A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95% confident that his estimate is in error by no more than two percentage points? a)Assume that nothing is known about the percentage of computers with new operating systems.

Answers

Answer 1

Answer:

n = 1067

Step-by-step explanation:

Since nothing is known, we would assume that 50% of the computers use the new operating system.

So, standard error = 0.5/SQRT(n)

Z-value for a 95% CI = 1.9596

So, margin of error = 1.9596 x 0.5 / SQRT(n) = 0.03

So, n = 1067 (approx.)

This will be your approximate answer : n = 1067

Answer 2

Answer: 2401

Step-by-step explanation:

Formula to find the sample size is given by :-

[tex]n= p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]

, where p = prior population proportion.

[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex]

E= Margin of error.

As per given , we have

Confidence level : [tex]1-\alpha=0.95[/tex]

⇒[tex]\alpha=1-0.95=0.05[/tex]

Two -tailed z-value for [tex]\alpha=0.05 : z_{\alpha/2}=1.96[/tex]

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if prior estimate of proportion is unknown.]

Required sample size will be :-

[tex]n= 0.5(1-0.5)(\dfrac{1.96}{0.02})^2\\\\ 0.25(98)^2=2401[/tex]

Hence, the number of computer must be surveyed = 2401


Related Questions

Radar detectors are either powered by their own battery or plug into the cigarette lighter socket. All radar detectors come in two models: no-frills and fancy. In addition, detectors powered by their own batteries detect either radar or laser, or both, whereas the plug-in types come in models that detect either radar or laser, but not both. How many different radar detectors can you buy?

Answers

Final answer:

There are 10 different radar detectors one can buy, considering the power source, detection capabilities (radar, laser, or both), and model type (no-frills or fancy).

Explanation:

To find out how many different radar detectors one can buy, we need to consider the options presented and calculate the total number of combinations. According to the problem statement, radar detectors are powered either by their own battery or by plugging into the cigarette lighter socket. They come in two models: no-frills and fancy. Moreover, battery-powered detectors can detect either radar, laser, or both, while plug-in types can only detect either radar or laser, but not both.

Battery-powered detectors:No-frills model (detects radar) - 1 optionFancy model (detects radar) - 1 optionNo-frills model (detects laser) - 1 optionFancy model (detects laser) - 1 optionNo-frills model (detects both) - 1 optionFancy model (detects both) - 1 optionPlug-in detectors:No-frills model (detects radar) - 1 optionFancy model (detects radar) - 1 optionNo-frills model (detects laser) - 1 optionFancy model (detects laser) - 1 option

Adding these up, we get a total of 6 options for battery-powered and 4 options for plug-in detectors, making a grand total of 10 different radar detectors one can buy.

The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 23 B, and 37 C. Show the frequency and relative frequency distributions (use nearest whole number for the frequency column and 2 decimal for the relative frequency column).

Answers

Answer with explanation:

We know that in a frequency table we write the frequency corresponding to each of the data.

The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.

Here we have a total sample as: 120

Also, the frequency corresponding to A is: 60

Corresponding to B is: 23

and corresponding to C is: 37

Hence, the Frequency table is as follows:

Data               Frequency

 A                          60  

 B                           23

 C                           37

The relative frequency table is given by:

Data               Relative Frequency          

 A                      60/120=0.5

 B                       23/120=0.19  

 C                       37/120=0.31

Hence, we get:

Data               Relative Frequency          

 A                           0.5

 B                           0.19

 C                           0.31

Final answer:

The frequency distribution for the responses A, B, and C are 60, 23, and 37 respectively. The relative frequency distribution for the responses A, B, and C are 0.50, 0.19, and 0.31 respectively. Sum of the relative frequencies equals to 1, indicating all portions of the sample have been accounted for.

Explanation:Frequency and Relative Frequency Distributions

To create these distributions for the given response data, we'll organize our observations into a table.

Frequency distribution: The frequency shows the number of times each response (A, B, or C) occurs in the sample.
- Response A: 60
- Response B: 23
- Response C: 37

Adding these frequencies would equal the total sample size, 120.

Relative frequency distribution: The relative frequency is calculated as the frequency of each response divided by the total sample size, expressed as a decimal.
- Response A: 60/120 = 0.50
- Response B: 23/120 = 0.19
- Response C: 37/120 = 0.31

Note that if we add up the relative frequencies, we should get a sum of 1, indicating that we've accounted for all portions of the sample.

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In this lab you will use Excel to plot a distance x on the vertical axis and the inverse of mass m on the horizontal axis. That is, a plot of x versus 1 m . Plotted this way, the data falls on a straight line. If x is in centimeters and m is in grams, what are the units of the slope of the line?

Answers

Answer:

When you find the gradient (slope) of a graph, you divide a change of value on the vertical-axis (the 'rise') by a change of value on the horizontal axis (the 'run').  

Gradient = rise/run.  

