Determine whether the given ordered pair is a solution of the equation. x2 + y2 - 8x + 8y = -7; (4, -1)
1 answer:
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Recall that a circle of radius 2 centered at the origin has equation
where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius
You have
Another way to verify this is to actually compute the integral. Let
Recall the half-angle identity for cosine:
This means the integral is equivalent to
Answer:
32.64% probability that you would have enough money to pay for all five baskets of fries
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are 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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sample means with size n can be approximated to a normal distribution with mean
In this problem, we have that:
You want to get 5 baskets of fries but you only have $28 in your pocket. What is the probability that you would have enough money to pay for all five baskets of fries?
28/5 = 5.6
So this is the pvalue of Z when X = 5.6.
By the Central Limit Theorem
has a pvalue of 0.3264
32.64% probability that you would have enough money to pay for all five baskets of fries