Answer:
37
Step-by-step explanation:
The first thing is to calculate critical z factor
the alpha and the critical z score for a confidence level of 90% is calculated as follows:
two sided alpha = (100% - 90%) / 200 = 0.05
critical z factor for two sided alpha of .05 is calculated as follows:
critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:
critical z factor = 2.58
Now we have the following formula:
ME = z * (sd / sqrt (N) ^ (1/2))
where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58
N the sample size and we want to know it, replacing:
6 = 2.58 * (14 / (N) ^ (1/2))
solving for N we have:
N = (2.58 * 14/6) ^ 2
N = 36.24
Which means that the sample size was 37.
Answer:
7.5 L of 10% solution and 22.5 L of 30% solution
Step-by-step explanation:
Volume of 10% solution plus volume of 30% solution = total volume of 25% volume.
x + y = 30
Acid in 10% solution plus acid in 30% solution = total acid in 25% solution.
0.10 x + 0.30 y = 30 × 0.25
0.10 x + 0.30 y = 7.5
Solve the system of equations, using either substitution or elimination. I'll use substitution:
x = 30 − y
0.10 (30 − y) + 0.30 y = 7.5
3 − 0.10 y + 0.30 y = 7.5
0.20 y = 4.5
y = 22.5
x = 30 − y
x = 7.5
Sarah needs 7.5 L of 10% solution and 22.5 L of 30% solution.
Step-by-step explanation:
if you need any explanation you can ask
Ninety-nine hundredths.
Hope this helps!
and you can expand the numerator if you wish, it won't be simplified further though.
