I'm sure it's only 15 miles :)
Hope that helps
Male Female Total
Income over $50,000 485 385 870
Income below $50,000 65 65 130
<span>Total 550 450 1,000
Probability of being male: 550/1000 = 0.55
Probability of earning over $50,000: 870/1000 = 0.87
0.55 x 0.87 = 0.4785
Probability of being male and earning over $50,000: 485/550 = 0.8818
</span><span>C) No, P(being male | the person earns over $50,000) ≠ P(being male)</span><span>
</span>
is in quadrant I, so
.
is in quadrant II, so
.
Recall that for any angle
,

Then with the conditions determined above, we get

and

Now recall the compound angle formulas:




as well as the definition of tangent:

Then
1. 
2. 
3. 
4. 
5. 
6. 
7. A bit more work required here. Recall the half-angle identities:



Because
is in quadrant II, we know that
is in quadrant I. Specifically, we know
, so
. In this quadrant, we have
, so

8. 
Answer: 0.0136
Step-by-step explanation:
Given : Mean : 
Standard deviation : 
Sample size : 
The formula to calculate the z-score :-

For x = 24

The p-value = 
Hence, the probability that the sample mean age for 50 randomly selected women to marry is at most 24 years = 0.0136