The vertical axis has units of cm, so the rise in in cm.  

The horizontal axis has units of 1/grams = g⁻¹, so the rise is in g⁻¹.  

units for slip are  

rise/run ≡ cm/g⁻¹ ≡ cm.g

Step-by-step explanation:

Final answer:

The slope in the plotted graph in Excel is determined by the change in the vertical value ('x' - distance, in centimeters) with the change in the horizontal value ('1/m' - inverse of mass, in grams). Therefore, the unit of the slope will be grams centimeters (g.cm).

Explanation:

In this lab experiment using Excel to plot a graph, it's vital to understand the concept of slope. In a line graph, slope indicates the amount of vertical 'rise' for every unit of horizontal 'increase' and is calculated by the change in the dependent variable (in this case 'x' or distance, which is on the vertical axis) over the change in the independent variable (here, it is 1/mass or 1/m, on the horizontal axis).

Since 'x' is measured in centimeters (cm) and 'm', the mass, is measured in grams (g), when calculating the slope, we do a division of cm by the inverse of grams (1/g), which is equivalent to multiplication by its reciprocal (g/1). Therefore, the unit of the slope of the line would be g.cm, which is grams centimeters.

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A bag contains 3 red marbles, 2 blue marbles, and 2 green marbles. One marble is picked, then another marble. Assume that the selections are made with replacement. A) Find the probability of picking two red marbles with replacement. B) find the probability of picking a red marble and a blue marble. Assume the selections are made without replacement. C) Find the probability of picking two red marbles without replacement. D) find the probability of picking a red marble and a blue marble without replacement.

Answers

Answer:

A.) 3/7

B.) 5/7

C.) 2/7

D.) 2/7

Help with this math question

Rationalize the denominator or is it rationalized already ? -13/√x

Answers

Answer:

[tex]-\frac{13\sqrt{x} }{x}[/tex]

Step-by-step explanation:

We have been given the following expression;

-13/√x

In order to rationalize the denominator, we multiply the numerator and the denominator by √x;

[tex]-\frac{13}{\sqrt{x}}=-\frac{13\sqrt{x} }{\sqrt{x}\sqrt{x}}\\ \\-\frac{13\sqrt{x} }{\sqrt{x^{2} } }\\\\-\frac{13\sqrt{x} }{x}[/tex]

Final answer:

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of √x is -√x. Multiply -13/√x by -√x/-√x to get -13√x / x.

Explanation:

To rationalize the denominator, we need to eliminate the square root from the denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of √x is -√x. So, multiplying the numerator and denominator by -√x gives us:

-13/√x * (-√x)/(-√x) = 13√x/(-x) = -13√x / x

Therefore, the rationalized form of -13/√x is -13√x / x.

Problem Page
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 15% vinegar. The chef wants to make 240 milliliters of a dressing that is 13% vinegar. How much of each brand should she use?

Answers

Let [tex]x[/tex] be the amount (in mL) of the first brand (7% vinegar) and [tex]y[/tex] the amount of the second brand (15% vinegar). She wants to end up with a mixture with volume 240 mL, so that

[tex]x+y=240[/tex]

and she wants it contain 13% vinegar. Each mL of the first brand contributes 0.07 mL (i.e. 7% of 1 mL) vinegar, while each mL of the second brand contributes 0.15 mL (i.e. 15% of 1 mL). The final mixture needs to contribute 0.13 mL (i.e. 13% of 1 mL) for each mL of dressing, so that

[tex]0.07x+0.15y=0.13(x+y)=31.2[/tex]

Now solve:

[tex]x+y=240\implies y=240-x[/tex]

[tex]0.07x+0.15y=31.2\implies0.07x+0.15(240-x)=31.2[/tex]

[tex]\implies-0.08x+36=31.2[/tex]

[tex]\implies4.8=0.08x[/tex]

[tex]\implies\boxed{x=60}[/tex]

[tex]y=240-x\implies\boxed{y=180}[/tex]

The chef needs to use 60 mL of the first brand and 180 mL of the second brand.

Answer:

First brand: 60 milliliters

Second brand: 180 milliliters

Step-by-step explanation:

Let's call m the amount of the first dressing mark that contains 7% vinegar

Let's call n the amount of the second dressing mark that contains 15% vinegar

The resulting mixture should have 13% vinegar and 240 milliliters.

Then we know that the total amount of mixture will be:

[tex]m + n = 240[/tex]

Then the total amount of vinegar in the mixture will be:

[tex]0.07m + 0.15n = 0.13 * 240[/tex]

[tex]0.07m + 0.15n = 31.2[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.15 and add it to the second equation:

[tex]-0.15m -0.15n = 240 * (- 0.15)[/tex]

[tex]-0.15m -0.15n = -36[/tex]

[tex]-0.15m -0.15n = -36[/tex]

              +

[tex]0.07m + 0.15n = 31.2[/tex]

--------------------------------------

[tex]-0.08m = -4.8[/tex]

[tex]m = \frac{-4.8}{-0.08}[/tex]

[tex]m = 60\ milliliters[/tex]

We substitute the value of m into one of the two equations and solve for n.

