Answer:
Each pitcher has the same fraction of the other drink.
Step-by-step explanation:
After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).
The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.
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You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.
Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:
tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2
Answer:
Each box has 800 spoons.
Step-by-step explanation:
4800/6=800
The correct question is
The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases. What is the volume of the composite figure<span>
?</span>
the complete question in the attached figure
we know that
[volume of a cone]=[area of the base]*h/3
[area of the base]=22*10/2-------> 110 units²
h=19.5 units
[volume of a cone]=[110]*19.5/3------> 715 units³
[volume of a triangular prism]=[area of the base]*h
[area of the base]=110 units²
h=25 units
[volume of a a triangular prism]=[110]*25------------> 2750 units³
[volume of a the composite figure]=[volume of a cone]+[volume of a <span>a triangular prism]
</span>[volume of a the composite figure]=[715]+[2750]-------> 3465 units³
the answer is
The volume of a the composite figure is 3465 units³
Move constant to other side
add 1
4c^2-8c=1
divide by 4 to make leading coeficient 1
c^2-2c=1/4
take 1/2 of linear coeficient and square it
-2/2=-1, (-1)^2=1
add that to both sides
c^2-2c+1=1/4+1
factor perfect squaer and add
(c-1)^2=5/4
square root both sides
c-1=+/-(√5)/2
add 1
c=1+/-(√5)/2
c=2.12 or -0.12
Hey there! :)
Answer:
x = 242 mm.
Step-by-step explanation:
Begin by setting up a proportion between the actual college building and the drawing.

Cross multiply:
99 × 22 = 9 × x
2178 = 9x
Divide both sides by 9:
2178/9 = 9x/9
x = 242 mm.