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The sum of n consecutive integers, where n is an odd positive integer, is divisible by n.

To prove the statement, let's consider a set of n consecutive integers starting from a.

The sum of n consecutive integers can be expressed as:

S = a + (a+1) + (a+2) + ... + (a+n-1)

To find the sum, we can use the formula for the sum of an arithmetic series:

S = (n/2) × (2a + (n-1))

Since n is an odd positive integer, we can represent it as n = 2k + 1, where k is a non-negative integer.

Substituting this value of n into the sum formula, we get:

S = ((2k+1)/2) × (2a + ((2k+1)-1))

Simplifying further:

S = (k+1) × (2a + 2k)

S = 2(k+1)(a + k)

Since k is an integer, (k+1) is also an integer. Therefore, we can rewrite the sum as:

S = 2m(a + k)

Now, we can see that S is divisible by n = 2k + 1, where m = (k+1).

Thus, we have proven that the sum of n consecutive integers, where n is an odd positive integer, is divisible by n.

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The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.

Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.

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Answer and Step-by-step explanation:

Divide -5 from both sides of the inequality.

x < -5 is the answer.

Here's Why:

If you were to add 5x to both sides, it results in this:

0 > 25 + 5x

Now, we subtract 25 from both sides.

-25 > 5x

When we divide 5 from both sides, we see that it results in -5 > x, which is the same as x < -5.

#teamtrees #PAW (Plant And Water)

Answer:

supplementary (add together to = 180°)

Step-by-step explanation:

Step-by-step explanation:

Supplementary angles add up to 180

complementary angles add up to 90

75+105=180

so the angles are supplementary

Hope that helps :)

Answer: x=3/5

Step-by-step explanation:

Answer:

k=62

Step-by-step explanation:

K divided by 5 = 12.4

Multiply both sides by 5

5k/5=12.4×5

Simplify;

k=62

Hope this helped!!

Answer:

k = 62

Step-by-step explanation:

To solve we need to get k on one side alone.

To do this we can multiply buth sides by 5

[tex]\frac{k}{5} =12.4[/tex] --->  =12.4*5

This gives us x=62

You can check this by putting 62 in for k and solving the problem.

Answer:

The First Choice

Step-by-step explanation:

1/4 is equal to .25

.25 x 4= 1.00

25 x 4= 100

Answer:

No coz 2:3 is 2+3=5

1:2 is 1+2=3 so they are not equivalent.

The standard deviation of the fish Zagreus will catch is approximately 0.6833.

Given probability of catching fish by Zagreus in a single run of Hades is as follows: P(0 fish) = 0.10 P(1 fish) = 0.40 P(2 fish) = 0.35 P(3 fish) = 0.15

To calculate the standard deviation of the fish Zagreus will catch, we need to follow these steps:

Find the expected value, µ, of the fish he will catch.

Then, calculate the variance, σ², using the formula:σ² = Σ [(x - µ)² P(x)]

Finally, calculate the standard deviation, σ, which is the square root of the variance.μ = Σ [xP(x)]μ = (0 × 0.10) + (1 × 0.40) + (2 × 0.35) + (3 × 0.15)μ = 0.75

The expected value, µ, of the fish he will catch is 0.75.

To find the variance:σ² = [(0 - 0.75)² × 0.10] + [(1 - 0.75)² × 0.40] + [(2 - 0.75)² × 0.35] + [(3 - 0.75)² × 0.15]σ² = 0.4675

Finally, the standard deviation, σ, is the square root of the variance:σ = √σ²σ = √0.4675σ ≈ 0.6833

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Given: In a single run of hades, zagreus has a 10% chance of catching 0 fish, 40% chance of catching 1 fish, 35% chance of catching 2 fish, and a 15% chance of catching 3 fish. The standard deviation of the fish that Zagreus will catch is 0.49 fish.

The standard deviation of the fish that Zagreus will catch can be calculated using the following formula

σ = sqrt [∑(x-μ)²/N], where σ is the standard deviation, ∑ is the sum of, x is the fish, μ is the mean, and N is the total number of chances.