[tex]m + n = 240[/tex]

[tex]60 + n = 240[/tex]

[tex]n = 180\ milliliters[/tex]

The life span at birth of humans has a mean of 89.87 years and a standard deviation of 16.63 years. Calculate the upper and lower bounds of an interval containing 95% of the sample mean life spans at birth based on samples of 105 people. Give your answers to 2 decimal places.

Answers

Final answer:

To calculate the 95% confidence interval for the mean life span of a sample of 105 people, use the formula Confidence interval = sample mean ± (z-score)*(standard deviation/√n). The z-score for a 95% confidence level is approximately 1.96.

Explanation:

The subject of this question is regarding statistics, specifically the calculation of confidence intervals for a sample mean. In this case, we will use the formula for a confidence interval for the mean:

Confidence interval = sample mean ± (z-score)*(standard deviation/√n)

Where the sample mean is the mean life span of humans (89.87 years), n is the sample size (105 people), the standard deviation is 16.63 years and the z-score corresponds with 95% confidence level (approximately 1.96). After performing the necessary computations:

Confidence interval = 89.87 ± (1.96 * 16.63/√105)

The final step would be calculating the upper and lower bounds by adding and subtracting the product from the mean respectively. Your results will indicate the range within which 95% of sample means of life spans at birth are expected to fall.

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Find the sum of the geometric sequence 3, 15, 75, 375, … when there are 9 terms and select the correct answer below.

a. -976,563
b. 976,563
c. 1,464,843
d. 976,562

Answers

Answer:

  c.  1,464,843

Step-by-step explanation:

The sum of n terms of a geometric sequence with first term a1 and common ratio r is given by ...

  sn = a1(r^n -1)/(r -1)

Filling in the values a1=3, r=5, n=9, we get ...

  s9 = 3(5^9 -1)/(5 -1) = 1,464,843

Answer: -976,563 PLEASE READ DESCRIPTION

Step-by-step explanation:

My question had the same exact numbers but some of them were negative! Please be sure that you have the exact same numbers as me before putting my answer!!

"Find the sum of the geometric sequence −3, 15, −75, 375, ... when there are 9 terms and select the correct answer below"

-3 X -5 = 15 X -5 = -75 X -5 = 375.

Ratio = -5

Use the formula [tex]s_{n} = \frac{a_{1 - a_1 (r)^{n} }}{1 - r}[/tex].

Our [tex]a_1[/tex] (first term) = -3, r (ratio)= -5, and n (number of terms) = 9. Knowing this, plug them into the equation.

[tex]s_9 = \frac{-3 - (-3)(-5)^9}{1-(-5)}[/tex].

First, simplify the exponent. -5 to the ninth power = -1,953,125. Multiply this by the nearest number in exponents (-3). -1,953,125 X -3 = 5,859,375. Continue simplifying your numerator. -3 - (5,859,375) = -5,859,378. Now, simplify your denominator. 1 - (-5) = 6.

Divide.

[tex]s_9 = \frac{-5,859,372}{6}[/tex] = -976,563

I tried to make sure there weren't any typos, but please comment if there's something wrong!

Please help!!!!!>>>>>>

Answers

Answer:

-3.3

Step-by-step explanation:

-2.3-(4.5-3 1/2)=-2.3-(4.5-3.5)=-2.3-(1)=-3.3

what is the solution to the equation 9^(x+1) =27

Answers

ANSWER

[tex]x = \frac{1}{2} [/tex]

EXPLANATION

The given exponential equation is

[tex] {9}^{x + 1} = 27[/tex]

The greatest common factor of 9 and 27 is 3.

We rewrite the each side of the equation to base 3.

[tex]{3}^{2(x + 1)} = {3}^{3} [/tex]

Since the bases are equal, we can equate the exponents.

[tex]2(x + 1) = 3[/tex]

Expand the parenthesis to get:

[tex]2x + 2 = 3[/tex]

Group similar terms

[tex]2x = 3 - 2[/tex]

[tex]2x = 1[/tex]

[tex]x = \frac{1}{2} [/tex]

For this case we must solve the following equation:

[tex]9 ^ {x + 1} = 27[/tex]

We rewrite:

[tex]9 = 3 * 3 = 3 ^ 2\\27 = 3 * 3 * 3 = 3 ^ 3[/tex]

Then the expression is:

[tex]3^ {2 (x + 1)} = 3 ^ 3[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

[tex]2 (x + 1) = 3[/tex]

We apply distributive property to the terms within parentheses:

[tex]2x + 2 = 3[/tex]

Subtracting 2 on both sides of the equation:

[tex]2x = 3-2\\2x = 1[/tex]

Dividing between 2 on both sides of the equation:

[tex]x = \frac {1} {2}[/tex]

Answer:

[tex]x = \frac {1} {2}[/tex]

Given that y varies directly with x in the table below, what is the value of y if the value of x is 7? x 2 4 6 10 y 12 24 36 60 37 42 48 54

Answers

Answer:

42

Step-by-step explanation:

Note that as x increases by 2 from 2 to 4, y increases by 12 from 12 to 24.  Thus, the slope of the line connecting the given points is m = rise / run = 12/2, or m = 6.  Thus, this direct proportion is written as y = 6x.

If x = 7, y = 6(7) = 42

Answer:

42

Step-by-step explanation:

g Let P be the plane that goes through the points A(1, 3, 2), B(2, 3, 0), and C(0, 5, 3). Let ` be the line through the point Q(1, 2, 0) and parallel to the line x = 5, y = 3−t, z = 6+2t. Find the (x, y, z) point of intersection of the line ` and the plane P.

Answers

Answer:

  (x, y, z) = (1, 1/3, 3 1/3)

Step-by-step explanation:

The normal to plane ABC can be found as the cross product ...

  AB×BC = (1, 0, 2)×(2, -2, -3) = (4, 1, 2)

Then the equation of the plane is ...

  4x +y +2z = 4·0 +5 +2·3 . . . . using point C to find the constant

  4x +y +2z = 11

__

The direction vector of the reference line is the vector of coefficients of t: (0, -1, 2). Then the line through point Q is ...

  (x, y, z) = (1, 2, 0) +t(0, -1, 2) = (1, 2-t, 2t)

__

The value of t that puts a point on this line in plane ABC can be found by substituting these values for x, y, and z in the plane's equation.

  4(1) +(2 -t) +2(2t) = 11

Solving for t gives ...

  t = 5/3

so the point of intersection of the plane and the line is

  (x, y, z) = (1, 2-t, 2t) = (1, 2-5/3, 2·5/3) = (1, 1/3, 3 1/3)

Two competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?

Gym B charges $1.05 less per hour than Gym A.
Gym B charges $1.50 less per hour than Gym A.
Gym B charges $5.25 less per hour than Gym A.
Gym B and Gym A charge the same hourly rate for childcare.

Answers

The answer is D. Gym B and Gym A charge the same hourly rate for childcare.

Answer:

  Gym B and Gym A charge the same hourly rate for childcare

Step-by-step explanation:

The rate of $0.75 per 5 minutes is ...

  $0.75/(5/60 h) = $0.75×12/h = $9.00/h

Gym B's hourly rate is $9.00, the same as that of Gym A.

At a local college, 102 of the male students are smokers and 408 are non-smokers. Of the female students, 240 are smokers and 360 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers? Do not round your answer.

Answers

Answer: Probability that both are non smokers is 0.48.

Step-by-step explanation:

Since we have given that

Number of male smokers = 102

Number of male non smokers = 408

Total male = 102+408=510

Number of female smokers = 240

Number of female non smokers = 360

Total female = 240+360 = 600

According to question,

A male student and a female student from the college are randomly selected for a survey,

So, Probability that both are non smokers is given by

P(both are smokers ) = P(Male smoker) × P(female smoker)

[tex]P(both)=\dfrac{360}{600}\times \dfrac{408}{510}\\\\P(both)=\dfrac{146880}{306000}\\\\P(both)=0.48[/tex]

Hence, probability that both are non smokers is 0.48.

Final answer:

The probability that both the randomly selected male and female students from the college are non-smokers is 0.48.

Explanation:

To compute the probability that both the randomly selected male and female students are non-smokers, we start by finding the total number of male and female students. The total number of male students is 510 (102 smokers + 408 non-smokers), and the total number of female students is 600 (240 smokers + 360 non-smokers). Then, we calculate the individual probabilities of selecting a non-smoking male and a non-smoking female. The probability of selecting a non-smoking male is 408 / 510, and the probability of selecting a non-smoking female is 360 / 600.

To find the combined probability, we multiply these individual probabilities. So, the probability that both the male and the female students selected are non-smokers, is (408 / 510) * (360 / 600) = 0.8 * 0.6 = 0.48.

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Use Fermat's Little Theorem to determine 7^542 mod 13.

Answers

[tex]a^{p-1} \equiv 1 \pmod p[/tex] where [tex]p[/tex] is prime, [tex]a\in\mathbb{Z}[/tex] and [tex]a[/tex] is not divisible by [tex]p[/tex].

[tex]7^{13-1}\equiv 1 \pmod {13}\\7^{12}\equiv 1 \pmod {13}\\\\542=45\cdot12+2\\\\7^{45\cdot 12}\equiv 1 \pmod {13}\\7^{45\cdot 12+2}\equiv 7^2 \pmod {13}\\7^{542}\equiv 49 \pmod{13}[/tex]

Answer:

49 mod 13 = 10.

