<u>Answer:</u>
A) 720 ways
B) 15 ways
C) 6 ways
<u>Step-by-step explanation:</u>
A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Alicia can arrange her paintings in 720 ways.
B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:


Therefore, Alicia can choose any 4 of her paintings in 15 ways.
C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways
Answer:
The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.
Step-by-step explanation:
Assuming that the shortest side of this triangle has a length of "x" feet, then one side is "x + 4" feet and the third is "2*x - 4" feet. Since the perimeter of the deck is 80 feet, then the sum of the length of these sides should be equal to that.

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.
Angle AOD = 180
4x-2 + 5x+10 + 2x+14 = 180
11x + 22 = 180
11x = 180 - 22 = 158
x = 158/11
Answer:
50
Step-by-step explanation:
The equation that represent the total cost is in form of equation of a line y = mx+c
m is the gradient of the line
c is the intercept (The point where the line cuts the y - axis
If the equation given y = 150x + 50 is graphed, it will look like a straight line and the y- intercept will represent 50 when compared with the general equation of a line.
Answer:
easy one
Step-by-step explanation:
first factorise 600 as 2*2*2*3*5*5
then write as 2^3 * 3*5^2= 2^a*b*c^d
equating corresponding elements as a=3
b=1and c= 2 is the answer