Product of prime numbers in exponential form
1 answer:
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Answer:
(x - 8)² + (y + 6)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (8, - 6 ) , then
(x - 8)² + (y - (- 6))² = r² , that is
(x - 8)² + (y + 6)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r =
with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )
r =
=
=
=
=
= 5
Then equation of circle is
(x - 8)² + (y + 6)² = 5² , that is
(x - 8)² + (y + 6)² = 25
Answer:
a: 0.8884
b: 0.9934
Step-by-step explanation:
We have µ = 300 and σ = 70. The sample size, n = 125.
For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:
P(292 < x < 308).
We need to find the z-scores that correspond to these values using the given data. See attached photo 1 for the calculation of these scores.
We have P(292 < x < 308) = 0.8884
Next we want the probability of the sample mean to be within 17 units of the population mean, so we want the values from 283 to 317. We want to find
P(283 < x < 317)
We need to find the z-scores that correspond to these values. See photo 2 for the calculation of these scores.
We have P(283 < x < 317) = 0.9934
