Answer:
16%
Step-by-step explanation:
The Empirical Rule claims that 68% of the values in a normal distribution are within 1 standard deviation of the mean, 95% are within 2 standard deviations, and 99.7% are within 3. Using this here, we can see that 102 is exactly 1 standard deviation from the mean, as 94 + 8 * 1 = 102.
We also know that a normal distribution is symmetric, meaning that there is an equal distribution on both sides of the mean. Therefore, we can say that 50% of the values are above the mean. Next, 68% of values are within 1 standard deviation of the mean, so here, we can say that 34% of values are between the mean and 1 positive standard deviation of the mean. We want to find how many values are greater than 1 standard deviation of the mean. This is equal to (total amount of values greater than the mean) - (total amount of values greater than the mean but not greater than 1 standard deviation of the mean) = 50% - 34% = 16%
Answer:
≈ 1.32471795725...
Explanation:
If x is one less than its cube, then
x = x³ - 1,
x³ - x - 1 = 0
so f(x) = ? would be an appropriate (continuous) function to apply the Intermedate Value Theorem on some appropriate interval to see if it takes on the value 0 in that interval.
f(x) = x³ - x - 1
For large x the left hand side is positive, for x = 0 it is negative. The root can be calculated exactly, it is given by:
![\sqrt[3]{\frac{1}{2} + \sqrt{\frac{1}{4} - \frac{1}{27} } } + \sqrt[3]{\frac{1}{2} - \sqrt{\frac{1}{4} - \frac{1}{27} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%20-%20%5Cfrac%7B1%7D%7B27%7D%20%7D%20%20%7D%20%2B%20%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%20-%20%5Cfrac%7B1%7D%7B27%7D%20%7D%20%20%7D)
≈ 1.32471795725...
Pythagorean theorem is used to solve this
Answer:
Step-by-step explanation:
Domain: Input values; independent variables.
Range: Output values; dependent variables.