Two lines meet at a point that is also the vertex of an angle set up and solve an appropriate equation for x and y.

In reference to data given in question, the exponential smoothing forecast for Week 4 with a smoothing constant alpha of 0.5 is 1262.5

Exponential smoothing is a popular forecasting method that assigns exponentially decreasing weights to the past observations while placing greater emphasis on more recent observations. It is a simple and effective method to forecast time series data, and is widely used in various industries.

The formula for exponential smoothing is as follows:

F(t+1) = αDt + (1 - α)Ft

where:

F(t+1) is the forecast for the next period,

Ft is the forecast for the current period,

Dt is the actual demand for the current period, and

α is the smoothing constant or the weight given to the most recent observation.

In this case, we are given the actual demand for the first three weeks (i.e., Dt for weeks 1 to 3) and the forecast for the first week (i.e., Ft for week 1). Using a smoothing constant of 0.5, we can calculate the forecast for each week as follows:

F(1) = 1100 (given)

F(2) = 0.5(1000) + 0.5(1100) = 1050

F(3) = 0.5(1200) + 0.5(1050) = 1125

F(4) = 0.5(1400) + 0.5(1125) = 1262.5

Therefore, the exponential smoothing forecast for Week 4 with a smoothing constant alpha of 0.5 is 1262.5, which is option C

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The equation of line that passes through (6, 4) and is perpendicular to the line passing through ( 0,12) and (2,7) is 5y = 2x + 8

Two lines a re said to be perpendicular is the meet at rights angles.

Which means the two lines form an angle of 90°

Also if the product of the gradients of both lines is -1, those lines are said to be perpendicular.

when  a line passes through (0,12) and (2,7),

Its slope(\(m_{1}\)) = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

so ,

slope = 7-12 / 2 - 0

slope( \(m_{1}\)) = -5/2          

Since both lines are perpendicular, \(m_{1}\)\(m_{2}\) = -1

making \(m_{2}\) subject of the equation

\(m_{2}\) = -1/\(m_{1}\)

\(m_{2}\) = -1/-5/2

     = 2/5

Equation of line in slope intercept form is y = mx + c

where  m= slope, c = intercept

coordinates of the point of the first line (6, 4)

so if m = 2/5, x = 6, y = 4, and substituting these values into the above equation, we have

4= 2/5(6) + c

4 = 12/5 + c

c = 4 - 12/5

c = 8/5

Therefore the equation of the line is y = 2/5x + 8/5

Further simplified as 5y = 2x + 8

In conclusion, the equation of the line is 5y =2x + 8

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The function g(x) represents the bonus earned by a salesperson on weekly sales over $5000. It is calculated as 3% of the sales amount over $5000.

The function h(x) represents the amount of sales over $5000. It calculates the difference between the total sales (x) and the threshold amount of $5000.

In the given functions, g(x) and h(x), we can analyze their representations and purpose.

The function g(x) = 0.03x represents the bonus earned by a salesperson. It is a linear function that multiplies the sales amount (x) by the bonus rate of 0.03, which is equivalent to 3%. The purpose of this function is to calculate the additional earnings on the portion of sales that exceeds $5000. For example, if a salesperson makes $6000 in sales, the bonus earned would be g(6000) = 0.03 * (6000 - 5000) = $30.

The function h(x) = x - 5000 represents the amount of sales over $5000. It is a linear function that subtracts the threshold amount of $5000 from the total sales (x). The purpose of this function is to determine the additional sales amount that is eligible for the bonus calculation. For instance, if a salesperson makes $7000 in sales, the amount over $5000 would be h(7000) = 7000 - 5000 = $2000.

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Based on the information provided, the total tax this person will need to pay is $2,622,2.

The amount of money you pay for taxes depends on your income as there are specific percentages to be paid. In the case the income is $25000, this income matches the range $7,825 - $31,850, and therefore you should pay 50 plus 15 percent of the amount over 7,825. Based on this, let's calculate the money to be paid:

$25,000 - $7852 = $17, 148 x 0.15 (15%) = $2,572.2 + $50 = $2622.2

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A sample in which each individual in the population has an equal chance to be selected is a "simple random sampling".

A subset of such a statistical population called a simple random sample is one where each member has an equal chance of being chosen. A straightforward random sample is intended to offer an objective depiction of a group.

Some key features of simple random sampling are-

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The chosen online news article highlights the growing concerns regarding the impact of social media on freedom of speech.

The article, titled "Social Media Platforms and the Challenge to Free Speech," examines the complex relationship between social media platforms and freedom of speech. It raises key concepts discussed in the chapter regarding the limitations and challenges posed by online platforms to this fundamental right.

The article acknowledges the significant role that social media platforms play in facilitating public discourse, allowing individuals to express their opinions and engage in discussions on various topics. However, it also highlights the potential limitations on freedom of speech that arise due to the power wielded by these platforms.

It discusses instances where social media companies have imposed content restrictions, suspended or banned users, or altered algorithms, leading to concerns about censorship and the stifling of diverse viewpoints.

The article further explores the legal framework surrounding freedom of speech in relation to social media platforms.

It mentions the tension between protecting free expression and addressing issues such as hate speech, disinformation, and online harassment. It delves into the challenges of finding a balance between safeguarding individual liberties and ensuring a safe and inclusive online environment.

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Based on the amount of Nacho cheese corn chips and the calories per gram, the calories per party bag is 1,094.6 calories

First, convert ounces to grams:

= 1 ounce is 28.3495 grams

Party bag in grams:

= 15 x 28.3495

= 425.243 grams

The amount of calories is:

= 425.243 x 28.6% x 9

= 1,094.6 calories

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The equation is equivalent to the r = d/t.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

We have to find which equation is equivalent to the formula d = rt.

Formula given: d = rt

Divide both sides by t

d/t = rt / t

d/t = r

Thus, the equation is equivalent to the r = d/t.

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Answer:

\(\sf y \leq \dfrac34x\)

Step-by-step explanation:

Choose 2 points on the line:  (0, 0) and (4, 3)

\(\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-0}{4-0}=\dfrac34\)

point-slope form of linear equation:  \(\sf y-y_1=m(x-x_1)\)

\(\implies \sf y-0=\dfrac34(x-0)\)

\(\implies \sf y=\dfrac34x\)

Solid line : ≤ or ≥

Dashed line: < or >

Therefore as the line is solid, and the shading is below the line,

\(\implies \sf y \leq \dfrac34x\)

Slope:-

\(\\ \tt\Rrightarrow m=\dfrac{6+3}{8+4}=\dfrac{9}{12}=\dfrac{3}{4}\)

Equation of line in point slope form

\(\\ \tt\Rrightarrow y+3=3/4(x+4)\)

\(\\ \tt\Rrightarrow y+3=3/4x+3\)

\(\\ \tt\Rrightarrow y=3/4x\)

equation of shaded region

\(\\ \tt\Rrightarrow y\leqslant 3/4x\)

Answer:

the median is 80.5

Step-by-step explanation:

first we put them in order

75,76,77,79,80,81,85,86,90,91

the median is the middle number...however, in cases where there are an even number of numbers, ur gonna have 2 middle numbers....so u take the average of those 2 numbers...basically, u add them and divide by 2.

So we have 2 numbers in the middle.....we add them and divide by 2 to get the median.

(80 + 81) / 2 = 161/2 = 80.5 <== the median

Answer:

80.5

Step-by-step explanation:

The following are the amount each person receive:

a. 6 : 4

Total ratio = 6 + 4

= 10

6/10 × 500

= $300

4/10 × 500

= $200

b. 1 : 4 : 5

Total ratio = 1 + 4 + 5

= 10

1/10 × 500

= $50

4/10 × 500

= $200

5/10 × 500

= $250

c. 1 : 8 : 1

Total ratio = 1 + 8 + 1

= 10

1/10 × 500

= $50

8/10 × 500

= $400

1/10 × 500

= $50

d. 8 : 9 : 8

Total ratio = 8 + 9 + 8

= 25

8/25 × 500

= $160

9/25 × 500

= $180

8/25 × 500

= $160

e. 10 : 5 : 4 : 1

Total ratio = 10 + 5 + 4 + 1

= 20

10/20 × 500

= $250

5/20 × 500

= $125

4/20 × 500

= $100

1/20 × 500

= $25

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Answer:

33 ounces.

Step-by-step explanation:

There are 16 ounces in a pound, so multiply 33/4 by 16, which gives you 132 ounces.  We can then divide this number by 4, 132/4, giving us 33 ounces of rice in each container.

