Write an equation that represents the line.

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Part a

we have that

the volume of the box is equal to

V=L*W*H

so

In this problem

the height H is equal to H=x

L=(10-2x) in

W=(8-2x) in

substitute in the formula

V=(10-2x)(8-2x)(x) in3

apply distributive property

V=(80-20x-16x+4x^2)(x)

V=(4x^3-36x^2+80x) in3

Part b

For x=0.7 in

V=4(0.7)^3-36(0.7)^2+80(0.7)

V=39.732 in3

For x=2.3 in

V=4(2.3)^3-36(2.3)^2+80(2.3)

V=42.228 in3

so

the change in the box volume increases (42.228-39.732)=2.5 in3

For x=3.2 in

V=4(3.2)^3-36(3.2)^2+80(3.2)

V=18.432 in3

the change in the box volume decreases (42.228-18.432)=23.8 in3

Two of them have the same remaining. The proof using the pigeonhole principle is now complete.

When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.

If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.

So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.

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The total amount of kinetic and potential energy in a system is called mechanical energy.

Mechanical energy is the sum of kinetic energy and potential energy within a system. Kinetic energy (KE) is the energy possessed by an object due to its motion, and it is calculated using the formula KE = (1/2)mv², where m is the mass of the object and v is its velocity. Potential energy (PE) is the energy possessed by an object due to its position or condition, and it can be gravitational potential energy, elastic potential energy, or other forms. The total mechanical energy (ME) is obtained by adding the kinetic and potential energy together, so ME = KE + PE.

In summary, the total amount of kinetic and potential energy in a system is referred to as mechanical energy. This energy accounts for both the motion and position-related energies within the system. The calculation of mechanical energy involves summing the kinetic energy, which depends on the mass and velocity of the objects, with the potential energy, which can arise from factors such as gravity or elasticity. Understanding and analyzing the mechanical energy in a system can provide insights into its overall energy distribution and behavior.

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Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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Here are the factored forms of the given trinomials:
1. p^2 - 13p + 30 = (p - 10)(p - 3)
2. n^2 - 8n - 65 = (n - 13)(n + 5)
3. x^2 + 6x + 9 = (x + 3)(x + 3) or (x + 3)^2


To factor a trinomial, we need to find two numbers that multiply to the constant term (the last term) and add up to the coefficient of the middle term. Once we find these two numbers, we can write the trinomial as the product of two binomials in the form (x + a)(x + b), where a and b are the two numbers we found.

Let's use the first trinomial as an example. We need to find two numbers that multiply to 30 and add up to -13. One possible pair of numbers is -10 and -3, because (-10)(-3) = 30 and (-10) + (-3) = -13. Therefore, we can write p^2 - 13p + 30 as (p - 10)(p - 3).

We can use the same method to factor the other two trinomials. For n^2 - 8n - 65, we need two numbers that multiply to -65 and add up to -8. One possible pair of numbers is -13 and 5, because (-13)(5) = -65 and (-13) + 5 = -8. Therefore, we can write n^2 - 8n - 65 as (n - 13)(n + 5).

For x^2 + 6x + 9, we need two numbers that multiply to 9 and add up to 6. The only possible pair of numbers is 3 and 3, because (3)(3) = 9 and 3 + 3 = 6. Therefore, we can write x^2 + 6x + 9 as (x + 3)(x + 3) or (x + 3)^2.


To factor a trinomial, we need to find two numbers that multiply to the constant term and add up to the coefficient of the middle term. Once we find these two numbers, we can write the trinomial as the product of two binomials in the form (x + a)(x + b), where a and b are the two numbers we found. In the examples given, we found the factored forms of p^2 - 13p + 30, n^2 - 8n - 65, and x^2 + 6x + 9.

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Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

Answer:

  the correct choice is marked

Step-by-step explanation:

Let x represent the smaller number. Then the larger number is 8x, and the difference is ...

  8x -x = 280

  7x = 280 . . . . . simplify

  x = 40 . . . . . . divide by 7

The larger number is 8x = 8(40) = 320.

_____

Additional comment

Effectively, we have solved for the multiplier (40) that gives the ratio with 320 on top and a difference between top and bottom of 280:

  \(\dfrac{8}{1}=\dfrac{8\cdot40}{1\cdot40}=\dfrac{320}{40}\)

Answer:

x = 107

Step-by-step explanation:

44+29+107=180

a triangle equals 180 with all the degrees added together :)

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

The sum of the expression is 3.5x+6.8.

Given that are two expressions, we need to find the sum of the expressions,

The expression is a mathematical statement which is constructed by putting arithmetical operations, variables and numbers together.

So, finding the sum.

(-4.25x + 9) and (8x - 2.2)

Putting the sign of addition,

= (-4.25x + 9) + (8x - 2.2)

Opening the brackets,

= -4.5x + 9 + 8x - 2.2

Combining the like terms.

