The value of 4 in 34,258 is 10 times the value of the 4 in 47,163.
Answer:
5.1 days
Step-by-step explanation:
Given in the question,
initial amount of substance = 34 grams
k-value = 0.137
To find the half life of this substance we will use following formula
here N(0) is initial amount of substance
t is time in days
Plug values in the formula
1/2 = e^{-0.137t}
Take logarithm on both sides
ln(1/2) = ln( e^{-0.137t})
ln(1/2) = -0.137t
t = ln(1/2) / -0.137
t = 5.059
t ≈ 5.1 days (nearest to tenths)
Answer: choice A. 40 liters
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Explanation:
x = number of liters of the 50% alcohol solution
If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).
So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below
0.50*x + 36 = 0.70*(40+x)
0.50*x + 36 = 0.70*(40)+0.70*(x)
0.50*x + 36 = 28+0.70*x
36 - 28 = 0.70*x - 0.50x
8 = 0.20x
0.20x = 8
x = 8/0.20
x = 40
So that is why the answer is choice A. 40 liters
Answer: F (cos(230)).
Explanation:
Cosine corresponds to the x coordinate of points on a circle when the radius is drawn in like this, so the answer would be the cos of that angle, but you have to account for the fact that the 50 degree angle marked is just the reference angle not the entire angle so you have to add 180 degrees to that to get 230.