Using the Empirical Rule, it is found that there is a 68% probability that a student scored between 66 and 82.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, considering the mean of 74 and the standard deviation of 8, we have that:
74 - 8 = 66
74 + 8 = 82.
Hence, there is a 68% probability that a student scored between 66 and 82.
More can be learned about the Empirical Rule at brainly.com/question/24537145
Answer:
27x⁴y⁵
Step-by-step explanation:
9xy⁴ₓ3x³y =
= 9ₓ3ₓx¹⁺³ₓy⁴⁺¹
= 27x⁴y⁵
Start by drawing a right triangle with legs matching the given point.
Horizontal leg = -8, Vertical leg = 3
The hypotenuse should be identical to a line going from given point to origin.
Next, use pythagorean theorem to find length of hypotenuse.
= sqrt((-8)^2 + 3^2) = sqrt(64+9) = sqrt(73)
Finally use trig ratios for cos, csc, and tan. (csc = 1/sin)
SOH --> sin = opp/hyp = 3/sqrt(73)
csc = 1/sin = sqrt(73)/3
CAH---> cos = adj/hyp = -8/sqrt(73) = (-8*sqrt(73))/73
TOA ---> tan = opp/adj = -3/8