What is 10 and one half minus 8 and one half
1 answer:
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Answer:
The forecast for November is 235 if August's forecast was 145.
Step-by-step explanation:
The formula for calculating forecast using exponential smoothing is:
Where Ft = New month forecast
Ft-1 = Previous month forecast
At-1 = Previous month actual value
α = smoothing constant
We are given F₈ = 145 (forecast for August), A₈ = 200 (Actual Value for August), α = 2, and we need to compute the forecast for November. So, We will first calculate the forecast for September then October and then November, step-by-step.
So, forecast for September is:
F₉ = F₈ + α (A₈ - F₈)
= 145 + 2*(200-145)
= 145 + 2*55
F₉ = 255
Then, forecast for October is:
F₁₀ = F₉ + α (A₉ - F₉)
= 255 + 2*(220-255)
= 255 + 2*(-35)
F₁₀ = 185
The forecast for November is:
F₁₁ = F₁₀ + α (A₁₀ - F₁₀)
= 185 + 2*(210 - 185)
F₁₁ = 235
So, both equations are essentially linear equations.
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
---------------------------------------------------------------------------------------------------------------
Part A
the slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4
y = 5x - 3
m = 5; b = -3
The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***
Part B: x = 1; y = 2
Linear equations are written in the format y = mx+b, where m represents the slope/slope intercept and b represents the y-intercept.
---------------------------------------------------------------------------------------------------------------
Part A
the slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4
y = 5x - 3
m = 5; b = -3
The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***
Part B: x = 1; y = 2
Answer:
Number of t-shirts Trevor have are 16
If Trevor have 16 t-shirts, than Marissa will have 10 t-shirts.
Step-by-step explanation:
Let, the number of t-shirts Trevor has = x and number of t-shirts Marissa has = y.
Since, they both have total of 26 t-shirts. We get,
Moreover, Marissa has 6 t-shirts less than that of Trevor.
So, we have,
On solving the system of equations, we get,
implies
implies
i.e. 2x= 32 i.e. x= 16.
So, implies
i.e y= 10.
Hence, the number of t-shirts Trevor and Marissa have are 16 and 10 respectively.
That is, If Trevor have 16 t-shirts, than Marissa will have 10 t-shirts.