MATHEMATICS COLLEGE

What sample size would be required to estimate the true proportion of American female business executives who prefer the title "Ms.," with an error of ±0.025 and 98 percent confidence? (Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.) Sample size

Answers

Answer 1

Answer:

Answer:

$n=(0.5(1-0.5))/(((0.05)/(2.326))^2)=2164.1104$

And rounded up we have that n=2165

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

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 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by:

$z_(\alpha/2)=-2.326, z_(1-\alpha/2)=2.326$

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

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

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

(b)

We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=(0.5(1-0.5))/(((0.05)/(2.326))^2)=2164.1104$

And rounded up we have that n=2165

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A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.

Answers

Answer:

(a) 3178

(b) 14231

Step-by-step explanation:

Given

$y = (269573)/(1+985e^(-0.308t))$

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

$y = (269573)/(1+985e^(-0.308*8))$

$y = (269573)/(1+985e^(-2.464))$

$y = (269573)/(1+985*0.08509)$

$y = (269573)/(84.81365)$

$y = 3178$ --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

$y = (269573)/(1+985e^(-0.308*13))$

$y = (269573)/(1+985e^(-4.004))$

$y = (269573)/(1+985*0.01824)$

$y = (269573)/(18.9664)$

$y = 14213$ --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

$y = (269573)/(1+985e^(-0.308*16))$

$y = (269573)/(1+985e^(-4.928))$

$y = (269573)/(1+985*0.00724)$

$y = (269573)/(8.1314)$

$y = 33152$ --- approximated

The sum of two consecutive integers is -39. List the two numbers from smallest to greatest

Answers

Answer:

-20, -19

Step-by-step explanation:

The average of the two numbers is -39/2 = -19.5. The smaller number is 0.5 less than this, -20, and the larger number is 0.5 more than -19.5, so is -19.

_____

Comment on the problem and solution

I find that working consecutive integer problems is often simplified by working with the average value of those integers:

the average of two consecutive odd integers is the even integer between them
the average of two consecutive even integers is the odd integer between them
the average of an odd number of integers of the same type (consecutive, consecutive odd, consecutive even) is the middle one
The average of an even number of consecutive integers is the "half" number between the middle two (as in this problem).

Which function represents the graph?

Answers

Answer:

option 3

Step-by-step explanation:

We know this is a cube-root parent function due to the shape of the curve. Option C moves the graphed function from the origin (0,0) to two units to the left and one unit upward.

Each of the following tables defines a relationship between an input x and an output y. Which of the relationships represent functions? Table A x -8 -3 0 6 y 24 4 9 72 Table B x 9 15 24 38 y -14 -16 53 29 Table C x 15 24 24 100 y -16 53 29 7 Table D x -8 6 0 6 y 24 4 9 72 a. Table A and Table C b. Table A and Table B c. Table B and Table C d. Table C and Table D Please select the best answer from the choices provided

Answers

The relationship representing the function as per the input and output value is given by option b. Table A and Table B.

In order for a relationship between an input x and an output y to represent a function,

each input value x must be associated with exactly one output value y. Let's analyze the given tables:

Table A:

x -8 -3 0 6

y 24 4 9 72

Table B:

x 9 15 24 38

y -14 -16 53 29

Table C:

x 15 24 24 100

y -16 53 29 7

Table D:

x -8 6 0 6

y 24 4 9 72

Let's examine the options:

a. Table A and Table C: Table A represents a function because each x value corresponds to a unique y value.

Table C has duplicate x values, which means it doesn't represent a function.

b. Table A and Table B: Both Table A and Table B represent functions because each x value is associated with a single unique y value in both tables.

c. Table B and Table C: Table B does not represent a function

because the x value 24 is associated with two different y values (-16 and 53) in Table B.

Table C does not represent a function either because of the duplicate x value 24.

d. Table C and Table D: Similar to options a and c,

Table C does not represent a function due to duplicate x values.

Table D represents a function as each x value is associated with a unique y value.

Therefore, based on the analysis above, the correct answer for the function is option b. Table A and Table B.

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Answer: is B. table A and Table B

Step-by-step explanation:

MilesToGo Transport verified that it had a receipt showing that 45 air conditioning units had been delivered to its warehouse and are scheduled for delivery to the wholesaler next week. What type of receipt would show this information

Answers

Answer: Bill of loading

Step-by-step explanation:

The bill of loading is a detailed list which is in a form of receipt on the merchandise that is being transported given by the carrier to the person that is consigning the goods.

The purpose of the bill of loading is to serve functions such as a contract, a receipt to show that the carrier has received the goods, and a document of title.

Therefore, the bill of loading will show that MilesToGo Transport verified that it had a receipt showing that 45 air conditioning units had been delivered to its warehouse and are scheduled for delivery to the wholesaler next week.

Final answer:

A Delivery Receipt is used to confirm the delivery of goods. In the scenario, the document verifies the reception of 45 air conditioning units by MilesToGo Transport and can guide the future delivery of these units to the wholesaler.

Explanation:

The receipt that would show this information is called a Delivery Receipt. A Delivery Receipt is a document that confirms delivery of goods. It is typically issued by the carrier (in this case, MilesToGo Transport) and it provides details about the goods delivered, their quantity (45 air conditioning units in this scenario), delivery date, and recipient. This receipt informs the recipient about what goods have been received and what are expected to be delivered.

For instance, when MilesToGo Transport received the 45 air conditioning units in its warehouse, a Delivery Receipt would have been issued to confirm that the units had arrived. This receipt can subsequently be used to verify and schedule the further delivery of these units to a wholesaler the next week.

Learn more about Delivery Receipt here:

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The hours since a person has eaten and the strength of hunger they feel. what is the independent and dependent variable?

Answers

The hours are independent, time keeps flowing. but the hunger depends on hours. If time itself stopped, so would all matter, and thus, you would never be hungry.

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