The length of a rectangle is eight more than twice it's width. the perimeter is 96 feet. find the dimensions

Variables:


equation:



Solution:​

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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a) The probability that they're not all right-handed is approximately 0.684.

b) The probability that they're not all left-handed is approximately 0.002.

c) The probability that there are no more than 5 righties is approximately 0.034.

d) The probability that there are exactly 4 of each handedness is approximately 0.167.

e) The probability that the majority is right-handed is approximately 0.678.

a) To calculate the probability that they're not all right-handed, we need to find the complement of the event that all of them are right-handed. Assuming each person is right-handed with a probability of 0.85, the probability of a person being non-right-handed is 1 - 0.85 = 0.15. Since the handedness of each person is independent, the probability that they're not all right-handed is (0.15)^10, which is approximately 0.684.

b) Similarly, the probability that they're not all left-handed can be calculated as (0.15)^10, which is approximately 0.002. This assumes that the probability of being left-handed is also 0.15.

c) To find the probability that there are no more than 5 righties, we need to sum the probabilities of having 0, 1, 2, 3, 4, or 5 right-handed individuals. We can calculate each probability using the binomial distribution. Assuming the probability of a person being right-handed is 0.85, the probability of having exactly k right-handed individuals out of 10 is given by (10 choose k) * (0.85)^k * (0.15)^(10-k). By summing these probabilities for k from 0 to 5, we find that the probability is approximately 0.034.

d) The probability of having exactly 4 of each handedness can also be calculated using the binomial distribution. We calculate the probability of having exactly 4 righties and 4 non-righties, which is given by (10 choose 4) * (0.85)^4 * (0.15)^6. Since there are two possibilities for each group (righties and non-righties), we multiply this probability by 2 to account for the two groups. The probability of having exactly 4 of each handedness is approximately 0.167.

e) Finally, to calculate the probability that the majority is right-handed, we need to find the probability of having 6, 7, 8, 9, or 10 right-handed individuals. Similar to part c, we sum the probabilities of these outcomes using the binomial distribution. By summing the probabilities for k from 6 to 10, we find that the probability is approximately 0.678.

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As regards iron, the tuna offers more calorie count.

Now, let's look at the math behind the comparison of beef stew and tuna. According to the statement, three ounces of beef stew and three ounces of water-packed tuna contain about the same amount of iron. However, the beef stew provides over 300 calories, while the tuna provides only about 100 calories.

Calories are a measure of energy, specifically the energy that food provides to your body when you eat it. When you consume more calories than your body needs, the excess is stored as fat, which can lead to weight gain over time. On the other hand, if you don't get enough calories, you may feel tired and sluggish, and your body may not be able to function properly.

So, why does the beef stew provide more calories than the tuna? One reason is that beef is a higher-fat food than tuna, and fat contains more calories per gram than carbohydrates or protein. Additionally, the beef stew may contain other ingredients that contribute to its calorie count, such as potatoes or other vegetables.

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Answer:

Step-by-step explanation:

\(7^{2} +x^{2} =24^{2} \\49+x^{2} =576\\x^{2} =418\\x=\sqrt{418}\)

Answer:

FGH DEJ .................

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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The solution to the given question is given below:(a) f(x) = 3x^2+4/x^2+2To differentiate the given function, we will use the quotient rule of differentiation.

which is given by,(f(x)/g(x))'=[f'(x)g(x)-f(x)g'(x)]/[g(x)]2Now, putting the given values into the formula, we get,f(x) = 3x2+4/x2+2Let f(x) = 3x2+4 and g(x) = x2+2Now,f'(x) = d/dx[3x2+4] = 6xg'(x) = d/dx[x2+2] = 2xAfter substituting all the values in the quotient rule, we get,(f(x)/g(x))'=(6x(x2+2)-2x(3x2+4))/(x2+2)2=(-6x^3-8x+12x^3+16x)/[x^4+4x^2+4] = (6x^3+8x)/[x^4+4x^2+4]Hence, f'(x) = (6x^3+8x)/[x^4+4x^2+4].Therefore, the required derivative of the given function is (6x^3+8x)/[x^4+4x^2+4].(b) f(x) = (x2 - 7x)12To differentiate the given function, we will use the chain rule of differentiation which is given by, d/dx[f(g(x))] = f'(g(x)).g'(x)Now, putting the given values into the formula, we get,Let f(x) = x^12 and g(x) = x2-7xThen,f'(x) = 12x^11g'(x) = d/dx[x2-7x] = 2x-7After substituting all the values in the chain rule, we get,d/dx[f(g(x))] = f'(g(x)).g'(x) = 12(x2-7x)11.(2x-7)Therefore, the required derivative of the given function is 12(x2-7x)11.(2x-7).(c) f(x) = x^4√6x+5To differentiate the given function, we will use the product rule of differentiation which is given by, (fg)' = f'g + fg'Now, putting the given values into the formula, we get,Let f(x) = x^4 and g(x) = √6x+5Then,f'(x) = d/dx[x4] = 4x3g'(x) = d/dx[√6x+5] = 3/√6x+5After substituting all the values in the product rule, we get,(fg)' = f'g + fg' = (4x3).(√6x+5) + (x^4).(3/√6x+5)Hence, f'(x) = (4x3).(√6x+5) + (x^4).(3/√6x+5).Therefore, the required derivative of the given function is (4x3).(√6x+5) + (x^4).(3/√6x+5).

