Hey!
Finding the factorial for the first few numbers, we have:
1!=1
2!=2
3!=6
4!=24
5!=120
6!=720
7!=720*7
8!=720*56
What we can see as a clear pattern from 5! and on is that our number ends with a 0, making the units digit 0. Therefore, when we add the units digit of 5! and on, we have a result of 0. So, we can simply add the units digits of 1!, 2!, 3!, and 4!, which is 1+2+6+4=13. Since the units digit is the last number, we can drop the tens place to get an answer of 3.
Feel free to ask further questions!
Hello! :)
Find the derivative using the quotient rule:
In this instance:
Use the following properties to find the derivative of f(x) and g(x):
Use the quotient rule:
Simplify the numerator:
Factor out 
Factor out -1 from the numerator:
And we're done! Thanks for posting the question to my 1000th answer!
Answer:
Final factor is (x-9)(x+4)
Step-by-step explanation:
Given expression is 
.
Now we need to factor that expression
Find two numbers whose product is -36 and sum is -5.
Two such numbers oare -9 and +4. So we get:
Hence final factor is (x-9)(x+4)
Answer:
Part A:
The probability of hitting the black circle is the ratio between the area of the black circle and the white square (including the black circle)
Area of circle:
Ac = pi x r^2 = pi x (2/2)^2 = pi (diameter = 2)
Area of square:
As = side^2 = 11^2 = 121 (side = 11)
=> P = pi/121 = ~0.025 (P = 0.025 < 0.5 => P is closer to 0 than 1)
Part B:
The probability of hitting the white portion could be calculated in a similar way as shown in part A. However, the event of hitting the white portion is the complement event of the event of hitting the black circle.
Because P(event) + P(complement of event) = 1
=> P = 1 - 0.025 = 0. 975 (P = 0.975 > 0.5 => P is closer to 1 than 0)
