Answer:
<em>x = 15°</em>
<em>x = 135°</em>
<em>x = -45°</em>
<em>x = -180°</em>
Step-by-step explanation:
<u>Trigonometric Equations</u>
Solve
cos(2x + 30°) = 0.5 for -180° ≤ x ≤ 180°
Applying the inverse cosine function:
2x + 30° = arccos(0.5)
There are several angles whose cosine is 0.5. They are 60°, 300°, -60° and -300°, thus we have these candidate solutions:
2x + 30° = 60°
2x + 30° = 300°
2x + 30° = -60°
2x + 30° = -300°
Subtracting 30° to all the equations:
2x = 60° - 30° = 30°
2x = 300° - 30° = 270°
2x = -60° - 30° = -90°
2x = -60° - 300° = -360°
Dividing by 2 we have the complete set of solutions:
x = 15°
x = 135°
x = -45°
x = -180°
Answer:7x >= -14 and 3x + 2 < 17
Step-by-step explanation: >= or <= means a closed circle, whereas < or > is an open circle. If you divide -14 by 7 you get x >= -2 and 17-2 is 15, which once you divide by 3 equals x < 5.
A. The empirical rule tells you that 68% of observations fall within one standard deviation of the mean for a normal distribution. [32, 38] = 35 ±3, so your interval is within one standard deviation of the mean.
68% of observations will fall between 32 and 38
B. The distribution is symmetrical about the mean, so half of the observations in part A will be below the mean.
34% of observations will fall between 32 and 35
C. The distribution is symmetrical about the mean, so half the observations fall above the mean.
50% of observations will fall above 35
D. The distribution is symmetrical about the mean, so half the observations will fall below the mean, 35. As in part B, 34% will fall between the mean and one standard deviation above the mean, 38. The sum of these percentages is 84%.
84% of observations will fall below 38
