With ASA, we need two angles and an included side. An included side is one that is between the two angles.
But, we need to make sure the sides match up. So, triangle KJI is congruent to triangle ZYX.
Therefore, we need to know that side JI is congruent to YX.
Hope this helps!
Answer:
d = 6
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 23 and a₁₁ = 65 , then
a₁ + 3d = 23 → (1)
a₁ + 10d = 65 → (2)
Subtract (1) from (2) term by term to eliminate a₁
10d - 3d = 65 - 23
7d = 42 ( divide both sides by 7 )
d = 6
Answer:
Explanation:
You can find the theoretical probability of the event "the sum of the numbers is at least 4".
The theoretical probability is:
- number of positive outcomes / number of possible outcomes.
<u>1. Number of positive outcomes.</u>
The number of positive outcomes is the amount of ways for which the sum of the numbers is at least 4.
Those are:
- Sum = 4: (1,3); (2,2), (3,1) → 3 ways
- Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 ways
- Sum = 6: (1,5), (2, 4), (3, 3), (4, 2), (5,1) → 5 ways
- Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 ways
- Sum = 8: (2,6), (3,5), (4,4), (3,5), (2,6) → 5 ways
- Sum = 9: (3,6), (4,5), (5,4), (6,3) → 4 ways
- Sum = 10: (4,6), (5,5), (6,4) → 3 ways
- Sum = 11: (5, 6), (6,5) → 2 ways
Thus, the total number of ways to have a sum of at least 4 is: 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.
<u>2. Number of possible outcomes</u>
The total number of possible outcomes is found by multiplying the ways each die can be rolled, this is: 6 × 6 = 36.
<u>3. Probability</u>
Then, the searched probability is 33/36 = 11/12 ≈ 0.92
