D because it is the only one that is unpredictable
2/3 is the simplified form of 18/27
Assume that the amount needed from the 5% solution is x and that the amount needed from the 65% solution is y.
We are given that, the final solution should be 42 ml, this means that:
x + y = 42 ...........> equation I
This can also be written as:
x = 42-y .......> equation II
We are also given that the final concentration should be 45%, this means that:
5% x + 65% y = 45% (x+y)
0.05x + 0.65y = 0.45(x+y)
We have x+y = 42 from equation I, therefore:
0.05x + 0.65y = 0.45(42)
0.05x + 0.65y = 18.9 .........> equation III
Substitute with equation II in equation III as follows:
0.05x + 0.65y = 18.9
0.05(42-y) + 0.65y = 18.9
2.1 - 0.05y + 0.65y = 18.9
0.6y = 18.9 - 2.1
0.6y = 16.8
y = 28 ml
Substitute with y in equation II to get x as follows:
x = 42-y
x = 42 - 28
x = 14 ml
Based on the above calculations:
amount of 5% solution = x = 14 ml
amount of 65% solution = y = 28 ml
The correct choice is:
The teacher will need 14 mL of the 5% solution and 28 mL of the 65% solution.
Scenario B - 143 (Year 1), 109 (Year 2), 141 (Year 3)
In this scenario, the total income is 35,370. This is calculated by getting the sum of the number of garments in the span of three years and multiplying it by the rate of $90 per garment. Your income of 35,370 is lesser than your fixed cost for three years of 40,000.
Answer:
There is not sufficient evidence to support the claim μ > 54.4.
Step-by-step explanation:
1) Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
2) Solution to the problem
On this case we want to test is 
and the system of hypothesi on this case are:
Null Hypothesis: 
Alternative hypothesis:
On this case is our decision is FAILS to reject the null hypothesis then we can conclude that we don't have enough evidence to support the claim at the significance level provided. So the correct conclusion would be:
There is not sufficient evidence to support the claim μ > 54.4.
