Answer:
<em>99.93%</em>
Step-by-step explanation:
<u>Probability of Independent Events</u>
Given the probability of success of each detector is 0.84 independently of the others, their combined success/failure probability can be computed with the product rule.
We can calculate the required probability by using the binomial distribution, but it's easier to calculate the probability of the negated event an subtract from 1.
We want to know the probability that a least one of the 4 systems detects the occurrence of theft. That probability is the sum of the probabilities that one of them, two of them, three of them or all of them succeed. The negated event is that NONE of them actually detects the theft. Being p the individual probability of success, p=0.84. Being q the probability of failure, q=0.16.
The probability that none of the systems detect the theft is
Thus, the probability that at least one of the systems detect the theft is
That means a 99.93%
Answer:
y=9x+2
Step-by-step explanation:
The standard form for a linear equation is y=mx+b. m=9 since it is slope and b=2 which is the y intercept. So the equation would be y=9x+2.
Answer:
Option c -2.8571
Step-by-step explanation:
z-score are calculated as
.
We are given that mean=120 and standard deviation=S.D=35 as X~N(120,35).
Sample size=n=25.
We have to find z-score for x-bar=100. So,
z-score=[100-120]/[35/√25]
z-score=[-20]/[35/5]
z-score=-20/7
z-score=-2.8571.
Thus, the z-score associated with x-bar = 100 is -2.8571.
The hotel is $250 plus $25 per person so the equation would be
y= 25x + 250
(Y is the total cost and x is the number of people)
the restaurant is $100 plus $40 per person so the equation would be
y = 40x + 100
What we want to know is which x value would make the y values equal to each other. So you can just replace the "y" in one equation with the other equation:
25x + 250 = 40x + 100
and then solve...
1. subtract 100 from both sides
25x + 150 = 40x
2. subtract 25x from both sides
150 = 15 x
3. divide both sides by 15
10 = x
you can check by plugging 10 into the original equations
25(10) + 250
250 + 250 = 500
and
40(10) + 100
400 + 100 = 500
they both cost $500 when you invite 10 people
The correct answer to your question is 8.
