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The cube of any integer is of the form 9k, 9k+1, or 9k-1.

Let's consider the cube of an integer n, represented as n^3. We can express n as either a multiple of 3 (3k), one more than a multiple of 3 (3k+1), or one less than a multiple of 3 (3k-1), where k is an integer.

When we cube these three forms, we get:

(3k)^3 = 27k^3 = 9(3k^3) = 9m (where m = 3k^3)

(3k+1)^3 = 27k^3 + 27k^2 + 9k + 1 = 9(3k^3 + 3k^2 + k) + 1 = 9m + 1 (where m = 3k^3 + 3k^2 + k)

(3k-1)^3 = 27k^3 - 27k^2 + 9k - 1 = 9(3k^3 - 3k^2 + k) - 1 = 9m - 1 (where m = 3k^3 - 3k^2 + k)

From these expressions, we can see that the cube of any integer can be written in the form 9k, 9k+1, or 9k-1, where k is an integer.

Therefore, the statement is proven, and the cube of any integer is of the form 9k, 9k+1, or 9k-1.

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The order of equations based on their solutions from greatest to smallest is:3(2x - 2) > -3x + 6 = 2x + 1 > -413(x) - 2 = 3x.

We are to arrange the given equations based on their solutions and place the equation with the greatest solution on top.So, let us solve each of the given equations and check their solutions.

1. -3x + 6 = 2x + 1

We will first bring all the x terms on one side and the constants on the other side.

-3x - 2x = 1 - 6 (transferring 2x to the other side and 6 to this side)

-5x = -5 (Simplifying)

x = 1 (dividing both sides by -5)

Therefore, the solution of this equation is x = 1.

2. -413(x) - 2 = 3x

Transferring 3x to the left side,

-413(x) - 3x = 2

- (Equation modified)

-416x = 2 x = -1/208

The solution of this equation is x = -1/208.

3. 3(2x - 2)

We can solve this equation directly by multiplying the constant with the expression inside the brackets.

3(2x - 2) = 6x - 6

Therefore, the solution of this equation is x = 2.

We can see that the equation with the greatest solution is the third one as the solution is x = 2, which is greater than x = 1 and x = -1/208.

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Answer:

2 solutions

-1 and 3 is the real solutions

Answer:

b-2x=n

b-2x+2x=n+2x

b=n+2x

Step-by-step explanation:

add 2x to both sides of the equation and simplify

In order to caculate the perimeter of the given polygon, you first determine the length of each side of the polygon, just as follow:

side RS = 2 - (-2) = 2 + 2 = 4

side ST = 1 - (-3) = 1 + 4 = 5

side TQ = 2 - (-2) = 2 + 2 = 4

side QR = 1 - (-3) = 1 + 4 = 5

finally you sume all lengths:

4 + 5 + 4 + 5 = 18

Hence, the perimeters of the given polygon is 18 units

EXPLANATION

Given the equation 4.5x = 45

Dividing both sides by 4.5:

x= 45/4.5

Simplifying:

x=10

The answer is x=10

Answer:

$142.64

Step-by-step explanation:

If the numbers after the 63 are greater than 5 you round up if not you round down.

Answer:

$142.64

Step-by-step explanation:

rendering the amount with only two numbers after the decimal point, then you have come to the right post.

Answer:

18vw²y^9 + 24v^6w^5

= 6vw²( 3y^9 + 4v^5w³)

Hope this helps.

Answer:

6vw^2(3y^9 + 4v^5w^3)

Step-by-step explanation:

If you were to multiply the equation 6vw^2(3y^9 + 4v^5w^3) then the result would be

18vw^2y^9 + 24v^6w^5

Hope this helps!

Step-by-step explanation:

Answer: see in the picture.

I hope it helps...

