Find the volume of the following prism using the formula V = Bh.
2 answers:
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Answer:
First brand of antifreeze: 21 gallons
Second brand of antifreeze: 9 gallons
Step-by-step explanation:
Let's call A the amount of first brand of antifreeze. 20% pure antifreeze
Let's call B the amount of second brand of antifreeze. 70% pure antifreeze
The resulting mixture should have 35% pure antifreeze, and 30 gallons.
Then we know that the total amount of mixture will be:
Then the total amount of pure antifreeze in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.7 and add it to the second equation:
+
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We substitute the value of A into one of the two equations and solve for B.
<u>Answer: </u>
A standard six-sided die is rolled twice and the top faces are observed and the probability that the sum of the numbers on the top faces is 10 is
<u>Solution: </u>
The sample space of two dice outcomes is given as follows:
{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3, 1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4, 1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5, 1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6, 1) (6,2) (6,3) (6,4) (6,5) (6,6) }
Total number of events n(s) = 36
Expected Outcomes = {(4, 6), (5, 5), (6, 4)}
Number of favorable outcomes n(E) = 3
Probability (sum of numbers on the top faces is 10) = =
=
Therefore the probability that the sum of the numbers on the top faces is 10 is