Suppose there is a pile of quarters, dimes, and pennies with a total value of $1.08

Mathematics

1 answer:

WINSTONCH [101]3 years ago

6 0

Answer:

if 1 quarter = $ 0.25

1 dime = $ 0.10

1 penny = $ 0.01

so to make the total of $1.08 and its is also required to calculate the number of each coins present without being able to make change for a dollar

therefore we say;

1 Quarter + 8 dimes + 3 penny

: ( 1 × 0.25 ) + ( 8 × 0.10 ) + ( 3 × 0.01 )

: 0.25 + 0.80 + 0.03 = $ 1.08

Now if you have a 4 Quarters, you have change for $1.

If you have 5 dimes, you have change for 2 Quarters.

If you have nickel; one of those can combine with 2 dimes to have a change for a Quarter.

If you have 5 pennies, you have enough change for 1 nickel

Therefore

(4-1)×0.25 + (5-1)×0.1 + (0×0.05) + (5-1)×0.01 = x

(3 × 0.25) + ( 4 × 0.1) + 0 + ( 4 × 0.01) = x

x = 0.75 + 0.4 + 0.04

x = $ 1.19

PROVED

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In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system

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Answer:

n=206

Step-by-step explanation:

Previous concepts

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.09$ , we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got: