Prove that a regular 9-gon is not constructible (with a compass and straight-edge), but a regular 20-gon is. For the impossibility of the of the regular 9-gon, your proof should mimic the proof we did in class that 20 is not constructible. That is, your proof should talk about field extensions and polynomials (do not just argue that t is impossible because if we could construct it, we would then be able to construct 20 which we know is impossible).

The solution to the equation -4x + 21 = x is x = 21/5.

We can move all the x terms to one side of the equation and the constant terms to the other side in order to solve the equation -4x + 21 = x:

-4x - x = -21combining comparable phrases-5x = -21

Divide both sides of the equation by -5 to separate x: x = (-21) / (-5)

Making the right side simpler:

x = 21/5As a result, x = 21/5 is the answer to the equation -4x + 21 = x.

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Answer:

like wise. I too agree with your contribution

Step-by-step explanation:

a.

the coordinates of the center of the circle are exactly in the middle between the 2 points.

since the y values are the same, this diameter is a horizontal line, and we can simply calculate the middle of the x values :

(15 - 6) / 2 = 9/2 = 4.5

and the x coordinate if the center is then 6 + 4.5 = 10.5

so, the coordinates are

(10.5, 8)

b.

the diameter is the length of the line between the 2 points

since the y values are the same, the length is simply the difference in x values : 15 - 6 = 9

c.

the radius is half of the diameter, so, 9/2 = 4.5

Answer:

20 percent

Step-by-step explanation:

10% of 60 is 6

6 times 2 is 12, 10% times 2 is 20%. so 20%

Answer:

20%

Step-by-step explanation:

20%

Answer:

the answer is a

Step-by-step explanation:

hope it help

First we add 0.3 to 3.7, that way we will have an integer and it would be more easy to make the operations. Then we have 4.

Then we can substract the 4 to the 9.4, getting 5.4.

Finally we add once again 0.3 (because in the difference we have an extra .3) to the 5.4, getting 5.7.

Then Tamela swims 5.7 more than Blake every day.

Peter is 19 years old and Sylvia is 9 years old now.

Let's use algebra to solve this problem.

Let's assume Peter's current age is P, and Sylvia's current age is S.

We can create two equations based on the information given:

Four years ago, Peter was three times as old as Sylvia:

P - 4 = 3(S - 4)

In 5 years, the sum of their ages will be 38:

(P + 5) + (S + 5) = 38

Now we can solve for P and S.

P - 4 = 3(S - 4)

P - 4 = 3S - 12

P = 3S - 8

(P + 5) + (S + 5) = 38

P + S + 10 = 38

P + S = 28

Now we can substitute P = 3S - 8 from the first equation into the second equation:

3S - 8 + S = 28

4S = 36

S = 9

So Sylvia's current age is 9.

We can use P + S = 28 from the second equation to find Peter's current age:

P + 9 = 28

P = 19

Therefore, Peter's current age is 19.

So currently Peter is 19 years old and Sylvia is 9 years old.

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To fully answer this question, I would need the information presented in Figure 3.14 that provides the computer solution. Unfortunately, I cannot access or view specific figures or external sources. However, I can explain the general approach to solving such a problem and provide a LaTeX code snippet to format the question.

To solve the given problem, it appears to be a linear programming problem where the goal is to optimize the total annual return subject to certain constraints. The decision variables are the number of shares of US Oil (U) and Huber Steel (H) to be purchased.

a. The optimal solution would provide the values of U and H that maximize the total annual return while satisfying the given constraints. The value of the total annual return would be the objective function value at the optimal solution.

b. The binding constraints are those that are active and determine the solution. These constraints limit the risk index, the total investment amount, and the maximum number of shares of US Oil. Interpretation of these constraints would depend on the specific problem and its context.

c. The dual values for the constraints represent the marginal values or shadow prices associated with each constraint. They indicate the rate of change in the objective function value for a small change in the right-hand side of the constraint. Interpretation of dual values would also depend on the specific problem and its context.

d. The impact of increasing the maximum amount invested in US Oil would depend on the objective function and the constraints. It could lead to a higher total annual return if US Oil has a higher return rate and the constraint on the risk index or total investment amount allows for it. However, if the maximum number of shares of US Oil is already binding, increasing the maximum investment amount would not be beneficial.

Please provide any additional information or specific values from Figure \(3.14\) if you have access to it, and I can assist further.

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The answer to your question is that the only way to demonstrate causation is to conduct a controlled experiment. This domain involves manipulating one variable and measuring the effect it has on another variable while holding all other variables constant.

correlation simply shows a relationship between two variables, but it doesn't prove that one variable causes the other. There could be other factors at play that are influencing both variables. For example, there may be a correlation between ice cream sales and crime rates, but this doesn't mean that ice cream causes crime or vice versa. It's possible that a third variable, such as temperature, is influencing both ice cream sales and crime rates.

further into the complexities of establishing causation, such as the need for random assignment in experimental studies, the importance of replicating findings, and the challenges of applying experimental findings to real-world situations. However, the key point is that a controlled experiment is the most reliable method for establishing a causal relationship between variables.

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Answer:

- 5

Step-by-step explanation:

Given

(- 2 × 2 - 6) ÷ 2

Evaluate the parenthesis performing the multiplication before subtracting.

= (- 4 - 6) ÷ 2

= - 10 ÷ 2

= - 5

Answer:

See below

Step-by-step explanation:

Answer:

(a) $818.50

(b) 820 glow sticks

Step-by-step explanation:

(a) P= 0.91(350)+500

= 318.50+500

= $818.50

(b) 1246.20-500=746.20

n= 746.20÷0.91

= 820

Answer:

\($\frac{5\sqrt{2} }{2}$\)

Step-by-step explanation:

\(x: \text{opposite side of the angle of 45\º}\)

\(5: \text{hypotenuse of the right triangle}\)

\($\sin(\theta)=\frac{\text{opp}}{\text{hyp}} \Rightarrow \sin(45\º)=\frac{x}{5} $\)

\($\text{Once }\sin(45\º)=\frac{\sqrt{2} }{2} $\)

\($\frac{\sqrt{2} }{2} =\frac{x}{5} \Rightarrow 2x=5\sqrt{2} \Rightarrow x=\frac{5\sqrt{2} }{2} $\)

You can just remember that 5 is the diagonal of a square of side length x.

\($5=x\sqrt{2} \Rightarrow x=\frac{5}{\sqrt{2} } \Rightarrow x=\frac{5}{\sqrt{2} } \cdot \frac{\sqrt{2} }{\sqrt{2} } = \frac{5\sqrt{2} }{2} $\)

Answer:

See below for answers and explanations (along with a graph)

Step-by-step explanation:

Refer to the equations for a limaçon:

y=a+bcos∅ (horizontal line of symmetry) and y=a+bsin∅ (vertical line of symmetry) where a/b determines the type of limaçon.

This is an inner loop limaçon because 36/70<1, so its horizontal axis intercepts are 36 and -36 (marked in red) and its vertical axis intercepts are 0, 36+70=106 and 70-36=34 (marked in green)

Answer:

3(24+56)

Step-by-step explanation:

3 times sum of 24 and 56 so your adding 24 and 56 and multiplying it by 3

3(24+56)

Answer:

3(24 +56)

Step-by-step explanation:

sum of 24 and 56 means addition

3 times the sum means multiplication

the format you'd use in math would be 3(24 +56)

Answer:

7 calls in a day

Step-by-step explanation:

You divide 252 by 36 which equals 7

Answer:7 calls in a day

Step-by-step explanation:

Answer:

(-2, -3)

Step-by-step explanation:

Sorry if im wrong but I looked it up and the person who wrote it got 131 thanks' so im guessing its this.

Consider giving brainlist :D

Answer:

d

Step-by-step explanation:

We can make 37 , 3-letter strings  from the letters a, b, c, and d.

1 . AAA    - This word could be written in 1 way.

