Determine if each statement is always, sometimes, or never true.
2 answers:
1. Parallel lines are always coplanar.
<em>The right answer is </em><em>always.</em>
This is indicated in Figure 1. You can see that the red line and the blue one lie on the same plane, therefore parallel lines are always co-planar.
2. Perpendicular lines are always coplanar.
<em>The right answer is </em><em>always.</em>
This is illustrated in Figure 2. As you can see, the red and blue lines are perpendicular. Notice that the red line lies on the plane M and also on the plane N, and the blue line only lies on the plane N. Therefore, both lines lie on the plane N. In conclusion, perpendicular lines are always coplanar.
3. Distance around an unmarked circle can never be measured.
<em>The right answer is </em><em>never</em>
We need to have a marked circle to measure the distance. So, the distance from the center of the circle to one point of it is the radius. Moreover, the distance between two points of the circle taking a line passing through the center is the diameter of the circle.
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Answer:
68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade
Step-by-step explanation:
We use the binomial approximation to the normal to solve this question.
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
Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.
This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So
has a pvalue of 0.3121
1 - 0.3121 = 0.6879
68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade
Answer:
Step-by-step explanation:
If you graph there would be two different regions. The first one would be
And the second one would be
.
If you rotate the first region around the "y" axis you get that
And if you rotate the second region around the "y" axis you get that
And the sum would be 2.51+4.188 = 6.698
If you revolve just the outer curve you get
If you rotate the first region around the x axis you get that
And if you rotate the second region around the x axis you get that
And the sum would be 1.5708+1.0472 = 2.618
