The snack shop makes 3 mixes of nuts in the following proportions.
1 answer:
Answer:
Step-by-step explanation:
It is given that the snack shop makes 3 mixes of nuts in the following proportions.
Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.
Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.
Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.
they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.
We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.
Mix I Mix II Mix III
peanuts 6 5 3
cashews 2 3 4
pecans 2 2 2
The product of both matrices is
Therefore matrix AB gives the total number of lbs of each nut required to fill the order.
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Answer:
The probability that the household has only cell phones and has high-speed Internet is 0.408
Step-by-step explanation:
Let A be the event that represents U.S. households has only cell phones
Let B be the event that represents U.S. households have high-speed Internet.
We are given that 51% of U.S. households has only cell phones
P(A)=0.51
We are given that 70% of the U.S. households have high-speed Internet.
P(B)=0.7
We are given that U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected.
P(B|A)=0.8
Hence the probability that the household has only cell phones and has high-speed Internet is 0.408
Taking into account the definition of a system of linear equations, the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.
<h3>System of linear equations</h3>A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
<h3>Amount of ticket sold</h3>In this case, a system of linear equations must be proposed taking into account that:
- "x" is the amount of adult tickets sold.
- "y" is the amount of child tickets sold.
The maximum capacity for seating in a theater is 500 people. If they sold out on a certain showtime, this is represented by x+y=500.
On the other side, the theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each and the made a total of $3,157. This is represented by 7.25x +4y=3157.
So, the system of equations to be solved is
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable x from the first equation you get:
x=500 - y
Substituting this expression in the second equation you get:
7.25× (500 -y) +4y=3157
7.25×500 - 7.25y +4y=3157
3625 - 7.25y +4y=3157
- 7.25y +4y=3157 -3625
-3.25y= -468
y= (-468)÷ (-3.25)
<u><em>y= 144</em></u>
Substituting this value in the expression x=500 - y you get:
x=500 - 144
<u><em>x=356</em></u>
Remembering that "x" is the amount of adult tickets sold and "y" is the amount of child tickets sold, you get that the amount of adult tickets sold is 356 and the amount of child tickets sold is 144.
Learn more about system of equations:
<u>brainly.com/question/14323743</u>
<u>brainly.com/question/1365672</u>