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3 years ago

List all the numbers between 20 and 30 that are prime

Mathematics

2 answers:

sesenic [268]3 years ago

5 0

the answer was 23, and 29

hope that helps you

Alchen [17]3 years ago

3 0

23 and 29 are the two numbers that are prime

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Lenovo uses the zx-81 chip in some of its laptop computers. the prices for the chip during the last 12 months were as follows:

Stella [2.4K]

Given the table below of the prices for the Lenovo zx-81 chip during the last 12 months

$\begin{tabular}
{|c|c|c|c|}
Month&Price per Chip&Month&Price per Chip\\[1ex]
January&\$1.90&July&\$1.80\\
February&\$1.61&August&\$1.83\\
March&\$1.60&September&\$1.60\\
April&\$1.85&October&\$1.57\\
May&\$1.90&November&\$1.62\\
June&\$1.95&December&\$1.75
\end{tabular}$

The forcast for a period $F_{t+1}$ is given by the formular

$F_{t+1}=\alpha A_t+(1-\alpha)F_t$

where $A_t$ is the actual value for the preceding period and $F_t$ is the forcast for the preceding period.

Part 1A:
Given α = 0.1 and the initial forecast for october of $1.83, the actual value for october is $1.57.

Thus, the forecast for period 11 is given by:

$F_{11}=\alpha A_{10}+(1-\alpha)F_{10} \\ \\ =0.1(1.57)+(1-0.1)(1.83) \\ \\ =0.157+0.9(1.83)=0.157+1.647 \\ \\ =1.804$

Therefore, the foreast for period 11 is $1.80

Part 1B:

Given α = 0.1 and the forecast for november of $1.80, the actual value for november is $1.62

Thus, the forecast for period 12 is given by:

$F_{12}=\alpha
 A_{11}+(1-\alpha)F_{11} \\ \\ =0.1(1.62)+(1-0.1)(1.80) \\ \\ 
=0.162+0.9(1.80)=0.162+1.62 \\ \\ =1.782$

Therefore, the foreast for period 12 is $1.78

Part 2A:

Given α = 0.3 and the initial forecast for october of $1.76, the actual value for October is $1.57.

Thus, the forecast for period 11 is given by:

$F_{11}=\alpha
 A_{10}+(1-\alpha)F_{10} \\ \\ =0.3(1.57)+(1-0.3)(1.76) \\ \\ 
=0.471+0.7(1.76)=0.471+1.232 \\ \\ =1.703$

Therefore, the foreast for period 11 is $1.70


Part 2B:

Given α = 0.3 and the forecast for November of $1.70, the actual value for november is $1.62

Thus, the forecast for period 12 is given by:

$F_{12}=\alpha
 A_{11}+(1-\alpha)F_{11} \\ \\ =0.3(1.62)+(1-0.3)(1.70) \\ \\ 
=0.486+0.7(1.70)=0.486+1.19 \\ \\ =1.676$

Therefore, the foreast for period 12 is $1.68


Part 3A:

Given α = 0.5 and the initial forecast for october of $1.72, the actual value for October is $1.57.

Thus, the forecast for period 11 is given by:

$F_{11}=\alpha
 A_{10}+(1-\alpha)F_{10} \\ \\ =0.5(1.57)+(1-0.5)(1.72) \\ \\ 
=0.785+0.5(1.72)=0.785+0.86 \\ \\ =1.645$

Therefore, the forecast for period 11 is $1.65


Part 3B:

Given α = 0.5 and the forecast for November of $1.65, the actual value for November is $1.62

Thus, the forecast for period 12 is given by:

$F_{12}=\alpha
 A_{11}+(1-\alpha)F_{11} \\ \\ =0.5(1.62)+(1-0.5)(1.65) \\ \\ 
=0.81+0.5(1.65)=0.81+0.825 \\ \\ =1.635$

Therefore, the forecast for period 12 is $1.64

Part 4:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.3, we obtained that the forcasted values of october, november and december are: $1.83, $1.80, $1.78

Thus, the mean absolute deviation is given by:

$\frac{|1.57-1.83|+|1.62-1.80|+|1.75-1.78|}{3} = \frac{|-0.26|+|-0.18|+|-0.03|}{3} \\ \\ = \frac{0.26+0.18+0.03}{3} = \frac{0.47}{3} \approx0.16$

Therefore, the mean absolute deviation using exponential smoothing where α = 0.1 of October, November and December is given by: 0.157

Part 5:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.3, we obtained that the forcasted values of october, november and december are: $1.76, $1.70, $1.68

Thus, the mean absolute deviation is given by:

$
 \frac{|1.57-1.76|+|1.62-1.70|+|1.75-1.68|}{3} = 
\frac{|-0.17|+|-0.08|+|-0.07|}{3} \\ \\ = \frac{0.17+0.08+0.07}{3} = 
\frac{0.32}{3} \approx0.107$

Therefore, the mean absolute deviation using exponential smoothing where α = 0.3 of October, November and December is given by: 0.107


Part 6:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.5, we obtained that the forcasted values of october, november and december are: $1.72, $1.65, $1.64

Thus, the mean absolute deviation is given by:

$
 \frac{|1.57-1.72|+|1.62-1.65|+|1.75-1.64|}{3} = 
\frac{|-0.15|+|-0.03|+|0.11|}{3} \\ \\ = \frac{0.15+0.03+0.11}{3} = 
\frac{29}{3} \approx0.097$

Therefore, the mean absolute deviation using exponential smoothing where α = 0.5 of October, November and December is given by: 0.097

5 0

3 years ago

What is the volume of a cylinder with a height of 13 and radius 6?

olga_2 [115]

1470.27

v = pi r^2 (H)

v = 3.14 (6^2) (13)

v = 3.14 (36) (13)

v = 1470.27 (about)

3 0

3 years ago

Read 2 more answers

Which of the following best describes the slope of the line below? -5 O A. Undefined O B. Zero O c. Positive OD. Negative

lana66690 [7]

negative is the answer

3 0

3 years ago

100%

Pavlova-9 [17]

The answer is E.$1,170

7 0

3 years ago

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Cement was poured to make two rectangular prism the prism were stacked as shown 4 feet 3 feet 4 feet 3 feet 2 feet what are leng

Mars2501 [29]

Answer:

V_t = 72 ft^3

Step-by-step explanation:

Solution:-

- The complete question is given in the attachment.

- The length of the smaller rectangular prism ( l ) is the side that runs along horizontal to the page and marked by l = 4 feet.

- The width of the smaller rectangular prism ( w ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by w = 2 feet.

- The height of the smaller rectangular prism ( h ) is the side that runs vertical to the page and marked by h = 3 feet.

- So the dimensions of the smaller rectangular prism are:

( l , w , h ) = ( 4 , 2 , 3 ) feet

- Similarly, for the larger rectangular prism:

- The length of the larger rectangular prism ( L ) is the side that runs along horizontal to the page and the sum of smaller and upper exposed face length, totaling to L = ( 4 + 4 ) = 8 feet.

- The width of the larger rectangular prism ( W ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by W = 2 feet.

- The height of the larger rectangular prism ( h ) is the side that runs vertical to the page and marked by H = 3 feet.

- So the dimensions of the larger rectangular prism are:

( L , W , H ) = ( 8 , 2 , 3 ) feet

- The total amount of cement in cubic feet required to make two rectangular prism with dimensions evaluated above is the sum of smaller and larger rectangular prism volumes.

- The volume of a rectangular prism is given by:

V-prism = Length*width*height

- So the total volume V_t would be:

V_t = V_small + V _large

V_t = ( l*w*h ) + ( L*W*H )

V_t = ( 4*2*3 ) + ( 8*2*3 )

V_t = ( 24 ) + ( 48 )

V_t = 72 ft^3

4 0

3 years ago