125x^6 – 8
We write the numbers in exponential form
125= 5*5*5 = 5^3
8 = 2*2*2= 2^3
Now 125x^6 - 8 becomes 5^3x^6 - 3^3
We got the expression in cube form a^3- b^3= (a-b)(a^2+ab+b^2)
a= 5x^2 and b= 2
The correct answer is: d=9m
Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.
Then, using the Pythagorean Theorem we have:
20^2 = h^2 + (d+7)^2 (Eq. 1)
400 = h^2 + d^2 + 2*7*d + 7^2 (expanding the theorem)
400 = (h^2 + d^2) + 14*d + 49 (Eq. 2)
15^2 = h^2 + (d)^2 (Eq. 3)
Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):
400 = (15^2) + 14*d + 49
400 = 225 + 14*d + 49
14*d = 400 - 225 - 49 (clearing the variable d)
14*d = 126
d = 9 m
And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.
And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building
a) 9.52% probability that, in a year, there will be 4 hurricanes.
b) 4.284 years are expected to have 4 hurricanes.
c) The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
6.9 per year.
This means that
a. Find the probability that, in a year, there will be 4 hurricanes.
This is P(X = 4).
9.52% probability that, in a year, there will be 4 hurricanes.
b. In a 45-year period, how many years are expected to have 4 hurricanes?
For each year, the probability is 0.0952.
Multiplying by 45
45*0.0952 = 4.284.
4.284 years are expected to have 4 hurricanes.
c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here?
The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
down 2 affects the y, so 1-2=-1
Left 4 affects the x, so 3-4=-1