Q1: Use simple exponential smoothing with a = 0.75 to forecast the water pumps sales for February through May. Assume that the forecast for January was for 25 units. [4 marks) Month January February March April Air-condition sales 28 72 98 126

Answer:

The same line.

Step-by-step explanation:

We have to decide whether the lines are perpendicular, neither parallel nor perpendicular, parallel, or the same line. We can check if a line is perpendicular by finding the slope. The line is perpendicular if the slope of one line is the negative reciprocal of the second line.

Let's try to solve for the Y-intercept (where X = 0) of both of these functions.

y + 3x = -4

y + 3(0) = -4

y + 0 = -4

:. y = -4

And now the other one:

y = -3x-4

y = -3(0) - 4

:. y = -4

Since y = -4 in both cases, well, now we have our answer. The answer is it's the same line, so the fourth answer is correct. All the other ones - perpendicular, neither parallel nor perpendicular, and parallel - are incorrect by process of elimination. We don't actually have to keep going from here. But we can (although I won't).

The width of the rectangle is x + 4

Since the area of the rectangle is x^2 + 15x + 44, the product that give the value can be solved by factorization

To factorize the expression x^2 + 15x + 44, we need to find two numbers whose product is 44 and whose sum is 15. These numbers are 11 and 4, because 11 times 4 is 44 and 11 plus 4 is 15.

Now we can write the expression as:

x^2 + 11x + 4x + 44

Grouping the terms in pairs:

(x^2 + 11x) + (4x + 44)

Factoring out the greatest common factor from each pair:

x(x + 11) + 4(x + 11)

Now we can see that we have a common factor of (x + 11):

(x + 11)(x + 4)

Therefore, the factored form of x^2 + 15x + 44 is:

(x + 11)(x + 4)

the width of the rectangle is x + 4

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The volume of the bookshelf is 1/4 cubic units.

The amount of space a three-dimensional object occupies is measured by its volume.

A cubic unit, such as a cubic foot, cubic metre, or cubic metre is typically used to express it.

An object's volume can be calculated by figuring out how much space is contained within its boundaries. Depending on the shape of the object, different mathematical formulas can be used to accomplish this.

To calculate the volume of the bookshelf, we need to add the volumes of the two cubes together.

The length of one side cubed determines a cube's volume.

Since each cube has a side of (1/2), the volume of each cube can be calculated as:

(1/2)³ = 1/8

To get the total volume of the bookshelf, we can add the volumes of the two cubes:

1/8 x 2 = 1/4

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A graph of four points with integer coordinates that are each 3 units away from (2, 3) is shown in the image attached below.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).

Where:

In order to write an equation that models the four points with integer coordinates that are each 3 units away from (2, 3), we would have to apply a set of translation to f(x) by 3 units:

A (5, 3)

B (-1, 3)

C (2, 6)

D (2, 0)

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Answer:

Step-by-step explanation:

THE ANSWER IS 21

The simplified expression using rational numbers is 82.25.

First, let's start by defining what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. For example, 2/3, 5, and -7/2 are all rational numbers.

Now, let's simplify the expression using rational numbers. We can start by simplifying (5.5)² and 9(5.5)².

(5.5)² is equal to 30.25, which is a rational number because it can be expressed as 121/4.

9(5.5)² is equal to 9 times 30.25, which is equal to 272.25. This is also a rational number because it can be expressed as 109/4.

Next, let's simplify √5.75. To do this, we need to express the square root as a rational number. We can do this by rationalizing the denominator.

To rationalize the denominator, we multiply both the numerator and denominator of the expression by the conjugate of the denominator. In this case, the conjugate of √5.75 is √5.75.

So, 5.75√ can be simplified as follows:

5.75√ = 5.75√5.75/√5.75

= 5.75√5.75/5.75

= √5.75

Now, we can rewrite the expression as:

(121/4) + √5.75 + (109/4) + 5.75 + 9

Combining like terms, we get:

(121/4) + (109/4) + 15.75 + 9

Simplifying further, we get:

(230/4) + 15.75 + 9

= 57.5 + 15.75 + 9

= 82.25

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(a) Total number of trips = 270

(b) There are 33 different visits that could make.

We have the information:

There are 18 major sea islands in the queen Elizabeth islands of Canada. There are 15 major lakes in Saskatchewan, Canada.

Let us say that A indicates the major sea Islands and B indicates the major lakes.

Taking both the cases as events, we will use multiplication principle.

Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

(a) A × B = 18 × 15

Total number of trips = 270

(b) |A| = 18

|B| = 15

A ∩B = θ         (as we cannot visit both an island and lake)

Addition Principle: There are |A| + |B| ways to choose an element form

A ∪ B , when A and B are the finite sets with A ∩B = θ

|A ∪ B| = |A| + |B| = 18 + 15 = 33

Thus, There are 33 different visits that could make.

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Roehr Corporation Additional Paid-in Capital--Common account will increase by $110,000 by issuing 20,000 shares of $0.50 par common stock for $6 per share.

When a corporation issues common stock, the par value of the stock is recorded in the Common Stock account, and any amount received above the par value is recorded in the Additional Paid-in Capital--Common account. In this case, Roehr Corporation The par value of the common stock is

Total par value = Par value per share x Number of shares

= $0.50 x 20,000

= $10,000

The total amount received from issuing the stock is $6 per share x 20,000 shares = $120,000.

The additional paid-in capital is calculated as the difference between the total amount received and the total par value:

Additional paid-in capital = Total amount received - Total par value

= $120,000 - $10,000

= $110,000

Therefore, the answer is (B) $110,000.

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Step-by-step explanation:

Let A(x1,y1)=(-3,1), B(x2,y2)=(5,6)  be the points of a line segment.

Mid point = [tex]\sf{ \dfrac{x1+x2}{2} , \dfrac{y1+y2}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-3+1}{2} , \dfrac{1+6}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-2}{2} , \dfrac{7}{2} }[/tex]

Step-by-step explanation:

Put '16' where 'x' is and compute

3/4 ( 16 ) + 7 = f(16) = 19

In the number 425.871, the digit with the greatest value is 4 because it is in the hundreds place, representing a value of 400.

In the number 425.871, each digit has a position and a value based on where it's located in the number. The position starting from the right of the decimal point we call the tenths, hundredths, and thousandths place, respectively. Similarly, the position to the left of the decimal point is called the ones, tens, hundreds place, etc., respectively. In this case, the digit with the greatest value is the one in the hundreds place, which is 4. This is because it represents 400, which is greater than any other individual digit's value in the number 425.871.

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The estimated area is about 22.5 square units

To estimate the perimeter of a patio, you need to measure the length of each side and then add those lengths together.

Here's a step-by-step guide to help you:

Determine the shape of your patio: Before you can estimate the perimeter, identify whether your patio is a rectangle, square, circle, or any other shape. The method for calculating the perimeter will vary depending on the shape.

Measure the sides:

a. For rectangular or square patios: Measure the length (L) and width (W) of the patio using a measuring tape. Ensure that the measurements are taken in the same unit (e.g., feet, meters, etc.).

b. For circular patios: Measure the diameter (D) or radius (R) of the patio. The radius is the distance from the center of the circle to any point on its edge.

c. For irregularly-shaped patios: Break the patio down into smaller, regular shapes (like rectangles, squares, or triangles), and measure each side of these smaller shapes.

Calculate the perimeter:

a. For rectangular or square patios: Use the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

b. For circular patios: Use the formula P = 2πR or P = πD, where P is the perimeter, R is the radius, and D is the diameter. π (pi) is approximately 3.14159.

c. For irregularly-shaped patios: Add up the side lengths of each smaller shape that you've broken the patio into. The sum of these lengths will give you the total perimeter.

(look at the image)

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A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = [tex]x^2[/tex] * h = 8500

Solving for h, we get:

h = 8500 / [tex]x^2[/tex]

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = [tex]2x^2[/tex] + 4x(8500 / [tex]x^2[/tex]) = 2[tex]x^2[/tex]+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/[tex]x^2[/tex] = 0

Multiplying both sides by [tex]x^2[/tex] and solving for x, we get:

x = (8500/2[tex])^(1/3)[/tex] ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / [tex]x^2[/tex] ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = [tex]X^2 + 34000/X[/tex]

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

[tex]X^{2Y} = 8500[/tex]

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = [tex]X^2 + 4XY[/tex]

We can substitute the value of Y from the equation for volume, giving:

Surface Area = [tex]X^2 + 4X(8500/X^2)[/tex]

Surface Area = [tex]X^2 + 34000/X[/tex]

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = [tex]20.5^2 + 4(20.5)(8500/20.5^2)[/tex]= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

[tex]X^2Y = 8500[/tex]

[tex](20.5)^2 Y = 8500[/tex]

[tex]Y = 8500/(20.5)^2 = 16.87[/tex] inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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Answer:

3/5 = 60% = 0.6

In the bottom row, 3/5 is the wrong fraction. 2/3 is the correct fraction.

in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

The equation of the line parallel to PQ that passes through the point (6, -1) is y = (-5/6)x + 4.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that: the coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).

We can find the slope of line PQ.

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively.

m = (-2 - 8) / (9 - (-3))

m = -10 / 12

m = -5/6

Since we want the equation of a line parallel to PQ, it will have the same slope.

Hence, the equation of the line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point (6, -1) and m is the slope we found earlier.

Plugging in the values, we get:

y - (-1) = (-5/6)(x - 6)

y + 1 = (-5/6)x + 5

y = (-5/6)x + 5 - 1

y = (-5/6)x + 4

Therefore, the equation of the parallel line to PQ is y = (-5/6)x + 4.

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Answer: Luis will spend a total of $22,868.48 on his lease.

Step-by-step explanation: To calculate the total cost of Luis's lease, we need to multiply the monthly cost by the number of months in the lease:

Total cost = monthly cost x number of months

The number of months in 4 years is 4 x 12 = 48 months.

Therefore, the total cost of Luis's lease is:

Total cost = $475.86/month x 48 months

Total cost = $22,868.48

So Luis will spend a total of $22,868.48 on his lease.

Answer:

  5 meters

Step-by-step explanation:

You want to know the width of a rectangular living room that is 12 m along one side and 13 m along the diagonal.

The diagonal of a rectangle is the hypotenuse of each of the right triangles it creates by dividing the rectangle in half. If one side length is 12 and the diagonal is 13, these measures are part of the {5, 12, 13} Pythagorean triple.

The width of the living room is 5 meters.

__

Additional comment

You can use the Pythagorean theorem to find the missing length:

  13² = 12² +w²

  169 -144 = w²

  w = √25 = 5

The width of the living room is 5 meters.

Other Pythagorean triples you see in algebra, trig, and geometry problems are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41} and their multiples.

The polynomials that are equivalent to  (x-3y+72)2 are

A polynomial is described as an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

A polynomial equation in two variables is an equation of the form

p(x, y) = q(x, y) where both p(x, y) and q(x, y) are polynomials in two variables.

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The digit 5 in 89.059 is greater than the digit 5 in 78.365.

To compare the digit 5 in the numbers 89.059 and 78.365, we need to look at the place value of the digit 5 in both numbers. In 89.059, the digit 5 is in the thousandth place, while in 78.365, the digit 5 is in the hundredth place.

Since the digit 5 in the thousandth place has a greater place value than the digit 5 in the hundredth place, it means that the digit 5 in 89.059 is greater than the digit 5 in 78.365.

To understand this concept better, consider the place value system of decimal numbers, where each digit represents a specific place value. The rightmost digit represents the units, the next digit to the left represents the tens, and so on.

Moving leftwards, each digit's place value increases by a factor of 10. Thus, the digit 5 in the thousandth place has a place value of 0.001, which is greater than the place value of the digit 5 in the hundredth place, which is 0.01. Therefore, the digit 5 in 89.059 is greater than the digit 5 in 78.365.

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Using percentages we know that Terrel has the best free throw statistics which is 70.83%.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

So, in the given situation where we need to get whose statistics are the best.

We need to calculate the percentages in all cases as follows:

Jack: 18/39*100 = 46.15%

Henry: 54%

Terrel: 17/24*100 = 70.83%

Riley: 9/23*100 = 39.13%

Since Terrel has the highest %, so he has the best free throw statistics.

Therefore, using percentages we know that Terrel has the best free throw statistics which is 70.83%.

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If your business starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness is b) 66 weeks

Compound growth denotes the procedure of generating profits not only on the investment's principal amount, but also on the accumulated interest.

It is essentially reallocating its earnings where the investor's interest is integrated with the beginning sum, while additional interest is contingent on this amplified amount.

The purposeful act of compounding can yield noteworthy accomplishments over time, since interest earned from pre-existing income inflates drastically in value due to accruing interest outlays, and hence boosts the final outcome substantially and rapidly- resulting in exponential growth of the given input.

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The equation of the circle centered at (4, -5) with radius 7 is (x - 4)²+ (y + 5)² = 49.

A circle is a two-dimensional form that may be described as a collection of points (locus) that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)²= r²

In this case, the center of the circle is (4, -5), and the radius is 7. So the equation of the circle is:

(x - 4)² + (y - (-5))² = 7²

(x - 4)² + (y + 5)² = 49

Therefore, the equation of the circle centered at (4, -5) with radius 7 is (x - 4)² + (y + 5)² = 49.

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The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.

Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.

Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.

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To proof that ΔLMQ ≅ ΔNPQ; we use the given statement "∠L is congruent to ∠N"

To complete the proof that ΔLMQ is congruent to ΔNPQ, we have to follow the following steps.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

We will apply ASA method to proof that ΔLMQ ≅ ΔNPQ;

∠L is congruent to ∠N

Length LM is congruent to length NP

Looking at the options, only one was stated. (∠L is congruent to ∠N).

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Answer: is option (3) -4x²-6.

Step-by-step explanation: First, we need to add the two given polynomials:

4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3

Now, we need to multiply this sum by 2:

2(-2x^2 - 3) = -4x^2 - 6

Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4

The fewest number of minutes it will take Jeremy and Michael to solve 10 Rubik's cube is 16 with a speed such that Jeremy solve one in 4 minutes and Michael solves 5 in 12 minutes.

To solve the following word problem,

Time taken by Jeremy to solve one cube = 4 minutes = 240 seconds

Time taken by Michael to solve 5 cubes = 12 minutes

Time taken by Michael to solve 1 cube = [tex]\frac{12}{5}[/tex] minutes = 144 seconds

Since one solves the cube alone, they do it individually,

For the first 12 minutes,  Michael solves 5 cubes and Jeremy solves 3 cubes ([tex]\frac{12}{3}[/tex])

Then, to solve 2 or more cubes Michael takes 288 seconds

And if Michael and Jeremy each solve one cube it takes them 144 seconds and 240 seconds respectively.

Therefore, the second situation is responsible for solving in the least time which comes out to be 12 minutes + 4 minutes (240 seconds) is 16 minutes.

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Answer:

Let's use a system of equations to solve the problem.

Let x be the number of regular admission tickets sold, and y be the number of fast pass tickets sold.

From the problem, we know that:

x + y = 104 (equation 1)

and

8x + 22y = 1280 (equation 2)

We can use equation 1 to solve for x in terms of y:

x = 104 - y

Substituting this expression for x into equation 2, we get:

8(104 - y) + 22y = 1280

Simplifying and solving for y, we get:

832 - 8y + 22y = 1280

14y = 448

y = 32

So the student sold 32 fast pass tickets.

To find the number of regular admission tickets sold, we can substitute y = 32 into equation 1 and solve for x:

x + 32 = 104

x = 72

So the student sold 72 regular admission tickets.

Therefore, the student sold 72 regular admission tickets and 32 fast pass tickets.

There are almost 8 different dessert options that can be served.

Given that there are four fruit alternatives (watermelon, cantaloupe, pineapple and mango) and two ice cream selections (lemon or piquin chilli), the question asks how many different dessert options are offered. We can utilise the multiplication principle of counting. In this case, there are 4 ways to choose a fruit and 2 ways to choose an ice cream flavor. Using the multiplication principle, we can multiply these choices to find the total number of dessert options:

4 (fruit options) x 2 (ice cream options) = 8

Therefore, there are 8 different dessert options that can be served.

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--The complete Question is, Today's dessert is any of these fruits: watermelon, cantaloupe, pineapple or mango, accompanied by lemon or piquin chili ice cream. How many different desserts can be served? --

Answer: 2/3

Step-by-step explanation: 1/2 converted to 6ths is 3/6 add them together and it’s 4/6 simplify that and it’s 2/3