Compare 9 . 10^4 to 3 . 10^2
a. 9 . 10^4 is 3 times larger than 3 . 10^ 2
b. 9 . 10^4 is 30 times larger than 3 . 10^2
c. 9 . 10^ 4 is 300 times larger than 3 . 10^2
d. 9 . 10^4 is 3000 times larger than 3 . 10^2


c. 30 times The Richter scale is a logarithmic scale for the energy release during an earth quake. For every increase by 1 in magnitude, the energy released is about 31.6 times larger. So calculate the magnitude difference by subtracting. 6.5 - 5.5 = 1.0 And then multiply by 31.6, giving 31.6. And since we're just looking for approximate values, select the answer that's closest which is option "c. 30 times"

d) 1000 times


As we know that difference of sound level is given as

L_2 - L_1 = 10 Log \frac{I_2}{I_1}

so here we need to find the ratio of two intensity

it is given as

Log\frac{I_2}{I_1} = \frac{(L_2- L_1)}{10}

Log\frac{I_2}{I_1} = \frac{60 - 30}{10}

Log\frac{I_2}{I_1} = 3

now we have

\frac{I_2}{I_1} = 10^3

so it is

d) 1000 times


Step-by-step explanation:

Since, 3*3=9, just add the needed 0s at the end.

500 times

Step-by-step explanation:

well, by using formula n•P

we get 3000\times \frac{1}{6}=500


Step-by-step explanation:



Step-by-step explanation:



The provided statement talks about an estimate of energy release by an Earthquake with a magnitude of 4 to a magnitude of 7. According to the statement, for the moment magnitude scale, 31.5 times more energy is released with increase of one magnitude scale. Therefore, if we take a rounded value of 31.5 as 30 and multiply it three times (30 X 30 X 30) to represent 3 scales (4 to 7) on moment magnitude scale, we will get 27,000 times more energy.

2124.03764889 K


Luminosity of Sun = L

New luminosity of Sun = 3000L

T_1 = Current temperature of Earth = 287 K (assumed)

Luminosity is given by

L=4\pi r^2\sigma T^4


L\propto T

\dfrac{3000L}{L}=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000=\dfrac{T_2^4}{T_1^4}\\\Rightarrow 3000^{\dfrac{1}{4}}=\dfrac{T_2}{T_1}\\\Rightarrow T_2=3000^{\dfrac{1}{4}}\times 287\\\Rightarrow T_2=2124.03764889\ K

The temperature of the Earth's surface is 2124.03764889 K

 a) 0.18, b) 720, c) 500

Step-by-step explanation:

Since we have given that

Score-1 Frequency-11

Score-2 Frequency-5

Score-3 Frequency-7

Score-4 Frequency-9

Score-5 Frequency-12

Score-6 Frequency-50-(11+5+7+9+12)=6

a) relative frequency of scoring a 4 would be :


b) how many times would you expect to roll a 5 when this dice is thrown 3000 times?

It would become:

\dfrac{12}{50}\times 3000\\\\=12\times 60\\\\=720

c) how many times would you expect to roll a 5 when a FAIR dice is thrown 3000 times?

It would become

\dfrac{1}{6}\times 3000\\\\=500

As we know that probability of getting a 5 from the fair die is given by:


Hence, a) 0.18, b) 720, c) 500

(C) 30 times

Richter scale is used to determine the magnitude of an earthquake from the arrival time of P and S waves. It determines the total amount of energy released during an earthquake.
If Richter magnitude scale measures 6.5 then it produces 30 times more energy than 1 Richter scale magnitude during an earthquake. The magnitude of an earthquake is plotted on a logarithmic scale from 1 to 9 and increases 10 folds by one magnitude. If 6.5 is the magnitude, it means it is 10 times more than 5.5 magnitude earthquake. Similarly the amount of energy is calculated as 30 folds. So 6.5 magnitude will have 30 folds more energy released than that with 5.5 magnitude earthquake.

Do you know the answer?

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