Answer:
3rd option
Step-by-step explanation:
substitute x = f(x) into g(x)
g(f(x))
= g(x² + 2)
= 4(x² + 2) - 1
= 4x² + 8 - 1
= 4x² + 7
First, you have to set a system of equations to determine the number of fiction and of nonfiction books.Call f the number of fiction books and n the number of nonfiction books. Then 400 = f + n. And f = n + 40 => n = f - 40 => 400 = f + f - 40 => 400 - 40 = 2f => f = 360 / 2 = 180. Now to find the probability of picking two fiction books, take into account the the Audrey will pick from 180 fiction books out of 400, and Ryan will pick from 179 fiction books out of 399, so the probability will be<span> (180/ 400) * (179/399) = 0.20 (rounded to two decimals). Answer: 0.20</span>
Answer:
θ = 38°
Step-by-step explanation:
The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...
sin(θ)/9 = sin(20°)/5
sin(θ) = (9/5)sin(20°)
θ = arcsin(9/5·sin(20°)) ≈ 38°
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Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.
