Answer: Choice B) {3, 5, sqrt(34)}
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Explanation:
We can only have a right triangle if and only if a^2+b^2 = c^2 is a true equation. The 'c' is the longest side, aka hypotenuse. The legs 'a' and 'b' can be in any order you want.
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For choice A,
a = 2
b = 3
c = sqrt(10)
So,
a^2+b^2 = 2^2+3^2 = 4+9 = 13
but
c^2 = (sqrt(10))^2 = 10
which is not equal to 13 from above. Cross choice A off the list.
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Checking choice B
a = 3
b = 5
c = sqrt(34)
Square each equation
a^2 = 3^2 = 9
b^2 = 5^2 = 25
c^2 = (sqrt(34))^2 = 34
We can see that
a^2+b^2 = 9+25 = 34
which is exactly equal to c^2 above. This confirms the answer.
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Let's check choice C
a = 5, b = 8, c = 12
a^2 = 25, b^2 = 64, c^2 = 144
So,
a^2+b^2 = c^2
25+64 = 144
89 = 144
which is a false equation allowing us to cross choice C off the list.
Answer:
p-value = 0.1277
Step-by-step explanation:
p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.
Firstly we find the mean and standard deviation of the given data set.
⇒ Mean = 
⇒ Mean = 4.368
where, 
is mean of the distribution.
⇒ Standard Deviation = 0.034
Applying t- test:
Let out hypothesis is:
H₀: μ = 4.35
H₁: μ ≠ 4.35
Now,
Here, μ = Population Mean = 4.35
= Sample Mean = 4.368
σ = Standard Deviation = 0.034
n = 10
Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.
Then the p-value at 99% level of significance.
⇒ p-value = 0.1277
