Since the figures are similar, we can establish a rule of three as follows.
We know that the area of the smaller figure is
, and its volume is
. We also know that the area of the larger figure is
; since we don't now its volume, lets represent it with
:
We can conclude that the volume of the larger figure is
; therefore, the correct answer is
a.
Answer:
x = 2
Step-by-step explanation:
Taking antilogs, you have ...
2³ × 8 = (4x)²
64 = 16x²
x = √(64/16) = √4
x = 2 . . . . . . . . (the negative square root is not a solution)
___
You can also work more directly with the logs, if you like.
3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2
3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents
6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify
2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)
ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2
2 = x . . . . . . . . . . . . . . . . . . . take the antilogs
Answer:
0.6708 or 67.08%
Step-by-step explanation:
Helen can only make both free throws if she makes the first. The probability that she makes the first free throw is P(C) = 0.78, now given that she has already made the first one, the probability that she makes the second is P(D|C) = 0.86. Therefore, the probability of Helen making both free throws is:
There is a 0.6708 probability that Helen makes both free throws.
AB is proportional to XY since they are similar triangles making it 25:10 or 5:2
so then AC:XZ would be 5x:2x and 5x:6 so then its 15:6 since x is 3 basically set up proportions and so value of the big triangle to the small triangle would be at rails os 5:2
Answer:
The number is -3.
Step-by-step explanation:
X = a number
X + 12 = 9
Rearrange to get X on its own.
X = 9 - 12
X = -3