Step-by-step explanation:

Fermat's little theorem states that

x^p = x mod p where p is a prime number.

Note that 542 = 41*13 + 9 so

7^542 = 7^(41*13 + 9)  = 7^9 * (7^41))^13

By FLT (7^41)^13 = 7^41 mod 13

So 7^542 = ( 7^9 *  7(41)^13) mod 13

= (7^9 * 7^41) mod 13

= 7^50 mod 13

Now we apply FLT to this:

50 = 3*13 + 11

In a similar method to the above we get

7^50 = (7^11 * (7^3))13)  mod 13

=  (7^11 * 7^3) mod 13

= (7 * 7^13) mod 13

= ( 7* 7) mod 13

= 49 mod 13

= 10 (answer).

solve 8 + 5^x = 1008. Round to the nearest ten-thousandth.

Answers

Answer: 4.29203

Explanation:

5^x=1008-8

5^x=1000

take the log of both sides

x=3 log 5 (10)

x=3+3log5(2)

or 4.29203

For this case we must solve the following equation:

[tex]8 + 5 ^ x = 1008[/tex]

Subtracting 8 on both sides of the equation:

[tex]5 ^ x = 1008-8\\5 ^ x = 1000[/tex]

We apply Neperian logarithm to both sides of the equation:

[tex]ln (5 ^ x) = ln (1000)[/tex]

We use the rules of the logarithms to draw x

of the exponent.

[tex]xln (5) = ln (1000)[/tex]

We divide both sides of the equation between[tex]ln (5)[/tex]:

[tex]x = \frac {ln (1000)} {ln (5)}\\x = 4.29202967[/tex]

Rounding:

[tex]x = 4.2920[/tex]

Answer:

[tex]x = 4.2920[/tex]

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2 + yy0 b2 + zz0 c2 = 1 Find the equation of the tangent plane to the hyperboloid x2/a2 + y2/b2 − z2/c2 = 1 at (x0, y0, z0) and express it in a form similar to the one for the ellipsoid.

Answers

The equation of the tangent plane to the ellipsoid at the given point is [tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} - \frac{zz^0}{c^2} = 1[/tex]

The equation of the tangent plane to the ellipsoid is given as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1[/tex]

The point on the ellipsoid is given as:

(x0, y0, z0)

The equation of the tangent plane to the ellipsoid at the given point can be written as:

[tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} + \frac{zz^0}{c^2} = 1[/tex]

Given that the equation of the tangent plane to the hyperboloid is

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} = 1[/tex]

The equations at the tangents of the ellipsoid and the hyperboloid take the same form.

So, the equation of the tangent plane to the ellipsoid at the given point is [tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} - \frac{zz^0}{c^2} = 1[/tex]

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Find the twenty-fifth term of an arithmetic sequence if the first term is-1 and the common difference is 5. Write the first three terms of an arithmetic sequence in which the twenty-first term is 17 and the fiftieth term is 75. 10. 11

Answers

Final answer:

The twenty-fifth term of the arithmetic sequence is 119. The first three terms of another arithmetic sequence are 17, 19, 21.

Explanation:

To find the twenty-fifth term of an arithmetic sequence, we can use the formula:
nth term = first term + (n-1) * common difference

Substituting the given values:
nth term = -1 + (25-1) * 5 = -1 + 24 * 5 = -1 + 120 = 119

Therefore, the twenty-fifth term of the arithmetic sequence is 119.

For the second part of the question, to find the common difference, we can use the formula:
common difference = (fiftieth term - twenty-first term) / (50 - 21)

Substituting the given values:
common difference = (75 - 17) / (50 - 21) = 58 / 29 = 2

Using the first term of 17 and the common difference of 2, we can write the first three terms of the arithmetic sequence:
17, 19, 21

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at General Electric selects every 20th refrigerator that comes off the assembly line starting with the sixth until she obtains a sample of 130 refrigerators. What type of sampling is used? (a) Simple random (b) Systematic (c) Cluster (d)Convenience (e) Stratified

Answers

Answer:  (b) Systematic

Step-by-step explanation:

A systematic random sampling is kind of sampling method in which samples are chosen from a larger population based on a random beginning point that has a definite and periodic interval.

Given statement : To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at General Electric selects every 20th refrigerator that comes off the assembly line starting with the sixth until she obtains a sample of 130 refrigerators.

Periodic interval : Every 20th

Beginning point : 6th

Sample size : 130

Hence, this type of sampling is a systematic random sampling.

Final answer:

The type of sampling used by the General Electric quality control manager is systematic sampling. This method involves selecting subjects at fixed regular intervals, providing a balance between bias and needed sample size.

Explanation:

The quality control manager at General Electric is using systematic sampling to estimate the percentage of defects in a recent manufacturing batch. Systematic sampling involves selecting subjects at regular intervals from the population, in this case, every 20th refrigerator starting with the sixth one to achieve a sample of 130 refrigerators. This type of sampling is situated between other sampling methods such as random sampling and judgmental sampling in terms of bias and sample size needed to characterize the population adequately.

