There are 20 gallons of 20% butterbeer solution.
Assume there are x gallons of 80% solution.
So total amount of the solution will be (x+20) gallons
The final solution is 50%.
So, we can set up the equation as:
.
Thus, there will be 20 gallons of 80% butterbeer solution that is needed to be mixed with 20 gallons of 20% butterbeer solution.
You are given two points on a line, and told that the function is "direct variation." You can save a lot of time by recognizing that the y-intercept here is zero (0). Thus, the line passes through the origin.
A line through (2,14) and (4,38) is NOT direct variation, because the line connecting those two points does NOT pass through the origin, and thus has a vertical intercept.
Answer:
Step-by-step explanation:
We assume that there are 100 sour candies, Thus-
26 % of candy are grape implies that 26% of 100 candies are grape that is equal to 26
Now remaing candies that are not grape are 100-26 = 74
Based on the rule of multiplication:
P(A ∩ B) = P(A)/ P(B|A)
In the beginning, there are 26grape candies, probability of choosing first grape candy = 26C1 = 26
After the first selection, we replace the selected grape candy so there are still 100 candies in the bag P(B|A) = 100C3 = 100 x 99 x 98 x 97!/3! X 97!
= 50 x 33 x 98
So probability =1/ 50 x 33 x 98 x 26
= 1/4204200
Answer:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of 
to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = of the sides of ΔABC
Area of ΔA'B'C' = 
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
Assuming that the topping order is not important, you need to use the combination to solve this question. The number of toppings is 12 and then added 2, so the number will become: 12+2= 14 toppings
From 14 toppings, ian need to choose 3. The possible ways would be:
14C3= 14!/(14-3)!3!= 14*13*12/ 3*2= 364 possible ways
