The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is _____.

The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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Answer:

Step-by-step explanation:

2 1/3 because I learned this exact question at school

Answer:

The angle SQR is half the intercepted arc SR which is 43°

Answer: 20.8

Step-by-step explanation: .

\(f(x) =2 x+1 \\\\ \text{If x = 2,}\\\\f(2) = 2(2) +1 = 4+1 = 5\)

Answer:

5

Step-by-step explanation:

plug 2 in for x

f(2) = 2(2) + 1

f(2) = 5 [Asnwer]

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

The area under the curve y = \(8e^{(4x)\) from x = 0 to x = ln(2) is 30.

To determine the area under the curve y = \(8e^{(4x)}\) from x = 0 to x = ln(2), follow these steps:

1. Integrate the function y = \(8e^{(4x)\) with respect to x:
\(\int(8e^{(4x)}) dx = (8/4)e^{(4x)} + C = 2e^{(4x) }+ C\)

2. Evaluate the definite integral from x = 0 to x = ln(2):
Area = \(\int(8e^{(4x)})\) dx from x=0 to x=ln(2) = \([2e^{(4x)}]\)(from 0 to ln(2))

3. Plug in the upper limit, x = ln(2), and subtract the result when plugging in the lower limit, x = 0:
Area = \(2e^{(4*ln(2)}) - 2e^{(4*0)\)

4. Simplify the expression:
Area = \(2e^{(4*ln(2))-} 2e^0\)
Area = \(2*(e^{(ln(2^4))}) - 2*1\)
Area = \(2*(2^4) - 2\)
Area = 2*16 - 2

5. Calculate the final value:
Area = 32 - 2
Area = 30

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Answer:

$35

Step-by-step explanation:

multiply 35 by the number of weeks (6) to get $210, subtract $210 from $250 to get $35

Answer:

The second one, I got that question

x ≤ 10

The Angle Bisector Equidistant Theorem Converse (ABET Converse) states that if a point is equidistant from the sides of an angle, then it lies on the angle bisector.

To understand the ABET Converse, we first need to understand the Angle Bisector Equidistant Theorem (ABET). The ABET states that if a point lies on the angle bisector of an angle, then it is equidistant from the sides of the angle. In other words, if we draw an angle and then bisect it (i.e., draw a line that splits the angle into two equal parts), any point on that line will be equidistant from the sides of the angle. The ABET Converse simply flips this idea around. It states that if a point is equidistant from the sides of an angle, then it must lie on the angle bisector. So, if we have a point that is the same distance from both sides of an angle, then that point must lie on the line that bisects the angle.

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The coordinates of three possible additional vertices of the kite are  (3, 6),(3,2), (7,4), (−9,4)

The length of the shorter diagonal is d and the length of the longer diagonal is 4d.

Area = (1/2) × Product of Diagonals.

We are given that the area of the kite is 32, so we can write the equation as follows:

32 = (1/2) × d × (4d)

32 = 2d²

16 = d²

d = ±4

Since distance cannot be negative, we take the positive value, so d = 4.

Therefore, the length of the shorter diagonal is 4, and the length of the longer diagonal is 4d = 4 × 4 = 16.

The longer diagonal is at A (3, 6)

4 less the longer diagonal

shorted diagonal is B (3,2)

The length of our longer diagonal is 16. This can be broken up in multiple ways as 4 and 12. The longer diagonal will be a horizontal line segment since the diagonals meet at 90∘ angles. So, 4 to the right and 12 to the left. We then get our last two vertices of (7,4) which is and (−9,4).

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To find the volume of the solid, we need to integrate the area of each square section perpendicular to the x-axis over the range of x values that correspond to the base of the solid.

The base of the solid is the region enclosed by the parabola y = 4x^2, the line x=1, and the x-axis in the first quadrant. To find the bounds of integration, we need to find the x values where the parabola intersects the line x=1.

Setting y = 4x^2 equal to x=1, we get:

4x^2 = 1

x^2 = 1/4

x = ±1/2

Since we are only interested in the first quadrant, we take x=0 to x=1/2 as the bounds of integration.

