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2 answers:
Answer:
The first blank: 65
The second blank: 24
The third blank: 16
The last blank is: 41
Step-by-step explanation:
The Phthagorean theorm is as follows: c^2=a^2+b^2
Where a and b are the legs of the triangle and c is the hypotenuse
To fill in the first blank space you need to find c, and it's given a and b: a=25 b=60
You substitute the known values into the equation of the Pythagorean theorm: c^2=25^2+60^2
And solve to find c
c^2=4225
c=
c=65
The answer for the first blank
For the second blank you given a and c: a=7 c=25
Substitute the value into Pythagorean theorm:c^2=a^2+b^2
25^5=7^2+b^2
625=49+b^2
To solve b you got to subtract 49 to both sides
625-49=b^2
576=b^2
24=b
Which is your answer
For the third blank its given b and c: b=30 c=34
Substitute the value into Pythagorean theorm
c^2=a^2+b^2
34^2=a^2+30^2
Solve the exponential terms: 1156=a^2+900
Then you solve the variable that you need to find. In this case, you got to solve a^2 by subtracting 900 of both sides of the equation:1156-900=a^2
256=a^2
16=a which is your answer
Finally your last blank,its given the values and b
a=9
b=40
Substitute the value into Pythagorean theorm
c^2=9^2+40^2
And solve for c
c^2=81+1600
c^2=1681
Which gives you c=41 which is your answer
Let me know if this helps
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Answer:
a) The expected value is given by:
and the variance is given by:
b)
And we can find this probability with the following Excel code:
=1-BINOM.DIST(25,50,0.4,TRUE)
And we got:
c) 1) Random sample (assumed)
2) np= 50*0.4= 20 >10
n(1-p) =50*0.6= 30>10
3) Independence (assumed)
Since the 3 conditions are satisfied we can use the normal approximation:
d)
e)
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
The expected value is given by:
and the variance is given by:
Part b
For this case we want to find this probability:
And we can find this probability with the following Excel code:
=1-BINOM.DIST(25,50,0.4,TRUE)
And we got:
Part c
1) Random sample (assumed)
2) np= 50*0.4= 20 >10
n(1-p) =50*0.6= 30>10
3) Independence (assumed)
Since the 3 conditions are satisfied we can use the normal approximation:
Part d
We want this probability:
Part e
For this case we use the continuity correction and we have this: