Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent​ switches, each one set on or off. The receiver​ (wired to the​ door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches​ independently, what is the probability of at least one pair of neighbors using the same​ settings?

Answer:

We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Step-by-step explanation:

We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.

We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Let p = proportion of Americans who only use their cell phones to access the internet

SO, Null Hypothesis, [tex]H_0[/tex] : p = 38%  {means that the proportion of Americans who only use their cell phones to access the internet is same as that of Chinese proportion of 38%}

Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 38%  {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}

The test statistics that will be used here is One-sample z proportion statistics;

                 T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of cell phone owners who browse the internet

                 exclusively on their phone in a survey of 2,254 adults = 17%

          n  = sample of adults = 2,254

So, test statistics = [tex]\frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }[/tex]

                            = -26.542

Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.

Answer:

40

Step-by-step explanation:

8*5

Answer:

Step-by-step explanation:

The set that represents the notation Ø is E ∩ O

Venn diagrams are used to represent sets and the relationship between them using diagrams

The sets are given as:

O = Odd

E = Even

P = Prime

The notation Ø represents an empty set.

In the number system, a number cannot be even and odd at the same time

Hence, the set that represents Ø is E ∩ O

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Answer:

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

Step-by-step explanation:

Data provided

[tex]\bar X=9797[/tex] represent the sample mean for the steps

[tex]\mu[/tex] population mean

s=2313 represent the sample standard deviation

n=61 represent the sample size  

Solution

The confidence interval for the true population mean is given by :

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:

[tex]df=n-1=61-1=60[/tex]

The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]

Now we have everything in order to replace into formula (1):

[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]    

[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]    

And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57

90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.

To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:

Confidence Interval = X ± Z * (σ/√n)

Where:

X is the sample mean (9,797 steps).

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).

σ is the population standard deviation (2,313 steps).

n is the sample size (61).

Now, let's plug in the values and calculate the confidence interval:

Z for a 90% confidence level is approximately 1.645.

Confidence Interval = 9,797 ± 1.645 * (2,313/√61)

Confidence Interval = 9,797 ± 1.645 * (299.98)

Confidence Interval ≈ 9,797 ± 494.06

Now, calculate the lower and upper bounds of the confidence interval

Lower Bound = 9,797 - 494.06 ≈ 9,302.94

Upper Bound = 9,797 + 494.06 ≈ 10,291.06

Interpretation:

We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.

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Answer:

You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times of the year show an increase in the sales of outdoor soccer shoes.

Step-by-step explanation:

Answer:

Subtract 9 I agree with the 1st question but can you help me back just comment if you wanna

Answer:

  f(r) = (x -1)(x -4+√7)(x -4-√7)

Step-by-step explanation:

The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.

The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.

Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:

  r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7

This is zero when ...

  (r -4)^2 = 7

  r -4 = ±√7

  r = 4±√7

Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...

  f(r) = (r -1)(r -4 -√7)(r -4 +√7)

_____

Comment on the graph

I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)

Answer:

49.4 km

Step-by-step explanation:

you add 27.54 plus 21.86 so 49.4 km total between school and to your friends house

You drive a total distance of 49.4 kilometers when you travel 27.54 kilometers to school and then 21.86 kilometers to your friend's house.

When you drive 27.54 km to school and then 21.86 km to your friend's place, you are covering a total distance of 49.4 kilometers. To calculate this, you simply add the two distances together:

Distance to school: 27.54 km

Distance to friend's place: 21.86 km

Total distance = 27.54 km + 21.86 km = 49.4 km

So, you drive a total of 49.4 kilometers when you travel to both school and your friend's house. This cumulative distance is the sum of the individual distances you cover for each leg of your journey. It's important to keep track of such distances, especially if you want to estimate fuel consumption, plan your commute, or calculate travel time accurately. In this case, you've covered 49.4 kilometers in total, which is the combined distance for your trip.

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Answer:

[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]

Step-by-step explanation:

Here is one example:

[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]

[tex]\sin 0.5x \cdot \cos 0.5x + \cos 0.5x\cdot \sin 0.5x[/tex]

[tex]\sin (0.5x + 0.5x)[/tex]

[tex]\sin x[/tex]

Answer:

No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed

Completed question;

Max travels to see his brother's family by car. He drives 216 miles in 4 hours. What is his rate in miles per hour? Suppose he makes two stops of 10 minutes each during his journey. Will he be able to reach the town in 4 hours if he keeps the speed the same?

Step-by-step explanation:

Average speed = total distance travelled/time taken

Given;

Total distance travelled= 216 miles

Total time taken = 4 hours

Average speed v = 216/4 = 54 miles per hour

v = 54 mph

Suppose he makes two stops of 10 minutes each during his journey.

Total time on stops = 2 × 10 = 20 minutes = 0.33 hours

Total time spent on motion = 4 - 0.33 hours = 3.67 hours

Total distance covered in 4 hours with two stops;

d = 3.67 × 54 mph = 198.18 miles

Since d < 216 miles

No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed

Answer:

25

Step-by-step explanation:

Answer:

72 degrees

Step-by-step explanation:

We need to know the total circumference in order to determine the arc measure for ABC before we figure out AC

Circumference   =2πr   →  =2π(10)   →   =20π

We know the length of ABC

so we set up a proportion to figure out its arc measure.

arc length/ circumference = arc measure/ degrees in a circle

16π/ 20π = arc measure/ 360 degrees

arc measure= 360 x 16π/ 20π =228 degrees

The arc measure of ABC is 228 degrees

If we combine the major arc ABC, and the minor arc AC we have the entire circle.