Answer: true

Step-by-step explanation:

You can buy 10 for $7.80

$3.90 × 2 = $7.80

Answer:

∠a =50

∠b = 100

∠c = 30

Step-by-step explanation:

Answer:

About 706.5 or 707

Explanation:

3.14 • 5² (5² is also 25) = 78.5

78.5 • 9 = 706.5 or 707

Edit: Also posted a better picture for explanation. See the attachment.

To calculate the point estimate of a population proportion, collect a representative sample, determine the number of individuals with the characteristic of interest, divide it by the sample size, and the resulting value is the point estimate of the population proportion.

The point estimate of a population proportion is a single value that represents an estimate of the proportion of a certain characteristic in a population based on a sample. To calculate the point estimate, follow these steps:

Collect a representative sample from the population of interest. The sample should be randomly selected to ensure it is unbiased and reflects the population.

Determine the number of individuals in the sample who possess the characteristic of interest. Let's denote this as "x".

Calculate the sample proportion by dividing "x" by the sample size, denoted as "n". The sample proportion is the estimated proportion of the characteristic in the sample.

Sample Proportion (p-hat) = x / n

The point estimate of the population proportion is equal to the sample proportion. Therefore, the point estimate is the value calculated in step 3.

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The point estimate of a population proportion is calculated by dividing the number of successes in the sample by the sample size.

To calculate the point estimate of a population proportion, you need to follow these steps:

Mathematically, the formula for calculating the point estimate is:

Point Estimate = (Number of Successes in Sample) / (Sample Size)

Remember that the point estimate is just an estimate and may not be exactly equal to the true population proportion. The accuracy of the point estimate depends on the sample size and the variability in the population.

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Answer:

.63

Step-by-step explanation:

bc the first three numbers are less then 0 so add the three probabilities and boom magic.

To use the elimination method, we want to eliminate one of the variables (either x or y) by adding or subtracting the two equations. Let's eliminate x by multiplying the first equation by -1 and adding the two equations:

-x dt/dt - y = -t^2
-x + dy/dt = 1
--------------------
dy/dt - y = -t^2 + 1

This is a first-order linear differential equation, which we can solve using an integrating factor. The integrating factor is e^(-t), so we multiply both sides by e^(-t):

e^(-t) dy/dt - e^(-t) y = -t^2 e^(-t) + e^(-t)

The left side can be written as the derivative of (e^(-t) y), so we integrate both sides:

e^(-t) y = ∫(-t^2 e^(-t) + e^(-t)) dt + C
e^(-t) y = (t^2 - 1) e^(-t) + C
y = t^2 - 1 + Ce^t

Now we can substitute this expression for y into either of the original equations to find x. Let's use the first equation:

dx/dt + y = t^2
dx/dt + t^2 - 1 + Ce^t = t^2
dx/dt = 1 - Ce^t
x = t - Ce^t + D

So the general solution to the linear system is:

x = t - Ce^t + D
y = t^2 - 1 + Ce^t

where C and D are constants determined by initial conditions.

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Answer:

78.3

Step-by-step explanation:

To find the area do 9.1 X 8.6.

The answer is 78.26 but we have to round it to the nearest tenth. When he round it to the nearest tenth, it's 78.3.

Cheers!

Answer:

The answer is 78.3

Step-by-step explanation:

9.1 x 8.6 = 78.26

Rounded to the nearest tenth is 78.3

Answer:

P=5x3+17  P=32

Step-by-step explanation:

Answer: I believe that the answer would be "In an isosceles triangle, two of the angles are congruent."

Step-by-step explanation:

Answer:

In an isosceles triangle, two of the angles are congruent.

hope this helps :)

Answer: 4

Step-by-step explanation:

=( −2 /3)( −1 /6)

=( −2 /3 )( 6 /−1 )

= (−2)(6)/ (3)(−1)

= −12 /−3

=4

Answer:

4

Step-by-step explanation:

Since you can't divide a fraction by another fraction, you start by flipping the second fraction (-1/6 becomes -6/1) and changing the division sign to multiplication.

-2/3 x -6/1

Multiply across, numerator with numerator and denominator with denominator. Also, when multiplying or dividing negative numbers, two negatives make a positive (i.e. -2 x -6 = +12)

-2/3 x -6/1 = 12/3

12/3 = 4

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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(B) On a coordinate plane, two lines are graphed. The growing line's Y intercept is - 6, whereas the decreasing line's Y intercept is zero. the place where the lines converge ( 1, - 5).

Consider the system of equations,

y = - 5x and y = x - 6

To graph the equation y = - 5x we need to determine the points on the line.

When x = 0,

y = 0

When x = 1,

y = - 5

When x = 2.

y = - 5(2) = - 10

When x = - 1,

y = - 5( - 1 ) = 5

When x = - 2,

y = - 5 ( - 2 ) = 10

So, the point on the graph y = - 5x are ( 0, 0 ), ( 1, - 5 ), ( 2, - 10), ( - 1, 5 ), and ( - 2, 10 ).

Consider the equation,

y = x - 6

When x = 0,

y = - 6

When x = 1,

y = 1 - 6 = - 5

When x = 2,

y = 2 - 6 = - 4

When x = - 1,

y = - 1 - 6 = - 7

When x = - 2,

y = - 2 - 6 = - 8

So, the points are ( 0, - 6 ), ( 1, - 5 ), ( 2, - 4 ), ( - 1, - 7), and ( - 2, - 8).

So, the two lines intersect each other at ( 1, - 5 ).

The increasing line's y-intercept is at - 6 and the decreasing line's y-intercept is at 0.

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To test the claim that meal preference and gender are not related, you can use a chi-squared test for independence.

The null hypothesis for this test is that there is no relationship between the variables, while the alternative hypothesis is that there is a relationship. To conduct the test, you will need to calculate the chi-squared statistic and compare it to the critical value from a chi-squared distribution with one degree of freedom. The degrees of freedom for this test are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2-1)*(2-1) = 1.

To calculate the chi-squared statistic, you will need to compare the observed frequencies in the table to the expected frequencies if the null hypothesis were true. The expected frequency for each cell is calculated as the row total * column total / sample size.

For example, the expected frequency for females who prefer hamburgers is (39 * 15)/59 = 12.71. The chi-squared statistic is then calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-squared statistic would be:

((15-12.71)^2/12.71) + ((23-26.29)^2/26.29) + ((24-26.29)^2/26.29) + ((16-12.71)^2/12.71) = 7.39

To determine whether this result is statistically significant, you would compare the chi-squared statistic to the critical value from a chi-squared distribution with one degree of freedom. At a significance level of 0.05, the critical value is 3.84. Since the chi-squared statistic (7.39) is greater than the critical value (3.84), you can reject the null hypothesis and conclude that there is a relationship between meal preference and gender in this sample.

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The two triangles are equivalent triangles

Flowchart proofs are organized with boxes and arrows.

The statements given are written in the box and the reason of that statement is written just below the box.

Every statement if flowchart proof complements other statement.

The correct answer is

∠AZ = ∠BX

The two triangles are equivalent triangles.

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Answer:

1/3 = 1 serving

2/3 =2 servings

1 cup= 3 servings

so if one cup is 3 servings we can multiply 3 x 6 for an answer of 18 servings

Answer: -68.97x+ 41.61y+11.4

Step-by-step explanation:

Answer:

The median will remain unchanged and the mean will increase.

Step-by-step explanation:

The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

The Median represents the middle value of the given data when arranged in a particular order.

WE have been given boxplot that displays the average number of apple pies consumed in eating contests across a particular state.

The higher outlier is from a professional,the heavyweight contest, and the lower outlier is from a children's eating contest.

The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.

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11 1/4

Step-by-step explanation:

the yards have to be converted to feet

1 yards = 3 feet

5 yards x 3 = 15 feet

Area of a rectangle = length x width

15 x 2 1/4

15 x 9/4 = 33 3/4

33 3/4 x 1/3 = 135 /12 = 11 1/4