Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: Number of winning caps out of 5 bottles.
Checking the binomial criteria:
- Number of trials is fixed n=5 bottles of soda
- Only two possible outcomes per trial: "success": winning cap; "failure": regular cap.
- The trial are independent.
- The probability of success is constant trough the experiment p= 1/12= 0.083
This variable has a binomial distribution with parameters n= 5 and p= 0.083
You have to calculate the probability of getting 4 out of 5 winning caps
P(X=4)
Using the following formula:

Or using the tables for accumulated probabilities:
P(X=4)= P(X≤4)-P(X≤3)= 0.9999 - 0.9997= 0.0002
Answer:
Step-by-step explanation:
1.
To write the form of the partial fraction decomposition of the rational expression:
We have:

2.
Using partial fraction decomposition to find the definite integral of:

By using the long division method; we have:


<u> </u>

So;

By using partial fraction decomposition:


x + 20 = A(x + 2) + B(x - 10)
x + 20 = (A + B)x + (2A - 10B)
Now; we have to relate like terms on both sides; we have:
A + B = 1 ; 2A - 10 B = 20
By solvong the expressions above; we have:

Now;

Thus;

Now; the integral is:


3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.
Please check to the attached image below for the solution to question number 3.
3.1 Solve<span> : </span>4x2<span>+3 = 0. Subtract 3 from both sides of the equation : </span><span>4x2 = -3</span>. Divide both sides of the equation by 4: x2<span> = -3</span>/4 = -0.750. When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ -3/4. In Math, i is called the imaginary unit. It satisfies i 2<span> =-1.</span>
Establish two right triangles, both with the height of the pole, h.
Call x the distance from the pole to one stake. Then the distance from the other stake to the pole is 6 -x.
Apply Pytagora's equation to both triangles.
1) h^2 = 7^2 - x^2
2) h^2 = 8^2 - (6-x)^2
Eaual 1 to 2
7^2 - x^2 = 8^2 - 6^2 +12x -x^2
12x = 7^2 -8^2 +6^2 = 49 -64 + 36 = 21
x = 1.75
Substitue x-value in 1
h^2 = 49 - (1.75)^2 = 45.94
h = sqrt(45.94) = 6.78
Answer: option d.