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The derivatives of the functions of the differentiation of the given functions has been calculated.

(a) The rule of differentiation applied to

f(x) = 3x²+4/x²+2 is as follows:

f'(x) = [12x(x²+2)-(6x)(4)] / [(x²+2)²]

=> f'(x) = [12x³-24x] / [(x²+2)²]

=> f'(x) = 12x(1-x²)/[(x²+2)²].

(b) The rule of differentiation applied to f(x) = (x² - 7x)^12 is as follows:

f'(x) = 12(x²-7x)^11(2x-7).

We apply the chain rule, which is the following:

[f(g(x))]' = f'(g(x)) * g'(x).(c)

The rule of differentiation applied to f(x) = x⁴√(6x+5) is as follows:

f'(x) = 4x³ * (6x+5)¹∕² + x⁴ * 1/2(6x+5)^-1/2 * 6

=> f'(x) = [24x³(6x+5) + 3x⁴(6)]/[2(6x+5)¹∕²]

=> f'(x) = [3x³(8x²+15)]/[(6x+5)¹∕²].

Thus, the differentiation of the given functions has been calculated.

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The length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

To determine the length of t in triangle TUV, we can use the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we have:

- u = 380 inches (the length of side u)

- m∠V = 151° (the measure of angle V)

- m∠T = 25° (the measure of angle T)

We need to find the length of side t.

Using the law of sines, we can set up the equation;

sin(25°) / t = sin(151°) / 380

To solve for t, we can cross multiply and then divide by sin(25°):

t = (380 x sin(25°)) / sin(151°)

t ≈ 85.6 inches

Therefore, the length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

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The ordered pairs which make the open sentence true are:

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:

For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.

When ordered pairs = (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When ordered pairs = (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When ordered pairs = (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When ordered pairs = (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (True).

When ordered pairs = (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (True).

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Answer: DM, M, CM

Step-by-step explanation:

Answer:

Meters

Step-by-step explanation:

Meters are 100 times bigger than centimeters and 1000 times larger than a millimeter.

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

can u rewrite your answer in the chat thingy bc your equations are so close together it's hard to tell which is apart of which, I tried to answer them but I don't want you to get them wrong so rewrite it and I'll tell you the answers :)  

Answer:

The equation's result: 32,000 (Rounded)

Goal: Find the closest or equivalent result in another expression

Step-by-step explanation:

\((1.5^{15})/(0.7^{12})\\(1.5^{15})/(0.7^{12}) = (437.894)/(0.7^{12})\\437.894/(0.014)\\31636.79\)

How we got to 31,636 was by dividing from left to right.

Remember: When dividing decimals, it's like multiplying whole numbers in a way. The number(the quotient, also) ends up bigger instead of being smaller like when dividing whole numbers. If you multiply decimals, they(the product) end up smaller.

Therefore, A is the correct answer.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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The probability of at least 10 cities out 45 have a commute time greater than 30 minutes is 0.893 or 89.3%

Apply the complement rule.

Probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes,

The complement of the event is 'none of the 10 cities have a commute time greater than 30 minutes'.

The probability of the complement event can be calculated by ,

Multiplying probabilities of selecting a city with a commute time less than or equal to 30 minutes for each of 10 selections.

P(none of 10 cities have a commute time > 30 minutes) = (35/45) x (35/45) x ... x (35/45) (10 times)

Because there are 35 cities out of the total 45 that have a commute time less than or equal to 30 minutes.

