We have seen in the Triangle Sum<span> Conjecture that the</span>sum<span> of the </span>angles<span> in any triangle is 180 degrees. The</span>Quadrilateral Sum<span> Conjecture tells us the </span>sum<span> of the</span>angles<span> in any convex </span>quadrilateral<span> is 360 degrees. Remember that a polygon is convex if each of its</span>interior angles<span> is less that 180 degree.</span>
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Answer:
π square inches
Step-by-step explanation:
The area of the whole circle is ...
A = πr²
A = π(2 in)² = 4π in²
A 90° sector is 1/4 of the circle, so its area is ...
(1/4)(4π in²) = π in²
Answer:
UCL (x bar) = 424
LCL (x bar) = 376
Step-by-step explanation:
Given:
Average calories contained, μ = 400
Standard deviation, σ = 30 calories
Sample size, n = 25
a) UCL (x bar) =
On substituting the respective values, we get
UCL (x bar) = 
or
UCL (x bar) = 424
Similarly,
LCL (x bar) =
On substituting the respective values, we get
LCL (x bar) = 
or
LCL (x bar) = 376
Answer:
0.1667
Step-by-step explanation:
There are 6! ways to arrange the hats. The number of ways for which no guest will receive the proper hat is 5! (since there are 5 wrong hats for the first guest, 4 for the second guest, and so on). The probability that no guest will receive the proper hat is:

The probability is 0.1667.