Janice has just bought a new pack of levels in her favorite game, Candy Crush. She knows that she can win a new level on the fir
1 answer:
Answer:
0.0039 = 0.39% probability that she beats all 4 levels on the first try.
Step-by-step explanation:
For each level, there are only two possible outcomes. Either she can win the new level on the first try, or she cannot. The probability of winning a level on the first try is independent of any other level. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
She knows that she can win a new level on the first try 25% of the time.
This means that
Janice plays through 4 levels.
This means that
What is the probability that she beats all 4 levels on the first try?
This is P(X = 4). So
0.0039 = 0.39% probability that she beats all 4 levels on the first try.
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Answer:
We would have
where " l " is length, " w" is width and "h" is height.
Step-by-step explanation:
Step 1
Remember that
Surface area for a box with no top =
where " l " is length, " w" is width and "h" is height.
Step 2.
Remember as well that
Volume of the box =
Step 3
We can now use lagrange multipliers. Lets say,
and
By the lagrange multipliers method we know that
Step 4
Remember that
and
So basically you will have the system of equations
Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get
Then you would get
You can get rid of from these equations and you would get
And from those equations you would get
Now remember the original equation
If we plug in what we just got, we would have
We are told to use simple interest rate. Formula for this is:
Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years
We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.
To solve this problem we will assume that we are putting same amount each month on the bank account.
We are given:
A=$19500
P=?
r=1.5%
t=5 years
First step is to transform r into decimal number:
Now we get back to our formula and we solve it for P:
We insert numbers and we get our principal:
We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.
Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years
We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.
To solve this problem we will assume that we are putting same amount each month on the bank account.
We are given:
A=$19500
P=?
r=1.5%
t=5 years
First step is to transform r into decimal number:
Now we get back to our formula and we solve it for P:
We insert numbers and we get our principal:
We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.