For each value of x, the plane section perpendicular to the x-axis is a square with side length equal to the y-value of the point on the parabola at that x-value. Thus, the area of the square section is (4x^2)^2 = 16x^4.

To find the volume of the solid, we integrate the area of each square section over the range of x values:

V = ∫(0 to 1/2) 16x^4 dx

V = [16/5 x^5] (0 to 1/2)

V = (16/5)(1/2)^5

V = 1/20

Therefore, the volume of the solid is 1/20 cubic units.

The volume of the solid is  8 cubic units.

Integrate the area of each square cross-section perpendicular to the x-axis to determine the solid's volume.

Find the parabolic region's equation in terms of y first. We get to x = ±√(y/4).  after solving y = 4x^2 for x. Since only the area in the first quadrant is of interest to us, we take the positive square root:  = √(y/4) = (1/2)√y.

Consider a square cross-section now, except this time it's y height above the x-axis. The area of the cross-section, which is a square, is equal to the square of the length of its side. Let s represent the square's side length. Next, we have

s is the length of the square's side projection onto the x-axis,

= 2x

= √y

As a result, s2 = y is the area of the square cross-section at height y.

We must establish the bounds of integration for y in order to build up the integral for the solid's volume. The limits of integration for y are 0 to 4 since the parabolic area intersects the line x = 1 at y = 4. As a result, the solid's volume is:

V = ∫[0,4] y dy

= (1/2)y^2 |_0^4

= (1/2)(4^2 - 0^2)

= 8

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a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Taking the square root of both sides, we get: y = ±sqrt(C)(x^2 + 78). This is the final solution to the differential equation. Note that we have included a constant of integration, which could take on any value and would affect the specific solution to the equation.

In this problem, we are given an equation that needs to be separated into variables, with x-terms on one side and y-terms on the other. We also need to avoid placing dy or dx in a denominator. Following this strategy, we can rewrite the original equation as:
y dy = x/(x^2 + 78) dx
Next, we need to integrate each side of the differential equation. Ignoring the constant of integration, we can integrate the left-hand side of the equation as follows:
∫ y dy = 1/2 y^2
To integrate the right-hand side of the equation, we can use the substitution u = x^2 + 78, which gives us du/dx = 2x and dx = du/2x. Substituting this back into the original equation, we get:
∫ x/(x^2 + 78) dx = ∫ 1/u du
The integral of 1/u is ln|u| + C, where C is the constant of integration. Substituting back for u, we get:
∫ x/(x^2 + 78) dx = ln|x^2 + 78|/2 + C
Putting this all together, we get:
1/2 y^2 = ln|x^2 + 78|/2 + C
Multiplying both sides by 2 and exponentiating, we get:
y^2 = Ce^(2ln|x^2 + 78|)
Simplifying this expression, we get:
y^2 = C(x^2 + 78)^2
Taking the square root of both sides, we get:
y = ±sqrt(C)(x^2 + 78)
This is the final solution to the differential equation. Note that we have included a constant of integration, which could take on any value and would affect the specific solution to the equation.

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Answer: Operations properties

Step-by-step explanation:

Operations properties are a series of properties, rules, or laws associated with mathematical operations and equality.

There are 4 operations properties namely: Commutative(applies to addition), Associative (also applies to addition), Distributive (applies to addition and multiplication) and Identity (applies to addition and multiplication).

Answer:

x=10

Step-by-step explanation:

Using Pythagorean theorem,

(√13^2-12^2)×2

(√169-144)×2

(√25)×2

5×2=10

The quadratic equation has a negative value that is a maximum if vertex constant is negative but vertex y-coordinate is negative, while it has a positive value that is a minimum if vertex constant is positive by vertex y-coordinate is positive.

Graphically speaking, quadratic functions are parabolae and their absolute extremes are called vertices. There are three ways to describe quadratic functions:

Standard form

y = a · x² + b · x + c

Factor form

y = a · (x - r₁) · (x - r₂)

Vertex form

y - k = C · (x - h)²

Where:

Vertex form offers us a quick possibility to answer this question, from its understanding we get the following conclusions:

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The given problem is a 0-1 integer programming problem, which involves finding the maximum value of a linear objective function subject to a set of linear constraints, with the additional requirement that the decision variables must take binary values (0 or 1).

