The area of each triangular face is
.. A = (1/2)*b*h
.. Aside = (1/2)*(6 cm)*(5 cm) = 15 cm^2
The area of the triangular base is
.. Abase = ((√3)/4)*s^2 = (√3)/4*(6 cm)^2 = 9√3 cm^2
The total surface area is the base area plus the area of the three sides.
.. Atotal = Abase + 3*Aside
.. = 9√3 cm^2 +3*15 cm^2
.. = (45 +9√3) cm^2
.. ≈ 60.6 cm^2
Actually, there's an error in the picture. The height of the side should be 4, and the length of the edge should be 5. Making that adjustment, the total area is 51.6 cm^2.
It is hard to tell what is intended. Not all answers are showing, so we can't "reverse-engineer" the problem from the answers.
Answer:
see explanation
Step-by-step explanation:
The bar above the 3 indicates the 3 is being repeated, that is
0.13333....
We require to make 2 equations with the repeating 3 after the decimal point.
let x = 0.13333... , then multiply both sides by 10 then 100
10x = 1.3333 ← equation with repeating 3 after the decimal point
100x = 13.3333 ← second equation with repeated 3 after the decimal point
Subtracting the equations eliminates the repeated 3, that is
100x - 10x = 13.333 - 1.333
90x = 12 ( divide both sides by 90 )
x =
← divide numerator/denominator by 6, hence
0.1333... = 
Since the time to failure distribution is
exponential, the distribution is F (n) = 1 – e ^ (-x/48)
The probability of failure between months 60
and 72 is the same as the probability that the battery will fail in 12 months,
since the exponential distribution is memoryless F (12) = 0.221
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Answer:
99% Confidence interval: (50.9,61.3)
Step-by-step explanation:
We are given the following in the question:
Sample mean,
= 56.1
Sample size, n = 72
Alpha, α = 0.01
Sample standard deviation, σ = 16.7
Degree of freedom = n - 1 = 71
99% Confidence interval:
Putting the values, we get,