Independent events are such events where the occurrence of any one event does not affect the occurrence of any other event.
<u>Part A:</u> rolling two number cubes at same time does not affect outcome of any one cube. It would be Independent events.
<u>Part B:</u> choosing a card, then flipping a coin according to favourable outcome can affect the result. It would be dependent events.
<u>Part C:</u> choosing a winner, keeping it, then choosing another name depends upon remaining persons. It would be dependent events.
<u>Part D:</u> drawing a marble, replacing it, then drawing another marble does not affect number of marbles in the bag. It would be Independent events.
<u>Part E:</u> flipping any coin three times does not affect past or future outcomes. It would be Independent events.
Hence, options A, D, and E are Independent events.
Answer: D.680
Step-by-step explanation:
Answer:
<em>Answer: C.Fraction 11 and 1 over 4 cubic inches</em>
Step-by-step explanation:
The volume of a rectangular prism of length L, width W, and height H is given by:
V=LWH
The prism is packed with cubes of a side length of a=1/2 inch. The volume of each cube is:

The prism is packed with L=5, W=3, and H=6, thus the volume (in cubes) is:
V=5*3*6=90\ cubes
Since each cube has a volume of
:

Expressing as a mixed fraction:

Answer: C.Fraction 11 and 1 over 4 cubic inches
Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
<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.
The area within 0.9 standard deviations of the mean is the <u>p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841)</u>, hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
More can be learned about the normal distribution at brainly.com/question/4079902
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