Answer:
<h2><u>
(9, 76)</u></h2>
Step-by-step explanation:
y = 7x + 13
y = 3x + 49
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We can solve this in either of two ways: Mathematically and graphically.
<h2><u>
Math</u></h2>
Set the equations equal to each other (after all, y does equal y).
7x + 13 = 3x + 49
4x = 36
x = 9
Then use x = 9 to solve for y:
y = 7x + 13
y = 7(9) + 13
x = 76
<h2><u>
Graph</u></h2>
Plot the two equations. I use Desmos - its online and free. The intersection of the two lines reveals to answer: (9,76). See the attachment.
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.
120 x 1/100 = 120/100
120/100 = 12/10 = 6/5
The answer is 6/5
Answer:
Number 2 is A
Step-by-step explanation:
5 is 380% because 405-22 is 383 if you round that it is 380%
Answer:
450.4
Step-by-step explanation:
