5-28. Sophie claims that whenever she increases the perimeter of a rectangle, its area increases. 5-28 HW eTool Homework Help ✎
a. She showed the rectangle at right and said, “If I make the base twice as long, then the area increases.” Is her statement correct for this figure? Draw a diagram of the rectangle she described and explain whether the area is greater or less than the rectangle at right.
b. Is her claim about the relationship of area and perimeter correct for all figures? For example, is there any way that she could have a rectangle with a greater perimeter than the figure in part (a) but with the same area? Give examples and explain your reasoning.
b. Is her claim about the relationship of area and perimeter correct for all figures? For example, is there any way that she could have a rectangle with a greater perimeter than the figure in part (a) but with the same area? Give examples and explain your reasoning.
1 answer:
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Answer:
B) .35
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem:
Then
So the correct answer is:
B) .35
The second question:
Consider the division expression . Select all multiplication equations that correspond to this division expression.
Answer:
1. See Explanation
2. and
Step-by-step explanation:
Solving (a):
Given
Required
Interpret in 2 ways
<u>Interpretation 1:</u> Number of groups if there are 5 students in each
<u>Interpretation 2:</u> Number of students in each group if there are 5 groups
<u>Solving the quotient</u>
<u>For Interpretation 1:</u>
The quotient means: 12 groups
<u>For Interpretation 2:</u>
The quotient means: 12 students
Solving (b):
Given
Required
Select all equivalent multiplication equations
Let ? be the quotient of t
So, we have:
Multiply through by 2
Rewrite as:
--- This is 1 equivalent expression
Apply commutative law of addition:
--- This is another equivalent expression