Answer:
Step-by-step explanation:
diameter= 22 mm
Radius is half of diameter
r = 22/2 = 11mm
Area of circle = πr²
= 3.14 * 11*11
= 379.94 mm²
Answer:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find this probability:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find this probability:
Answer: the z score is - 5.33
Step-by-step explanation:
Since the results for the standardized test are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = test reults
µ = mean score
σ = standard deviation
From the information given,
µ = 1700 points
σ = 75 points
We want to the Z-score test result of 1300 points.
For x = 1300,
z = (1300 - 1700)/75 = - 400/75 =
- 5.33
Answer:
Step-by-step explanation:
Given
--- The radius of each
Required
The area between them
See attachment for illustration of the question. (figure 1)
First, calculate the height of the equilateral triangle formed by the 3 radii (See figure 2)
Using Pythagoras theorem, we have:
Collect like terms
Take square roots
Expand
Split
Now, the area of the equilateral triangle can be calculated using:
Where
Next, is to calculate the area of the sector formed by 2 radii in each circle (figure 3).
Since the radii formed an equilateral triangle, then the central angle will be 60. So:
For the three circles, the area is:
Subtract the areas of the sectors (A2) from the area of the equilateral triangle (A1), to get the area between them.
Approximate