This is a doozy so pay attention. First thing you have to recognize is that is a trig identity, the sum identity for cosine to be exact. That formula is
.
So that means you need to find the cosine of alpha and the sin of beta. We are given the sin of alpha being 4/5 in the first quadrant. If you set up the sin ratio which is side opposite over hypotenuse of a right triangle, you put the 4 on the side opposite the reference angle, alpha, and the hypotenuse of 5 on the terminal ray and then you have to find the missing side of the right triangle you created. Using Pythagorean's theorem, you find that the missing side, which is the adjacent side to alpha, is 3. Now you can find the cosine of alpha as well, since cosine is the side adjacent, 3, over the hypotenuse, 5. So far wwe have
and
for that first angle. Now moving on to the second angle. The cosine of beta is side adjacent, 5, over the hypotenuse, 13, and we are missing the side opposite the reference angle beta. Using Pythagorean's theorem again to find the side opposite, we have that that side measures 12. Now we can find the sine of beta using that opposite side, 12, over the hypotenuse, 13. What we have now is
and
. According to the identity, we have to multiply those ratios now:
.
When you do that you get
.
Of course in order to subtract those 2 fractions you need a common denominator which is 65 so
which gives you a final answer of 
which is the first choice given above. There you go!
The way the equation is written
Solve for G:F = (G m^3)/r^2
F = (G m^3)/r^2 is equivalent to (G m^3)/r^2 = F:(G m^3)/r^2 = F
Divide both sides by m^3/r^2:Answer: G = (F r^2)/m^3
Answer you multiple it by 10
Step-by-step explanation:
Answer:
The answer is 8 please Brainlist me
Step-by-step explanation:
6^2+h^2=10^2
36+h^2=100
Solving for h gives 8
Complete Question
Express the confidence interval 0.555 less than p less than 0.777 in the form Modifying above p with caret plus or minus Upper E.
Answer:
The modified representation is 
Step-by-step explanation:
From the question we are told that
The confidence interval interval is 
Now looking at the values that make up the up confidence interval we see that this is a symmetric confidence interval(This because the interval covers 95% of the area under the normal curve which mean that the probability of a value falling outside the interval is 0.05 which is divided into two , the first half on the left -tail and the second half on the right tail as shown on the figure in the first uploaded image(reference - Yale University ) ) which means
Now since the confidence interval is symmetric , we can obtain the sample proportion as follows
Generally the margin of error is mathematically represented as
Where K is the length of the confidence interval which iis mathematically represented as
Hence
So the confidence interval can now be represented as