To solve this problem by implicit enumeration, we systematically evaluate all possible combinations of values for the decision variables and check if they satisfy the constraints. The objective function is then evaluated for each feasible solution, and the maximum value is determined.

In this case, there are three decision variables: x1, x2, and x3. Each variable can take a value of either 0 or 1. We need to evaluate the objective function 2x1 - x2 - x3 for each feasible solution that satisfies the given constraints.

By systematically evaluating all possible combinations, checking the feasibility of each solution, and calculating the objective function, we can determine the solution that maximizes the objective function value.

The explanation of the solution process, including the enumeration of feasible solutions and the calculation of the objective function, can be done using a table or a step-by-step analysis of each combination.

This process would involve substituting the values of the decision variables into the constraints and evaluating the objective function. The maximum value obtained from the feasible solutions will be the optimal solution to the problem.

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The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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Answer:

1. 5x^2 − 3x − 2

2. 4s^2 −28s + 49

3. 4y^2 + 9y + 8

Answer:

Explanation:

Remove Parenthesis: (a) = a

3x² + 4 - (-2x² + 3x + 6)

Simplify -(-2x² + 3x + 6): 2x² - 3x - 6

3x² + 4 + 2x² - 3x - 6

Simplify 3x² + 4 + 2x² - 3x - 6

5x² - 3x - 2

Apply Perfect Square Formula: (a - b)² = a² - 2ab + b²²: a = 2s, b = 7

(2s)² - 2 · 2s · 7 + 7²

Simplify (2s)² - 2 · 2s · 7 + 7²

4s² - 28s + 49

Remove Parenthesis: (a) = a

7y² + 9y - 2 - 3y² + 10

Group Like Terms

7y² - 3y² + 9y - 2 + 10

Add Similar Elements: 7y² - 3y² = 4y²

4y² + 9y - 2 + 10

Add: -2 + 10 = 8

4y² + 9y + 8

rise / run

13 + 6 / - 2 + 5 = 19 / - 3 = - 6.333 or - 6 and 1 / 3

The correct value of the inequality as solves is x > 14 , and the error made by the student was that he directly divided the RHS by 7.

To simplify the equation we will multiply 7 on both the sides.

Then we will get the result as 7x > 98

Thus, we can say that the new inequality will be x > 14 ,

Hence , the mistake made by the student was that he didn't divided both the sides by 7 but only one side.

So a result, he obtained the incorrect result x>2.

Inequality is a concept in mathematics and uses symbols such as > , < , <= , >= etc.

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There is percent decrease of 30%

50 pounds to 35 pounds

Original amount = 50 pounds

New amount= 35 pounds

Since, New amount is less than the original amount, this is a percentage of decrease.

Change in amount = 35 -50

Change in amount = -15 pounds

Substitute the given values we have;

% change = (change/original value) x 100

% change = -(15/50) x 100

% change = - 30%

Therefore, there is percent of decrease which is 30%.

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The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.

For the stated question -

The formula for the z score -

z = (x - μ)/σ

In which,

μ = 140  and σ = 20

Put the values-

z = (150 - 140)/20

z = 0.5

p(x > 105.0) = p(z > 0.5)

p(x > 105.0) = 0.6915

Thus, the value of the probability p(x > 105.0) for the given  normal random variable is found as 0.6915.

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The complete question is-

suppose x is a normal random variable with μ = 140  and σ = 20 and find p(x > 105.0).

Answer:  None of the above

Step-by-step explanation: It's none because we need to divide the 70 apples by the 4 in the sample ratio. That's 17.5. Now, we need to multiply 3 by that. So, 17.5 * 3 = 52.5. That's equal to about 53 oranges. But, as we see that is not an answer choice. So, I believe it's none of the above.

