Well, we need to consider the x and y coordinates of the giben points, and check wether the y coordinate is greater than twice the x coordinate minus 1 (i.e. 2x-1):
- For the first point, the x coordinate is 0. So, 2x-1 = -1. The y coordinate is 2, and 2>-1. So, this point is a solution.
- For the second point, the x coordinate is 4. So, 2x-1 = 7. The y coordinate is 2, and 2<7. So, this point is not a solution.
- For the third point, the x coordinate is 0. So, 2x-1 = -1. The y coordinate is -10, and -10<-1. So, this point is not a solution.
- For the fourth point, the x coordinate is 4. So, 2x-1 = 7. The y coordinate is 1, and 1<7. So, this point is not a solution.
This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2
Hope this helps!!
Answer:
0.4444
Step-by-step explanation:
Use the following property to ease the calculation:
P(At least one)=1-P(None)
Total number of electrical components: 9
Number that does not function well :1
Number that functions well : 8
We have 
ways to to choose 4 good components from 8.
We have 
ways to choose 4 components from a total of 9.
If all function properly then none is bad, we 
way to do this.
P(At least one)=
P(At least one)=
P(At least one)=0.4444
The empirical rule states that in a normal distribution,
68% of data is within 1 std deviation of the mean
95% of data is within 2 std deviation of the mean
99.7% of data is within 3 std deviation of the mean
In this case 95% of the cases would be within two std deviations of the mean
mean - 8 and mean + 8
72 - 8 = 64 and 72 + 8 = 80
then 95% of the scores are between 64% and 80% on the test.
You would take the amount of increase and divide it by the amount of total cost over the time period of certain months. Then you would multiply that number by the percentage of increase gained, and subtract 96.12 to get your answer.
