Let x and y denote the coordinates of a point uniformly chosen in the circle of radius 1 centered at the origin. that is, their joint density is f(x, y) = 1 π for x 2 + y 2 ≤ 1. find the joint density function of the polar coordinates r = (x2 + y 2 ) 1/2 and θ = atan( y x ).

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

2/3

step-by-step explanation:

the answer is 18 units because there are 18 small cubes inside the rectangle

hope this and p.s i am also in k12

step-by-step explanation:

the ratios are reciprocals im positive

step-by-step explanation:

they are all positive numbers so it wouldn't be the other ones