The rule we'll use is
p^(q*r) = (p^q)^r
The exponents have been rearranged a bit.
In this case, p = 3.14, q = 159 and r = x, so,
p^(q*r) = (p^q)^r
3.14^(159*x) = (3.14^159)^x
This is in the form A^x with A = 3.14^159
Answer:
a) 0.7734
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:

(a) what proportion of children aged 13 to 15 years old have scores on this test above 83 ?
This is 1 subtracted by the pvalue of Z when X = 83. So



has a pvalue of 0.2266
1 - 0.2266 = 0.7734
The answer is 0.7734
Note first that several months have 30 days (each): April, June and September.
(A) could not be correct, since the month in question could have 28, 29 or 31 days.
(B) See (A), above. If the month in question does not have 30 days, then the month could NOT be April, June or September. Reject (B).
(C) You do this one, similarly to my responses to (A) and (B), above.
(D) This one is true, since we know that June has 30 days. If the month in question does NOT have 30 days, then that month could not possibly be June.
The answer is D. Because (18 x 10^6) + (5 x 10^4) = 18050000. And the answer to 1.805 x 10^7 also equals 18050000, if you do the math.