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The list of choices is missing so I am going to give my wording:
The fact that a set closed under a certain operation means that when the operation is applied to any element(s) of the set, the result will be also an element of the same set (as opposed to something that does not belong to the set).
In this case the set contains all polynomials. Multiplying any two polynomials results in another polynomial, therefore this set is closed with respect to multiplication. In contrast, the set is not closed with respect to division. Dividing two polynomials may lead to non-polynomial expressions with non-integer powers and so the set is not closed under division.
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is <u>one subtracted by the p-value of Z when X = 4</u>, hence:
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
More can be learned about the normal distribution at brainly.com/question/24663213
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Answer:
w =6 w=-2
Step-by-step explanation:
4/3|3w-6|=16
Multiply each side by 3/4 to isolate the absolute value
3/4 *4/3|3w-6|=16*3/4
|3w-6|=12
An absolute value has 2 solutions, one positive and one negative
3w-6 =12 3w-6 = -12
Add 6 to each side
3w-6+6 =12+6 3w-6+6=-12+6
3w = 18 3w = -6
Divide by 3
3w/3 = 18/3 3w/3 = -6/3
w = 6 w = -2
Zero seconds left in the last quarter