Answer:
![r=\sqrt[3]{\frac{3V}{4 \pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D)
Step-by-step explanation:
we know that
The formula of volume of the sphere is given by
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
Solve for r
That means ----> isolate the variable r
Multiply by 3 both sides
![3V=4 \pi r^3](https://tex.z-dn.net/?f=3V%3D4%20%5Cpi%20r%5E3)
Divide by
both sides
![r^{3} =\frac{3V}{4 \pi}](https://tex.z-dn.net/?f=r%5E%7B3%7D%20%3D%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D)
Elevate both sides to 1/3
![r =(\frac{3V}{4 \pi})^{\frac{1}{3}}](https://tex.z-dn.net/?f=r%20%3D%28%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![r=\sqrt[3]{\frac{3V}{4 \pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D)
Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- The sample has 20 pills, hence
.
- 100 - 4 = 96% are acceptable, hence
![p = 0.96](https://tex.z-dn.net/?f=p%20%3D%200.96)
The probability that <u>fewer that 5 in a sample of 20 pills</u> will be acceptable is:
![P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)](https://tex.z-dn.net/?f=P%28X%20%3C%205%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29)
In which
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B20%2C0%7D.%280.96%29%5E%7B0%7D.%280.04%29%5E%7B20%7D%20%3D%200)
![P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B20%2C1%7D.%280.96%29%5E%7B1%7D.%280.04%29%5E%7B19%7D%20%3D%200)
![P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B20%2C2%7D.%280.96%29%5E%7B2%7D.%280.04%29%5E%7B18%7D%20%3D%200)
![P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B20%2C3%7D.%280.96%29%5E%7B3%7D.%280.04%29%5E%7B17%7D%20%3D%200)
![P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B20%2C4%7D.%280.96%29%5E%7B4%7D.%280.04%29%5E%7B16%7D%20%3D%200)
0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
A similar problem is given at brainly.com/question/24863377
Answer:
The answer in the explanation
Step-by-step explanation:
we have
![\frac{1}{3}x-5=\frac{5}{2}x-\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx-5%3D%5Cfrac%7B5%7D%7B2%7Dx-%5Cfrac%7B2%7D%7B3%7D)
Step 1
Determine the least common denominator (LCD) of all fractions in the equation
The LCD is equal to
![(3)(2)=6](https://tex.z-dn.net/?f=%283%29%282%29%3D6)
Step 2
Multiply both sides of the equation by 6 to remove the fractions
![6[\frac{1}{3}x-5]=6[\frac{5}{2}x-\frac{2}{3}]](https://tex.z-dn.net/?f=6%5B%5Cfrac%7B1%7D%7B3%7Dx-5%5D%3D6%5B%5Cfrac%7B5%7D%7B2%7Dx-%5Cfrac%7B2%7D%7B3%7D%5D)
![2x-30=15x-4](https://tex.z-dn.net/?f=2x-30%3D15x-4)
Step 3
Solve for x
Group terms
![15x-2x=-30+4](https://tex.z-dn.net/?f=15x-2x%3D-30%2B4)
Combine like terms
![13x=-26](https://tex.z-dn.net/?f=13x%3D-26)
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Answer:
One number is 561
The other number is 23.6854
Step-by-step explanation:
x = y^2 One number = the square of another
x + y^2 = 1122 The sum of the two numbers is 1122
Substitute y^2 in for x on the second equation.
y^2 + y^2 = 1122 Combine like terms on the left
2y^2 = 1122 Divide by 2
y^2 = 1122/2
y^2 = 561 Take the square root of both sides.
y = 23.6854
x = y^2
x = 561
y^2 = 561
Answer: y=144
Step-by-step explanation:
y^1/2-6=6
y^1/2=12
y=144