Answer:
75.8% probability that a 31 square foot metal sheet has at least 4 defects.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
In this problem, we have that:
3 defects per 18 square feet.
So for 31 square feet, we have to solve a rule of three
3 defects - 18 square feet
x defects - 31 square feet
So 
Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.
Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.
So
We want 
So
In which
So
Finally
75.8% probability that a 31 square foot metal sheet has at least 4 defects.
Remember that ln=
and
means
convert
ln(x+7)=9 means
e^(9)=x+7
minus 7 from both sides
e^9-7=x
use calculator to evaluate
8096.08=x aprox
Answer:
White: 28 Blue: 20 Red: 32
Step-by-step explanation: Make ratios. If 35% are White strands then it would be 35/100 = ?/80 you can use the butterfly method to solve this:
35*80 = ?*100
? = 28
Blue: 25/100 = ?/80
(you can use the butterfly method or you can simplify 25/100 into 1/4)
1/4 = ?/80
1*80 = ?*4
? = 20
Red: 40/100 = ?/80 (once again, you can simplify if you want)
4/10 = ?/80
4*80 = ?*80
? = 32
The answer is: 3.
_________________
In the table, the relation (x, y) is not a function is the "missing value" of "x" is: 3.
_______________________________________
Explanation: We are given that the ordered pair: "(3,10)" exists. In other words, when x = 3, y =10.
______________________________________
The "missing value" refers to the "empty box" in the table shown (in the attached screenshot). The "empty box" shows a "y-coordinate" of "20"; but a "missing" corresponding "x-coordinate".
____________________________________
The problem asks:
_________________
In the table, the relation (x, y) is not a function is the "missing value" of "x" is: ____?
___________________
The answer is: 3.
_______________________
We know the answer is "3"; because we know that "3" already has 1 (one) corresponding y-coordinate.
By definition, a "function" cannot have ANY "x-coordinates" that have more than one "corresponding y-coordinate". As such:
_______________________________________
In the table, the relation (x, y) is not a function is the "missing value" of "x" is:
____________
3.
____________
Additional information:
____________
When examining an equation on an actual graph, we can use what is called the "vertical line test". That is, one can take a pencil and vertically go through the "y-axis", or even examine it visually, to see if there are any "x-values" that have more than one corresponding "y-coordinate".
If no, then it "passes" the "vertical line test" and is a "function".
If not, then it does NOT pass the "vertical line test" and is NOT a function.
__________________________________________
