Answer:
0.06 liters
Step-by-step explanation:
acid concentration of 65% means that it of 100 units of that solution 65 are acid, and the remaining 35 are water.
so, 100 units are 0.2 liters in this example.
that means that 65/100 × 0.2 = 0.13 liters are acid.
35/100 × 0.2 = 0.07 liters are water
we get a 50% concentration, when we have the same amount of water and acid in the solution (acid is only half of 50% of the solution).
the account of acid remains the same, as we are only adding water.
so, how much water do we need to get from 0.07 liters to 0.13 liters (the same as the already present acid) ?
0.13 - 0.07 = 0.06 liters
Answer:
1.5 grams of protein.
Step-by-step explanation:
The equation that represents the relationship between protein and fat is as follows :
4p + 9f = 60 ....(1)
We need to find the grams of protein are there if there are 6 grams of fat in the snack.
Put f = 6 in the above equation (1).
4p + 9(6)= 60
4p + 54 = 60
Subtract 54 to the both sides,
4p + 54-54 = 60-54
4p = 6
⇒ p = 1.5 grams
It means the snack contains 1.5 grams of protein.
This problem can be solved by the chicken rabbits method or you can just do simple algebra.
I.) Chicken and rabbits method
First assume all 110 coins are dimes and none are quarters.
We will have a total value of 11 dollars
Now for each dime we switch out for a quarter, we adds 15 cents to the total value.
18.50-11=7.50 dollars
There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.
This also meant that we need to switch out 50 dimes for 50 quarters.
So we have 50 quarters.
That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.
Let's say there are x dimes and y quarters.
Set up equation
x+y=110
10x+25y=1850
Now solve multiply first equation by 10
10x+10y=1100
subtract
15y=750
y=50
Now we set the numbers of quarters to y so the answer is 50 quarters.
I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.
Step-by-step explanation:
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Prove the LHS
Using trigonometric identities
That's
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<u>Rewrite the expression</u>
We have
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So we have
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Using trigonometric identities
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<u>Rewrite the expression</u>
That's
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Reduce the expression with cos a
We have the final answer as
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As proven
Hope this helps you
Answer:
50%
Step-by-step explanation:
The chances of getting either heads or tails on a coin is 50/50. Convert that to probability and that is 1/2. Convert it to percentage of 100 and it is 50%.
Only time a coin isn't 50/50 is if the coin itself is a weighted coin.