Orin solved an equation and justified his steps as shown in the table.
1 answer:
Answer:
Step-by-step explanation:
Given the equation as
apply multiplication property of equality where you multiply every term by 5
3x-15=60------------------apply addition property of equality
3x-15+15=60+15
3x=75--------------------------appy division property of equality by dividing both sides by 3
3x/3=75/3
x=25
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Answer:
(a) 0.4096
(b) 0.64
(c) 0.7942
Step-by-step explanation:
The probability that the player wins is,
Then the probability that the player losses is,
The player is playing the video game with 4 different opponents.
It is provided that when the player is defeated by an opponent the game ends.
All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)
(a)
The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.
The probability that the player defeats all four opponents in a game is,
P (Player defeats all 4 opponents) =
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b)
The probability that the player defeats at least two opponents in a game is,
P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) =
Thus, the probability that the player defeats at least two opponents in a game is 0.64.
(c)
Let <em>X</em> = number of times the player defeats all 4 opponents.
The probability that the player defeats all four opponents in a game is,
P(WWWW) = 0.4096.
Then the random variable
The probability distribution of binomial is:
The probability that the player defeats all the 4 opponents at least once is,
P (<em>X</em> ≥ 1) = 1 - P (<em>X</em> < 1)
= 1 - P (<em>X</em> = 0)
Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.
Answer:
The value of the account in the year 2009 will be $682.
Step-by-step explanation:
The acount's balance, in t years after 1999, can be modeled by the following equation.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999
This means that
$590 in the year 2007
2007 is 8 years after 1999, so P(8) = 590.
We use this to find r.
Applying ln to both sides:
Determine the value of the account, to the nearest dollar, in the year 2009.
2009 is 10 years after 1999, so this is A(10).
The value of the account in the year 2009 will be $682.