Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 \text{ m}2.8 m2, point, 8, start text, space,
2 answers:
Answer:
420 meters
Step-by-step explanation:
Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?
<u>Given</u>:
Circumference of circular tire = 2.8 meters
Tire revolves per second = 1.5 times
<u>Question asked:</u>
What is the distance Benjamin travels in 100 seconds?
<u>Solution:</u>
Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.
<em><u>Now, by unitary method:</u></em>
In 1 second, tire revolves = 1.5 times
In 100 seconds, tire revolves = 1.5 100
= 150 times
Distance covered by the tire when it revolves 1 time = 2.8 m
Distance covered by the tire when it revolves 150 times = 2.8 150
= 420 meters
Therefore, Benjamin travels 420 meters in 100 seconds.
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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