example, in a study investigating the effects of a new medication on blood pressure, participants may be randomly assigned to receive either the medication or a placebo. The researchers then measure and compare the participants' blood pressure readings to determine the medication's effectiveness. In another example, an experiment could be conducted to examine the impact of different fertilizers on plant growth by treating different groups of plants with specific fertilizers and measuring their growth rates.

Non-experimental data encompasses information collected without direct manipulation of variables. One example is observational data, where researchers observe and record naturally occurring events or behaviors. For instance, a study on animal behavior might involve observing a group of primates in their natural habitat and documenting their social interactions, feeding patterns, or communication. Another example of non-experimental data is survey data, which involves gathering information through questionnaires or interviews. For instance, a market research survey may ask consumers about their preferences for different brands of a product or their likelihood of purchasing certain items.

In experimental data, researchers have control over variables, allowing them to establish cause-and-effect relationships between the independent and dependent variables. Non-experimental data, however, lacks such control, making it more challenging to establish causal relationships. While experimental data provides strong evidence for drawing conclusions, non-experimental data is valuable for exploring relationships, describing phenomena, and generating hypotheses that can be further tested through experiments.

In summary, experimental data is collected through controlled experiments where variables are manipulated, while non-experimental data is obtained through observation or existing records without direct manipulation. Experimental data allows for establishing cause-and-effect relationships, while non-experimental data provides valuable insights for exploration and hypothesis generation. Examples of experimental data include studies on medication effects or fertilizer impact, while examples of non-experimental data include observational studies on animal behavior or surveys on consumer preferences.

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Answer:

4 x 20 - X

Step-by-step explanation:

4 times 20 - X

x is the unknown variable

Unknown variable = what you are trying to find.

Answer:

It should be D

Step-by-step explanation:

Answer:

the third option.

Step-by-step explanation:

angle 3 and 4 are complementary

so 90-35= 55

Answer:NO

Step-by-step explanation:

The paper clip costs $0.05 and the folder Costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

Let's solve this problem step by step:

Let's assume the cost of the paper clip is x dollars.

According to the information given, the folder costs $1.00 more than the paper clip, so the cost of the folder would be (x + $1.00).

The total cost of the folder and the paper clip is $1.10, so we can write the equation:

x + (x + $1.00) = $1.10

Combining like terms, we have:

2x + $1.00 = $1.10

Subtracting $1.00 from both sides of the equation, we get:

2x = $0.10

Dividing both sides by 2, we find the value of x:

x = $0.10 / 2

x = $0.05

Therefore, the paper clip costs $0.05.

In summary, the paper clip costs $0.05 and the folder costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

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Yes, it is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. By dilating the photo, it will be enlarged to fit the frame. Dilating a photo involves scaling it up or down to fit a particular size.

This is possible since dilating a photo is done proportionally. This implies that if the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same. Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame. It is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. Dilating a photo involves scaling it up or down to fit a particular size. This is possible since dilating a photo is done proportionally. If the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same.Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame. By dilating the photo, it will be enlarged to fit the frame.The process of dilating a photo can also be represented as a mathematical equation. The equation is as follows:y = kx where:y is the new height of the photo x is the original height of the photo k is the scale factor If the scale factor, k, is greater than 1, the photo will be enlarged, while if the scale factor is less than 1, the photo will be reduced. Therefore, if the scale factor, k, is 2, then the height of the photo will be multiplied by 2, resulting in a photo that is 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame.

In conclusion, it is possible to dilate a photo in order to fit the 8-inch by 10-inch frame. Dilating a photo involves scaling it up or down to fit a particular size. This is done proportionally, meaning that if the height and width of the photo are multiplied by the same number, the dimensions of the photo will increase or decrease in size while the proportions will remain the same. Therefore, if the 4-inch by 6-inch photo is dilated by a scale factor of 2, the resulting dimensions will be 8 inches by 12 inches. The photo can then be cut down to 8 inches by 10 inches to fit into the frame.

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Answer:

Option (B)

Step-by-step explanation:

By adding two polynomials,

(5xy² + 3x² - 7) + (3x²y² - xy² + 3y² + 4)

Now by adding the similar terms,

= (5xy² - xy²) + 3x² + 3x²y² + 3y² - 7 + 4

= 4xy²+ 3x² + 3x²y² + 3y² - 3

= 3x²y² + 4xy² + 3x² + 3y² - 3

Therefore, Option (B) will be the correct option.

