a jar contains nickels and pennies. there are 56 coins in the jar in all. the total value of the coins is 1.52. how many pennies
1 answer:
1 penny is just 1c
one nickel is 5 pennies or 5c
alrite...
p = amount of pennies in the jar
n = amount of nickels in the jar
we know there are 56 coins in the jar, thus whatever "p" and "n" are,
p + n = 56
we also know, the total value of all pennies and nickels is one buck and 52 cents, or 1.52.. that's 152 pennies.
now, we know there are 5 pennies in one nickel, so in "n" nickels, there are 5*n pennies, or 5n, thus
p + 5n = 152
solve for "p", to see how many penny coins are there.
what about the nickels? well, n = 56 - p.
one nickel is 5 pennies or 5c
alrite...
p = amount of pennies in the jar
n = amount of nickels in the jar
we know there are 56 coins in the jar, thus whatever "p" and "n" are,
p + n = 56
we also know, the total value of all pennies and nickels is one buck and 52 cents, or 1.52.. that's 152 pennies.
now, we know there are 5 pennies in one nickel, so in "n" nickels, there are 5*n pennies, or 5n, thus
p + 5n = 152
solve for "p", to see how many penny coins are there.
what about the nickels? well, n = 56 - p.
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Answer:
The required hypothesis to test is and
.
Step-by-step explanation:
Consider the provided information.
It is given that the nightclub has recently surveyed a random sample of n = 250 customers of the club.
She would now like to determine whether or not the mean age of her customers is over 30.
Null hypotheses is represents as . Thus the null hypotheses is shown as:
The alternative hypotheses is represents as . Thus the alternative hypotheses is shown as:
Hence, the required hypothesis to test is and
.
Answer:
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)
Step-by-step explanation:
Notation and definitions
n=50 represent the sample size
represent the sample mean
represent the sample standard deviation
m represent the margin of error
Confidence =88% or 0.88
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in R using the following formulas:
qt(0.06,49)
[1] -1.582366
qt(1-0.06,49)
[1] 1.582366
The critical value
Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
With R we can do this:
m=1.582366*(5.83/sqrt(50))
m
[1] 1.304639
Calculate the confidence interval
The interval for the mean is given by this formula:
And calculating the limits we got:
Using R the code is:
lower=27.02-m;lower
[1] 25.71536
upper=27.02+m;upper
[1] 28.32464
The 95% confidence interval is given by (25.71536 ;28.32464)
And if we need to round we can use the following excel code:
round(lower,2)
[1] 25.72
round(upper,2)
[1] 28.32
And the interval would be (25.72; 28.32)