The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive
2 answers:
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Answer:
And when we apply the limit we got that:
Step-by-step explanation:
Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"
We have the following formula in order to find the sum of cubes:
We can express this formula like this:
And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2
If we operate and we take out the 1/4 as a factor we got this:
We can cancel and we got
We can reorder the terms like this:
We can do some algebra and we got:
We can solve the square and we got:
And when we apply the limit we got that:
Answer:
he can expect to lose 0.5$
Step-by-step explanation:
To solve this problem we must calculate the expected value of the game.
If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:
When throwing a dice the possible values are:
x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12
The probability of obtaining any of these numbers is:
The gain when obtaining an even number is twice the number.
The loss to get an odd number is $ 9
So the expected gain is: