Answer:
7.1 points
Step-by-step explanation:
100/14=7.1 points
The model is 1:50 so take 11/5 and multiply it by 50 and you get 110, so the window is 110 inches long
Let Cameron be x years old now.
-
<u>Now:</u>
Cameron = x
Uncle =3x
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<u>4 years ago:</u>
Cameron = x - 4
Uncle = 3x - 4
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<u>4 years ago, Uncle is 4 times older:</u>
3x - 4 = 4(x - 4)
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<u>Find x:</u>
3x - 4 = 4(x - 4)
3x - 4 = 4x - 16
4x - 3x = 16 - 4
x = 12
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<u>Find the age:</u>
Cameron = x = 12
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Answer: Cameron is 12 years old now.
Answer:
<em>Choose the first alternative</em>
Step-by-step explanation:
<u>Probabilities</u>
The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions 
and the total number of possible choices 
, i.e.
There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total
We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.
To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5
The total number of possible choices is
The probability is then
Choose the first alternative
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
