Answer:
2.25 %
Explanation:
65-95-99.7 is a rule to remember the precentages that lies around the mean.
at the range of mean (
) plus or minus one standard deviation (
), ![P([\mu-\sigma \leq X \leq \mu+\sigma])\approx 68.3%](https://tex.z-dn.net/?f=P%28%5B%5Cmu-%5Csigma%20%5Cleq%20X%20%5Cleq%20%5Cmu%2B%5Csigma%5D%29%5Capprox%2068.3%25)
at the range of mean plus or minus two standard deviation, ![P([\mu -2\sigma \leq X \leq \mu+2\sigma])\approx 95.5%](https://tex.z-dn.net/?f=P%28%5B%5Cmu%20-2%5Csigma%20%5Cleq%20X%20%5Cleq%20%5Cmu%2B2%5Csigma%5D%29%5Capprox%2095.5%25)
at the range of mean plus or minus three standard deviation, ![P([\mu - 3\sigma\leq X \leq \mu+3\sigma])\approx 99.7%](https://tex.z-dn.net/?f=P%28%5B%5Cmu%20-%203%5Csigma%5Cleq%20X%20%5Cleq%20%5Cmu%2B3%5Csigma%5D%29%5Capprox%2099.7%25)
So, note that they are asking about the probability that it is greater than 0.32, that is the mean (0.3) plus two times the standard deviation (0.1) (
)
So we know that the 95.5% is between 
and 
, hence approximately the 4.5% (100%-95.5%) is greater than 0.32 or less than 0.28. But half (4.5%/2=2.25%) is greater than 0.32 and the other half is less than 0.28.
So 
Answer:
a) When its length is 23 cm, the elastic potential energy of the spring is
0.18 J
b) When the stretched length doubles, the potential energy increases by a factor of four to 0.72 J
Explanation:
Hi there!
a) The elastic potential energy (EPE) is calculated using the following equation:
EPE = 1/2 · k · x²
Where:
k = spring constant.
x = stretched lenght.
Let´s calculate the elastic potential energy of the spring when it is stretched 3 cm (0.03 m).
First, let´s convert the spring constant units into N/m:
4 N/cm · 100 cm/m = 400 N/m
EPE = 1/2 · 400 N/m · (0.03 m)²
EPE = 0.18 J
When its length is 23 cm, the elastic potential energy of the spring is 0.18 J
b) Now let´s calculate the elastic potential energy when the spring is stretched 0.06 m:
EPE = 1/2 · 400 N/m · (0.06 m)²
EPE = 0.72 J
When the stretched length doubles, the potential energy increases by a factor of four to 0.72 J
Answer:
Hz
Explanation:
We know that
1 cm = 0.01 m
= Length of the human ear canal = 2.5 cm = 0.025 m
= Speed of sound = 340 ms⁻¹
= First resonant frequency
The human ear canal behaves as a closed pipe and for a closed pipe, nth resonant frequency is given as
for first resonant frequency, we have n = 1
Inserting the values
Hz
Answer:
Explanation:
Since the front and back of the rocket simultaneously line up with forward and backward end of the platform respectively .
Then length of the platform = length of the train rocket .
A )
Time to cross a particular point on the platform
= length of rocket train / .96 x 3 x 10⁸
= 90 / .96 x 3 x 10⁸
= 31.25 x 10⁻⁸ s
B) Rest length of the rocket = length of platform = 90 m
C ) length of platform as viewed by moving observer =
= 
= 321 m
D ) For the observer on platform time taken = 31.25 x 10⁻⁸ s
for the observer in the rocket , time will be dilated so time recorded by observer in motion ,
8.75 x 10⁻⁸ s .
Answer:
7.894 Hours.
Explanation:
Based on information number hours that this battery will last with give load has mathematical relation of.
with load 60A t = 1h, 30A t = 2h so on and forth.
two head lights draw total current of 2x3.8A = 7.6A.
putting this in above relation gives.
.
That is how long will it be before battery is dead.
