Step-by-step explanation:
Permutation
:The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed.
Factorial
: There are n! ways of arranging n distinct objects into an ordered sequence.
Considering a situation when n = r in a permutation, nPr reduces to n!, a simple factorial of n.
Proof: 3P3 = 3!
n = 3 and r = 3
But 0! = 1
3P3 = 3!
Answer:
0.85
Step-by-step explanation:
Given two events A and B, the probability that either A or B occurs is given by:
where
the probability that A occurs
is the probability that B occurs
is the probability that both A and B occur at the same time
In this problem, we know the following facts:
is the probability that the car requires an oil change
is the probability that the car requires a brake repair
is the probability that the car requires both an oil change and brake repair
Therefore, the probability that either o (car requiring oil change) or b (car requiring brake repait) occur is:
Answer:
43.75 ft²
Step-by-step explanation:
= (l√(w/2)² + h²) + (w√(l/2)² + h²)
l & w become 3.5, and h becomes 6.
<em /><em> </em>= (3.5√(3.5/2)² + 6²) + (3.5√(3.5/2)² + 6²)
<em>Step 1:Because this is a square pyramid, what you see above essentially becomes what you see below.</em>
<em /> = 2(3.5√(3.5/2)² + 6²)
<em>Step 2: Divide 3.5 by 2 to get 1.75.</em>
<em /><em> </em>= 2(3.5√1.75² + 6²)
<em>Step 3: Square both 1.75 and 6 to get 3.0625 and 36 respectively.</em>
= 2(3.5√3.0625 + 36)
<em>Step 4: Add 3.0625 and 36 to get 39.0625.</em>
<em /> = 2(3.5√39.0625)
<em>Step 5: The square root of 39.0625 is 6.25.</em>
<em /><em> </em>= 2(3.5 * 6.25)
<em>Step 6: Multiply 3.5 by 6.25 to get 21.875.</em>
<em /> = 2(21.875)
<em>Step 7: Multiply 2 by 21.875 to get 43.75.</em>
<em /> = 43.75 ft²
The lateral area of this pyramid is 43.75 ft².
<em />
<em />
Answer:
The value of x is 200 in the equation 1/5x - 2/3y = 30, when y = 15
Step-by-step explanation:
<u>Given</u>
equation: x - 2/3y = 30
when y = 15
<em>Plug in y:</em>
1/5x - 2/3(15) = 30
1/5x - 10 = 30
<em>add</em> 10 to both sides,
1/5x - 10 + 10 = 30 + 10
1/5x = 40
<em>multiply</em> both sides by 5
1/5x * 5= 40 * 5
x = 200
Answer:
(1,B) (1,R) (2,B) (2,R) (3,B) (3,R)
