Answer:
Step-by-step explanation:
A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6. Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².
Answer:
5.78×10¹⁵
Step-by-step explanation:
The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.
The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.
The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.
The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.
The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.
Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.
So the total number of possible playlists is:
(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵
F(x) = 2x - 1
subtitute x = 0 to the equation:
f(0) = 2· 0 -1 = 0 - 1 = -1
f(0) = -1
Answer:
Height of the ball after 3 seconds = 27.4 feet.
Step-by-step explanation:
h(t) = -4.9t^2 + 22t + 5.5
h(3) means the height of the ball at time 3 seconds after the ball was thrown.
h(3) = -4.9(3)^2 + 22(3) + 5.5
= 27.4 feet
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