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
Answer:
Option D.
Step-by-step explanation:
In the given graph x-axis represents the number of owners and y-axis represents yearly cost of pets, in hundreds.
It is given that the graph passes through the points (1,15), (3,7) and (10,0).
We need to check whether (4.5, 6) is a realistic solution for the function or not. (4.5,6) point represents
Number of owners = 4.5
yearly cost of pets = 6
It is realistic that owners spend $600 a year on their pet(s).
Number of owners can not be a fraction value. So, it is not realistic to have 4.5 owners.
Therefore, the correct option is D.
Average speed is the total distance traveled by an object at a certain period of time. To calculate for the average speed we divide the total distance covered by the total time. We do as follows:
Average speed = 560 meters / 25 seconds = 22.4 m/s
Answer:
80 minutes or 1 h 20 minutes
Step-by-step explanation:
15-13=2
2/0.025=80
So we can conclude that it takes 80 minutes till it reaches 13 feet.
Answer:
The slope becomes 0.5625 and y intercept becomes 12.5.
$65.9375
Step-by-step explanation:
Given that
the total reimbursement function in terms of 
miles:
After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.
To find:
How to transform the graph of f.
Total reimbursement for a trip of 95 miles?
Solution:
can also be written as:
It is nothing but slope intercept form, comparing with 
M is the slope and C is the y intercept.
Slope of the graph is 0.45.
Y intercept is 5.
After change in the function, first of all add $5.
Now, multiply with 1.25
Resulting function becomes:
Kindly refer to the attached image for the graph of the two functions.
Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.
To find the reimbursement for a trip of 95 miles:
Put m = 95
