Match the pairs of equations that represent concentric circles

The 3rd equation on the left column  and second one on the right column.

Step-by-step explanation:

These 2 equations have same  coefficients of x and y if we divide the first one by 4 and the second by 2.

This gives the 2 equations

x^2 + y^2 - 4x + 6y - 7 = 0

x^2 + y^2 - 4x + 6y - 20 = 0

If we compete the square on these we get

(x - 2)^2 + (y + 3)^2 =  20

(x - 2(^2 + (y + 3)^2 =  33

These are in standard form . The center is the same (2, -3) but the radii are different so they are concentric.

a) This is because the Sunday customer purchases is skewed. b) For a highly skewed distribution, it is not possible but if it is slightly skewed, it is possible. c) approximately 0.0023  

Step-by-step explanation:

a) As stated in the question, the Sunday customer purchases is skewed, thus we cannot use the normal model to estimate the probability that the next Sunday customer will spend at least $40.

b) Using a sample of 10 Sunday customers won't be large enough to apply the Normal model for sampling. However, if it is just slightly skewed, the sample may be large enough for the analysis while if it is highly skewed it would be impossible to calculate the probability.

c) Using randomization principle, it can be assumed that 50 Sunday customer purchases can be considered a representative sample for all Sunday customer purchases. Using a 10% condition for the computation:

μ = μ = $32

σ = 20/ = 2.828

Then, the z-score is:

Thus:

P (z ≥ 2.83) = normalcdf (2.83, E99, 0.1) = 0.0023

Therefore, the probability that the average of the Sunday customer purchases is  at least $40 is 0.0023