The mean value of the fish Zagreus is expected to catch is given by:

μ = (0 x 10/100) + (1 x 40/100) + (2 x 35/100) + (3 x 15/100)

μ = 0 + 0.4 + 0.7 + 0.45

μ = 1.55.

Therefore, the mean value of the fish Zagreus will catch is 1.55 fish.

To calculate the standard deviation, we first calculate the deviation of each value from the mean as shown below: Deviation = x - μ

The deviations for each value of fish that Zagreus could catch are: -1.55, -0.55, 0.45, and 1.45.

Now, we can plug in these values into the formula above to calculate the standard deviation as shown below:

σ = sqrt [(-1.55² x 10/100) + (-0.55² x 40/100) + (0.45² x 35/100) + (1.45² x 15/100)]

σ = sqrt [0.24025]

σ = 0.49

Therefore, the standard deviation of the fish that Zagreus will catch is 0.49 fish.

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simply saying its circular measure

Answer:

x = 94

Step-by-step explanation:

(86 + x)/2 = 90

86 + x = 180

x = 94

The given statement “A correlation coefficient of −0.8 indicates strong indirect relationship” is true because it indicates a strong inverse or negative relationship between the variables.

A correlation coefficient is a statistical measure of the degree to which variables are related to one another. It is a numerical value that ranges from -1 to 1 and represents the strength and direction of the relationship between two variables.

If the correlation coefficient is -1, the relationship is strong and negative (inverse). On the other hand, if the correlation coefficient is 1, the relationship is strong and positive (direct).

When the correlation coefficient is zero, it indicates no relationship between the variables. When the correlation coefficient is near zero, it indicates a weak relationship between the variables.

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Answer:

Step-by-step explanation:

10^7 = 1 and 7 zeros after it.

=> 10000000

Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).

To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.

Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.

However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.

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Answer:

x=4

Step-by-step explanation:

Answer:

C-D = 6

A-B = 3.25

D = 118

Step-by-step explanation:

C-D = 6 because the line is the same as B-C

A-B = 3.25 because the line is the same as A-D

D = 118 because the angle of B is vertically opposite to D

Money needed to have accumulated if the RRSPs averaged a real return of four percent per year is $432,000

Amount of income stream = $25,000

Time = 30 years

According to the 4% rule, a retiree can risk not having enough money for at least 30 years by comfortably withdrawing 4% of their assets in their first year of retirement and adjusting that amount for inflation each year after that.

Calculating the present value -

[tex]PV = FV / (1 + r)^n[/tex]

Substituting the values -

[tex]PV = $25,000 / (1 + 0.04)^30[/tex]

[tex]PV = $25,000 / (1.04)^30[/tex]

= 432,309

Rounded the nearest thousand the return amount comes to $432,000

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Answer:

1.is 12

2. is 36

3. is 18

4. is 4.5

Step-by-step explanation:

sorry if im wrong

The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.

To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.

Starting with the given equation, we can simplify it step by step:

2 = -x√(x + 2) - x

Adding x to both sides:

2 + x = -x√(x + 2)

Squaring both sides to eliminate the square root:

(2 + x)^2 = (-x√(x + 2))^2

Expanding and simplifying:

4 + 4x + x^2 = x^2(x + 2)

Simplifying further:

4 + 4x = x^3 + 2x^2

Rearranging terms:

x^3 + 2x^2 - 4x - 4 = 0

Factoring the equation:

(x + 1)(x^2 + x - 4) = 0

Setting each factor to zero:

x + 1 = 0 or x^2 + x - 4 = 0

Solving the first equation, we find x = -1.

For the second equation, we can use the quadratic formula:

x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.

Hence, the set of all solutions to the equation is {x = -1}.

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Answer:

y = 3x + 2

Step-by-step explanation:

If the line is parallel, then the slope remains the same.

To find the y-intercept, just plug the coordinates into the equation

y = 3x + b

14 = 3(4) + b

14 = 12 + b

2 = b

The equation is y = 3x + 2

Answer:

Slope intercept form

y=3x^2−19x+42

or

Point slope form

y−14=(3x−7)⋅(x−4)

Step-by-step explanation:

:)

Answer:

A.) 0.25

B.) 0.125 (maybe don't trust me)

Step-by-step explanation:

Answer:

The 20 subjects constitutes the sample

Step-by-step explanation:

Given

[tex]Total = 150[/tex]

[tex]Selected = 20[/tex]

Required

What does 20 represent?

The 150 patients being treated is the population of the study. When a certain amount is selected from a population, the selected is referred to as a sample.

So, this means that, 20 represents sample of the study.

Answer:

4,684 km

Step-by-step explanation:

The system of linear equations has no solutions for any value of k except when k = 2, where it has infinitely many solutions.

(a) To reduce the augmented matrix for the system of linear equations to row-echelon form, we can write the system of equations as:

2 - y = kx

-y = k

To eliminate y in the first equation, we can multiply the second equation by (-1) and add it to the first equation:

(2 - y) - (-y) = kx - k

2 = kx - k

This gives us a new system of equations:

2 = kx - k

Now, we can represent this system in augmented matrix form:

[1 -k | 2]

(b) To find the values of k, we can examine the augmented matrix.

If the system has no solutions, it means that the rows of the augmented matrix result in an inconsistent equation, where the last row has a leading nonzero entry. In this case, for the system to have no solutions, the augmented matrix should have a row of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix [1 -k | 2] doesn't have this form, so there are no values of k that lead to no solutions.

If the system has exactly one solution, the augmented matrix should be in row-echelon form, with each row having at most one leading nonzero entry. In this case, the augmented matrix should not have any rows of the form [0 0 | c], where c ≠ 0. In our case, the augmented matrix can be reduced to row-echelon form as follows:

[1 -k | 2]

From this form, we can see that there are no restrictions on the value of k. For any value of k, the system will have exactly one solution.

If the system has infinitely many solutions, the augmented matrix should have at least one row of the form [0 0 | 0]. In our case, the augmented matrix can be reduced to:

[1 -k | 2]

From this form, we can see that if k = 2, the last row becomes [0 0 | 0]. Therefore, for k = 2, the system will have infinitely many solutions.

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Answer:

Pedro spent 9 weeks with his uncle and his friend.

Step-by-step explanation:

First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:

       [tex]3\frac{1}{2}[/tex]                   2

___________________

1       2       3       4       5       6       7       8       9       10        

[tex]3\frac{1}{2}+2=5\frac{1}{2}[/tex]

Now, you can find the and answer by adding up the number of weeks he spent with his uncle plus the weeks he spent with his friend:

       [tex]3\frac{1}{2}[/tex]                                   [tex]5\frac{1}{2}[/tex]

__________________________________

1       2       3       4       5       6       7       8       9       10  

[tex]3\frac{1}{2} + 5\frac{1}{2}=9[/tex]

According to this, the answer is that Pedro spent 9 weeks with his uncle and his friend.

Answer:

a=[tex]\sqrt{28.32}[/tex]≈5.3217 cm

Step-by-step explanation:

Use the Pythagorean Theorem

a^2+4.7^2=7.1^2

a^2+22.09=50.41

a^2=28.32

a=[tex]\sqrt{28.32}[/tex]

≈5.3217

Answer:

5.3

Step-by-step explanation:

Check the attached image for explanation if you are interested, as I did not feel like spending 20 minutes re-formatting the equations to work on Brainly.

Also, I did not do this

The new figure after the revolution is a cylinder of radius 5 and length 8

The volume is 200π

From the question, we have the following parameters that can be used in our computation:

The graph

The shape on the graph is a rectangle with

length = 5

width = 8

When revolved across the x-axis, we have the shape to be

A cylinder of radius 5 and length 8 (option a)

This is calculated as

V = πr²h

substitute the known values in the above equation, so, we have the following representation

V = π * 5² * 8

Evaluate

V = 200π

Hence, the volume is 200π

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