Answer:
4.5
Step-by-step explanation:
To find the hypotenuse of a right triangle, we use Pythagorean's Theorem which states that 
. Plugging in the values of the two legs given, we get 
. We can take the square root of each side and get that 
.
First, some housekeeping:
cos = 12/13 is incomplete; "cos" must have an argument (input).
cos x = 12/13 is fine; here "cos" has the argument (input) x.
Given that cos x = 12/13, find sin x. To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.
12^2 + opp^2 = 13^2, or opp^2 = 169-144 = 25.
Then the opp side could be either 5 or -5. Let's assume that it's +5, and that angle x is in the first quadrant.
Then sin x = opp / hyp = 5/13 (answer)
cos 2 is an entirely different kind of problem. Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).
Using a calculator: cos 2 = -0.416. Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.
Subtract 5 (Cameron) and 2 (Karlee) from 49.
Why: Denise's age is basically the basic number. Karlee would be 2 years older, so subtract 2 from 49. You get 47. Cameron is 5 years older than Denise, so subtract 5. You get 42 and divide that by 3 since there are 3 people.
49 - 7 = 42
42 divide by 3 = 14
Check:
14 + 5 = 19
14 + 2 = 16
14 + 0 = 14
19 + 16 + 14 = 49
19 (Cameron) - 16 (Karlee) = 3 years older
16 (Karlee) - 14 (Denise) = 2 years older
19 (Cameron) - 14 (Denise) = 5 years older
Hopes this helps!
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the men,
x = 318
n1 = 520
p1 = 318/520 = 0.61
For the women
x = 379
n2 = 460
p2 = 379/460 = 0.82
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.61(1 - 0.61)/520 + 0.82(1 - 0.82)/460]
= 1.96 × √0.0004575 + 0.00032086957)
= 0.055
Confidence interval = 0.61 - 0.82 ± 0.055
= - 0.21 ± 0.055
