By using trigonometric relations, we will find that:
sin(θ) = (√33)/7 = √(33/49)
<h3>How to find the value of the sine?</h3>
Remember that for a right triangle, we have the relations:
cos(a) = (adjacent cathetus)/(hypotenuse)
sin(a) = (opposite cathetus)/(hypotenuse).
Here we know that:
cos(θ) = 4/7
Then we can say that we have a triangle with an adjacent cathetus of 4 units and a hypotenuse of 7 units. Now we need to find the other cathetus.
opposite cathetus = √(7^2 - 4^2) = √33
Then we can write:
sin(θ) = (√33)/7 = √(33/49)
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Answer:
<h2><em><u>3</u></em></h2>
Step-by-step explanation:
<h3>
<u>Given</u><u> </u><u>question</u><u>:</u></h3>
<em>To</em><em> </em><em>simplify</em><em> </em><em>-</em><em> </em>
<h3>
<u>Solution</u><u>:</u></h3>
<em>According</em><em> </em><em>to</em><em> </em><em>PEMDAS</em><em> </em><em>rule</em><em>,</em>
- <em>[</em><em>First</em><em> </em><em>parenthesis</em><em>]</em>
- <em>[</em><em>Then</em><em> </em><em>exponents</em><em>]</em>
- <em>[</em><em>Then</em><em> </em><em>multiplication</em><em>]</em>
= 14 + 16 ÷ 8 - 21 ÷ 7 - 10
- <em>[</em><em>Then</em><em> </em><em>division</em><em>]</em>
= 14 + 2 - 3 - 10
- <em>[</em><em>Then</em><em> </em><em>addition</em><em>]</em>
= 16 - 13
- <em>[</em><em>Then</em><em> </em><em>subtraction</em><em>]</em>
= <em><u>3</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>
Answer:
<h2>B) (0, 6)</h2>
Step-by-step explanation:
If the point lies on the y-axis then the first coordinate of the point is equal 0.
(0, y) - y is any real number.
Answer:
Step-by-step explanation:
log(2)+log(8)
=
2
1.20412≠2
False
Answer:
- There is no significant evidence that p1 is different than p2 at 0.01 significance level.
- 99% confidence interval for p1-p2 is -0.171 ±0.237 that is (−0.408, 0.066)
Step-by-step explanation:
Let p1 be the proportion of the common attribute in population1
And p2 be the proportion of the same common attribute in population2
: p1-p2=0
: p1-p2≠0
Test statistic can be found using the equation:
where
- p1 is the sample proportion of the common attribute in population1 ()
- p2 is the sample proportion of the common attribute in population2 ()
- p is the pool proportion of p1 and p2 ()
- n1 is the sample size of the people from population1 (30)
- n2 is the sample size of the people from population2 (1900)
Then ≈ 2.03
p-value of the test statistic is 0.042>0.01, therefore we fail to reject the null hypothesis. There is no significant evidence that p1 is different than p2.
99% confidence interval estimate for p1-p2 can be calculated using the equation
p1-p2± where
- z is the z-statistic for the 99% confidence (2.58)
Thus 99% confidence interval is
0.533-0.704± ≈ -0.171 ±0.237 that is (−0.408, 0.066)