On the packaging for a triangular sail, the edge measurements for the sail are listed as 7ft x 15ft x 17ft without unfurling the
sail, you want to determine if the sail forms a right triangle, an acute triangle or an obtuse triangle
2 answers:
The law of cosines can be helpful here. The largest angle (C) will be opposite the longest side (c). That law tells us ...
... c² = a² + b² -2ab·cos(C)
Then
... cos(C) = (a² +b² -c²)/(2ab)
We don't actually need the angle. We only need to know the sign of the cosine.
... cos(C) = (7² +15² -17²)/(2·7·15) = -15/210 . . . . negative sign, so C > 90°
The sail has the shape of an obtuse triangle.
_____
A triangle solver app on your calculator, phone, tablet, or computer can give you the result easily.
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Answer:
(a) The probability that the store’s revenues were at least $9,000 is 0.0233.
(b) The revenue of the store on the worst 1% of such days is $7,631.57.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
It is provided that:
As the sample size is quite large, i.e. <em>n</em> = 310 > 30, the central limit theorem can be applied to approximate the sampling distribution of the store’s revenues for Sundays by a normal distribution.
(a)
Compute the probability that the store’s revenues were at least $9,000 as follows:
Thus, the probability that the store’s revenues were at least $9,000 is 0.0233.
(b)
Let <em>s</em> denote the revenue of the store on the worst 1% of such days.
Then, P (S < s) = 0.01.
The corresponding <em>z-</em>value is, -2.33.
Compute the value of <em>s</em> as follows:
Thus, the revenue of the store on the worst 1% of such days is $7,631.57.