Answer:
x = 51
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
x² = 45² + 24² = 2025 + 576 = 2601 ( take the square root of both sides )
x = = 51
Y and x have a proportional relationship, and y=4 when x=12
2 answers:
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<u>ANSWER: </u>
The probability that sum of numbers rolled is either 5 or 12 is
<u>SOLUTION: </u>
Given, Two dice are rolled.
We have to find what is the probability that the sum of numbers rolled is either 5 or 12
We know that, probability of an event =
Now, total outcomes for two dices = 6 for 1st dice x 6 for 2nd dice = 6 x 6 = 36.
Now, favourable outcomes = sum is 5 + sum is 12
= 4[(1,4), (2,3), (3, 2), (4, 1)] + 1[(6,6)]
= 5 total favourable outcomes.
Now, probability = 5/36
Hence, the probability that sum is either 5 or 12 is 5/36.
Answer:
20 gallons of the 40% solution, 60 gallons of the 80% solution
Step-by-step explanation:
Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the 70% solution mixture.
40% = 0.40,
80% = 0.80, respectively 70% = 0.70
As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,
0.40x + 0.80y = 0.70 80
At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.
( Multiply either side by 10 )
( Expand )
( Substitute to solve for x )
As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.