Can the numbers 12,6 , 6 be used to form the sides of a triangle
1 answer:
we have three sides, let's look at the two smaller sides first.
check the picture below, atop
if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side? Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 6 - 6 = 0. However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle. So whatever the third side may be, it must be greater than 0.
check the picture below, at the bottom
Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 6 + 6 = 12. However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle. So whatever the third side may be, it must be less than 12.
so, 12 is a no dice.
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Answer:
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Step-by-step explanation:
To solve this question, we need to use the binomial and the normal probability distributions.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
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:
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.
Probability the president will have an IQ of at least 107.5
IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that
This probability is 1 subtracted by the p-value of Z when X = 107.5. So
has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 probability that the president will have an IQ of at least 107.5.
Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So
has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:
In which
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?
0.3085 probability that the president will have an IQ of at least 107.5.
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Independent events, so we multiply the probabilities.
0.3082*0.0451 = 0.0139
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.