Answer:
Add 1.25 litres of oil.
Step-by-step explanation:
Contents in beaker A implies;
15% of oil in 1 litre = 0.15 litres of oil
So that, there are 0.15 litres of oil and 0.85 litres of vinegar in beaker A.
Contents in beaker B implies:
55% of oil in 2 litres = 1.1 litres of oil
So that, thee are 1.1 litres of oil and 0.9 litres of vinegar in beaker B.
Half of contents of B poured into A implies that beaker A now contains:
0.15 litres + 0.55 litres = 0.7 litres of oil
0.85 litres + 0.45 litres = 1.3 litres of vinegar
The percentage of oil in A now = 
x 100%
= 35%
To increase the percentage of oil to 60%, then:
0.7 litres + 1.25 litres = 1.95 litres of oil
But the new total litres of the content in beaker A = 3.25 litres
So that;
x 100% = 60%
Therefore, to produce a mixture which is 60% oil, add 1.25 litres of oil.
Answer:
The square root of 144 will be 12
Answer:
Left: The substance is decreasing by 1/2 every 12 years
Right: The substance is decreasing by 5.61% each year
Step-by-step explanation:
exponential decay
A = P(1-r)ᵇⁿ, where A is the final amount, P is the initial amount, r is the rate decreased each time period, b is the number of years, and n is the number of times compounded each year
let's write each formula in terms of this
left:
f(t) = 600(1/2)^(t/12)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1/2 -> r = 1/2
t/12 = bn -> b = number of years = t, so bn = b/12 -> n = 1/12. Thus, it is compounded 1/12 times each year, so it is compounded every t*12 = 12 years. If it was compounded each month, it would be compounded 12 times a year
Thus, this is decreasing by a rate of 1/2 each 12 years
right:
f(t) = 600(1-0.0561)^(t)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1 - 0.0561 -> r = 0.0561 = 5.61%
t = bn -> b = number of years = t, so bn = b -> n = 1. Thus, it is compounded annually (1 time each year)
Thus, this is decreasing by a rate of 5.61% each year
<h2>
Answer:</h2>
The statement which best describes the effect of replacing the function f(x) with g(x) is:
The graph shifts 7 units up.
<h2>
Step-by-step explanation:</h2>
The function f(x) is given by :
The function f(x) is a linear function with positive slope.
and the function g(x) is given by:
The function g(x) is a linear function with same positive slope.
Also, we know that any transformation of the type:
f(x) → f(x)+k
is a translation transformation such that it if k>0 then it is a shift k units upwards and if k<0 then it is a shift k units downward.
Here we have:
g(x)=2x+5-2+2
i.e.
g(x)=2x-2+7
i.e.
g(x)=f(x)+7
Hence, the function g(x) is a translation of the function f(x) 7 units upward.
