All categories

2 years ago

Please Help! Is the data set approximately periodic? If so, what are its period and amplitude?

Mathematics

1 answer:

n200080 [17]2 years ago

5 0

Answer:

Option C. Periodic

Step-by-step explanation:

This problem is set with the number of days passing by versus the book borrowed, possibly by a library.

In order to see this, let's recall the concept of period and amplitude. The period in this case would be how much a number or a pattern is repeated over time. The amplitude would be the result of the difference between the maximum value and the minimum value of the table, in this case, the number of books borrowed.

Now, if you watch closely the table, we can watch a pattern. Which pattern? well, let's divide the table in 3 parts.

The first 4 days, we have: 102. 76, 91, 140

The second 4 days: 98, 74, 88, 137

The last 4 days: 100, 75, 92, 139

As you can see, every 4 days we get a pattern of books borrowed and almost the same number. [In day 1, 102 books were borrowed, and in day 5, 98 books were borrowed. The difference between that and the first day is only 4 books.

Day 2, was 76 books and day 6 was 74, again a very small difference. If we do the same for the remaining day we can conclude that every 4 days, the number of books borrowed follows a pattern, so we can conclude that the period would be 4.

Now to get the amplitude, let's see the average of difference between the maximun and minimum value:

A = 140 - 74 / 2 = 33.

As we can see, the value it's not exactly 25, but it's close to 33, and the problem states if the data set is approximately periodic, so, we can go with this option.

You might be interested in

A simple random sample from a population with a normal distribution of 99 body temperatures has xbar = 99.10°F and s = 0.64°F. C

motikmotik

The general formula for the margin of error is e = (zs)/√n, when the sample size is 30 or more (otherwise, we'd need to to a t-interval).

Since we're needing a 99% confidence interval, we need to know what the positive z-score associated with this two-tailed area under the normal curve is. This can be a little tricky if you're using a standard normal table. What you want is a two-tailed interval that has an area of .99. What this means is that the remaining 0.01 is divided into 0.005 on each end. This then means that, to the right of the mean (which is 0), the area is 0.005 less than the total right-half area of 0.5, or 0.495. The total cumulative area, then, includes this plus the left half of .5, or 0.5 + 0.495 = .0995.

Then, if all we have to go on is a cumulative standard normal table, then we need to find the area closest to 0.995 and find the corresponding z-score. This z-score is 2.58.

Now that we have the z-score, we can now plug in all the values into the formula.

e = (2.58 · 0.66)/√102 = 0.1686.

So the 99% confidence interval will be that far above and below the mean (which is 98.8). So the lower limit is 98.8 - 0.1686 = 98.631, and the upper limit is 98.8 + 0.1686 = 98.967.

The TI-84 method:

This is much easier, if you're allowed to use this technology. You begin with the STAT button, and then move over to the TESTS menu. Then select ZInterval. We have summary stats rather than data in this problem, so we select Stats as the input. For the standard deviation, we put 0.66, for x-bar 98.8, for n 102, and for C-level 0.99. Then select Calculate, and it will provide the interval at the top of the screen (98.632, 98.968). Note that the lower limit is slightly different by this method. This is because, when doing it by hand, we had to approximate the z-score. This created a rounding error, albeit a small one.

4 0

3 years ago

PLEASE EXPLAIN YOUR ANSWER

umka21 [38]

Answer:

equivalent to 58/100

and 58%

Step-by-step explanation:

7 0

3 years ago

a coach asked two players how much water they drank before practice. Ashley said she drank 1/2 pint and Claire said she drank 0.

Andre45 [30]

1. The problem gives the following information: Ashley said she drank 1/2 pints and Claire said she drank 0.7 pints.

2. Therefore, to solve this problem you must follow the proccedure that is shown below:

3. You must sum the amount of water that Ashley and Claire drank before the practice. Then, you have:

1/2 pints=0.5 pints (Ashley)
0.7 pints (Claire)

x=0.5 pints+0.7 pints
x=1.2 pints

How many pints of water did Ashley and Claire drink combined?

The answer is: 1.2 pints or 1 1/5 pints

8 0

3 years ago

Solve and type in 'ab'

snow_tiger [21]

A=4 and b =29 hope this helps

4 0

3 years ago

Read 2 more answers

Which of the following sets are closed under multiplication? Select all that apply.

ivolga24 [154]

Answer:

Integers, whole numbers and polynomials are sets of closed under multiplication.

Only Irrational numbers are not the sets of closed under multiplication.

Step-by-step explanation:

To find : Which of the following sets are closed under multiplication?

1. Integers

Yes, integers is a sets of closed under multiplication as if you multiply an integer by an integer, you will always get another integer.

Example - $3\times 3=9$ is an integer

2. Irrational numbers

No, irrationals are not closed under multiplication.

Example - $\sqrt{3} \times \sqrt{3} =3$ is a rational number

3. Whole numbers

Yes, whole numbers is a sets of closed under multiplication as if you multiply a whole number by a whole number, you will always get another whole number.

Example - $5\times 5=25$ is a whole number

4. Polynomials

Yes, polynomial is sets of closed under multiplication as if you multiply the variables' exponents are added, and the exponents in polynomials are whole numbers so the new exponents will be whole numbers.

Example - $(x + 1)(x^2 + 4x + 3) = x^3 + 5x^2 + 7x + 3$ is a polynomial.

4 0

3 years ago

Read 2 more answers