Answer:
The explicit form is 
Step-by-step explanation:
The explicit form of a geometric sequence is given by:
where an is the nth term, a is the first term of the sequence and r is the common ratio.
In this case:
a=162
The value of the common ratio is obtained by dividing one term by the previous term.
For the first and second terms:
108/162=2/3
For the second and third terms (In order to prove that 2/3 is the common ratio)
72/108=2/3
Therefore:
r=2/3
Replacing a and r in the formula:
3. Alt. Interior Angles
4. definition of midpoint
Answer:
164.48 or 164.5
Step-by-step explanation:
So, to make it simpler, you can do the circle like this: 3.14×(8×8). Then you can work down!
3.14 × 64
200.96
and then because it's halved, you divide by 2
100.48
then that's the half circle
The square would just be 8×8=64
then add the circle and the square and viola!
164.48
Answer:
Check Explanation
Step-by-step explanation:
a) Yes, the two events are mutually exclusive. The true meaning of mutually exclusive is that both A1 and A2 have no sample points in common and cannot both occur at the same time.
The only sure mathematical way to tell is from P(A1 n A2) = 0.
Note that this is different from when two events are independent. Two events are independent when the chances of one occurring does not depend on the chances of the other event occurring at all. Independent events can both occur at the same time. Mathematically, independent events are described as P(A1|A2) = P(A1) and P(A2|A1) = P(A2)
b) To solve for P(B)
We use the mathematical definition of the conditional statement
P(B|A1) = P(B n A1)/P(A1)
P(B n A1) = P(B|A1) × P(A1) = 0.2 × 0.4 = 0.08
P(B|A2) = P(B n A2)/P(A2)
P(B n A2) = P(B|A2) × P(A2) = 0.05 × 0.6 = 0.03
P(B) = P(B n A1) + P(B n A2) (especially because A1 and A2 are mutually exclusive)
P(B) = 0.08 + 0.03 = 0.11
Hope this helps!!