When considering the provided exercises, the answers to the type of sampling used would be:

   

Q1. Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. What is the standard error of the distribution of the sample proportions? Round your answer to three decimal places.

Answers

Answer: 0.030

Step-by-step explanation:

Given: The percent of the items produced by a machine are defective  :[tex]P=10\%=0.10[/tex]

The percent of the items produced by machine which are not defective:[tex]Q=1-0.1=0.9[/tex]

Sample size : n = 100

Now, the standard error of the proportion is given by :-

[tex]\text{S.E.}=\sqrt{\dfrac{0.1\times0.9}{100}}\\\\\Rightarrow\text{S.E.}=0.030[/tex]

Hence, the the standard error of the distribution of the sample proportions=0.030

Final answer:

The standard error for the distribution of sample proportions of a machine producing 10% defective items determined from a random sample of 100 items is ±0.030.

Explanation:

Ten percent of the items produced by a machine are defective. From a random sample of 100 items, the standard error of the sample proportions is calculated using the formula for the standard error of a proportion, which is √(pq/n), where p is the proportion of successes, q is the proportion of failures (1-p), and n is the sample size.

In this case, p is 0.10 (the proportion defective), q is 0.90 (1-p, representing the proportion not defective), and n is 100 (the sample size). Substituting these values into the formula gives: √[(0.10)(0.90) / 100] which equals ±0.030 (rounded to three decimal places).

Therefore, the standard error for the distribution of sample proportions is ±0.030.

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Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.

Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)

Answers

Answer:

y = 85x + 55

Step-by-step explanation:

If we use the given prices as coordinates we will get the coordinates (2, 225) and (5, 480) and if we use the rise over run which in this case is 255/3 then we get the slope which is $85 and now we plug what we know into y = mx + b. we now have the equation 225 = (85)2 + b which can be simplified to 55 = b and now we can create the equation y = 85x + 55.

Hope this helps and please mark brainliest :)

In a lottery game, a player picks six numbers from 1 to 48. If 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?

Answers

[tex]|\Omega|={_{48}C_6}=\dfrac{48!}{6!42!}=\dfrac{43\cdot44\cdot45\cdot46\cdot47\cdot48}{720}=12271512\\|A|={_6C_4}=\dfrac{6!}{4!2!}=\dfrac{5\cdot6}{2}=15\\\\P(A)=\dfrac{15}{12271512}=\dfrac{5}{4090504}\approx1.2\%[/tex]

The probability that the player wins the prize from a drawn of six in 1 to 48 numbers is 0.001052.

Probability is usually expressed as the number of favorable outcomes divided by the number of desired outcomes.

Mathematically;

Probability of winning = [tex]\mathbf{\dfrac{favorable \ outcomes}{number \ of \ desired \ outcomes}}[/tex]

The probability that the player wins can be computed by taking the following combinations.

From the given information;

the number of ways in which 4 winning numbers can be selected out of six = [tex]\mathbf{^6C_4}[/tex]

the number of ways in which 2 non-winning numbers can be selected out of the 42 non-winning numbers i.e (48 - 6 = 42 ) = [tex]\mathbf{^{42}C_2}[/tex]

the number of ways to pick 6 numbers out of 48 = [tex]\mathbf{^{48}C_6}[/tex]

Thus, the probability of winning can now be computed as:

[tex]\mathbf{P(winning \ prize) = \dfrac{^6C_4 \times ^{42}C_2}{^{48}C_6}}[/tex]

[tex]\mathbf{P(winning \ prize) = \dfrac{\Big (\dfrac{6!}{4!(6-4)!} \Big )\times \Big (\dfrac{42!}{2!(42-2)!} \Big )}{\Big (\dfrac{48!}{6!(48-6)!} \Big )}}[/tex]

[tex]\mathbf{P(winning \ prize) = \dfrac{12915}{12271512}}[/tex]

[tex]\mathbf{P(winning \ prize) =0.001052}[/tex]

Therefore, the probability that the player wins the prize from a drawn of six in 1 to 48 numbers is 0.001052.

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f(x)= x-2/ x-4

Graph this equation and identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote.

Answers

Answer:

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵ [tex]f(x)=\frac{x-2}{x-4}[/tex]

- To find the point of discontinuity put the denominator = 0 and find

 the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

 and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

   equal to 0

There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes  

  of the denominator of the function

∵ The zero of the denominator is x = 4

The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

 intersection points between the graph and the x-axis

∵ f(x) = 0

∴ [tex]\frac{x-2}{x-4}=0[/tex] ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

 denominator, then the equation of the horizontal asymptote is

 y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

Determine whether the pair of triangles is congruent. If yes, include the theorem or postulate that applies.

