Yes and no, (4, 5) multiplied by 2 is (10, 8) but reversed. It depends on how you look at it because (10, 8) would be on the other side of the graph than (8, 10) which is the actually equivalent.
Answer:
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Explanation:
The figure attached shows the <em>Venn diagram </em>for the given sets.
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<em><u>a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?</u></em>
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From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.
There are a total of 7 multiples of 24, from 1 to 15.
Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:
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<em><u>b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?</u></em>
The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.
The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.
Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:
Answer: The value of x must be greater than 3
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Explanation:
The triangle inequality theorem will come into play here. The basic idea of this theorem is "take any two sides of a triangle and add them up. That sum must be larger than the third side".
So if we have
a = 12
b = x
c = 15
then the following must hold true (all three inequalities must be true)
a+b > c
a+c > b
b+c > a
Focus on the first inequality and plug in the given values. Then solve for x
a+b > c
12+x > 15
12+x-12 > 15-12
x > 3
So we see that x > 3. Repeat the same for the second inequality
a+c > b
12+15 > x
27 > x
x < 27
Repeat again for the third inequality
b+c > a
x+15 > 12
x+15-15 > 12-15
x > -3
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In summary so far, we have
x > 3
x < 27
x > -3
Combine all of those inequalities to form one single compound inequality which is 3 < x < 27
For some reason your teacher doesn't want you to focus on the "less than 27" part, so it seems like s/he only wants the "x > 3" portion.
So this is why x must be larger than 3 (up only til you get to 27 though).
Answer:
37.7 ft²
Step-by-step explanation:
2×3.14×r=30.77
<em>Divide both sides by 2</em>
3.14×r=15.385
<em>Divide both sides by 3.14</em>
r≈4.9
3.14×r²
3.14×4.9²=
24.01×3.14≈
75.4
75.4÷2=
37.7
