Answer: The correct option is 1, i.e., 
.
Explanation:
The geometric sequence is in the form of,
Where, a is the first term of the sequence and r is the common ratio of the sequence.
It means the 
term of the sequence is defined as,
So the the 
term of the sequence is defined as,
It means the geometric sequence is in the form of,
Where, r be any constant.
From the options only is in the form of with common ratio 
.
Therefore, the function can be used to model the graphed geometric sequence is .
According to the given information and what we know about a standard deck of cards, there are 4 fives in a deck of 52 cards.
To find the probability of drawing a five divide the number of fives by the total number of cards:
Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
- In the question it is given that the sprinklers activate correctly or not independently.
- The number of outcomes are two i.e. sprinklers activate correctly or not.
A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) = 
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
is calculated as:
= n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) =
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282
Mai ran 4,200 meters or 4.2 kilometers in 30 minutes.
