1. Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has mater
ial covering all six sides.
(a) What is the capacity of the container?
(b) How much material was used to make the container?
(a) What is the capacity of the container?
(b) How much material was used to make the container?
1 answer:
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Answer:
Step-by-step explanation:
The original expression given in the text is
(1)
And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:
(2)
Let's verify each of the other expressions separately. For the first one:
We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get
Which is equivalent to (1).
For the 2nd one:
This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.
If we write it explicitely in fact, we get
Which is different from (2).
For the 3rd one:
This one is equivalent. In fact, here we have applied the distributive property correctly. By solvign each term we get:
Using the Empirical Rule and the Central Limit Theorem, we have that:
- About 68% of the sample mean fall with in the intervals $1.64 and $1.82.
- About 99.7% of the sample mean fall with in the intervals $1.46 and $2.
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .
In this problem, the standard deviation of the distribution of sample means is:
68% of the means are within 1 standard deviation of the mean, hence the bounds are:
- 1.73 - 0.09 = $1.64.
- 1.73 + 0.09 = $1.82.
99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:
- 1.73 - 3 x 0.09 = $1.46.
- 1.73 + 3 x 0.09 = $2.
More can be learned about the Empirical Rule at brainly.com/question/24537145
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