Answer:
8
Step-by-step explanation:
if a set has 3 elements it has 8 subsets.
Answer:
x=-2/3 + 2
Step-by-step explanation:
Answer:
IQ scores of at least 130.81 are identified with the upper 2%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that ![\mu = 100, \sigma = 15](https://tex.z-dn.net/?f=%5Cmu%20%3D%20100%2C%20%5Csigma%20%3D%2015)
What IQ score is identified with the upper 2%?
IQ scores of at least the 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![2.054 = \frac{X - 100}{15}](https://tex.z-dn.net/?f=2.054%20%3D%20%5Cfrac%7BX%20-%20100%7D%7B15%7D)
![X - 100 = 15*2.054](https://tex.z-dn.net/?f=X%20-%20100%20%3D%2015%2A2.054)
![X = 130.81](https://tex.z-dn.net/?f=X%20%3D%20130.81)
IQ scores of at least 130.81 are identified with the upper 2%.
The explicit formula for an arithmetic sequence is an = a1 + d(n - 1) where a1 is the first term and d = common difference. For this sequence a1 is 7 and d = 13- 7 = 19 - 13 = 25 - 19 = 6
So explicit formula required = 7 + 6(n - 1)
Answer:
8 and 9.
Step-by-step explanation:
Let the two unknown numbers be a and b.
When added together, they equal 17. In other words:
a + b = 17.
The <em>difference</em> between five times the first number and three times the second number is 13. In other words:
5a - 3b = 13.
We have a system of equations. We can use substitution. From the first equation, we can derive a = 17 - b. Let's substitute this in:
5(17 - b) - 3b = 13
85 - 5b - 3b = 13
-8b = -72
b = 9
a = 17 - b.
a = 17 - 9 = 8.
Thus, the two numbers are 8 and 9.