Evaluate x + y + z if x = 3, y = -5, and z = -2
1 answer:
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Answer:
You have 15 dimes. You have 9 quarters. You have 12 nickels
Step-by-step explanation:
lets set some variables:
let "n" = the number of nickels
let "d" = the number of dimes
let "q" = the number of quarters
So, the total amount of money you have should be: $4.35 = 0.25q + 0.10d + 0.05n
Now let's look at the relationships between the coins:
"There are three fewer quarters than nickels": n - 3 = q
"six more dimes than quarters": q + 6 = d
So now you have three equations with three variables, all you need to do is solve.
first, you can substitute "n-3" for "q" (according to the 2nd equation) in the 1st and 3rd equation, you get:
You now only have two equations and two variables.
Simplify:
Now substitute "n+3" for "d" (according to the 2nd equation) in the 1st equation:
4.35=0.30n-0.75+0.10(n+3)
simplify:
4.35=0.30n-0.75+0.10n+0.30
4.35=0.40n-0.45
4.35+0.45=0.40n
4.80=0.40n
n=12
You have 12 nickels. Now sub "n" back into your equations to find the number of dimes and quarters:
n - 3 = q
12 - 3 = q
q = 9
You have 9 quarters.
q + 6 = d
9 + 6 = d
d = 15
You have 15 dimes.
Answer:
Confidence interval: (21.9, 32.9).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 26 - 1 = 25
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.485
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 27.4 - 5.5 = 21.9 hours
The upper end of the interval is the sample mean added to M. So it is 27.4 + 5.5 = 32.9 hours
Confidence interval: (21.9, 32.9).