The simple exponential smoothing model can be expressed asA)a simple average of past values of the data
.B)an expression combining the most recent forecast and actual data value. ***
C)a weighted average, where the weights sum to zero.
D)a weighted average, where the weights sum to the sample size.
E)None of the above.

Answer

One case of sprite costs 3 dollars, All four cases are $12. You can buy 16 cases of sprite with 48 dollars.

Step-by-step explanation:

How to get the cost for 1 case:

You have 4 cases of sprite which all four combined costs $12. You divide 12 by 4 and get 3.

How to get the amount of cases of sprite you can buy with $48:

divide 48 by 3 and you get 16. Why 3? Because 3 is the amount per case and 16 x 3 is 48. Thank me later!

Answer:

It costs $3 per case of Sprite

With 48 dollars, you could buy 16 cases.

Step-by-step explanation:

12/4 = 3    12 dollars divided buy 4 dollars each equals 3 dollars per case

48/3 = 16  48 dollars divided by 3 dollars per case equals 16 cases of sprite

Answer:o.75 you need to divide

Step-by-step explanation:

x < a/7 is the inequality which shows the  function f(x) = log (a-7x) positive

The logarithmic function is defined only for positive arguments, so for f(x) to be positive, the argument (a - 7x) must be positive:

a - 7x > 0

Solving for x, we get:

x < a/7

Therefore, the inequality is:

x < a/7

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The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:

1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.

2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.

3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.

So, the mean absolute deviation for the given dataset is approximately 0.996.


The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.


The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

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By applying direct proportion, the information should be filled in the table are as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented the following equation:

y = kx

Where:

Since the boat carried containers that weigh 4000 pounds each, we would multiply each of containers by 4000 as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

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The rent expense allocated to each department is as follows: Jewelry department: $30,800, Cosmetics department: $46,200, Housewares department: $21,000, Tools department: $9,000, Shoes department: $18,000.

The retailer allocates 70% of the total rent expense to the first floor and 30% to the second floor. Then, the rent expense for each floor is allocated to the departments based on the square footage they occupy. By applying these allocation percentages and calculations, we determined the rent expense for each department.

Rent expense allocation:

- Jewelry department (1,760 sq ft on the first floor): ($130,000 * 70% * 1,760 sq ft) / (1,760 sq ft + 2,640 sq ft) = $30,800

- Cosmetics department (2,640 sq ft on the first floor): ($130,000 * 70% * 2,640 sq ft) / (1,760 sq ft + 2,640 sq ft) = $46,200

- Housewares department (1,848 sq ft on the second floor): ($130,000 * 30% * 1,848 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $21,000

- Tools department (792 sq ft on the second floor): ($130,000 * 30% * 792 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $9,000

- Shoes department (1,760 sq ft on the second floor): ($130,000 * 30% * 1,760 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $18,000

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A retailer pays \( \$ 130,000 \) rent each year for its two-story building. Space in this building is occupied by five departments as shown here.

Jewelry department - 1,760 square feet of first-floor space

Cosmetics department - 2,640 square feet of first-floor space

Housewares department - 1,848 square feet of second-floor space

Tools department - 792 square feet of second-floor space

Shoes department - 1,760 square feet of second-floor space

The company allocates 70% of total rent expense to the first floor and 30% to the second floor, and then allocates rent expense for each floor to the departments occupying that floor on the basis of space Occupied.

Determine the rent expense to be allocated to each department

To plot and label the nullclines of the non-linear system given by dx/dt = -x - y - x^2 and dy/dt = y - 2xy, we can identify the points where the derivatives are zero, i.e., where dx/dt = 0 and dy/dt = 0.

These points correspond to the nullclines and help us understand the behavior of the system.

Nullcline for dx/dt = 0: Set dx/dt = 0 and solve for x and y. In this case, -x - y - x^2 = 0. This equation represents the nullcline for dx/dt = 0.

Nullcline for dy/dt = 0: Set dy/dt = 0 and solve for x and y. In this case, y - 2xy = 0. This equation represents the nullcline for dy/dt = 0.

Plotting the nullclines: Draw a Cartesian coordinate system with x and y axes labeled. On the graph, plot the points where dx/dt = 0 and dy/dt = 0. These points represent the nullclines.

Labeling the nullclines: Label the x-axis as "x" and the y-axis as "y". Label the nullcline for dx/dt = 0 and dy/dt = 0 accordingly, such as "Nullcline for dx/dt = 0" and "Nullcline for dy/dt = 0".

By following these steps, you can plot and label the nullclines for the given non-linear system. The nullclines represent the points where the derivatives are zero and provide insight into the behavior and stability of the system.

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The relative minimum is at t = 1/√2, the relative maximum is at t = -1/√2, the absolute minimum is at t = ±2, and the absolute maximum is at t = 1/√2.

To find the relative and absolute extrema of the function f(t) = t^2 - (1/t^2) over the domain [-2, 2], we first find the critical points by setting the derivative equal to zero:

f'(t) = 2t + 2/t^3 = 0

Solving for t, we get:

t = ±(1/√2)

We now check the second derivative to classify the critical points:

f''(t) = 2 - 6/t^4

At t = 1/√2, f''(t) > 0, so we have a relative minimum at t = 1/√2.

At t = -1/√2, f''(t) < 0, so we have a relative maximum at t = -1/√2.

To determine if there are any absolute extrema, we evaluate the function at the endpoints of the domain:

f(-2) = 4 - 1/4 = 15/4

f(2) = 4 - 1/4 = 15/4

Since f(t) is a continuous function over the closed interval [-2, 2], and the critical points and endpoints are finite, the extreme value theorem tells us that f(t) must have an absolute minimum and an absolute maximum on the interval.

Since f(-1/√2) is greater than both endpoints, the absolute minimum must occur at one of the endpoints.

Therefore, the absolute minimum of f(t) over the domain [-2, 2] is 15/4, which occurs at t = ±2.

Since f(1/√2) is less than both endpoints, the absolute maximum must occur at t = 1/√2.

Therefore, the absolute maximum of f(t) over the domain [-2, 2] is 7, which occurs at t = 1/√2.

In summary, the relative minimum is at t = 1/√2, the relative maximum is at t = -1/√2, the absolute minimum is at t = ±2, and the absolute maximum is at t = 1/√2.

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Answer:

4y^2 + 32y + 64

Step-by-step explanation:

To solve the expression (2y+8)^2, we can use the distributive property or the FOIL method. Let's use the distributive property to expand the expression:

(2y + 8) * (2y + 8)

Using the distributive property, we multiply each term in the first expression by each term in the second expression:

2y * 2y + 2y * 8 + 8 * 2y + 8 * 8

Simplifying each term, we get:

4y^2 + 16y + 16y + 64

Combining like terms, we have:

4y^2 + 32y + 64

So, the expanded form of (2y+8)^2 is 4y^2 + 32y + 64.

Answer:

A unit rate is a rate where the second quantity is one unit, such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. 1 minute=60 seconds1 hour=60 minutes (or) 3600 seconds1 day=24 hours (or) 1440 minutes.

Hope this helps :)

Answer:

Unit rates are like 2 liter per 30 min how much do you get in 1 hour 4

Step-by-step explanation:

The surface area of the portion in the first octant bounded by the plane 2 + 2x + 4y = 20 is approximately 98.995.

To find the surface area of the portion in the first octant bounded by the plane 2 + 2x + 4y = 20, we need to integrate the partial derivatives of x and y with respect to z over the region.

First, we solve the equation for z:

z = (20 - 2x - 4y)/2

z = 10 - x - 2y

The region in the first octant is bounded by the x-axis, y-axis, and plane 2 + 2x + 4y = 20. To find the limits of integration, we set each variable to 0 and solve for the other variable:

When x = 0, 2 + 4y = 20, y = 4

When y = 0, 2 + 2x = 20, x = 9

Now we can set up the integral for surface area:

Surface Area = ∫∫√(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA

∂z/∂x = -1

∂z/∂y = -2

Surface Area = ∫[0 to 9] ∫[0 to 4] √(1 + (-1)^2 + (-2)^2) dy dx

Surface Area = ∫[0 to 9] ∫[0 to 4] √6 dy dx

Evaluating the integral:

Surface Area = ∫[0 to 9] [√6y] [0 to 4] dx

Surface Area = ∫[0 to 9] 4√6 dx

Surface Area = 4√6 ∫[0 to 9] dx

Surface Area = 4√6 * [x] [0 to 9]

Surface Area = 4√6 * (9 - 0)

Surface Area = 36√6

Rounded to three decimal places, the surface area of the portion in the first octant is approximately 98.995.

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Answer:

in what? if you meant 8 hours in 24 hours than 3 times

Step-by-step explanation:

Answer:

The answer is 3 times.

Step-by-step explanation:

\(since \: 8 \times 3 =24

then \: you \: can \: fit \: 8 \: hours \: 3 \: times \: in \: 24 \: hours.\)

Answer:

4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

98 cm + 20 cm= 118. 98 cm + 12cm =110 118-110=8

The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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Step-by-step explanation:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer:

Step-by-step explanation:

Certainly! "Mean," "median," and "mode" are three different measures of central tendency used in statistics to describe a dataset. They help provide insight into the typical or central value within a set of data points.

1. **Mean:**

  - **Definition:** The mean, also known as the average, is calculated by adding up all the values in a dataset and then dividing by the total number of values.

  - **Calculation:** Mean = (Sum of all values) / (Number of values)

  - **Explanation:** The mean gives you the "typical" or "average" value in a dataset. It's the sum of all the values divided by the number of values. For example, if you have test scores of 80, 85, 90, 92, and 95, the mean score would be (80 + 85 + 90 + 92 + 95) / 5 = 88.4.

2. **Median:**

  - **Definition:** The median is the middle value in a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.

  - **Explanation:** The median is the middle value that separates the dataset into two equal halves. It is not influenced by extreme values (outliers) as much as the mean. For example, in the dataset 4, 7, 9, 12, 15, the median is 9 because it's the middle value.

3. **Mode:**

  - **Definition:** The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode if all values occur with the same frequency.

  - **Explanation:** The mode represents the most common value or values in a dataset. For example, in the dataset 2, 3, 3, 4, 4, 4, 5, the mode is 4 because it appears more frequently than any other value.

In summary, the mean is the average value, the median is the middle value, and the mode is the most frequently occurring value in a dataset. Each of these measures provides different insights into the central tendency of data and can be useful for various statistical analyses and interpretations.

a. \(123.1(1.069)^3 \approx 150.4\)

b. \(123.1(1.069)^{20} \approx 467.5\)

Answer:

67

is it multiple choise

The Laplace transform of a cos(ωt) b sin(ωt) is [(a + ib)s]/[(s^2) + ω^2].

We can use the identity cos(a)sin(b) = (1/2)(sin(a+b) - sin(a-b)) to write:

a cos(ωt) b sin(ωt) = (a/2)(e^(iωt) + e^(-iωt)) + (b/2i)(e^(iωt) - e^(-iωt))

Taking the Laplace transform of both sides, we get:

L{a cos(ωt) b sin(ωt)} = (a/2)L{e^(iωt)} + (a/2)L{e^(-iωt)} + (b/2i)L{e^(iωt)} - (b/2i)L{e^(-iωt)}

Using the fact that L{e^(at)} = 1/(s-a), we can evaluate each term:

L{a cos(ωt) b sin(ωt)} = (a/2)((1)/(s-iω)) + (a/2)((1)/(s+iω)) + (b/2i)((1)/(s-iω)) - (b/2i)((1)/(s+iω))

Combining like terms, we get:

L{a cos(ωt) b sin(ωt)} = [(a + ib)/(2i)][(1)/(s-iω)] + [(a - ib)/(2i)][(1)/(s+iω)]

Simplifying the expression, we obtain:

L{a cos(ωt) b sin(ωt)} = [(a + ib)s]/[(s^2) + ω^2]

Therefore, the Laplace transform of a cos(ωt) b sin(ωt) is [(a + ib)s]/[(s^2) + ω^2].

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The Laplace transform of acos(ωt) + bsin(ωt) is (as + bω) / (s^2 + ω^2).

To find the Laplace transform of a function, we can use the standard formulas and properties of Laplace transforms.

Let's start with the Laplace transform of a cosine function:

L{cos(ωt)} = s / (s^2 + ω^2)

Next, we'll find the Laplace transform of a sine function:

L{sin(ωt)} = ω / (s^2 + ω^2)

Using these formulas, we can find the Laplace transform of the given function acos(ωt) + bsin(ωt) as follows:

L{acos(ωt) + bsin(ωt)} = a * L{cos(ωt)} + b * L{sin(ωt)}

= a * (s / (s^2 + ω^2)) + b * (ω / (s^2 + ω^2))

= (as + bω) / (s^2 + ω^2)

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Answer:

1599995904

Step-by-step explanation:

first, you must do the top part of the fraction. you can start by doing the power numbers such as 2 power 4, 4 power 6 and 4 power 4.

the complete answer for the top part is: 12x 16x 4069x 8x 2x 256 which equals: 3199991808

then, you must divide by 2 which gives you the answer of: 1599995904

Problem:

Which of the following is the result of the equation below after completing the square and factoring?

Solution:

To complete the square of the polynomial

we add to both sides of the above equation the fraction:

in our case we have that a = 1, b = 3, c = 8 and d = 6 .Then we have that:

adding the above number on both sides of the given polynomial, we obtain:

this is equivalent to:

then we have:

Answer:

1/2 divided by 5

Step-by-step explanation:

Answer:

The first answer

Step-by-step explanation:

Answer:

Perimeter of a square = 40 acres

Step-by-step explanation:

Given the following data;

Area of square = 100 acres

The area of a square is given by the formula;

Area of square = l²

Where: l is the length of its sides.

100 = l²

Taking the square root of both sides, we have;

l = 10 acres

Now to find the perimeter;

Perimeter of a square = 4 * length of sides

Perimeter of a square = 4 * 10

Perimeter of a square = 40 acres

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The average deviation from the mean is 0.19 that can be calculated from the mean.

An average is calculated for a set of numbers that are of the same value range.

Mean = (32.52+32.14+32.61+32.75)/4 = %32.50

Standard deviation =

|32.50-32.52| = 0.02

|32.50-32.14| = 0.36

|32.50-32.61| = 0.11

|32.50-32.75| = 0.25

(.02+.36+.11+.25)/4= 0.19

So the standard deviation is 0.19

Relative deviation = .19/32.50=0.0058 or %0.58

Yes, %32.14, because it deviates too far from the average.

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