Jeff has a square of art paper .He cut it from one corner to the opposite corner to make two pieces.what is the total number of
side and angles in both of the new shape?
1 answer:
Okay. I drew a little diagram to help us out--make sure to look at that. So if he cut a square from one corner to the opposite corner, what shapes does he get? He gets two triangles!
Now, let's count the sides. Since they're asking about BOTH of the new shapes, we have to count them both together, not separately. We get 6!
What about angles? Remember, that's where two lines meet! Let's count again: we get 6!
Answer: There are 6 sides and 6 angles total.
Now, let's count the sides. Since they're asking about BOTH of the new shapes, we have to count them both together, not separately. We get 6!
What about angles? Remember, that's where two lines meet! Let's count again: we get 6!
Answer: There are 6 sides and 6 angles total.
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We have the following:
therefore, the answer is 3.35 x 10^6
Answer:
6.18% probability that more than 150 first-year students attend this college.
Step-by-step explanation:
We use the binomial approximation to the normal to solve this question.
For each item selected, there are only two possible outcomes. Either it is defective, or it is not. This means that we use concepts of the binomial probability distribution to solve this problem.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
Approximate the probability that more than 150 first-year students attend this college.
This is 1 subtracted by the pvalue of Z when X = 150. So
has a pvalue of 0.9382
1 - 0.9382 = 0.0618
6.18% probability that more than 150 first-year students attend this college.