Describe the roots of the equation shown below.
64x^2 - 16x + 1=0

a. there are two complex roots
b. there is one real, double root
c. there are two real, irrational roots
d. there are two real, rational roots

B. There is one real, double root

Step-by-step explanation:

For ax² + bx + c = 0, the discriminant is b² − 4ac.

If the discriminant is positive and a perfect square, there are two real, rational roots.

If the discriminant is positive and not a perfect square, there are two real, irrational roots.

If the discriminant is 0, there is one real, double root.

If the discriminant is negative, there are two complex roots.

Here, a = 64, b = -16, and c = 1.

b² − 4ac

= (-16)² − 4(64)(1)

= 0

The discriminant is 0.  Therefore, there is one real, double root

.19875994384

step-by-step explanation:

1699/ 8548

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560