Answer: a) 0.0058
b) 0.0026
Step-by-step explanation:
Given : The probability of having clear sunny skies in Seattle in July : p= 0.40
The number of days spent in Seattle in July: n= 18
a) Using, Binomial probability formula :
The probability of having clear sunny skies on at least 13 of those days:-
b) On converting binomial to normal distribution, we have
Let x be the number of days having clear sunny skies in Seattle in July.
Then, using we have
P-value =
The sum of the given sequence is -6384.
<u>Step-by-step explanation:</u>
The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).
- The first term of the sequence = 14
- The last term of the sequence = -280
- The common difference ⇒ 14 - 8 = 6
<u>To find the number of terms in the sequence :</u>
The formula used is
where,
- n is the number of terms.
- is the late term which is -280.
- is the first term which is 14.
- d is the common difference which is 6.
Therefore,
⇒
⇒
⇒
⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
<u>To find the sum of the arithmetic progression :</u>
The formula used is
where,
- S is the sum of the sequence.
- is the first term which is 14.
- is the late term which is -280.
Therefore,
⇒
⇒
⇒
∴ The sum of the given sequence is -6384.
No solution...............
Answer: v = -4
Step-by-step explanation:
Simplifying
4v + -7 = 5 + 7v
Reorder the terms:
-7 + 4v = 5 + 7v
Solving
-7 + 4v = 5 + 7v
Solving for variable 'v'.
Move all terms containing v to the left, all other terms to the right.
Add '-7v' to each side of the equation.
-7 + 4v + -7v = 5 + 7v + -7v
Combine like terms: 4v + -7v = -3v
-7 + -3v = 5 + 7v + -7v
Combine like terms: 7v + -7v = 0
-7 + -3v = 5 + 0
-7 + -3v = 5
Add '7' to each side of the equation.
-7 + 7 + -3v = 5 + 7
Combine like terms: -7 + 7 = 0
0 + -3v = 5 + 7
-3v = 5 + 7
Combine like terms: 5 + 7 = 12
-3v = 12
Divide each side by '-3'.
v = -4
Simplifying
v = -4