Answer:
8, 12, 16, 20, 24, 28, 32, 36
Step-by-step explanation:
the nth term of an arithmetic sequence is
= a₁ + (n - 1)d
a₁ is the first term and d the common difference
given a₁ = 4 and a₁₀= 40 , then
4 + 9d = 40 ( subtract 4 from both sides )
9d = 36 ( divide both sides by 9 )
d = 4
add d to each term to obtain the next term
4 + 4 = 8
8 + 4 = 12
12 + 4 = 16
16 + 4 = 20
20 + 4 = 24
24 + 4 = 28
28 + 4 = 32
32 + 4 = 36
the 8 terms between 4 and 40 are
8, 12, 16, 20, 24, 28, 32, 36
Answer:
The probability of Thomas inviting Madeline to the party over the phone is 0.143.
Step-by-step explanation:
Consider the tree diagram below.
The events are denoted as follows:
<em>A</em> = Thomas bumps into Madeline at school
<em>B</em> = Thomas call Madeline on the phone
<em>X</em> = Thomas asks Madeline to the party
The information provided is:
P (A) = 0.80
P (B) = 1 - P (A) = 1 - 0.80 = 0.20
P (X|A) = 0.90
⇒ P (X'|A) = 1 - P (X|A) = 1 - 0.90 = 0.10
P (X|B) = 0.60
⇒ P (X'|B) = 1 - P (X|B) = 1 - 0.60 = 0.40
The conditional probability of event <em>U</em> given that another events <em>V</em> has already occurred is:
The law of total probability states that:
In this case we need to determine the probability that Thomas invites Madeline to the party over the phone, i.e. P (B|X).
Use the law of total probability to determine the value of P (X) as follows:
Compute the value of P (B|X) as follows:
Thus, the probability of Thomas inviting Madeline to the party over the phone is 0.143.