Answer:
- 6 2/3 qt 80%
- 13 1/3 qt 20%
Step-by-step explanation:
It is often convenient to solve a mixture problem by letting a variable represent the quantity of the higher-concentration contributor to the mix.
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We can let x represent the number of quarts of 80% solution needed. Then (20-x) is the number of quarts of 20% solution needed. The amount of salt in the final mix is ...
0.80x +0.20(20-x) = 0.40(20)
0.60x = 0.20(20) . . . . . . . . subtract 0.20(20) and simplify
x = 20/3 = 6 2/3 . . . . . . . . . divide by 0.60; quarts of 80% solution
(20 -x) = 13 1/3 . . . . . . . . . . amount of 20% solution needed
The teacher should mix 6 2/3 quarts of 80% solution with 13 1/3 quarts of 20% solution.
Answer:
-6
Step-by-step explanation:
Answer:
Events E and F are independent.
Step-by-step explanation:
E = {multiple of 3} = {3, 6, 9, 12}
P(E) = 4/12
F = {even number} = {2, 4, 6, 8. 10, 12}
P(F) = 6/12
E and F = {even and multiple of 3} = {6, 12}
P(E∩F) = 2/12
In order for two events to be independent the following relationship must be true:
Testing this property:
The relationship holds true, thus events E and F are independent.
A) angle 1 = angle 2 - Incorrect
These angles are only on one of the following lines, which means that they do not show that lines C and D are parallel. In addition, angles 1 and 2 are supplementary, so they could not be equal.
B) angle 1 + angle 2 = 180 - Incorrect
Though this is true, this does not prove that lines C and D are parallel because both of these angles are on the same line.
C) angle 2 = angle 3 - Correct
These angles are alternate interior angles and there are angles on both lines, which proves that lines C and D are parallel.
D) angle 2 + angle 3 = 180 - Incorrect
These angles are equivalent, so they cannot add up to 180 degrees unless the intersecting line was perpendicular to both lines C and D.
Hope this helps!! :)