= 8x-4.5x + 9-2.2

Operating the like terms,

= 3.5x+6.8

Hence, the sum of the expression is 3.5x+6.8.

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The length of the rectangle is 8 feet or 4 feet and the breadth of the rectangle is 4 feet and 8 feet.

What are the area and perimeter of a rectangle?

Area:- It is the quantity that expresses the extent of the rectangle. The formula to find the area of a rectangle is = l×b, where l is the length of the rectangle and b is the breadth of the rectangle.

perimeter:- It is the length of the close path that outlines the rectangle. The formula to find the perimeter of a rectangle is = 2×(l+b); where l is the length of the rectangle and b is the breadth of the rectangle.

Given,

the area of the rectangle, l×b = 32 square feet -----(1)

the perimeter of the rectangle, 2×(l+b) = 24 feet -----(2)

from equation(1),

\(l \times b = 32\)

\(l = \frac{32}{b} \)

putting the value of l in equation (2) we get,

\(2 \times ( \frac{32}{b} + b) = 24\)

\(2 \times \frac{32}{b} + 2b = 24\)

\( \frac{64}{b} + 2b = 24\)

\( \frac{64 + 2 {b}^{2} }{b} = 24\)

\(64 + 2 {b}^{2} = 24b\)

\(2 {b}^{2} - 24b + 64 = 0\)

\(2 {b}^{2} - 16 {b}^{2} - 8b + 64 = 0 \)

\(2b(b - 8) - 8(b - 8) = 0\)

\((2b - 8)(b - 8) = 0\)

\(2b - 8 = 0 \: or \: l - 8 = 0\)

\(b = \frac{8}{2} \: or \: b = 8\)

\(b = 4 \: or \: b = 8\)

putting values of b in,

\(l = \frac{32}{b} \)

\(l = \frac{32}{4} \: or \: l = \frac{32}{8} \)

\(l = 8 \: or \: l = 4\)

Hence, the possible values of the length of the rectangle are 8 feet or 4 feet, and the breadth of the rectangle is 4 feet or 8 feet.

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Answer:

5 1/3 bags

Step-by-step explanation:

12/9 = 1 1/3 bags per pot

4 * 1 1/3 = 5 1/3 bags to fill the pots

Answer:

3 bags

Step-by-step explanation:

Given

Solving

The factors of 54m³ - 32y³ are 2m³, 3 - 2y, and 9 + 6y + 4y². The expression can be written as 2m³(3 - 2y)(9 + 6y + 4y²) after factoring out the GCF and recognizing the expression inside the parentheses as a difference of cubes.

To factor 54m³ - 32y³, we can start by finding the greatest common factor (GCF) of the two terms. The GCF of 54m³ and 32y³ is 2m³, so we can write:

54m³ - 32y³ = 2m³(27 - 16y³)

Now we have factored out the GCF, and we can further simplify the expression inside the parentheses by recognizing that it is a difference of cubes. Specifically, we can use the formula:

a³ - b³ = (a - b)(a² + ab + b²)

If we let a = 3 and b = 2y, then we have:

27 - 16y³ = (3)³ - (2y)³ = (3 - 2y)(9 + 6y + 4y²)

Putting this back into our original expression, we get:

54m³ - 32y³ = 2m³(27 - 16y³) = 2m³(3 - 2y)(9 + 6y + 4y²)

Therefore, the factors of 54m³ - 32y³ are 2m³, 3 - 2y, and 9 + 6y + 4y².

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Answer:

B

Step-by-step explanation:

√((-20)²+21²)=√(400+441)=√841=29

cos θ=-20/29

sec θ=-29/20

Answer:e

Step-by-step explanation:

The volume of a rectangular box could be 24 cubic meters.

"It is the measure of the three-dimensional space enclosed by a surface, measured in cubic units."

\(V=l\times w\times h\), where 'l' represents the length, w represents the width and h represents the height of the rectangular box.

For given example,

Since, the volume is measured in cubic units, the volume of a rectangular box could be 24 cubic meters.

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Answer:

Correct option: third one -> x > 2

Step-by-step explanation:

Writing the inequation from the sentence in the question, we have:

\((5/6)x - 1/3 > 1\ 1/3\)

To solve this inequation we can do the following steps:

\((5/6)x > 1\ 2/3\)

\((5/6)x > 5/3\)

\(x > (5/3) / (5/6)\)

\(x > (5/3) * (6/5)\)

\(x > 2\)

So the correct option is the third one: x > 2

Answer:

The answer is C.

x>2

Step-by-step explanation:

on edge

Answer:

Step-by-step explanation:

400 + 0.03x > 700

Answer:

2 is the slope

Step-by-step explanation:

the equation is y=mx+b so if it is

y= 2x+7 that means the slope is 2

Answer:

2

Step-by-step explanation:

This equation is in y=mx+b form.

