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The confidence interval of a standard deviation is given by:

Given a sample size of 31 charge sales, the degree of freedom is 30 and for 90% confidence interval,

Therefore, the 90% confidence interval for the standard deviation is given by

Given a sample size of 31 charge sales, the degree of freedom is 30 and for 90% confidence interval,

Therefore, the 90% confidence interval for the standard deviation is given by

Question

A map has the scale 2 centimeters = 1 kilometer. on a map, the area of a forest preserve is 3.8 square centimeters. what is the area of the actual forest preserve

Solution 1

We know that

the scale is 2 cm/1 km

on a map, the area of a forest preserve is 3.8 cm²

assuming it has a square shape

the length side of the square is √3.8 cm

so

if 2 cm on a map-----------------> is a 1 km in the actual

√3.8 cm------------------------> x

x=√3.8/2 km

the area of the actual forest preserve is

(√3.8/2)*(√3.8/2)----> 3.8/4---> 0.95 km²

**the answer is**

**0.95 km²**

the scale is 2 cm/1 km

on a map, the area of a forest preserve is 3.8 cm²

assuming it has a square shape

the length side of the square is √3.8 cm

so

if 2 cm on a map-----------------> is a 1 km in the actual

√3.8 cm------------------------> x

x=√3.8/2 km

the area of the actual forest preserve is

(√3.8/2)*(√3.8/2)----> 3.8/4---> 0.95 km²

Question

(a) [5 points] using only the definition, find the laplace transform y (s) of y(t) = e a t where a is a constant. for what values of s does the laplace transform y (s) exist? (b) [10 points] solve, using laplace transforms, the initial value problem: y 00 − 4y 0 + 4y = 3, y(0) = 0, y0 (0) = 1.

Solution 1

Find the Laplace transform y (s) of y (t) = e a t. Here, a is a constant. Which value of s exists for the Laplace transform y (s)? (0) = 0, y 0 (0) = 0, y (0) = 0,

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