Answer:
The probability that the coins are thrown more than three times to show the same face is 0.3164.
Step-by-step explanation:
The problem is related to Geometric distribution.
The Geometric distribution defines the probability distribution of <em>X</em> failures before the first success.
The probability distribution function is:
First compute the probability that in the 
throw all the three coins will show the same face.
P (All the 3 coins shows the same face) = P (All the three coins shows Heads) + P (All the three coins shows Tails)
Now compute the probability that it takes more than 3 throws for the coins to show the same face.
P (<em>X</em> > 3) = 1 - P (<em>X</em> ≤ 3)
![=1-[P(X=1)+P(X=2)+P(X=3)]\\=1-[[(1-\frac{1}{4} )^{0}\times\frac{1}{4}]+[(1-\frac{1}{4} )^{1}\times\frac{1}{4}]+ [(1-\frac{1}{4} )^{2}\times\frac{1}{4}]+[(1-\frac{1}{4} )^{3}\times\frac{1}{4}]]\\=1-[0.2500+0.1875+0.1406+0.1055]\\=1-0.6836\\=0.3164](https://tex.z-dn.net/?f=%3D1-%5BP%28X%3D1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%5C%5C%3D1-%5B%5B%281-%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7B0%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%5D%2B%5B%281-%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7B1%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%5D%2B%20%5B%281-%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7B2%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%5D%2B%5B%281-%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7B3%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%5D%5D%5C%5C%3D1-%5B0.2500%2B0.1875%2B0.1406%2B0.1055%5D%5C%5C%3D1-0.6836%5C%5C%3D0.3164)
Thus, the probability that it takes more than 3 throws for the coins to show the same face is 0.3164.
Answer:
m = 4
Step-by-step explanation:
The complete question is:
Given:
6.33 x 10
⁹ / 1.79 x 10⁵ ≈ 3 x 
To find:
To best estimate the quotient in scientific notation. what number should replace m?
Solution:
The equation is:
6.33 x 10
⁹ / 1.79 x 10⁵ = 3 x
Let x = 9 and y = 5 then the above equation becomes:
6.33 x 
/ 1.79 x 
= 3 x
Since we know that the exponent property is:
quotient 
Now converting the given equation in the form above we get:
6.33 / 1.79 x 
6.33 / 1.79 x 
Now the quotient is 6.33/1.79 ≈ 3.536313
quotient x
3.536313 x
Since 9-5 = 4 So
3.536313 x 
3.536 x
Hence
6.33 x 10
⁹ / 1.79 x 10⁵ ≈ 3.5 x
Hence m = 4
Answer:
![\boxed{\boxed{\sqrt[3]{d}\cdot \sqrt[3]{d}\cdot \sqrt[3]{d}=d}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%5Csqrt%5B3%5D%7Bd%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bd%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bd%7D%3Dd%7D%7D)
Step-by-step explanation:
The given expression is,
![=\sqrt[3]{d}\cdot \sqrt[3]{d}\cdot \sqrt[3]{d}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7Bd%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bd%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bd%7D)
It can also be written as,
The exponent product rule of algebra states that, while multiplying two powers that have the same base, the exponents can be added.
As here all the terms have same base i.e d, so applying the rule
You can make it with 10 because 10%times 5% is 50%
23/30 can't be simplified any further because 23 is a prime number.
