Answer:
a) Binomial distribution B(n=12,p=0.01)
b) P=0.007
c) P=0.999924
d) P=0.366
Step-by-step explanation:
a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.
b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

Then,

c) In this case, the distribution is B(1200,0.01)

d) In this case, the distribution is B(100,0.01)
We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

Answer:
See explanation
Step-by-step explanation:
Let x be the number of simple arrangements and y be the number of grand arrangements.
1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

2. A florist can make a grand arrangement in 18 minutes
hour, then he can make y arrangements in
hours.
A florist can make a simple arrangement in 10 minutes
hour, so he can make x arrangements in
hours.
The florist can work only 40 hours per week, then

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.
The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.
Total profit: $(10x+25y)
Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines
and 
But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

![(\sqrt[5]{x^{7}})^{3}=(x^{\frac{7}{5}})^{3}=x^{\frac{7\cdot3}{5}}=x^{\frac{21}{5}}](https://tex.z-dn.net/?f=%28%5Csqrt%5B5%5D%7Bx%5E%7B7%7D%7D%29%5E%7B3%7D%3D%28x%5E%7B%5Cfrac%7B7%7D%7B5%7D%7D%29%5E%7B3%7D%3Dx%5E%7B%5Cfrac%7B7%5Ccdot3%7D%7B5%7D%7D%3Dx%5E%7B%5Cfrac%7B21%7D%7B5%7D%7D)
The root is equivalent to a fractional power with that number as the denominator. Otherwise, the rules of exponents apply.
Its1. every number/variable that has a power to the zero, its goin to turn out to be just one
Answer:converge at 
Step-by-step explanation:
Given
Improper Integral I is given as

integration of
is -
![I=\left [ -\frac{1}{x}\right ]^{\infty}_3](https://tex.z-dn.net/?f=I%3D%5Cleft%20%5B%20-%5Cfrac%7B1%7D%7Bx%7D%5Cright%20%5D%5E%7B%5Cinfty%7D_3)
substituting value
![I=-\left [ \frac{1}{\infty }-\frac{1}{3}\right ]](https://tex.z-dn.net/?f=I%3D-%5Cleft%20%5B%20%5Cfrac%7B1%7D%7B%5Cinfty%20%7D-%5Cfrac%7B1%7D%7B3%7D%5Cright%20%5D)
![I=-\left [ 0-\frac{1}{3}\right ]](https://tex.z-dn.net/?f=I%3D-%5Cleft%20%5B%200-%5Cfrac%7B1%7D%7B3%7D%5Cright%20%5D)

so the value of integral converges at 