Question 6 options:


yes; The triangles are congruent by hypotenuse-angle congruence.


yes; The triangles are congruent by leg-leg congruence.


no; The triangles are not congruent.


There is not enough information to determine congruency.

---------------------------------------------------------------------

Determine whether the pair of triangles is congruent. If yes, include the theorem or postulate that applies.


Question 9 options:


yes; The triangles are congruent by hypotenuse-angle congruence.


yes; The triangles are congruent by hypotenuse-leg congruence.


no; The triangles are not congruent.


there is not enough information to determine congruency.


ANSWER IN 5 MINUTES TO RECEIVE BRAINLIEST.

Answers

Answer:

Question 6

There is not enough information to determine congruency

Question 9

yes; The triangles are congruent by hypotenuse-leg congruence

Step-by-step explanation:

* Lets revise the cases of congruence  

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles  

 and one side in the 2ndΔ

- HL ⇒ hypotenuse - leg of the first right angle triangle ≅ hypotenuse

 - leg of the 2nd right angle Δ

- HA ⇒ hypotenuse - angle of the first right angle triangle ≅ hypotenuse

 - angle of the 2nd right angle Δ

- LL ⇒ leg - leg of the first right angle triangle ≅ leg - leg of the

 2nd right angle Δ

* Now lets solve the problem

# Question 6

- There are two right angle triangles

- They have two different legs

- There is no mention abut legs equal each other

- There is no mention about hypotenuses equal each other

- There is no mention about acute angels equal each other

∴ There is not enough information to determine congruency

# Question 9

- There are two right angle triangles

- Their hypotenuse is common

- There are two corresponding legs are equal

∵ The hypotenuse is a common in the two right triangles

∵ Two corresponding legs are equal

- By using hypotenuse-leg congruence

∴ yes; The triangles are congruent by hypotenuse-leg congruence

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 10x − 24, y = 0; about the x-axis

Answers

The volume of the solid is (81π - 128)/3 cubic units, found by integrating the volume of washer-shaped slices.

Sure, here is the step-by-step calculation of the volume V of the solid formed by rotating the region bounded by the curves y = −[tex]x^2[/tex] + 10x − 16, y = 0, about the x-axis:

Find the x-intercepts.

Set the two equations equal to each other to find the x-coordinates of the points of intersection:

[tex]-x^2 + 10x -16 = 0[/tex]

Factor the expression:

(x - 2)(x - 8) = 0

Therefore, the x-intercepts are x = 2 and x = 8.

Sketch the curves and the axis of rotation.

On a coordinate plane, graph the parabola y = −[tex]x^2[/tex] + 10x − 16 and the line y = 0. The x-axis is the axis of rotation.

Imagine the solid of revolution.

When the shaded region between the parabola and the x-axis is rotated about the x-axis, it forms a solid of revolution. This solid can be imagined as a collection of thin slices.

Consider one such slice.

Take a thin slice of the solid perpendicular to the x-axis. The slice is a cylinder with a hole in the middle, much like a washer. Let the thickness of the slice be dx and let the radius of the washer, as a function of x, be r(x).

Express the volume of the slice as a washer.

The volume of the washer is the difference between the volume of the larger cylinder and the volume of the smaller cylinder inside it. The volume of a cylinder is π[tex]r^2[/tex]h, where r is the radius and h is the height. In this case, the height of each cylinder is dx.

Therefore, the volume of the washer is:

π[([tex]r(x))^2 - (r'(x))^2[/tex])] dx

Express the radius as a function of x.

The radius of the washer is equal to the distance between the parabola and the x-axis. In other words, for any x-value, r(x) = −[tex]x^2[/tex] + 10x − 16.

Set up the definite integral.

To find the total volume of the solid, we need to sum the volumes of infinitely many such washers as the thickness dx approaches zero. This is done using a definite integral:

[tex]\int _a^b \pi[(r(x))^2 - (r'(x))^2] dx[/tex]

where a and b are the x-coordinates of the endpoints of the region. In this case, a = 2 and b = 8.

Differentiate r(x) to find r'(x).

r'(x) = -2x + 10

Evaluate the definite integral.

[tex]\int_2^8 \pi[(-x^2 + 10x - 16)^2 - (-2x + 10)^2] dx[/tex]

This integral can be evaluated using integration by parts or a computer algebra system. The result is:

(81π - 128)/3

Therefore, the volume V of the solid is (81π - 128)/3 cubic units.

Question:

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −[tex]x^2[/tex] + 10x − 16,    y =0;  about the x-axis.

The length of time for one individual to be erved at a cafeteria is a random variable having an ex- ponential distribution with a mean of 4 minutes. What is the probability that a person will be served in less than/3 minutes on at least 4 of the next 6 days?

Answers

Answer:

less than 3

Step-by-step explanation:

Find the geometric means in the following sequence. –6, ? , ? , ? , ? , –1,458?

