Take two orthogonal vectors u, v ε R". u v, and let X = (Xi, , X,) be a vector of n iid standard Gaussians. Xi ~ N(0, 1), yl E「r). Let llr-〈II, X〉 and vr-(v, X〉, Are ux and vr independent? Hin: First try to see if they are correlated; you may use the fact that jointly normal random variables are independent iff. they are uncorrelated.

the input value is the number of times you fold it. the input value is also known as the x-value. 

the output value is its thickness. the output value is the y-value.

when you don't fold it all, the thickness will remain the same, which is 1. the ordered pair would be (0,1).

when you fold it once, the thickness will double from 1 to  2. the ordered pair would be (1,2).

when you fold it a second time, the thickness will double from 2 to  4. the ordered pair would be (2,4).

fold it one more time, and the thickness will be 8. the ordered pair is (3,8)

fold it the fourth time, and the thickness doubles. 8 x 2 = 16. the ordered pair is (4,16)

fold it the fifth time, and the thickness goes from 16 to 32. the ordered pair is (5,32)

the ordered pairs would be:

(0,1)

(1,2)

(2,4)

(3,8)

(4,16)

(5,32)

(6,64)

(7,128)

and so on : p

the question asks for 6 ordered pairs, so i bolded the first six.

now, the equation for this would be 

if we graph that, and we do the vertical line test, then we know this is a function.

it is a function because each x-value has a different y-value. there are no y-values that have the same x-values.

i have attached the graph of that line.

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step-by-step explanation:

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

hey seth! : )

i’m not 100% sure, but i think it’s b

hope this ya : p

miss u!

- nicole

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.