Answer:
0.16 liters of water
Step-by-step explanation:
Samantha's recipe makes 0.06 liters of solution. She wants 0.48 liters of solution, an amount 0.48/0.06 = 8 times as great as made by one recipe.
The recipe calls for 0.02 liters of water. To make 8 times the amount of solution, Samantha will use 8 times as much water: 0.16 liters.
Samantha will use 0.16 liters of water to make 0.48 liters of solution.
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Alternate solution
The fraction of solution that is water is (0.02 L)/(0.06 L) = 1/3. For 0.48 L of solution, the water needed is 1/3×0.48 L = 0.16 liters.
Answer: it will take 14 years
Step-by-step explanation:
A savings account is started with an initial deposit of $600. This means that the principal P is
P = 600
It was compounded annually. This means that it was compounded once in a year. Therefore,
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
The duration of time that for which the money stayed in the account is t years. So
Time = t
The formula for compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years. Therefore,
a) the equation to represent the amount of money in the account as a function of time in years would be
A = 600 (1+0.021/1)^1×t
A = 600 (1.021)^t
b) the amount of time it takes for the account balance to reach $800 would be
800 = 600 (1.021)^t
Dividing both sides of the equation by 600, it becomes
1.33 = (1.021)^t
t = 14
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<h3>= 35% × $70 ÷ 100</h3><h3>= 24.5</h3><h3>= $70 - 24.5</h3><h3>= 45.5</h3><h3>= 5% × 45.5 ÷ 100</h3><h3>= 2.275</h3><h3>= 2.275 + 45.5</h3><h3>= ~$47.775</h3><h3>= <u>$</u><u>48</u></h3><h3>Janet Will Have Enough Money Left Over For A Movie Ticket.</h3>
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Answer:
f(x) = -5x - 4
Step-by-step explanation:
We want to get the inverse of the following function:
f^-1(x) = (-1/5)x - 4/5
To do that, we have to replace x with f(x) and f^-1(x) with x, as follows:
x = (-1/5)f(x) - 4/5
And then solve for f(x), the inverse of f^-1(x).
x + 4/5 = (-1/5)f(x)
f(x) = -5x + (-5)4/5
f(x) = -5x - 4
To check our result we compute a pair (x, f(x))
x f(x)
1 -5*1 - 4 = -9
which has to be equivalent to (-9, 1) in the original function
x f^-1(x)
-9 (-1/5)*(-9) - 4/5 = 1
