Answer:
a) 1/2
b) 1/n
c) 1/4
Step-by-step explanation:
a) For each permutation, either 1 precedes 2 or 2 precedes 1. For each permutation in which 1 precedes 2, we can swap 1 and 2 to obtain a permutation in which 2 preceds 1. Thus, half of the total permutations will involve in 1 preceding 2, hence, the probability for a permutation having 1 before 2 is 1/2.
c) If 2 is at the start of the permutation, then it is impossible for 1 to be before 2. If that is not the case, then 1 has a probability of 1/n-1 to be exactly in the position before 2. We can divide in 2 cases using the theorem of total probability,
P( 1 immediately preceds 2) = P (1 immediately precedes 2 | 2 is at position 1) * P(2 is at position 1) + P(1 immediately precedes 2 | 2 is not at position 1) * P(2 is not at position 1) = 0 * 1/n + (1/n-1)*(n-1/n) = 1/n.
d) We can divide the total of permutations in 4 different groups with equal cardinality:
- Those in which n precedes 1 and n-1 precedes 2
- those in which n precedes 1 and 2 precedes n-1
- those in which 1 precedes n and n-1 precedes 2
- those in which 1 precedes n and 2 precedes n-1
All this groups have equal cardinality because we can obtain any element from one group from another by making a permutations between 1 and n and/or 2 and n-1.
This means that the total amount of favourable cases (elements of the first group) are a quarter of the total, hence, the probability of the event is 1/4.
Answer:
The mass of the ice block is 2116 grams ⇒ a
Step-by-step explanation:
The formula of density is 
, where m is the mass and V is the volume
To find the mass from this formula multiply both sides by V,
then m = p.V
∵ The density of ice is approximately 0.92 g/cm³
∴ p = 0.92
- That means the mass of 1 cm³ is 0.92 g
∵ The volume of an ice block is 2300 cm³
∴ V = 2300
- Use the formula of the mass
∵ m = p.V
- Substitute the values of p and V in it
∴ m = (0.92)(2300)
∴ m = 2116 grams
The mass of the ice block is 2116 grams
Create and solve an equation of ratios:
10 ft 8 oz
------- = -------
x 48 oz (note that 3 lb = 48 oz)
Then 480 = 8x, and x = 60 ft (answer)
Answer:
x = 11
Step-by-step explanation:
We know that vertical angles (opposite angles when two lines cross), are equal.
2x - 6 = 6x - 50
4x = 44
x = 11
Answer: Inequality
Step-by-step explanation:
From the question, if we can describe 15×-10 as an expression, then we would describe 6×-2< 35 as an inequality. An
inequality is used to compare two values, and shows if one is less than, or greater than, or maybe not equal to the other value.
For example, a ≠ b means that a is not equal to b and a < b means a is less than b while a > b means a is greater than b. From the question, 6×-2< 35 means that 6x - 2 is less than 35.
