If the probability that the Islanders will beat the Rangers in a game is 0.38, what is the probability that the Islanders will w
1 answer:
Answer:
0.014
Step-by-step explanation:
The probability that the Islanders will win at least 6 out of seven is the probability of them winning exactly 6 games, P(X=6), added to the probability of them winning all seven games, P(X=7).
This problem can be treated as a binomial probability model with probability of success p = 0.38 in each of n = 7 games.
Thus:
The probability is:
The probability that the Islanders will win at least six out of seven games in a series against the Rangers is 0.014.
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Answer:
Summation notation:
or after using your function part:
After evaluating you get 11.125 square units.
Step-by-step explanation:
The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.
The distance between x=0 and x=3 is (3-0)=3.
We want to divide that length of 3 units by 6 which gives a length of a half per each base length.
We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).
The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).
The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).
The fourth rectangle will have a height of f(2-.5)=f(1.5).
The fifth one will have a height of f(1.5-.5)=f(1).
The last one because it is the sixth one will have a height of f(1-.5)=f(.5).
So to find the area of a rectangle you do base*time.
So we just need to evaluate:
or by factoring out the 1/2 part:
To find f(3) replace x in -x^2+2x+4 with 3:
-3^2+2(3)+4
-9+6+4
1
To find f(2.5) replace x in -x^2+2x+4 with 2.5:
-2.5^2+2(2.5)+4
-6.25+5+4
2.75
To find f(2) replace x in -x^2+2x+4 with 2:
-2^2+2(2)+4
-4+4+4
4
To find (1.5) replace x in -x^2+2x+4 with 1.5:
-1.5^2+2(1.5)+4
-2.25+3+4
4.75
To find f(1) replace x in -x^2+2x+4 with 1:
-1^2+2(1)+4
-1+2+4
5
To find f(.5) replace x in -x^2+2x+4 with .5:
-.5^2+2(.5)+4
-.25+1+4
4.75
Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:
Okay now if you wanted the summation notation for:
is it
or after simplifying a bit:
If you are wondering how I obtain the .5+.5(k-1):
I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)