38. By the commutative property, 3(w +9) is
2 answers:
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Question 1.
Step 1. Add the total cost of purchasing the luxury items:
You will spend $135.85 purchasing the luxury items.
Step 2. Add the total cost of purchasing the name brand items:
You will spend $80.07 purchasing the name brand items.
Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.
Question 2:
Part 1. To find the how many months will take to pay the card debt, we are going to use the credit card equation:
where
is the months to pay the card
is the balance
is the monthly payment
is the interest rate in decimal form
We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so
and 
. To find convert the interest rate to decimal form, we are going to divide the rate by 100%
.
Now that we have all we need, lets replace the values in our credit card equation:
It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.
Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
We can conclude that the total amount paid including interest is $1,600
Step 1. Add the total cost of purchasing the luxury items:
You will spend $135.85 purchasing the luxury items.
Step 2. Add the total cost of purchasing the name brand items:
You will spend $80.07 purchasing the name brand items.
Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.
Question 2:
Part 1. To find the how many months will take to pay the card debt, we are going to use the credit card equation:
where
We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so
Now that we have all we need, lets replace the values in our credit card equation:
It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.
Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
We can conclude that the total amount paid including interest is $1,600
We assume the lunch prices we observe are drawn from a normal distribution with true mean and standard deviation 0.68 in dollars.
We average samples to get
.
The standard deviation of the average (an experiment where we collect 45 samples and average them) is the square root of n times smaller than than the standard deviation of the individual samples. We'll write
Our goal is to come up with a confidence interval (a,b) that we can be 90% sure contains .
Our interval takes the form of as
is our best guess at the middle of the interval. We have to find the z that gives us 90% of the area of the bell in the "middle".
Since we're given the standard deviation of the true distribution we don't need a t distribution or anything like that. n=45 is big enough (more than 30 or so) that we can substitute the normal distribution for the t distribution anyway.
Usually the questioner is nice enough to ask for a 95% confidence interval, which by the 68-95-99.7 rule is plus or minus two sigma. Here it's a bit less; we have to look it up.
With the right table or computer we find z that corresponds to a probability p=.90 the integral of the unit normal from -z to z. Unfortunately these tables come in various flavors and we have to convert the probability to suit. Sometimes that's a one sided probability from zero to z. That would be an area aka probability of 0.45 from 0 to z (the "body") or a probability of 0.05 from z to infinity (the "tail"). Often the table is the integral of the bell from -infinity to positive z, so we'd have to find p=0.95 in that table. We know that the answer would be z=2 if our original p had been 95% so we expect a number a bit less than 2, a smaller number of standard deviations to include a bit less of the probability.
We find z=1.65 in the typical table has p=.95 from -infinity to z. So our 90% confidence interval is
in other words a margin of error of
dollars
That's around plus or minus 17 cents.