Answer:
23.1 hours
Step-by-step explanation:
the mean is calculated as
mean = ∑ fx ÷ ∑ f
where x is the midpoint of the time intervals
0 < h ≤ 10 ⇒ x = 5
10 < h ≤ 20 ⇒ x = 15
20 < h ≤ 30 ⇒ x = 25
30 < h ≤ 40 ⇒ x = 35
then
∑ fx = (5 × 5) + (15 × 15) + (50 × 25) + (10 × 35)
= 25 + 225 + 1250 + 350
= 1850
∑ f = 5 + 15 + 50 + 10 = 80
then
mean = 1850 ÷ 80 ≈ 23.1 hours (to 1 dp )
Answer:
{-18, -6}
Step-by-step explanation:
Here there are only two inputs: {-2, 2}. There are only two outputs: {f(-2), f(2)}, which, in turn, can be written as {3(-2) - 12, 3(2) - 12}, or {-18, -6}. This corresponds to Answer B.
(5, 3) is the solution to this ordered pair
Use the Euclidean algorithm to express 1 as a linear combination of 
and 
.
a. 
because
77 = 1*52 + 25
52 = 2*25 + 2
25 = 12*2 + 1
so we can write
1 = 25 - 12*2 = 25*25 - 12*52 = (77 - 52)(77 - 52) - 12*52 = 77^2 - 2*52*77 + 52^2 - 12*52
Taken modulo 77 leaves us with
b. First, 
, so really we're looking for the inverse of 25 mod 52. We've basically done the work in part (a) already:
1 = 25*25 - 12*52
Taken modulo 52, we're left with
c. The EA gives
71 = 1*53 + 18
53 = 2*18 + 17
18 = 1*17 + 1
so we get
1 = 18 - 17 = 3*18 - 53 = 3*71 - 4*53
so that taken module 71, we find
d. Same process as with (b). First we have 
, and we've already shown that
1 = 3*18 - 53
which means, taken modulo 53, that
Answer:
the answer is 50%
Step-by-step explanation:
