You are standing at point b. point b is 21 feet from the center of the circular water storage tank and 20 feet from point a. \frac{ }{ab} a b is tangent to \odot ⊙ o at a. find the radius of the tank.

r = 6.40 feet

Step-by-step explanation:

Given line AB is tangent to circle O at point A, this means ∡OAB = 90°

Hence this is a right angle triangle and we can use the Pythagorean theorem.

r² + 20² = 21²

r²  = 21² - 20²

r²  = 441 - 400

r²  = 41

r  = √41 = 6.40 feet

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;

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )