We are told that the first term is 2. The next term is 7(2) = 14; the third term is 7(14) = 98. And so on. So, the first term and the common ratio (7) are known.
The nth term of this geometric series is a_n = 2(7)^(n-1).
Check: What is the first term? We expect it is 2. 2(7)^(1-1) = 2(1) = 2. Correct.
What is the third term? We expect it is 98. 2(7)^(3-1) = 2(7)^2 = 98. Right.<span />
Answer:
23
Step-by-step explanation:
<span>c^2 + 5c - 14 = 0 </span>
<span>(c-2)(c+7) = 0 </span>
<span>c-2 = 0 or c+7 = 0 </span>
<span>c = 2 or c = -7 </span>
<span>c^2 - 2c - 15 = 0 </span>
<span>(c-5)(c+3) = 0 </span>
<span>c-5 = 0 or c+3 = 0 </span>
<span>c = 5 or c = -3</span>
Answer: The probability of getting a prime number exactly five times = 0.1908
Step-by-step explanation:
Prime numbers from 1 to 30 are 2,3,5,7,11, 13, 17, 19, 23, 29.
The probability of getting a prime number p= 
Number of trials n = 12
Binomial probability formula:
, where x= number of successes
n= number of trials.
x = Number of successes
p= probability of getting one success.
The probability of getting a prime number exactly five times:
Hence, the probability of getting a prime number exactly five times = 0.1908
Answer:
P(0,0) = 2/12 times 1/11 = 1/66
Step-by-step explanation:
For probability questions, think of each event happening separately, it makes the maths easier to understand. For example, in this question, do not think of the two boys taking a fruit at the same time - that makes the maths complicated
.
Let Daniel take a fruit first, then Sean can take a fruit. There are two parts to consider.
P
r
o
b
a
b
i
l
i
t
y
=
number of desirable outcomes
total number of possible outcomes
For Daniel: there are 12 different pieces of fruit in the bowl, he just takes one without choosing a specific fruit. (random)
The chance that Daniel takes an orange is
2
12
Of the 12 pieces of fruit. 2 are oranges.
Now Sean: the numbers of fruit in the bowl have changed. There are now only 11 pieces of fruit in the bowl, and only 1 is an orange.
The chance that Sean takes an orange is
1
11
