What is the simplest form of the expression (14.2a + 9.8b) – (13.1b – 0.2a) – (3.7a + 4.8b)?
2 answers:
Answer:
Step-by-step explanation:
the simplest form of the expression (14.2a + 9.8b) - (13.1b - 0.2a) - (3.7a + 4.8b)
To subtract the expressions we multiply negative sign inside the second parenthesis, change the sign of each term in second and third parenthesis
Now we combine like terms
So the expression becomes
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Answer:
0.82 = 82% probability that at least one party will not order drinks
Step-by-step explanation:
For each party, there are only two possible outcomes. Either they will order drinks with their meal, or they will not. The probability of a party ordering drinks with their meal is independent of other parties. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal.
This means that
During one hour, Ryan served 6 parties. Assuming that each party is equally likely to order drinks, what is the probability that at least one party will not order drinks?
6 parties, so n = 6.
Either all parties will order drinks, or at least one will not. The sum of the probabilities of these events is decimal 1. So
We want P(X < 6). So
In which
0.82 = 82% probability that at least one party will not order drinks
I took a picture of the answer for you.
The
formula , where r! is 1*2*3*...r
is the formula which gives us the total number of ways of forming groups of r objects, out of n objects.
for example, given 10 objects, there are C(10,6) ways of forming groups of 6, out of the 10 objects.
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Selecting 4 people out of 12 can be done in :
many ways.
All the possible groups of 4 people, where the husband and wife are included, can be done in C(10, 2) many ways, since we only calculate the possible choices of 2 out of 10 people, to complete the groups of 4.
Thus, the
<span>probability that both the husband and wife are hired is 45/495=0.09Part 2)
The probability that one is hired and the other is not =
P(husband hired, wife not hired) + P(wife hired, husband not hired)
these 2 are clearly equal, so it is enough to calculate one.
Consider the case : husband hired, wife not hired.
assuming the husband is hired, we have to calculate the possible groups of 3 that can be formed from 11-1 (the wife)=10 people.
this is
</span>
thus,
P(husband hired, wife not hired)=120/495=0.24
thus,
The probability that one is hired and the other is not =
P(husband hired, wife not hired) + P(wife hired, husband not hired) =
0.24+0.24=0.48
Answer:
A) 0.09
B) 0.48