Answer:

b^2-c^2-10b+10c

Step-by-step explanation:

b^2-c^2-10(b-c)

b^2-c^2-10b+10c

The area of the region enclosed by the curves y=8x^2, y=8√x, x=1/4 and x=1 is 7.875. The first step is to sketch the curves. The curve y=8x^2 is a parabola that opens upwards. The curve y=8√x is a curve that increases rapidly at first, then levels off.

The line x=1/4 is a vertical line, and the line x=1 is a horizontal line. The region enclosed by the curves is a triangle. The base of the triangle is 3/4, and the height of the triangle is 8. Therefore, the area of the triangle is (1/2) * 3/4 * 8 = 7.875.

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Answer:

5.048

5.48

5.4871

5.7

Step-by-step explanation:

5.48 is 0.0071 less than 5.4871

Fractions are termed as a portion or section of any quantity, if t = 1/3s then, the value of s when t = 1/2 is 3.

Fractions are termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and lower part is the denominator.

we know that the value of t = 1/3s and that we have to find the value of s, we are also given with the value of t being 1/2 that is exactly half, therefore,

t = 1/3s

t is also 1/2, therefore,

1/2 = 1/3s x 1/2

1/2 = 1/6 x s

s = 6/2 = 3/1 = 3

therefore s = 3

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Answer:

the third one

Step-by-step explanation:

do you need and explanation

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

The Solution.

The correct answer is 2 right angles.

Answer: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25.

Step-by-step explanation: The point (-2, 4) is on the circle (x - 5)^2 + (y + 3)^2 = 25. To check if a point is on the circle, we can substitute the point's x and y coordinates into the equation of the circle. If the equation is true, then the point is on the circle. In this case, substituting (-2, 4) into the equation of the circle.

Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

If Rashid spent 30 minutes on each piece of homework for three subjects, we can calculate the total time he spent by multiplying the time spent per subject (30 minutes) by the number of subjects (3).

30 minutes * 3 = 90 minutes.

To convert this into hours and minutes, we divide 90 minutes by 60 since there are 60 minutes in an hour.

90 minutes ÷ 60 = 1 hour and 30 minutes.

Therefore, Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

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Answer:

the answer is x=4

Step-by-step explanation:

Answer:

C. 4≤x≤6

Step-by-step explanation:

First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.

Hope that helps! Have a fantastic day!

Answer:

Answer: 84 meters squared. (i.e. 84m^2).

Step-by-step explanation:

Area of the path = total area of path and plot - plot area only

First, let’s find the area of the plot:

20m x 20m = 400m^2

The path is 1m wide and runs all the way around, so, it describes an ‘outer square’ of 22m x 22m (2 x 1m larger because there are 1m of the path on each side).

The area of this ‘outer square’ is equivalent to the ‘total area of path and plot’

22m x 22m = 484m^2

So:

Area of the path = total area of path and plot - plot area only

= 484 - 400 = 84m^2

When dividing 456.3 by 100, how should the decimal point be moved is:

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point. 12.5 is a decimal number, for instance.

In mathematics, the decimal system—also known as the Hindu-Arabic number system or the Arabic number system—is a positional numeral system that uses 10 as its base and calls for the use of 10 different numbers, including 0, 1, 2, 3, 4, 5, 6, 7, and 8. To indicate decimal fractions, a dot (decimal point) is also necessary.

We use decimals on a daily basis when dealing with things like money, weight, and length. Decimal numbers are used when higher accuracy is required than full numbers can provide.

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The statements with the correct relationships are:

A. ∠1 and ∠8 are alternate exterior angles.

B. ∠4 and ∠6 are same side interior angles.

E. ∠3 and ∠6 are alternate interior angles.

Alternate interior angles and alternate exterior angles are pairs of angles that are formed when a transversal intersects two parallel lines.

Alternate interior angles are a pair of nonadjacent interior angles that are on opposite sides of the transversal and are located between the two parallel lines. In other words, they are the interior angles that are not adjacent to the corresponding exterior angle on the same side of the transversal. Alternate interior angles are always congruent if the two parallel lines are cut by a transversal.

In the diagram above, angle 1 and angle 8 are alternate exterior angles while angle 3 and angle 6 are alternate interior angles.

Also, angles 4 and 6 form same side interior angles.

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