Answer:
The probability that A selects the first red ball is 0.5833.
Step-by-step explanation:
Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.
To find : What is the probability that A selects the first red ball?
Solution :
A wins if the first red ball is drawn 1st,3rd,5th or 7th.
A red ball drawn first, there are 
places in which the other 2 red balls can be placed.
A red ball drawn third, there are 
places in which the other 2 red balls can be placed.
A red ball drawn fifth, there are 
places in which the other 2 red balls can be placed.
A red ball drawn seventh, there are 
places in which the other 2 red balls can be placed.
The total number of total event is 
The probability that A selects the first red ball is
Step-by-step explanation:
By rotating a figure,
The length of its sides remain the same.
Therefore line AB = line A'B'.
=> 5x - 14 = 4x + 4
=> x = 18
Hence, line AB = 5(18) - 14 = 76.
Answer:
see explanation
Step-by-step explanation:
The n th term ( explicit formula ) of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₁₂ = - 95 and a₃₇ = - 270 , then
a₁ + 11d = - 95 → (1)
a₁ + 36d = - 270 → (2)
Subtract (1) from (2) term by term to eliminate a₁
25d = - 175 ( divide both sides by 25 )
d = - 7
Substitute d = - 7 into (1) and solve for a₁
a₁ + 11(- 7) = - 95
a₁ - 77 = - 95 ( add 77 to both sides )
a₁ = - 18 , thus
= - 18 - 7(n - 1) = - 18 - 7n + 7 = - 7n - 11
= - 7n - 11 ← explicit formula
--------------------------------------------------------------
The recursive formula allows a term in the sequence to be found by adding the common difference d to the previous term, thus
= 
- 7 with a₁ = - 18 ← recursive formula
Answer:
Step-by-step explanation:
Part A: You can only use Pythagorean's Theorem on a right triangle.
Part B: The side across from the right angle is the hypotenuse. It has a length of 15.
Part C: To find the missing side using Pythagorean's Theorem:
and
and
and
a = 10.20
