7w−(2+w)=2(3w−1)
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Given:
Slips of paper numbered 1 to 15 are placed in a box.
To find:
The probability that the number picked is either a multiple of 5 or an odd number.
Solution:
We have,
Total outcomes = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
No. of total outcomes = 15
Multiple of 5 are 5, 10, 15.
Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15.
Number that are either a multiple of 5 or an odd number are 1, 3, 5, 7, 9, 10, 11, 13, 15.
No. of favorable outcomes = 9
We know that,
Therefore, the probability that the number picked is either a multiple of 5 or an odd number is 0.6.
Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
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For the complete question, refer to the attachment.
