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krek1111 [17]
3 years ago
14

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Mathematics
1 answer:
Daniel [21]3 years ago
6 0
Answer: x = 11 degrees

Step by step explanation:
Triangle rule states that all angles of a trundle must equal to 180 degrees. So we have two known angles, therefore we can subtract them from the 180 degree total.
180-109-43
=28
Now to solve for x we have the equation
4x-16=28
We add 16 to both sides to isolate x
4x=44
Now we divide each side by 4 to get rid of the coefficient
x=11
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The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past sever
mrs_skeptik [129]

Answer:

The answers to the question are

(a) The time series plot is given as attached

(b) The parameters for the line that minimizes MSE for the time series are;

y-intercept, b₀ = 19.993

Slope, b₁ =  1.77

MSE = 19.44

T_t = 19.993  + 1.774·t

(c) The average cost increase that the firm is realizing per year is $ 1.77

(d) The estimate of the cost/unit for next year is $35.96.

Step-by-step explanation:

(a) Using the provided data, the time series plot is given as attached

(b) Given hat the y-intercept, = b₀

Slope = b₁

Therefore the  linear trend forecast equation is given s

T_t = b₀ + b₁·t

The linear trend line slope is given as

b₁ = \frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2}

b₀ = \overline{\rm Y} - b₁·\overline{\rm t}

Where:

Y_t = Time series plot value at t

n =  Time period number

\overline{\rm Y} = Time series data average value and

\overline{\rm t} = Average time, t

Therefore, \overline{\rm t} = \frac{\Sigma^n _{t=1} t}{n}  = \frac{36}{8} =4.5

\overline{\rm t} = 4.5

\overline{\rm Y}  =  \frac{\Sigma^n _{t=1} Y_t}{n}  = \frac{223.8}{8} =27.975

\overline{\rm Y}  =  27.975

Therefore the linear trend line equation T_t, is

b₁ = \frac{\Sigma^n_{t=1}(t-\overline{\rm t)}(Y_t-\overline{\rm Y)}}{\Sigma^n_{t=1}(t-\overline{\rm t} )^2} =  = \frac{74.5}{42} = 1.774

b₀ = \overline{\rm Y} - b₁·\overline{\rm t} = 27.975 - 1.774×4.5 = 19.993

Therefore the trend equation for the linear trend is

T_t = 19.993  + 1.774·t

MSE = \frac{1}{2} \Sigma(Y-\overline{\rm Y)^ }^2 = \frac{155.495}{8} = 19.44

(c) From the linear trend equation, the average is given as the slope of the curve or b₁ which is equal to 1.774

Therefore the average cost increase that the firm has been realizing per year is $ 1.77

(b) From the equation of the future trend, we have when y = 9

T_t  is given as

T_t = 19.993  + 1.774×9 = 35.96

The cost/unit for 9th year is $35.96

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Answer: 60 calories in 1/8 cup...how many calories in 3/4 cup

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6:16

explanation:
6+10=16
6 is the amount in outer space
ration is 6:16
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