All categories

2 years ago

65. If the diameter of the sphere is halved, what will be the difference in volume?

Mathematics

1 answer:

Murrr4er [49]2 years ago

7 0

Answer:

Hi there !

A. 1/8 of the original volume
24 is the mode

<h2>Step-by-step explanation:</h2>

<h3>Question 1 :-</h3>

LET RADIUS OF SPHERE= R

VOLUME OF SPHERE= $( \frac{4}{3})\pi \: {r}^{3}$

WHEN RADIUS IS HALVED RADIUS IF SPHERE=R/2

VOLUME= $( \frac{4}{3} )\pi( \frac{r}{2})^{3}$ = {(4/3)πR^3}/8

THE VOLUME WILL BECOME 1/8 TH OF THE ORIGINAL VOLUME.

<h2>Question 2 :-</h2>

Wehave,

Mode+2×Mean=3×Median

⇒Mode=3×Median−2×Mean

Given : Mean=21 and Median=22

Putting the given values, we get

Mode=3×22−2×21=66−42=24.

Hope it helps u....

Stay safe, stay healthy and blessed

Have a great day !

Thank you

You might be interested in

Rectangle A is a scaled version of rectangle B. The dimensions of rectangle A are three times the dimensions of rectangle B. The

Firlakuza [10]

Answer:

1458 sq cm

Step-by-step explanation:

because each dimension of A is 3 tomes each dimension of B, that will mean that both the length and width of B are multiplied by 3 in order to get the length and width of A, so the area of B is length×width=162 and the area of A (in terms of B's dimensions) is 3xlength×3×width=9×length×width=9×162=1458 sq cm

7 0

4 years ago

Is 3/5 mile closer than 1/2 mile

Romashka [77]

Yes to both, and for future help, if you find a common denominator(the bottom one) by multiplication and one is higher, boom you have your answer.

6 0

4 years ago

Keith bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are n

AysviL [449]

Answer:

85 cards

Step-by-step explanation:

8 0

3 years ago

Subtract and reduce to lowest terms: 4 1/7 - 2 4/7

tatyana61 [14]

Answer:

Step-by-step explanation:

Both terms have the same denominator, 7. So combining them is relatively easy. Rewrite 2 4/7 as 18/7 and then subtract 18/7 from 1/7:

1/7 - 18/7 = -17/7

Choose Answer 4: None of these are correct.

5 0

4 years ago

Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all possibl

serg [7]

Answer:

P(X=i) where i = 1,2,3,4,5,6,7,8,9,10 = 1/2, 5/18, 5/36, 5/84, 5/252, 1/252, 0, 0, 0, 0.

Step-by-step explanation:

X denotes the highest ranking achieved by the woman.

When X=1, the top ranked person is a female.

When X=2, the first person is a male and the second ranked person is a female.

Similarly, when X=3, the first two ranked persons are male and the third one is a female.

When X=4, the first three persons are male and the fourth one is a female.

When X=5, the first four persons are males and the fifth person is a female.

When X=6, the first five people are males and the sixth person is a female. The rest of the four people are also females since there are only five men in a sample space.

The probability for X=7, 8, 9, 10 is zero because there are only five men who can achieve the first five positions and the last highest rank that can be achieved by a woman is 6.

To compute the probabilities, we will use the formula:

<u>No. of ways a female can be ranked X/Total number of ways to rank 10 people</u>

Note that the total number of ways of ranking 10 different people is 10P10 or 10!

For X=1, the first position can be taken by any of the 5 women. The possible ways of the first person being a woman is 5C1. The rest of the 9 people can take any of the ranks. They can be ordered in 9P9 ways.

So, P(X=1) = (5C1)(9P9)/(10P10) = (5 x 362880)/(3628800) = 1/2

For X=2, the first rank must be taken by a male. The number of ways to arrange the first person as a male out of the 5 men can be calculated by 5P1. The second position must be taken by a female and rest of the 8 positions can be taken by any of the 8 people in 8P8 ways.

So, P(X=2) = (5P1)(5C1)(8P8)/(10P10) = (5 x 5 x 40320)/(3628800) = 5/18

For X=3, first two people must be men and the number of ways to arrange 2 out of 5 males at the first two positions is 5P2. The third position is a female. The rest of the 7 people can be ordered in 7P7 ways.

P(X=3) = (5P2)(5C1)(7P7)/(10P10) = (20 x 5 x 5040)/(3628800) = 5/36

P(X=4) = (5P3)(5C1)(6P6)/(10P10) = (60 x 5 x 720)/(3628800) = 5/84

P(X=5) = (5P4)(5C1)(5P5)/(10P10) = (120 x 5 x 120)/(3628800) = 5/252

P(X=6) = (5P5)(5C1)(4P4)/(10P10) = (120 x 5 x 24)/(3628800) = 1/252

P(X=7) = 0

P(X=8) = 0

P(X=9) = 0

P(X=10) = 0

7 0

3 years ago