Answer:
You can say there is no solution for a system of linear equation when the graphs are PARALLEL to each other.
ONE solution: when both lines intersect at one point
INFINITE solution: when the line goes on forever
NO solution: is when the lines are parallel to each other.
Answer:
= 5n - 1
Step-by-step explanation:
There is a common difference between consecutive terms , that is
9 - 4 = 14 - 9 = 19 - 14 = 5
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 4 and d = 5 , then
= 4 + 5(n - 1) = 4 + 5n - 5 = 5n - 1
Let
A = event that the student is on the honor roll
B = event that the student has a part-time job
C = event that the student is on the honor roll and has a part-time job
We are given
P(A) = 0.40
P(B) = 0.60
P(C) = 0.22
note: P(C) = P(A and B)
We want to find out P(A|B) which is "the probability of getting event A given that we know event B is true". This is a conditional probability
P(A|B) = [P(A and B)]/P(B)
P(A|B) = P(C)/P(B)
P(A|B) = 0.22/0.6
P(A|B) = 0.3667 which is approximate
Convert this to a percentage to get roughly 36.67% and this rounds to 37%
Final Answer: 37%
Answer:
a) possible progressions are 5
b) the smallest and largest possible values of the first term are 16 and 82
Step-by-step explanation:
<u>Sum of terms:</u>
- Sₙ = n/2(a₁ + aₙ) = n/2(2a₁ + (n-1)d)
- S₂₀ = 20/2(2a₁ + 19d) = 10(2a₁ + 19d)
- 2020 = 10(2a₁ + 19d)
- 202 = 2a₁ + 19d
<u>In order a₁ to be an integer, d must be even number, so d = 2k</u>
- 202 = 2a₁ + 38k
- 101 = a₁ + 19k
<u>Possible values of k= 1,2,3,4,5</u>
- k = 1 ⇒ a₁ = 101 - 19 = 82
- k = 2 ⇒ a₁ = 101 - 38 = 63
- k = 3 ⇒ a₁ = 101 - 57 = 44
- k = 4 ⇒ a₁ = 101 - 76 = 25
- k = 5 ⇒ a₁ = 101 - 95 = 16
<u>As per above, </u>
- a) possible progressions are 5
- b) the smallest and largest possible values of the first term are 16 and 82
