Answer:
or 
Step-by-step explanation:
3*60 = 180 minutes
80/180 = 0.44
1-0.44 = 0.56
it was a 56% decrease in commute time
Answer:

Step-by-step explanation:
<u>Fundamental Theorem of Calculus</u>

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

<u>Integration by substitution</u>
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Find the derivative of x and rewrite it so that dx is on its own:


<u>Substitute</u> everything into the original integral:

Take out the constant:











Learn more about integration by substitution here:
brainly.com/question/28156101
brainly.com/question/28155016
Answer:
a)0.7
b) 10.03
c) 0.0801
Step-by-step explanation:
Rate of return Probability
9.5 0.1
9.8 0.2
10 0.3
10.2 0.3
10.6 0.1
a.
P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)
P(Rate of return is at least 10%)=0.3+0.3+0.1
P(Rate of return is at least 10%)=0.7
b)
Expected rate of return=E(x)=sum(x*p(x))
Rate of return(x) Probability(p(x)) x*p(x)
9.5 0.1 0.95
9.8 0.2 1.96
10 0.3 3
10.2 0.3 3.06
10.6 0.1 1.06
Expected rate of return=E(x)=sum(x*p(x))
Expected rate of return=0.95+1.96+3+3.06+1.06=10.03
c)
variance of the rate of return=V(x)=![sum(x^2p(x))-[sum(x*p(x))]^2](https://tex.z-dn.net/?f=sum%28x%5E2p%28x%29%29-%5Bsum%28x%2Ap%28x%29%29%5D%5E2)
Rate of return(x) Probability(p(x)) x*p(x) x²*p(x)
9.5 0.1 0.95 9.025
9.8 0.2 1.96 19.208
10 0.3 3 30
10.2 0.3 3.06 31.212
10.6 0.1 1.06 11.236
sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681
variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²
variance of the rate of return=V(x)=100.681-(10.03)²
variance of the rate of return=V(x)=100.681-100.6009
variance of the rate of return=V(x)=0.0801
5/6 of a yard divided by 5 is 1/6 of a yard.
Each piece is 1/6 yards long.