Answer:

1

Step-by-step explanation:

In golf, if you are over par, then your score is represented by values over zero and with a plus. Since Jewels' score was 5 over on the first hole (dang... that's a quintuple bogey (which is horrible)), she had a +5 on the first hole. But for the next 9 holes, she scored  4 under, which is represented by -4. Add 5 and -4 and you get +1. She still has 8 holes left in that round if she wants to get below par.

The difference between p = l/n(100) and p*(n+1) lies in the way they calculate a percentage value.

The former divides a number (l) by the total number of items (n) and then multiplies it by 100, while the latter multiplies a proportion (p) by the total number of items plus one (n+1). Let's illustrate this with an example. Suppose we have a survey with 100 participants, and we are interested in calculating the percentage of participants who prefer apples. If 30 participants indicate their preference for apples, we can calculate the percentage using both formulas. Using p = l/n(100), we have p = 30/100(100) = 30%. This means that 30% of the participants prefer apples. Using p*(n+1), we have p*(100+1) = p*101. If we consider p as 30/100, then p*101 = (30/100)*101 = 30.3. So, according to this calculation, approximately 30.3% of the participants prefer apples. The key distinction is that p = l/n(100) directly calculates the percentage based on the given number (l) and the total number (n), while p*(n+1) scales the proportion (p) by considering the total number of items plus one (n+1).

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We need to determine whether the set {P₁, P₂, P₃} is linearly independent in P₂, where P₁ = 2 + x + 3x² + 4x³, P₂ = 4 + 3x + 2x² + x³, and P₃ = 1 + 2x + 3x² + 4x³. In this problem, we will perform the necessary calculations to determine the linear independence of the set.

To determine the linear independence of the set {P₁, P₂, P₃}, we need to check if the only solution to the equations c₁P₁ + c₂P₂ + c₃P₃ = 0, where c₁, c₂, and c₃ are constants, is the trivial solution (c₁ = c₂ = c₃ = 0).

We set up the equation as follows:

c₁(2 + x + 3x² + 4x³) + c₂(4 + 3x + 2x² + x³) + c₃(1 + 2x + 3x² + 4x³) = 0

Multiplying through and combining like terms, we get:

(2c₁ + 4c₂ + c₃) + (c₁ + 3c₂ + 2c₃)x + (3c₁ + 2c₂ + 3c₃)x² + (4c₁ + c₂ + 4c₃)x³ = 0

For this equation to hold true for all values of x, each coefficient of x and its powers must be zero. Therefore, we have the following system of equations:

2c₁ + 4c₂ + c₃ = 0 (1)

c₁ + 3c₂ + 2c₃ = 0 (2)

3c₁ + 2c₂ + 3c₃ = 0 (3)

4c₁ + c₂ + 4c₃ = 0 (4)

Solving this system of equations, we find that the only solution is c₁ = c₂ = c₃ = 0. This implies that the set {P₁, P₂, P₃} is linearly independent in P₂.

Therefore, the set {P₁, P₂, P₃} is linearly independent in P₂.

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Friend is incorrect and the permutations rule should be used instead of just 5!.

Permutations are a process in which the order of items in a set matters. In other words, it refers to the different arrangements that can be made by selecting r items from n different objects, without repeating any of them.

Calculating permutations manually can be time-consuming.

However, the permutations rule simplifies the process.

The permutations rule states that the number of permutations of n distinct objects, taken r at a time, is equal to

nPr = n!/(n-r)!,

where "n" represents the total number of distinct objects and

"r" represents the number of items selected for each arrangement.

So, if you want to find the number of arrangements possible for five distinct letters, you need to use the permutation rule and not just 5!.

This is because 5! represents the number of ways to arrange five distinct objects (letters) in a line, without restrictions, meaning that the same letter can appear twice, or more, in the arrangement.

However, if the five distinct letters are taken two, three, four, or five at a time, then the permutations rule would have to be used.

For example, the number of different arrangements of two letters out of five distinct letters is equal to

5P2 = 5!/3!

= 5 × 4

= 20.

Therefore, your friend is incorrect and the permutations rule should be used instead of just 5!.

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Answer:

A and D

Step-by-step explanation:

no cap

The numbers that replace A, B and C on the tree diagram are given as follows:

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

At each node, the sum of the probabilities is of 1, hence the missing values are given as follows:

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Answer:

i cant see the question very well but go to cymath dot com

Step-by-step explanation:

Answer:

I cant see it well.

Step-by-step explanation: