Month Sales
Jan 34
Feb 36
Mar 39
Apr 37
May 38
June
Using exponential smoothing, with an alpha value of 0.2 and assuming the forecast for Jan is 34, what is the forecast for June?
a. 37.5
b. 36.1
c. 35.6
d. 32.4
What is the MAD value for the two-month moving average?
a. 2.67
b. 3.0
c. 4.5
d. 1.

To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

The partial fraction decomposition for the given fraction is:

(4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)) = A/x + B/x^(2) + C/(x+3) + D/(x^(2)+2x+9) + E/(x^(2)+1) + F/(x^(2)+1)^(2) + G/(x^(2)+1)^(3)

Where A, B, C, D, E, F, and G are constants that need to be determined.

To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

However, since the question only asks to set up the partial fraction decomposition, we do not need to solve for the constants at this time.

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The value of r when 2^(r)=(1)/(32) is -5. This can be derived by taking the logarithm of both sides of the equation. Since log2 (2^r) = r and log2 (1/32) = -5, then r = -5.

In order to work out the value of r when 2^(r) = 1/32, we need to use logarithms. Logarithms are a way of expressing a number as the power of another number. Specifically, the logarithm of a number x is the exponent y to which a given base must be raised to equal x.

In this case, the base is 2, so log2 (2^r) = r. Therefore, to work out the value of r, we need to find the logarithm of 1/32. This can be done by dividing 1 by 32 and taking the logarithm of the result. We get log2 (1/32) = -5. Therefore, r = -5.

Since the question specifies that we should give the answer as an integer or as a fraction in its simplest form, we must conclude that the answer is -5. It is impossible to reduce this fraction any further, so it is already in its simplest form.

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The volume of 9/5x2/3x is 2/15.

Volume is the amount of space an object or substance occupies or contains. It is measured in three-dimensional space and is often given in cubic units such as cubic centimeters, cubic meters, and cubic millimeters. Volume is an important concept in physics, chemistry, and other sciences, and is used to describe the size of all kinds of substances, from solids, liquids, and gases to particles and energy fields. Volume is also used to compare the relative sizes of different objects, and to measure the capacity of containers.

To calculate this, we first need to multiply 9/5 and 2/3 together. This gives us 18/15. Then, we multiply this by x. This gives us 2/15x. Therefore, the volume of 9/5x2/3x is 2/15.

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Answer:

This

Step-by-step explanation:

( x y z) = (-1,7,4) explanation is big

those are opposite angles therefore they are equal

3x - 3 = 2x + 13

solve for x

x = 16

Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x.

We should know that the 2 angles given are Vertical Angles.

Vertical Angles are angles that are opposite of each other. These angles are equal to each other if 2 or more lines are straight.

Let's set the angles equal to each other.

[tex]3x-3=2x+13[/tex]

Simplify:

[tex]x=16[/tex]

The value of x is 16.

Answer:

Step-by-step explanation:

2-Bs:  4 x 3.8 = 15.2     2 x 15.2 = 30.4 m²

2-Cs:  11.5 x 3.8 = 43.7   2 x 43.7 = 87.4 m²

Total S.A. = 92 + 30.4 + 87.4 = 209.8 m²

Answer: 2.98m squared i think im not sure im just guessing im still not fully awake yet bro.

Step-by-step explanation:

The missing angle as labelled in the task content and required to be determined is; 33°.

It follows from the task content that the missing angle is to be determined from the task content.

By the use of trigonometric ratios;

The missing angle, x can be determined as follows;

tan (x) = 9.09 / 14

x = tan-¹ (9.09/14).

x = 32.995°

The missing angle is therefore; 33°.

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The given equation is x2−9/18​−x−3/12​=x+3/x

(a) The restrictions on x are that x cannot equal 0, 6, or -4. This is because if x were to equal any of these values, the denominator of one of the fractions in the equation would equal 0, which is undefined.

(b) The least common denominator of the fractions in the equation is 36. This is because 36 is the smallest number that is divisible by 18, 12, and x.

(c) To solve the equation, we can multiply each term by the least common denominator to eliminate the fractions:

36x2 - 18(9) - 36x - 3(3) = 36x + 3(36)

Simplifying and rearranging the terms gives us:

36x2 - 72x - 207 = 0

Using the quadratic formula, we can find the values of x:

x = (-(-72) ± √((-72)2 - 4(36)(-207)))/(2(36))

Simplifying gives us:

x = (72 ± √12960)/72

So the solutions are x = (72 + √12960)/72 and x = (72 - √12960)/72.

However, we must check these solutions against the restrictions on x. The first solution, (72 + √12960)/72, is approximately 6.8, which does not violate any of the restrictions. The second solution, (72 - √12960)/72, is approximately -0.8, which also does not violate any of the restrictions. Therefore, the solutions to the equation are x = (72 + √12960)/72 and x = (72 - √12960)/72.

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To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.

In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6

Simplifying the equation, we get:
y = (1/6)x - 7/2

Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2

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Answer:

40

Step-by-step explanation:

The geometric mean will equal the square root of the product of the two numbers.

√64 * √25

   8  *     5  = 40

The y-intercept of the continuous function in the table is (0, –6) which can be determined by looking at the first point, (0, –6).

A continuous function is a function that is defined for all values of its independent variable, and whose graph is a continuous line without breaks or gaps. It typically means that a function's value for an input can be calculated without having to consider the values of the function for other inputs.

The y-intercept of a continuous function is the point at which the graph of the function crosses the y-axis. It is the point where the x-coordinate is zero. In other words, it is the point where the graph of the function intersects the y-axis.

In the given table, the y-intercept can be determined by looking at the first point, (0, –6). This means that the y-coordinate is –6 when the x-coordinate is 0. Therefore, the y-intercept of the continuous function in the table is (0, –6).

The y-intercept also helps us to determine the slope of the function. The slope is the rate at which the function changes as we move along the x-axis. The slope can be calculated by looking at the change in the y-coordinate for a given change in the x-coordinate.

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The y-intercept οf the cοntinuοus functiοn in the table is (0, –6) which can be determined by lοοking at the first pοint, (0, –6).

A cοntinuοus functiοn is a functiοn that is defined fοr all values οf its independent variable, and whοse graph is a cοntinuοus line withοut breaks οr gaps. It typically means that a functiοn's value fοr an input can be calculated withοut having tο cοnsider the values οf the functiοn fοr οther inputs.

The y-intercept οf a cοntinuοus functiοn is the pοint at which the graph οf the functiοn crοsses the y-axis. It is the pοint where the x-cοοrdinate is zerο. In οther wοrds, it is the pοint where the graph οf the functiοn intersects the y-axis.

In the given table, the y-intercept can be determined by lοοking at the first pοint, (0, –6). This means that the y-cοοrdinate is –6 when the x-cοοrdinate is 0. Therefοre, the y-intercept οf the cοntinuοus functiοn in the table is (0, –6).

The y-intercept alsο helps us tο determine the slοpe οf the functiοn. The slοpe is the rate at which the functiοn changes as we mοve alοng the x-axis. The slοpe can be calculated by lοοking at the change in the y-cοοrdinate fοr a given change in the x-cοοrdinate.

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Complete question:

Which is a y-intercept of the continuous function in the table?

The required with the help of trig ratios we have,
1. x = 30.69
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
1.

Apply the sine rule,
Sin21 = perpendicular/hypotenus
sin21 = 11 / x
x = 11/sin21
x = 30.69

Similarly,
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

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The angle between the vectors "[−12​] and [6−1​]α" is approximately 2.03 radians.

To find the angle between the vectors, we can use the formula:

cos(α) = ([tex]V{1}[/tex] • [tex]V{2}[/tex]) / (||[tex]V{1}[/tex]|| ||[tex]V{2}[/tex]||)

Where v1 and v2 are the two vectors, and ||[tex]V{1}[/tex]|| and ||[tex]V{2}[/tex]|| are the magnitudes of the vectors.

For the given vectors:

[tex]V{1}[/tex] = [−1 2] and [tex]V{2}[/tex] = [6 −1]

[tex]V{1}[/tex]• v2 = (−1)(6) + (2)(−1) = −6 + −2 = −8

||[tex]V{1}[/tex]|| = √((-1)^2 + 2^2) = √(5)

||[tex]V{2}[/tex]|| = √(6^2 + (-1)^2) = √(37)

cos(α) = (−8) / (√(5) √(37)) = −8 / √(185)

α = cos^-1(−8 / √(185))

α ≈ 2.03 radians

Therefore, the angle between the vectors is approximately 2.03 radians.

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Answer:

88

Step-by-step explanation:

METHOD 1:

Find 68% of 275:

275 * 0.68 = 187

Subtract 187 from the total:

275 - 187 = 88 coins

METHOD 2:

100% - 68% = 32%

Find 32% of total:

275 *0.32 = 88 coins

Option a) t= 4 years. The effective interest rate for the specified account is 9.31%. This is because the effective interest rate is the rate that actually applies to the balance in the account, taking into account the compounding frequency. The formula for the effective interest rate is:

Effective interest rate = (1 + nominal yield / compounding frequency) ^ compounding frequency - 1

In this case, the nominal yield is 9% and the compounding frequency is 2 (since it is compounded twice a year). Plugging these values into the formula, we get:

Effective interest rate = (1 + 0.09 / 2) ^ 2 - 1
Effective interest rate = (1.045) ^ 2 - 1
Effective interest rate = 1.092025 - 1
Effective interest rate = 0.092025

Converting this to a percentage, we get:

Effective interest rate = 9.31%

Therefore, the correct answer is 9.31%.

For the second part of the question, we can use the formula for future value to find the missing quantity. The formula is:

A = P(1 + rt)

Plugging in the given values, we get:

5580 = 4500(1 + 0.06t)

Solving for t, we get:

5580 = 4500 + 270t
1080 = 270t
t = 4

Therefore, the correct answer is t = 4 years, or choice A.

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The solution of the absolute value inequality is (-∞,-5] U [-3,∞) in interval notation and x ≥ -3 or x ≤ -5 in algebraic notation.

Step 1: To solve the absolute value inequality, we need to isolate the absolute value expression on one side of the inequality. We can do this by adding 1 to both sides of the inequality:

|x + 4| ≥ 1

Step 2: Now, we can split the inequality into two separate inequalities:

x + 4 ≥ 1 and x + 4 ≤ -1

Step 3: Solve each inequality for x:

x ≥ -3 and x ≤ -5

Step 4: Express the solution in interval notation and algebraic notation. In interval notation, the solution is (-∞,-5] U [-3,∞). In algebraic notation, the solution is x ≥ -3 or x ≤ -5.

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The monthly house payment will be $375.84. The annual payment  for A farmer that purchased 265 acres of land for $4,300/acre  will be $75,436.20. The annual payment  of  Larry purchased a new combine that cost $240,500will be $64,514.88.

To calculate the monthly house payment for a home loan of $55,000 at 5.25% APR for 20 years, we can use the formula:

M = P * (r / (1 - (1 + r)^(-n)))

Where M is the monthly payment, P is the principal amount, r is the monthly interest rate, and n is the number of monthly payments.

In this case, P = $55,000, r = 5.25% / 12 = 0.004375, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $55,000 * (0.004375 / (1 - (1 + 0.004375)^(-240)))

M = $375.84

Therefore, the monthly house payment will be $375.84.

#2
To calculate the annual payment for a loan of 265 acres of land at $4,300/acre with a 25% down payment and 6.75% APR over 20 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = 265 * $4,300 * (1 - 0.25) = $845,625, r = 6.75% / 12 = 0.005625, and n = 20 * 12 = 240.

Plugging in these values, we get:

M = $845,625 * (0.005625 / (1 - (1 + 0.005625)^(-240)))

M = $6,286.35

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $6,286.35 * 12 = $75,436.20

Therefore, the annual payment will be $75,436.20.

#3
To calculate the annual payment for a loan of $240,500 for a new combine with a rebate of $4,500, a trade-in of $9,500, and a down payment of $5,000 at 8% APR over 4 years, we can use the same formula as above, but with different values for P, r, and n.

In this case, P = $240,500 - $4,500 - $9,500 - $5,000 = $221,500, r = 8% / 12 = 0.006667, and n = 4 * 12 = 48.

Plugging in these values, we get:

M = $221,500 * (0.006667 / (1 - (1 + 0.006667)^(-48)))

M = $5,376.24

Since this is the monthly payment, we can multiply it by 12 to get the annual payment:

A = $5,376.24 * 12 = $64,514.88

Therefore, the annual payment will be $64,514.88.

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The ramp rises about 10.4 inches off the ground to the nearest inch.

A ramp is an inclined plane that connects two different levels, allowing people or objects to move between them with less force than if they had to be lifted vertically.

We can use trigonometry to solve this problem. Let's call the height of the ramp "h". Then we have:

tan(3.2°) = h/15

To solve for h, we can multiply both sides by 15:

h = 15 tan(3.2°)

Using a calculator, we get:

h ≈ 0.87 feet

To convert this to inches, we can multiply by 12:

h ≈ 10.4 inches

So, the ramp rises about 10.4 inches off the ground to the nearest inch.

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Anne and Maya drive for 2 1/2 hours.

A mixed fraction is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where the whole number is 2 and the proper fraction is 1/3.

To convert an improper fraction into a mixed fraction, Divide the numerator by the denominator and write down the whole number result as the whole number part of the mixed fraction.

Write down the remainder as the numerator of the fractional part of the mixed fraction.

Here we have

Anne and Maya each drive the same amount of time to complete the 5-hour trip.  

Let both of them be derived for 'x' hours

=> x + x = 5 hours

=> 2x = 5 hours

=> x = 5/2

Hence, Anne and Maya drive for 5/2 hours

Here 5/2 can be converted as 2 1/2  

Therefore,

Anne and Maya drive for 2 1/2 hours.  

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The probability of winning on the first try is 0.000003426 .

P(MUF) = P(M) + P(F) - P(M and F) = 73/293 + 79/293 - 14/293 = 138/293

P(B) = 80/293

P(E/S) = P(E and S)/P(S) = 20/293 / 78/293 = 20/78 = 10/39

P(ENS) = P(E and S and N) = 0 (since there is no N category in the table)

P(MUJUH) = P(M and J and H) = 0 (since there is no intersection of all three categories in the table)

P(SEUM) = P(SE and M) = 10/293

P(F/B) = P(F and B)/P(B)

=> 16/293 / 80/293

=> 16/80

=> 1/5

P(AUB) = P(A) + P(B) - P(A and B)

=> .4 + .35 - (.4 * .35)

=> .595
If order matters, the probability is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26) * 5!

=> 0.00002056

The probability of winning on the first try is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26)

=> 0.000003426

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Given vectors ū = (u1, u2) and ✓ = (v1, v2), we can find vector w = 4ữ - 5✓ by using the formula:
w = (4u1 - 5v1, 4u2 - 5v2)
To find the magnitude of vector w, we can use the formula:
|w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Since we do not have the exact values of u1, u2, v1, and v2, we cannot compute the exact values of w and |w|.
w = (4u1 - 5v1, 4u2 - 5v2), |w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Problem 4:
Given the point P(-15, 8) on the terminal side of angle O in standard position, we can find the values of the six trigonometric functions of O using the following formulas:
sin O = y/r
cos O = x/r
tan O = y/x
csc O = r/y
sec O = r/x
cot O = x/y
Where x = -15, y = 8, and r = √(x² + y²) = √((-15)² + 8²) = √(225 + 64) = √289 = 17

Therefore, the exact values of the six trigonometric functions of O are:
sin O = 8/17
cos O = -15/17
tan O = -8/15
csc O = 17/8
sec O = -17/15
cot O = -15/8

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The equation has two solutions:[tex]x=5[/tex] and [tex]x=-4[/tex].

To solve an absolute value equation, we need to consider both the positive and negative solutions. We can do this by setting up two separate equations and solving each one individually.

The first equation is:
[tex]2x-1 = 9[/tex]

We can solve for x by isolating the variable on one side of the equation:
[tex]2x = 10[/tex]
[tex]x = 5[/tex]

The second equation is:
[tex]2x-1 = -9[/tex]

We can also solve for [tex]x[/tex] in this equation:
[tex]2x = -8[/tex]
[tex]x = -4[/tex]

Therefore, the solution to the absolute value equation[tex]|2x-1|=9[/tex] is [tex]x=5[/tex] or [tex]x=-4[/tex].

In conclusion, the equation has two solutions: [tex]x=5[/tex] and [tex]x=-4[/tex].

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The guy wire's length should be approximately 120.5 feet.

To find out, we can use trigonometry. The guy wire, the tower, and the ground form a right triangle, with the guy wire as the hypotenuse. We know the angle between the guy wire and the ground (20°), and we know the height of the tower (578 feet). We want to find the length of the guy wire. Using the trigonometric function tangent, we can set up the following equation:

tan(20°) = 578 / (guy wire length - 6)

Solving for the guy wire length, we get:

guy wire length = 578 / tan(20°) + 6

guy wire length ≈ 120.5 feet

Therefore, the guy wire should be approximately 120.5 feet long.

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Answer:

The difference in elevation between the bottom of the canyon and the bird's nest is the sum of the depths, which is:

72 1/2 + 719 2/5

To add these two mixed numbers, we first convert them to improper fractions:

72 1/2 = 145/2

719 2/5 = (3595/5) + (2/5) = 3597/5

Now we can add them:

145/2 + 3597/5

To add fractions with different denominators, we need to find a common denominator. The smallest common multiple of 2 and 5 is 10, so we can rewrite the fractions with a denominator of 10:

145/2 × 5/5 = 725/10

3597/5 × 2/2 = 7194/10

Now we can add the fractions:

725/10 + 7194/10 = 7929/10

Finally, we can simplify the fraction and convert it back to a mixed number:

7929/10 = 792 9/10

Therefore, the difference in elevation between the bottom of the canyon and the bird's nest is 792 9/10 feet.

The ratio of pages to minutes is 3:4. If he read 16 minutes, then the number of pages is 12 pages. And Tyler has to read 24 pages for homework. Then the number of minutes is 32 minutes.

The utilization of two or more additional numbers that compares is known as the ratio.

Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,

Ratio = (3/4) / 1

Ratio = 3: 4

If he read 16 minutes, then the number of pages is calculated as,

⇒ (3/4) x 16

⇒ 3 x 4

⇒ 12 pages

Tyler has to read 24 pages for homework. Then the number of minutes is given as,

⇒ 24 / (3/4)

⇒ 24 x (4/3)

⇒ 8 x 4

⇒ 32 minutes

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Answer:

Distributive property

Step-by-step explanation:

In this problem, you are distributing the 5 to both the [tex]\sqrt{3}[/tex] and the 2. Therefore, the answer is the distributive property

Answer: Distributive property.

Step-by-step explanation: The initial terms are being multiplied by 5 into both terms and they are equivalent by the distributive properly.  

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Answer:

[tex]\boxed{R:-40.48}[/tex]

Step-by-step explanation:

Rewriting the statement we have:

[tex]-44+22 \times\frac{ 16}{100}[/tex]

According to the order of operations, we solve:

simplify:

[tex]-44+22 \times\frac{ 4}{25}\\=-44 +\frac{88}{25} \\=\frac{-44(25)+88}{25} = \frac{-1012}{25} \approx -40.48[/tex]

Answer:

Height = 8

Volume = 48

Step-by-step explanation:

(4x4)x3 = 48