1. Find the area of the region bounded above by y = e^x, bounded below by y = x, and bounded on the sides
1 answer:
The area of the region bounded above by y= eˣ bounded by y = x, and bounded on the sides; x =0; and x = 1 is given as e¹ - 1.5.
<h3>What is the significance of "Area under the curve"?</h3>This is the condition in which one process increases a quantity at a certain rate and another process decreases the same quantity at the same rate, and the "area" (actually the integral of the difference between those two rates integrated over a given period of time) is the accumulated effect of those two processes.
<h3>What is the justification for the above answer?</h3>Area =
=
= e¹-(1/2-0); or
Area = e -1.5 Squared Unit
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Answer:
<h2>L.A. = 384 cm²</h2><h2>S.A. = 640 cm²</h2>Step-by-step explanation:
Lateral Area:
We have four congruent triangles with base b = 16cm and height h = 12cm.
The formula of an area of a traingle:
Substitute:
Surface Area:
In the base we have the square with side s = 16cm. The formula of an area of a square:
Substitute:
Answer:
a)
And replacing we got:
b)
Step-by-step explanation:
Previous concepts
In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".
The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).
And the standard deviation of a random variable X is just the square root of the variance.
Solution to the problem
Part a
We have the following distribution function:
Y 0 1 2 3
P(Y) 0.45 0.2 0.3 0.05
And we can calculate the expected value with the following formula:
And replacing we got:
Part b
For this case the new expected value would be given by:
And replacing we got