Answers

Answer:

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374

Step-by-step explanation:

It is given a geometric sequence,

–6, ? , ? , ? , ? , –1,458?

From the given sequence we get first term a₁ = -6 and 6th term a₆ = -1458

To find the common ratio 'r'

6th term can be written as

a₆ = ar⁽⁶ ⁻ ¹⁾

-1458 = 6 * r⁽⁶⁻¹⁾

r⁵ = -1458/-6 = 243

r = ⁵√243 = 3

To find the sequence

We have a = -6, r = 3

a₂ = -6 * 3 = -18

a₃ = a₂*3 = -18* 3 = -54

a₄  = a₃*3 = -54 * 3 = -162

a₅ = a₄*3 = -162* 3 = -486

a₆ = - 1458

a₇ = a₂*3 =-1458 * 3= -4374

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374

Compute the value of the following improper integral if it converges. If it diverges, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise (hint: integrate by parts). ∫∞18ln(x)x2dx Determine whether ∑n=1∞(8ln(n)n2) is a convergent series. Enter C if the series is convergent, or D if it is divergent.

Answers

Answer:

INF for first while D for second

Step-by-step explanation:

Ok I think I read that integral with lower limit 1 and upper limit infinity

where the integrand is ln(x)*x^2

integrate(ln(x)*x^2)

=x^3/3 *ln(x)- integrate(x^3/3 *1/x)

Let's simplify

=x^3/3 *ln(x)-integrate(x^2/3)

=x^3/3*ln(x)-1/3*x^3/3

=x^3/3* ln(x)-x^3/9+C

Now apply the limits of integration where z goes to infinity

[z^3/3*ln(z)-z^3/9]-[1^3/3*ln(1)-1^3/9]

[z^3/3*ln(z)-z^3/9]- (1/9)

focuse on the part involving z... for now

z^3/9[ 3ln(z)-1]

Both parts are getting positive large for positive large values of z

So the integral diverges to infinity (INF)

By the integral test... the sum also diverges (D)

Final answer:

To compute the value of the improper integral, we can integrate by parts. Using the formula for integration by parts, we find that the integral converges to a finite value of -ln(x)/x as x approaches infinity.

Explanation:

To compute the value of the improper integral ∫∞18ln(x)/x2dx, we can integrate by parts. Let u = ln(x) and dv = 1/x2dx. Differentiating u with respect to x gives du = 1/x dx and integrating dv gives v = -1/x. Applying the formula for integration by parts, we get:

∫∞18ln(x)/x2dx = -ln(x)/x + ∫∞181/x2dx.

Simplifying the integral, we have:

∫∞181/x2dx = -1/x

As x approaches infinity, 1/x approaches 0. Therefore, the improper integral converges to a finite value of -ln(x)/x.

Refer to Interactive Solution 17.45 to review a method by which this problem can be solved. The fundamental frequencies of two air columns are the same. Column A is open at both ends, while column B is open at only one end. The length of column A is 0.504 m. What is the length of column B?

Answers

Answer:

  0.252 m

Step-by-step explanation:

At the fundamental frequency, a closed-end column has the same wavelength as an open-end column twice as long. Column B only needs to be half the length of Column A:

  0.504 m/2 = 0.252 m

Video Planet (VP) sells a big screen TV package consisting of a 60-inch plasma TV, a universal remote, and on-site installation by VP staff. The installation includes programming the remote to have the TV interface with other parts of the customer’s home entertainment system. VP concludes that the TV, remote, and installation service are separate performance obligations. VP sells the 60-inch TV separately for $1,500, sells the remote separately for $200, and offers the installation service separately for $300. The entire package sells for $1,900.How much revenue would be allocated to the TV, the remote, and the installation service?

Answers

Answer:

TV: $1425Remote: $190Installation: $285

Step-by-step explanation:

The combined price of the separate obligations is $2000, so the package price is 1900/2000 = 0.95 of the total of separate items. We assume the allocation matches that proportion, so the allocations are ...

  TV: 0.95×$1500 = $1425

  remote: 0.95×$200 = $190

  installation: 0.95×$300 = $285

The revenue that would be allocated to the TV, the remote, and the installation service are;

New revenue for TV = $1425

New revenue for remote = $190

New revenue for installation= $285

We are given the cost for individual obligations as;

Cost of 60-inch TV = $1,500

Cost of remote = $200

Installation service cost = $300

Total revenue to be generated when they pay individually = 1500 + 200 + 300 = $2000

Now, we are told that the entire package when done together instead of individually will generate a revenue of $1,900 when sold.

This means, the discount here is; 1900/2000 × 100 = 95% or 0.95

Now, based on this discount of 95%, we can calculate the revenue that will be generated from amount allocated to each obligation based on the entire package deal;

New revenue for TV: 0.95 × $1500 = $1425

New revenue for remote: 0.95 × $200 = $190

New revenue for installation: 0.95 × $300 = $285

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