What are dimensions of three rectangles that can be created with a perimeter of 24?
1 answer:
The perimeter of a rectangle is given by:
2 × length + 2 × width
2l + 2w
2(l+w)
We want the perimeter to be 24, so the equation is
, divide both sides by 2
We then think of combination of two numbers that sum gives 12
1 + 11
2 + 10
3 + 9
4 + 8
5 + 7
6 + 6 ⇒ This combination will give us a square, not a rectangle
7 + 5 ⇒ This repeat the other combination 5+7
So we can have rectangles with combination of length and width
1 by 11
2 by 10
3 by 9
4 by 8, and
5 by 7
2 × length + 2 × width
2l + 2w
2(l+w)
We want the perimeter to be 24, so the equation is
We then think of combination of two numbers that sum gives 12
1 + 11
2 + 10
3 + 9
4 + 8
5 + 7
6 + 6 ⇒ This combination will give us a square, not a rectangle
7 + 5 ⇒ This repeat the other combination 5+7
So we can have rectangles with combination of length and width
1 by 11
2 by 10
3 by 9
4 by 8, and
5 by 7
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Answer:
Step-by-step explanation:
The graph is shifted 3 units to the right
Answer:
a)
b)
c)
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and with the normal standard table or excel:
Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part c
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.
When u say whole over do u mean like this
