The answers are:
P(9, 2) = 72
P(5, 5) = 120
P(7, 7) = 5040
These are examples of permutations. The problems are asking us to find the total number of ways an event can happen.
In the first case, P(9, 2), we are asked to find the ways that 2 things can be chosen out of a group of 9.
9 x 8 = 72
P(5, 5) = 5 x 4 x 3 x 2 x 1
P(7, 7) = 7 x 6 x 5 x 4 x 3 x 2 x 1
Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.
Now, Pythagoras' Theorem is defined as follows:
c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:
c^2 = a^2 + b^2
24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)
b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)
b = √(24^2 - 8^2) (Take the square root of both sides)
b = √512 (Evaluate 24^2 - 8^2)
b = 16√2 (Simplify √512)
= 22.627 (to three decimal places)
I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.
Answer:
24 blocks will be needed to make the tower that is 4 feet high
Step-by-step explanation:
Let us use the ratio method to solve the question
∵ Charlie knows that 3 blocks are needed to make a tower that is
0.5 foot high
∵ He needs to make a tower that is 4 feet high
→ By using the ratio method
→ Blocks : height (ft)
→ 3 : 0.5
→ x : 4
→ By using the cross multiplication
∵ x × 0.5 = 3 × 4
∴ 0.5x = 12
→ Divide both sides by 0.5 to find x
∵ 
= 
∴ x = 24
∵ x represents the number of blocks
∴ 24 blocks will be needed to make the tower that is 4 feet high
Answer:
1.5 is not a prime number
Step-by-step explanation:
