ANSWER:
r =
Explaination:
Convert the given curve into the the polar form.
x = rcosθ
y = rsinθ
in f(x,y) = (x²-y²) - √(x²+y²) = 0
put the values of x & y in given curve equation.
We get at,
g(r,θ) = (r²cos²θ - r²sin²θ) - √(r²cos²θ + r²sin²θ) = 0
g(r,θ) = r²(cos²θ - sin²θ) - √r² = 0
We know that,
cos²θ - sin²θ = cos2θ
g(r,θ) = r²(cos2θ) - r = 0
Solve for r
Finally we get:
r =
Subtract the sides of the equation minus 3
Divided the sides of the equation by 2
So ;
_________________________________
And we're done.
Thanks for watching buddy good luck.
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Answer:
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
A statistician calculates that 8% of Americans own a Rolls Royce.
This means that
Sample of 595:
This means that
Mean and standard deviation:
What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05. So
By the Central Limit Theorem
has a p-value of 0.0035
2*0.0035 = 0.0070
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%