Slope = m

Y-intercept = b

This will give you the slope of 2 :)

Answer:

we divide by the number of data points, N. If the data is a sample from a larger population, we divide by one fewer than the number of data points in the sample, n − 1 n-1 n−1 .

Step-by-step explanation:

Answer:

25% of the mix is raisins

True, there are some undefined terms like line, point angle, distance between two points .

Which definition of angle is the best?

How does Euclid define angle?

A plane angle is the inclination toward one another of two intersecting, non-straight lines in the plane.

True, there are some undefined terms like line, point angle, distance between two points .

we intuitively know about the angle but can not give mathematical definition .

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\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{240\% of 25}}{\left( \cfrac{240}{100} \right)25}\implies 60~\hfill \underset{\textit{selling price}}{\stackrel{25+60}{85}}\)

As slope is undefined, then the slope of the line is parallel to the x axis.

In this problem we have a line that passes through two points, the slope is determined by definition of secant line:

m = [- 9 - (- 6)]/(8 - 8)

m = - 3/0

As slope is undefined, then the slope of the line is parallel to the x axis.

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Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

Answer:

I think x equals 7.5

Step-by-step explanation:

Please let me know if this was correct or what you were looking for. Thanks!

Answer:

0, 1, 2, 3, 4....

Step-by-step explanation:

Part A: Wednesday's stock value is 4 times Tuesday's. Friday's value is one-fifth of Thursday's.
Part B: Mr. Kwon should sell on Monday, the day with the highest number stock value.



Part A:
To find the value of the stock on Wednesday, we know that it was 4 times its value on Tuesday. Let's denote the value on Tuesday as x. Therefore, the value on Wednesday would be 4x.

Value on Wednesday = 4 * Value on Tuesday = 4 * x

To find the value of the stock on Friday, we know that it was one-fifth of what it was on Thursday. Let's denote the value on Thursday as y. Therefore, the value on Friday would be one-fifth of y.

Value on Friday = (1/5) * Value on Thursday = (1/5) * y

Part B:
Mr. Kwon should sell his stock on the day it has the greatest worth, which is when it will make the greatest profit. From the given information, we can see that the value of the stock decreases over time. Therefore, Mr. Kwon should sell his stock on Monday, the day when it initially costs $58. This ensures that he sells it at the highest value and makes the greatest profit.

For Question 7:
The correct answers indicating that multiplication should be used are A (times), C (product of), and F (at this rate). These phrases suggest the combining of quantities or the calculation of a total by multiplying values together. Multiplication is the appropriate operation when interpreting these phrases in a mathematical context.


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a) Activity that should be crashed first to reduce the project duration by 1 day is B.

b) Activity that should be crashed next to reduce the project duration by one additional day is C.

c) Total cost of crashing the project by 2 days = $10,000.

To determine the activities that should be crashed first and next, we need to consider the critical path method (CPM). The critical path is the longest sequence of activities that determines the total project duration. Crashing activities on the critical path will reduce the project duration.

Let's calculate the project duration and costs for each activity:

Activity A:

Normal Time: 7 days

Crash Time: 6 days

Normal Cost: $5000

Total Cost with Crashing: $5600

Activity B:

Normal Time: 4 days

Crash Time: 2 days

Normal Cost: $1500

Total Cost with Crashing: $3400

Immediate Predecessor(s): A

Activity C:

Normal Time: 11 days

Crash Time: 9 days

Normal Cost: $4200

Total Cost with Crashing: $6600

Immediate Predecessor(s): B

To find the critical path, we add the normal times of each activity:

Critical Path: A -> B -> C

a) Activity that should be crashed first to reduce the project duration by 1 day:

Since the critical path includes activities A, B, and C, we need to identify which activity's crash time can reduce the project duration by 1 day. The activity that can achieve this is B since its crash time is 2 days compared to activity A's crash time of 6 days. Therefore, activity B should be crashed first.

b) Activity that should be crashed next to reduce the project duration by one additional day:

After crashing activity B, the project duration will be reduced by 1 day. To further reduce the duration by an additional day, we need to determine which activity's crash time can achieve this. The activity that can achieve this is C since its crash time is 9 days compared to activity A's crash time of 6 days. Therefore, activity C should be crashed next.

c) Total cost of crashing the project by 2 days:

The total cost of crashing the project by 2 days is the sum of the total costs for the crashed activities:

Total cost of crashing = Total cost of crashing activity B + Total cost of crashing activity C

                   = $3400 + $6600

                   = $10,000

Therefore, the total cost of crashing the project by 2 days is $10,000.

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Complete Question:

Three activities are candidates for crashing on a project network for a large computer installation (all are, of course, critical). Activity details are in the following table.

a) Activity that should be crashed first to reduce the project duration by 1 day is

b) Activity that should be crashed next to reduce the project duration by one additional day is

c) Total cost of crashing the project by 2 days =