Answer:
Step-by-step explanation:
The given geometric series is:
243-162+108.....+64/3
The first term is .
The common ratio is:
The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.
The complete series is
243-162+108-72+48-32+64/3
The sum is:
18 = 2×3×3
30 = 2×3×5
The LCM will have factors of 2, 3², and 5. (Choose the highest power of each prime.)
2×3×3×5 = 90 is the LCM of 18 and 30.
X+(y+z) is equal to saying (x+y)+z
This is called the cumulative property when order doesn’t matter or doesn’t change the equation. As in 1+2 is the same as 2+1. No matter which way we get the same answer. This only works with multiplication and addition though. Hope this helps. Any questions please just ask!! Thank you so much!!
I believe that it equals 3 2/3 cuz 3 4/3-2/3= 3 2/3
Answer:
a) 336
b) 593775
c) 83160
d) P=0.14
e) P=0.0019
Step-by-step explanation:
We have wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet.
a) If he wants to serve 3 bottles of zinfandel and serving order is important. We get:
C=8·7·6=336
b) {30}_C_{6}=\frac{30!}{6!(30-6)!}
{30}_C_{6}=593775
c) {8}_C_{2} · {10}_C_{2} · {12}_C_{2}=
=\frac{8!}{2!(8-2)!} · \frac{10!}{2!(10-2)!} · \frac{12!}{2!(12-2)!}
=28 · 45 · 66
=83160
d) We calculate the number of possible combinations:
{30}_C_{6}=593775
We calculate the number of favorable combinations:
{8}_C_{2} · {10}_C_{2} · {12}_C_{2}=83160
The probability that this results in two bottles of each variety being is
P=83160/593775
P=0.14
e) We calculate the number of possible combinations:
{30}_C_{6}=593775
We calculate the number of favorable combinations:
{8}_C_{6} + {10}_C_{6} + {12}_C_{6}= 28+210+924=1162
The probability is
P=1162/593775
P=0.0019