Bria and Matt have a total of 400 stamps. Matt has three times as many stamps as Bria. Which system of equations can be used to
2 answers:
Answer:
Step-by-step explanation:
Let b be the number of stamps Bria has and m be the number of stamps Matt has.
Given : Bria and Matt have a total of 400 stamps.
i.e. No. of stamps Bria has + No. of stamps Matt has = 400
i.e. In terms of variables (1)
Also, Matt has three times as many stamps as Bria.
i.e. No. of stamps Matt has = 3 x (No. of stamps Bria has )
i.e. In terms of variables (2)
From (1) and (2) , the system of equations can be used to find the number of stamps Bria has, b, and the number of stamps Matt has, m will be :_
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Answer:
The ticket price that maximizes revenue is $50.
The maximum monthly revenue is $250,000.
Step-by-step explanation:
We have to write a function that describes the revenue of the airline.
We know one point of this function: when the price is $30, the amount of passengers is 7000.
We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.
Then, we can write the revenue as the multiplication of price and passengers:
where x is the variation in the price of the ticket.
Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.
We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:
The maximum monthly revenue is:
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