A fountain is made up of two semicircles and a quarter circle. Find the perimeter of the fountain. Round to the nearest hundredt
h.
1 answer:
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Answer:
a) There is a 2.28% probability that a new cup will overflow when filled by the automatic dispenser.
b) The mean amount dispensed by the machine should be set at 16.14 ounces to satisfy this wish.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Normal model with mean 16 ounces and standard deviation 0.31 ounces. This means that .
A new 16-ounce cup that is being considered for use actually holds 16.62 ounces of drink.
a. What is the probability that a new cup will overflow when filled by the automatic dispenser?
This probability is 1 subtracted by the pvalue of Z when . So
has a pvalue of 0.9772. This means that there is a 1-0.9772 = 0.0228 = 2.28% probability that a new cup will overflow when filled by the automatic dispenser.
b. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish?
This is the value of , with
when Z has a pvalue of 0.94. It is between
and
, so we use
.
The mean amount dispensed by the machine should be set at 16.14 ounces to satisfy this wish.
Answer:
24/25
20/29
Step-by-step explanation:
Trigonometry ratios:
where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse (longest side)
As angles A and C are complementary, this implies that side b is the hypotenuse and sides a and c are the legs of a right triangle.
Referring to the attached diagram:
sin(A) = O/H = a/b
cos(C) = A/H = a/b
Therefore, sin(A) ≡ cos(C)
If sin(A) = 24/25 , the value of cos(C) = 24/25
If cos(A) = 20/29, the value of sin(C) = 20/29