4:3 = 53:70 (about 53)

The cheapest price for ten (10) rolls would be = £25.50. That is option B.

The wallpapers are those designed paper materials that are used in decoration of a room.

The total number of wall paper that Salima needs to buy= 10 rolls.

A single roll of wallpaper = £9.20

A pack of 3 rolls= £25:50

That is 1 roll = X

make X the subject of formula;

£x = 25.50/3

£x = £8.5

A pack of 5 rolls = £43.05

That is 1 roll = X

make X the subject of formula;

£x = 43.05/3

£x = 14.35

Therefore, the cheapest price that can be used to buy 10 rolls would be = £25.50 because one roll would be = £8.5.

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Answer:

Pack of 3 rolls (total of £85.70

Step-by-step explanation:

25.5+25.5+25.5+9.20= £85.70

Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

The cost of labor per hour is $55, and Savannah spent a total of $441.50.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represents the cost of labor per hour, hence if the total was $441.50, hence:

441.50 = 4.5x + 194

x = 55

The cost of labor per hour is $55, and Savannah spent a total of $441.50.

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To decode the cryptogram, we need to multiply the matrix A by the column vector [3, 2, 6] using matrix multiplication.

Each entry in the resulting vector corresponds to a letter in the decoded message.

Let's perform the matrix multiplication:

A =

[1 1 3]

[1 1 4]

Column vector: [3, 2, 6]

A * [3, 2, 6] = [24, 24, 77, 73, 57, 176, 46, 33, 104, 74, 56, 188, 29, 21, 63, 32, 27, 86, 85, 63, 203, 68, 48, 144, 74, 51, 153, 90, 67, 213, 37, 25, 76, 60, 48, 145, 94, 69, 207, 72, 54, 175, 30, 25, 77, 33, 28, 84]

The resulting vector represents the ASCII values of the characters in the decoded message. Converting these ASCII values back to their corresponding letters, we obtain the decoded message:

"SEMPTEMBER THE ELEVENTH WILL ALWAYS REMEMBER"

Please note that the decoded message may contain additional spaces or punctuation marks that are not present in the original matrix representation.

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Given that the point (8, 5) is on the terminal side of an angle in standard position. We have to determine the exact values of the six trigonometric functions of the angle.Let's consider the point (8, 5) on the coordinate plane.From the above figure, we can see that the point (8, 5) is located in the first quadrant.

Therefore, the value of sin, cos, and tan will be positive and the value of sec, csc, and cot will also be positive.The length of the hypotenuse of the right-angled triangle formed by the given point with the x and y-axis is given by the distance formula. We have :

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{(8-0)^2+(5-0)^2}=\sqrt{64+25}=\sqrt{89}$

Now, we can determine the exact values of the six trigonometric functions of the angle:

1. sin θ = (opposite side/hypotenuse) = y/d = 5/√89.2. cos θ = (adjacent side/hypotenuse) = x/d = 8/√89.3. tan θ = (opposite side/adjacent side) = y/x = 5/8.4. csc θ = (hypotenuse/opposite side) = d/y = √89/5.5. sec θ = (hypotenuse/adjacent side) = d/x = √89/8.6. cot θ = (adjacent side/opposite side) = x/y = 8/5.Therefore, the exact values of the six trigonometric functions of the angle are: sin θ = 5/√89, cos θ = 8/√89, tan θ = 5/8, csc θ = √89/5, sec θ = √89/8, and cot θ = 8/5.

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Yes, These data suggest a statistically significant difference between the proportions of drug-resistant cases in the two cities.

In first city, the drug-resistant proportion is significant while In other city, It is not significant.

What is Ratio and proportion ?

A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another.

Let the first city to be City A and the other city as City B.

In city A, 14 cases are of drug-resistant out of total 221 cases.

In city B, 6 cases are of drug-resistant out of total 322 cases.

We'll find the proportion of drug-resistant cases of both cities,

City A = 14 / 221 = 0.06 > 0.02

City B = 6 / 322 = 0.018 < 0.02

If use a 0.02 level of significance then,

City A has significant drug-resistant cases while City B does not have significant cases.

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