What are the solutions to the equation
1 answer:
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Answer:
The cost of edging the flower beds with roll is $41.10.
Step-by-step explanation:
Given,
dimension of rectangular flower bed :
length = 40 ft
width = 15 ft
dimension of circular flower bed :
diameter = 16 ft
cost of each roll = $6.85
We need to find the cost of roll used to cover completely rectangular and circular flower bed.
Solution,
Firstly we will find out the perimeter of the rectangular flower bed.
Since we know that the perimeter of rectangle is equal to twice the sum of its length and width.
framing in equation form, we get;
Perimeter =
So the perimeter of 2 flower bed =
Again we will find out the circumference of the circular flower bed.
And we know that the circumference of the circle is equal to pi multiplied with the diameter.
framing in equation form, we get;
Circumference =
Now the total edge for covering is equal to the sum of the perimeter of two flowerbed and circumference of one circular flower bed.
Total edge =
Here also given that Plastic edging for flower beds comes in 50-foot per roll.
So we will find out the number of rolls required for edging.
For this we will use the unitary method.
50 ft = 1 roll
270.24 ft = number of roll
so we can say that there will be 6 rolls required for edging.
also given the cost of 1 roll is $6.85.
So the cost of 6 rolls =
Hence The cost of edging the flower beds with roll is $41.10.
Answer:
a. .
b.
Step-by-step explanation:
By the definition, the expected value of a random variable X with probability mass function p is given by where the sum runs over all the posible values of X. Given a function g, the random variable Y=g(X) is defined. Note that the function g induces a probability mass function P' given by P'(Y=k) = P(X=g^{-1}(k)) when the function g is bijective.
a. Note that for 1/3ln(2)+1/6ln(5) by choosing the function g(x) = ln(x) the expression coincides with E(g(x)), because if Y = g(x) then E(Y) = P'(Y=1)*ln(1)+P'(Y=2)*ln(2)+P'(Y=5)*ln(5) = P(X=1)*ln(1)+P(X=2)*ln(2)+P(X=5)*ln(5).
b. On the same fashion, the function g(x) = xe^{xt} fullfills the expression of E[g(X)]