Graph the function. Compare the graph to the graph of f(x)=x^2 g(x)=5x^2
1 answer:
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Answer:
1)
2)
Step-by-step explanation:
To find : Calculate the Laplace transforms of the following from the definition ?
Solution :
We know that,
Laplace transforms of is given by,
1)
Laplace of y,
here n=2
2)
Laplace of y,
here n=3
A) The two line plots are attached.
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = <span>{|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= </span>{4, 4, 0, 0, 0, 2, 2, 4<span>}
RM = </span><span>{|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= </span>{4, 2, 0, 0, 0, 0, 2, 4<span>}
Therefore,
MAD(MSH) = (</span>4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = <span>{|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= </span>{4, 4, 0, 0, 0, 2, 2, 4<span>}
RM = </span><span>{|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= </span>{4, 2, 0, 0, 0, 0, 2, 4<span>}
Therefore,
MAD(MSH) = (</span>4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).