2. AAB, AAC, AAD  

3.ABB, ACC, ADD

4. ABC, ABD, ACD      

Total = 1+9+9+18

        = 37

So, we can make 37  3-letter strings  from the letters a, b, c, and d by applying the method called permutation.

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Hu and colleagues (2001) addressed concerns about the lack of random assignment to treatment conditions by using a quasi-experimental design.

In their study, Hu and colleagues (2001) used a quasi-experimental design to examine how organizational citizenship behaviors (OCBs) of bank tellers affect customer service. A quasi-experimental design is a type of research design that lacks the random assignment of participants to treatment conditions, which is a key characteristic of true experimental designs.

To address the concerns about the lack of random assignment in their study, Hu and colleagues (2001) used statistical techniques to control for potential confounding variables and to increase the internal validity of their findings. They also carefully selected their sample of bank tellers and customers to ensure that the groups were as similar as possible, which helped to increase the external validity of their study.

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Explanation

Step 1

so, option 1 is true

Step 2

Step 3

so

Step 4

finally

so, the answer is

I hope this helps you

Answer: The width is 5.

Step-by-step explanation:

'(2+w)+(2+w)+2w=24

4+4w=24

W=5

Answer:

a = 9

Step-by-step explanation:

\(a^{2}\) = a*a

a = -3

-3 * -3 = 9

NOTE: 2 negative numbers multiplied by each other always equals a positive

So.... a = 9

The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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Answer:

2/10 + 7/10

9/10

Step-by-step explanation:

I did the test.

Answer:

The expression written in equivalent form with common denominators is

✔ 2/10 + 7/10

The sum is

✔ 9/10

Step-by-step explanation:

Adding two numbers combines their values

Subtracting one number from another finds the difference between the two values

Multiplying two numbers gives the product of their values

Dividing one number by another gives the quotient of their values

By performing the same operations on both sides, to maintain the balance and validity of the equation.

Arithmetic Operations with Whole Numbers, Integers, Fractions, and Decimals:

1. Addition: Adding two numbers combines their values. For example,

2 + 3 = 5.

This operation is commutative, meaning the order of numbers doesn't affect the result.

2. Subtraction: Subtracting one number from another finds the difference between the two values. For example,

5 - 3 = 2.

This operation is not commutative since changing the order of numbers will yield a different result.

3. Multiplication: Multiplying two numbers gives the product of their values.

For example, 2 * 3 = 6.

This operation is commutative.

4. Division: Dividing one number by another gives the quotient of their values. For example,

6 / 2 = 3.

Division is not commutative, and it's important to note that division by zero is undefined.

When solving equations, what is done to one side of the equation must also be done to the other side. This is because an equation represents a balance or equality between two expressions. The goal is to isolate the variable on one side of the equation and keep the equation balanced.

By performing the same operation on both sides of the equation, maintain equality. If  only performed an operation on one side, the equation would become unbalanced, and the equality would be lost.

For example, let's solve the equation 2x + 5 = 11 for x:

1. Start with the equation:

2x + 5 = 11.

2. To isolate the term with x, subtract 5 from both sides:

2x + 5 - 5 = 11 - 5.

  This simplifies to:

2x = 6.

3. Finally, divide both sides by 2 to solve for x:

(2x) / 2 = 6 / 2.

  This gives the solution:

x = 3.

If only subtracted 5 from one side of the equation, the equality would be broken, and the solution would be incorrect. By performing the same operations on both sides, maintain the balance and validity of the equation.

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The perimeter of half of the basketball court is 194 feet.

The basket ball court is divided into two equal halves. The perimeter of the halve of the basket ball court can be calculated as follows:

Therefore, the perimeter is the sum of the whole sides of half of the basket ball court.

Hence,

perimeter of half of the basket ball court = 94 / 2 + 94 / 2 + 50 + 50

perimeter of half of the basket ball court = 47 + 47 + 100

perimeter of half of the basket ball court = 94 + 100

perimeter of half of the basket ball court = 194 feet

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Answer:

Answer down below!

Step-by-step explanation:

The set (1, 2, 3) would have 8 sets in total

Answer:

slope of (16,8) (8,4) is 1/2