Answer: a) 6
<u>Step-by-step explanation:</u>
The mean is 375 which has a z-score of 0.
The standard deviation is 24 so:
- z-score of 1 is: 375 + 24 = 399
- z-score of 2 is: 399 + 24 = 423
- z-score of 3 is: 423 + 24 = 477
A z-score of 3 is 99.85% from the left <em>(or 1 - 99.85% from the right = 0.15%)</em>
Since we are looking for the "more than" a z-score of 3, it is 0.15% of the total.
4000
<u>× 0.0015</u>
6.0000
2cos(x) - 4sin(x) = 3
use identity [cos(x)]^2 +[ sin(x)]^2 = 1 => cos(x) = √[1 - (sin(x))^2]
2√[1 - (sin(x))^2] - 4 sin(x) = 3
2√[1 - (sin(x))^2] = 3 + 4 sin(x)
square both sides
4[1 - (sin(x))^2] = 9 + 24 sin(x) + 16 (sin(x))^2
expand, reagrup and add like terms
4 - 4[sin(x)]^2 = 9 + 24sin(x) + 16sin^2(x)
20[sin(x)]^2 + 24sin(x) +5 = 0
use quadratic formula and you get sin(x) = -0.93166 and sin(x) = -0.26834
Now use the inverse functions to find x:
arcsin(-0.93166) = 76.33 degrees
arcsin(-0.26834) = 17.30 degrees
Answer:
12
Step-by-step explanation:
You divide 96 by 8 and you get 12.
The population of the fish is given by P(t) = 750(1 + 0.083)^t; where t is the number of years after 2005.
Here, t = 2050 - 2005 = 45
Population in 2050 = 750(1.083)^45 = 750(36.16) = 27,123