So the probability that at least one of the 10 cities has a commute time greater than 30 minutes is,

1 - P(none of the 10 cities have a commute time greater than 30 minutes)

= 1 - (35/45) x (35/45) x ... x (35/45) (10 times)

= 1 - 0.1073

= 0.8926

Therefore, the probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes is 0.893 or 89.3%.

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The above question is incomplete, the complete question is:

If i randomly sample two cities from this group (consider these 45 the 'population' if you will) then what is the probability that at least one of the 10 cities i select will have a commute time greater than 30 minutes?

Answer:

Adjacent

Step-by-step explanation:

Since angle a and b are right next to each other, they would be adjacent.

Answer:

-247/7

Step-by-step explanation:

-40+8-23/7

=-40+(56-23)/7

=-40+33/7

=(-280+33)/7

=-247/7

The root of this equation is determined to be approximately 0.567143.The root is found to be approximately -0.673253.

The Newton-Raphson method is an iterative numerical technique used to find the roots of equations. In the first equation, y = f(x) = e^x - x, the initial approximation x0 is set to 0. By applying the Newton-Raphson method, successive approximations of the root are calculated until convergence is achieved. The root of this equation is determined to be approximately 0.567143.

In the second equation, x^3 + 2x^2 + 6x + 3 = 0, the root is sought within the range (-1, 0). The Newton-Raphson method is employed again, starting with an initial approximation x0 of -1. Through iterative calculations, the root is found to be approximately -0.673253.

Both equations demonstrate the effectiveness of the Newton-Raphson method in finding roots within specific ranges by iteratively refining approximations until a satisfactory solution is obtained.

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The number of children are there in the given scenario are 400.

Given that, the ratio of children to adults on a school trip is initially 10:1.

Here, the given ratio can be written as 10x:1x

5 more children and 5 more adults join the trip so that the ratio is now 9:1

10x+5:1x+5

The new ratio is (10x+5)/(x+5) = 9/1

10x+5=9(x+5)

10x+5=9x+45

10x-9x=45-5

x=40

So, the number of children =10x=400

Therefore, the number of children are there in the given scenario are 400.

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Answer:

the equation for the function m(t) point-stope form will be:

Hence, option D is correct.

The graph is attached below.

Step-by-step explanation:

Given

Point (10, 25)

Slope m = 2.5

To determine

Write the equation for the function m(t) point-stope form.

We know that the point-slope form of the line equation is

\(y-y_1=m\left(x-x_1\right)\)

where

In our case:

so

substituting the values m = 2.5 and the point (10, 25) in the equation

\(y-y_1=m\left(x-x_1\right)\)

\(y - 25 = 2.5 (x - 10)\)

Therefore, the equation for the function m(t) point-stope form will be:

Hence, option D is correct.

The graph is attached below.

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

The coordinates of point A = (-5, -4),

The coordinates of the point B = (-3, 3)

Let the point at the distance 3/4 from A to B = P

The coordinates of point 3/4 from A to B = P

At the x-coordinate, the distance from B to A is =  -3-(-5) = 2 units.

At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.

Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)

                                            P = (-5 + (3/4×(2), -4 + 3/4×(7))

                                            P = (-3.5, 1.25)

Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).

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The complete question is -

What are the coordinates of the point 3/4 of the way from A to B?

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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The simplified form of 2cos²θ - cos2θ simplifies to 1 using trigonometric identities.

To simplify the expression 2cos²θ - cos2θ, we'll use trigonometric identities to rewrite the terms in a more manageable form.

1. Start with the double angle identity for cosine: cos2θ = 2cos²θ - 1

2. Substitute the above identity into the expression:

2cos²θ - (2cos²θ - 1)

3. Distribute the negative sign:

2cos²θ - 2cos²θ + 1

4. Combine like terms:

1

So, the simplified expression is 1.

The given expression 2cos²θ - cos2θ simplifies to 1.

This result can be verified using the double angle identity for cosine, which states that cos2θ = 2cos²θ - 1.

By substituting this identity into the expression, we get 2cos²θ - (2cos²θ - 1), and simplifying further yields 2cos²θ - 2cos²θ + 1, which simplifies to 1.

This simplified form can be useful in various mathematical and trigonometric calculations.

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The class which has a greater percent of students who ride the bus is Walter's class

Walter's class:

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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Answer:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.

$8 .   YES

$9 .    HELL NO

$11 .   DEFINITLY NOT

$13 .  GET OUTTA HERE

$14 .   MMM YES

Step-by-step explanation:

Answer:

A and E or 8, 14

Step-by-step explanation:

The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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Answer:

n^2-8 is the answer

Step-by-step explanation: