The nth term of a quadratic sequence is an^2 + bn + c. Here are its first four terms.
4 12 26 46
Find the values of a, b and c.

a = 3, b = -1, c = 2

Step-by-step explanation:

an^2 + bn + c

n = 1:

a + b + c = 4    Eq. 1

n = 2:

4a + 2b + c = 12    Eq. 2

n = 3:

9a + 3b + c = 26    Eq. 3

Eq. 2 minus Eq. 1

3a + b = 8    Eq. 4

Eq. 3 minus Eq. 2

5a + b = 14    Eq. 5

Eq. 5 minus Eq. 4

2a = 6

a = 3

Plug in a = 3 into Eq. 4

3(3) + b = 8

b = -1

Plug in a = 3 and b = -1 into Eq. 1.

3 - 1 + c = 4

c = 2

a = 3, b = -1, c = 2

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

answer is (b.

164 ft2)

a base  

18

b base  

7

h height  

8