in class, matthew stated "i think that a negative is like an opposite. That is why multiplying a negative times a negative equal
2 answers:
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Answer:
The polar coordinates are as follow:
a. (6,2π)
b. (18, π/3)
c. (2√2 , 3π/4)
d. (2, 5π /6)
Step-by-step explanation:
To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .
To calculate r, we use Pythagorean theorem:
r = ---- (1)
To calculate the θ, first we will find out the θ ' using the inverse of cosine as it is easy to calculate.
So, θ ' = cos ⁻¹ (x/r)
If y ≥ 0 then θ = ∅
If y < 0 then θ = 2 π − ∅
For a. (6,0)
Sol:
Using the formula in equation (1). we get the value of r as:
r =
r = 6
And ∅ = cos ⁻¹ (x/r)
∅ = cos ⁻¹ (6/6)
∅ =cos ⁻¹ (1) = 2π
As If y ≥ 0 then θ = ∅
So ∅ = 2π
The polar coordinates are (6,2π)
For a. (9,9/)
Sol:
r = 9 + 3(3) = 18
and ∅ = cos ⁻¹ (x/r)
∅ = cos ⁻¹ (9/18)
∅ = cos ⁻¹ (1/2) = π/3
As If y ≥ 0 then θ = ∅
then θ = π/3
The polar coordinates are (18, π/3)
For (-2,2)
Sol:
r =√( (-2)²+(2)² )
r = 2 √2
and ∅ = cos ⁻¹ (x/r)
∅ = cos ⁻¹ (-2/ 2 √2)
∅ = 3π/4
As If y ≥ 0 then θ = ∅
then θ = 3π/4
The polar coordinates are (2√2 , 3π/4)
For (-√3, 1)
Sol:
r = √ ((-√3)² + 1²)
r = 2
and ∅ = cos ⁻¹ (x/r)
∅ = cos ⁻¹ ( -√3/2)
∅ = 5π /6
As If y ≥ 0 then θ = ∅
So θ = 5π /6
The polar coordinates are (2, 5π /6)
Answer:
a. The point estimate of the corresponding population mean is of $8213.
b. The margin of error is of $103.
c. The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
a. What is the point estimate of the corresponding population mean?
The sample mean is of $8213. So, by the Central Limit Theorem, the point estimate of the corresponding population mean is of $8213.
b. What is the margin of error for this estimate (use2 standard deviations (divided by Vn) to either side of the mean is used when no specific confidence level is stated).
Sample of 450, standard deviation of $2185. So
The margin of error is of $103.
c. Create and interpret a 98% confidence interval for the corresponding population mean.
The confidence interval is given by:
In which is the sample mean and z is the value related to the confidence level.
98% confidence level
So , z is the value of Z that has a pvalue of
, so
.
Then
The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.