Given:
The sequence is -8, -12, -16.
To find:
The nth and 52th term of the given sequence.
Solution:
We have,
-8, -12, -16
It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is
The nth term of an AP is
Where, a is first term and d is common difference.
Putting a=-8 and d=-4, we get
Putting n=52, we get
Therefore, the equation for the nth term of the given sequence is and the 52nd term of the sequence is -212.
Using the binomial distribution, it is found that there is a 0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.
For each water, there are only two possible outcomes, either it is correctly identified, or it is not. The probability of a water being correctly identified is independent of any other water, hence the binomial distribution is used to solve this question.
<h3>What is the binomial distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- The friend guesses among 3 types, hence .
- 3 cups will be identified, hence .
The probability that each of the 3 cups is correctly identified is P(X = 3), hence:
0.037 = 3.7% probability that Adina's friend correctly identifies each of the 3 cups of water.
You can learn more about the binomial distribution at brainly.com/question/24863377
Answer:
x=40
Step-by-step explanation:
y=kx
36=16k
k=9/4
y=9/4 x
90=9/4 x
x=40
Answer:
(x, y) ⇒ (x, y+6)
Step-by-step explanation:
Reflection of a value a across a point p to make b requires that a, b, and p satisfy the relation ...
p = (a+b)/2
2p = a + b
b = 2p - a
This is true for any sort of reflection. Here we have a reflection across the horizontal line y=-1, followed by a reflection across the horizontal line y=2. These reflections do not change the x-coordinate of a point, but they change the y-coordinate in accordance with the above relation.
Reflection across y = -1:
(x, y) ⇒ (x, 2(-1)-y) = (x, -2-y)
Reflection of that across y = 2:
(x, -2-y) ⇒ (x, 2(2) -(-2-y)) = (x, y+6)
The composition of the two reflections results in a translation upward of 6 units: (x, y) ⇒ (x, y+6)
Answer:
12km/hour
Step-by-step explanation:
The formula for how far he was jogging = Speed
Speed = Distance /Time
In the question,
Distance = 5km
Time = 5/12 hour
Speed = 5km / 5/12 hour
= 5 km ÷ 5/12 hour
= 5km × 12/5 hour
= 12km/hour
Therefore,Ezra was jogging as fast as 12 km/hour