In this problem we evaluate the series:
1 answer:
Answer:
A. 1/(n(n+2)) = (1/2)/n - (1/2)/(n+2)
B. 14651/19800
Step-by-step explanation:
<h3>A.</h3>The coefficients of the partial-fraction expansion can be found from ...
f(n) = 1/(n(n+2)) = A/n +B/(n+2)
n·f(x) = 1/(n+2) = A +Bn/(n+2)
For n=0, this becomes ...
1/(0 +2) = A = 1/2
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Similarly, ...
(n+2)·f(n) = 1/n = A(n+2)/n +B
For n = -2, this becomes ...
1/(-2) = B = -1/2
The n-th term can be written ...
1/(n(n+2)) = (1/2)/n - (1/2)/(n+2)
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<h3>B.</h3>The sum is ...
1/(1·3) +1/(2·4) +1/(3·5) +... +1/(98·100)
= 1/2(1/1 -1/3 +1/2 -1/4 +1/3 -1/5 +... +1/98 -1/100)
= 1/2((1/1 +1/2 +1/3 +...1/98) -(1/3 +1/4 +1/5 +...+1/100)
We notice that terms 3..98 cancel, so the sum is ...
= 1/2(1/1 +1/2 -1/99 -1/100) = (1/2)(3/2 -199/9900)
= 14651/19800
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Answer and Step-by-step explanation:
This is a complete question
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the nullhypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The computation is shown below:
The null and alternative hypothesis is
= 0.7629
Now Test statistic = z
= -0.91
Now
P-value = 0.1804
So, it is Fail to reject the null hypothesis.
There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.
Answer:
96 square units
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
- The length of the large rectangle is: 5
- The width of the large rectangle is: 7
=> Area of the large rectangle = length × width = 7*5 = 35 square units
- The length of the middle rectangle is: 7
- The width of the middle rectangle is: 4
=> Area of the middle rectangle = length × width = 7*4 = 28 square units
- The length of the small rectangle is: 7
- The width of the small rectangle is: 3
=> Area of the small rectangle = length × width = 7*3 = 21 square units
Area of top and the bottom triangles =2*
Total surface area = 35 + 28 + 21 + 12 = 96 square units
Answer:
The probability of using one or the other is 36%
Step-by-step explanation:
For solving this problem it is easy if we see it in a ven diagram, for this first we are going to name the initial conditions with some variables:
Probability of passing Professor Jones math class = 64% =0,64
P(J) = 0.64
Probabiliry of passing Professor Smith's physics class = 32% =0.32
P(S) = 0.32
Probability of passing both is = 30% = 0.30
P(JnS) = 0.30 (Is is an intersection so it is in the middle of the ven diagram
We need to know which is the probability of pasing one or the other for this we need to take out the probability of passing both for this we have to add the probability of passing Professor Jones math class with the probabiliry of passing Professor Smith's physics class and substract the probability of passing both for each one:
P(JuS) = (P(J) - P(JnS)) + (P(S) - P(JnS)) = (0.64 - 0.30) + (0.32 - 0.30) = 0.34 + 0.02 = 0.36 = 36%
If you check the ven diagram you can see that if we add all what is in red we will have the probability of passing Professor Jones math class and if we add all what is in blue we wiill have the probability of passing Professor Smith's physics class, and if we add just what is in each corner we will get the same value that is the probabilty of passsing one or the other.
