Does 3 times 48 equal 4 times 36
2 answers:
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Answers:
- (a) 73440
- (b) 3060
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Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
- 18 choices for slot A
- 17 choices for slot B
- 16 choices for slot C
- 15 choices for slot D
We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
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Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
which can be rearranged into
these formulas are handy to help us go back and forth between nCr or nPr.
Answer:
Canada was 418.912 sq miles smaller than the USSR.
Step-by-step explanation:
Note: I don't know if this question required a calculator so I'll answer without one.
Symbols:
- USSR area in sq miles = u
- Canada area in square miles = c
u<em> </em>= 8.649×106
c<em> </em>= 4.797×106
x = how much less area
u<em> </em>= c + x
- USSR area = Canada area + number of sq miles less
Math:
u = c + x
- plug in values
8.649×106 = 4.797×106 + x
- divide by 106 to get rid of the ridiculously large numbers.
8.649 = 4.797 +
- subtract (use calculator or just traditional subtraction methods)
3.952 =
- multiply both sides by 106 (use calculator or traditional methods)
418.912 = x
Interpreting the inequality, it is found that the correct option is given by F.
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- The first equation is of the line.
- The equal sign is present in the inequality, which means that the line is not dashed, which removes option G.
In standard form, the equation of the line is:
Thus it is a decreasing line, which removes options J.
- We are interested in the region on the plane below the line, that is, less than the line, which removes option H.
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- As for the second equation, the normalized equation is:
- Thus, a circle centered at the origin and with radius 2.
- Now, we have to check if the line
, with coefficients
, intersects the circle, of centre
- First, we find the following distance:
- Considering the coefficients of the line and the center of the circle.
- This distance is less than the radius, thus, the line intersects the circle, which removes option K, and states that the correct option is given by F.
A similar problem is given at brainly.com/question/16505684