X = the number of minutes the phone is used
<u>Plan A:</u>
40¢ per minute ($0.40)
no other costs
<em>Cost for 1 month = 0.4 x</em>
<u>Plan B:</u>
$30 a month, even if you don't use the phone at all
100 free minutes
then 50¢ per minute ($0.50)
Cost for 1 month:
If 'x' is less than 100: <em>Cost = 30</em>
<span>
If 'x' is greater than 100</span>:
Cost = 30 + 0.5(x - 100) (Because the first 100 minutes are free, and
you only pay for minutes past 100. There are [x-100] of those.)
Eliminate parentheses: Cost = 30 + 0.5x - 50
Combine like terms: <em> Cost = 0.5x - 20</em>
Which plan costs more ? It depends on how many minutes you use in a month.
If you use a small number of minutes, Plan A costs you more.
If you use a huge number of minutes, Plan B costs you more.
Where is the crossover point ? It's the number of minutes in one month
where the costs of both plans are equal.
<u>If you use the phone for less than 100 minutes a month,</u>
(where the cost of Plan B starts increasing with each minute):
0.4x = 30
Divide each side by 0.4: <em>x = 75</em>
Less than 75 minutes per month, Plan A costs less.
Past 75 minutes a month, Plan A costs more than $30, so Plan B costs less,
until Plan B starts charging for extra minutes.
<u>If you use the phone for more than 100 minutes a month: </u>
0.4 x = 0.5 x - 20
Add 20 to each side: 0.4 x + 20 = 0.5 x
Subtract 0.4x from each side: 20 = 0.1 x
Multiply each side by 10: <em> 200 = x</em>
There it is.
Now we can combine the results:
-- Less than 75 minutes in a month: Plan A costs less.
-- Between 75-200 minutes in a month: Plan B costs less.
-- More than 200 minutes a month: Plan A costs less again.
Complicated ? Absolutely ! That's why citizens' consumer groups are after
these companies, to try to get them to make their plans more understandable
to regular people. I know from personal experience that even a lot of the
salesmen in the phone stores could not figure this out and give you sound advice.
a quantity of carbon - 14 will take 1342.5 years to become 1/8 of its original size.
Step-by-step explanation:
1/2 of the atoms decayed after 5370 years
now half of( 1/2 of )the atoms decayed after 5370/ 2 years
i.e, 1/4 of the atoms decayed after 2685 years.
again half of (1/4 of the atoms ) decayed after 2685/2 years
i.e, 1/8 of the atoms decayed after 1342.5 y<u>ears.</u>
Given: The series ∑cₙ is convergent
To find: The series ∑cₙ is convergent or not.
Solution: If the radius of convergence R the we can conclude that R≥4
So, the series will converge as -3<9.
Answer:
0.9704 = 97.04% probability of getting a cookie with at least 3 chips
Step-by-step explanation:
We only have the mean number of chocolate chips. So we use the Poisson distribution to solve this question.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
A well-mixed cookie dough will produce cookies with a mean of 7 chocolate chips apiece.
This means that
What is the probability of getting a cookie with at least 3 chips?
Either we have less than 3 chips, or we have at least 3 chips. The sum of the probabilities of these events is decimal 1.
We want . Then
In which
0.9704 = 97.04% probability of getting a cookie with at least 3 chips
Answer:
292 inches^2
Step-by-step explanation:
So to start off this is a picture of the fish tank.
Next we will find the area of the bottom and top rectangles.
The side lenghts for those two is 7 and 8.
So the area of one is 56 and the area of 2 is 112 inches^2.
Now we will find the area of the left and right rectangles.
The side lenghts are 6 and 8.
So the area of 2 is 96 inches^2.
Now for the front and back rectangles.
The side lenghts for those two are 6 and 7.
So the area of both is 84 inches^2.
So after adding all the areas up the surface area is 292 inches^2.