Answer:
t ≥ 18
Step-by-step explanation:
He has run 12 miles plus some more miles t. He need to run at least 30 miles
12+t ≥ 30
Subtract 12 from each side
12+t-12 ≥ 30-12
t ≥ 18
We have the following equation:
2 (x-3) ^ 2 + 10 = 82
We must clear x.
We pass the constant terms to one side of the equation:
2 (x-3) ^ 2 = 82 - 10
2 (x-3) ^ 2 = 72
(x-3) ^ 2 = 72/2
(x-3) ^ 2 = 36
Square root to both members:
x-3 = +/- root (36)
x-3 = +/- 6
The solutions are:
x1 = 6 + 3 = 9
x2 = -6 + 3 = -3
Answer:
x1 = 9
x2 = -3
Answer: a) 683 b) 1067
Step-by-step explanation:
The confidence interval for population proportion is given by :-

a) Given : Significance level :
Critical value : 
Margin of error : 
Formula to calculate the sample size needed for interval estimate of population proportion :-

Hence, the required sample size would be 683 .
b) If no estimate of the sample proportion is available then the formula to calculate sample size will be :-

Hence, the required sample size would be 1067 .
Answer:
1577.8 US dollars are received for 1127 UK pounds.
5669.5 UK pounds are received for US$7937.3.
Step-by-step explanation:
The questions are solved by proportions, using a rule of three.
How many US dollars are received for 1127 UK pounds?
1 UK pound = 1.4 US dollars
1127 UK pounds - x US dollars
Applying cross multiplication:

1577.8 US dollars are received for 1127 UK pounds.
How many UK pounds are received for US$7937.3?
1 UK pound = 1.4 US dollars
x UK pounds - 7937.3 US dollars



5669.5 UK pounds are received for US$7937.3.