288 degrees  +m  AC= 360

m  AC= 72 degrees

The measure of AC is 72 degrees

(i got the explanation off of Klan Academy when i answered the question)

Answer:

a) P=0.091

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but it is still possible that there are 6 of each taste.

c) The probability of picking 4 vainilla in a row, if there are half of each taste, is P=0.030.

This is a very improbable case, so if this happens we would have reasons to think that there are more than half vainilla candies in the box.

Step-by-step explanation:

We can model this problem with the variable x: number of picked vainilla in a row, following a hypergeometric distribution:

[tex]P(x=k)=\dfrac{\binom{K}{k}\cdot \binom{N-K}{n-k}}{\binom{N}{n}}[/tex]

being:

N is the population size (12 candies),

K is the number of success states in the population (6 vainilla candies),

n is the number of draws (3 in point a, 4 in point c),

k is the number of observed successes (3 in point a, 4 in point c),

a) We can calculate this as:

[tex]P(x=3)=\dfrac{\binom{6}{3}\cdot \binom{12-6}{3-3}}{\binom{12}{3}}=\dfrac{\binom{6}{3}\cdot \binom{6}{0}}{\binom{12}{3}}=\dfrac{20\cdot 1}{220}=0.091[/tex]

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but is possible.

c) In the case k=4, we have:

[tex]P(x=3)=\dfrac{\binom{6}{4}\cdot \binom{6}{0}}{\binom{12}{4}}=\dfrac{15\cdot 1}{495}=0.030[/tex]

This is a very improbable case, so we would have reasons to think that there are more than half vainilla candies in the box.

Using the hypergeometric distribution, it is found that:

The candies are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Item a:

The probability that you would have picked three vanillas in a row is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,12,3,6) = \frac{C_{6,3}C_{6,0}}{C_{12,3}} = 0.0909[/tex]

0.0909 = 9.09% probability that you would have picked three vanillas in a row.

Item b:

The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.

Item c:

Now n = 4, and the probability is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,12,4,6) = \frac{C_{6,4}C_{6,0}}{C_{12,4}} = 0.0303[/tex]

The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.

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Answer:

  c. A line of credit against which additional debt may be drawn

Step-by-step explanation:

A line of credit is "open" if there are no specific payoff requirements (except perhaps a minimum payment according to the balance). There is usually a limit to the available credit, but as long as the amount borrowed is less than that limit, additional funds may be borrowed at any time.

A credit card is an example of an open line of credit.

Answer:

Step-by-step explanation:

1.

1/4 cup x 13 and 1/2 cup x 1

2.

1/2 cup x 7 1/4 cup x 1

The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.

Step-by-step explanation:

The given is,

               Radius of pentagon - 7 cm

Step:1

              Ref the attachment,

              The pentagon contain 10 right angled triangle.

                        Angle of Right angle triangle = [tex]\frac{360}{10}[/tex] = 36°        

              From the right angle OPQ triangle,

                                        sin ∅ = [tex]\frac{Opp}{Hyp}[/tex]

              Where,  ∅ = 36°  

                          Radius = Hyp = 7 cm

              Trigonometric ratio becomes,

                                 sin 36° = [tex]\frac{b}{7}[/tex]          

                                0.5878 = [tex]\frac{b}{7}[/tex]                  (∵ sin 36° = 0.5878 )

                                           b = ( 0.5878 × 7 )

                                           b = 4.115 cm

                From the right angle OPQ triangle,

                                    cos ∅ = [tex]\frac{Adj}{Hyp}[/tex]

                Where, Adj = h

                                   cos 36° = [tex]\frac{h}{7}[/tex]

                                0.809017 = [tex]\frac{h}{7}[/tex]

                                              h = ( 0.809017 × 7 )

                                              h = 5.663 cm

Step:2

                Area of triangle OPR,

                                             [tex]A = \frac{1}{2} (Height )(Base)[/tex]

              Where, Height, h = 5.663 cm

                                  Base = b + c = 4.115 + 4.115 = 8.23 cm

              Area of OPQ becomes,

                                       A = [tex]\frac{1}{2}[/tex] (8.23)(5.663)

                                          =  [tex]\frac{1}{2}[/tex] ( 46.6065)

                                     A = 23.30324 squared centimeters

Step:3

              Pentagon contain 5 triangles,

                         Area of pentagon = 5 × Area of triangle

                                                        = 5 × 23.30324

                                                        = 116.516 squared centimeters

                        Area of pentagon = 116.516 squared centimeters

Result:

          The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.

Answer:

Step-by-step explanation:

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . false

There is no value of x that will make this true, hence NO SOLUTION.

_____

Comment on the other choices

3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.

Answer:

Answer:

  15

Step-by-step explanation:

Tangents to the circle from the same point are the same length. Then rn = 7, and nt = 10. This means mt = 10, so ...

  st = sm +mt = 5 +10

  sm = 15

Answer:

D

Step-by-step explanation:

if m increases n increases too and vice versa

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Answer 98x1.10 =107.8

Step-by-step explanation:

Answer:

107.80

Step-by-step explanation:

98*.10+=107.80

Answer:

The treasure is hidden under 95.

Step-by-step explanation:

The numbers are:

[tex]1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\\21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40\\41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60\\61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80\\81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,100[/tex]

Clue A:Start at 3. The rule is: Subtract 2, and then add 5.

3-2+5=6

6-2+5=9

Therefore, this rule eliminates all multiples of 3.

[tex]1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20\\22, 23, 25,26, 28, 29, 31, 32, 34, 35, 37, 38, 40\\41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, \\61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80\\82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100[/tex]

Clue B:Start at 2. The rule is: Add 6.

The numbers are:2,8,14,...

We have left:

[tex]1, 4, 5, 7, 10, 11, 13, 16, 17, 19, \\22, 23, 25, 28, 29, 31, 34, 35, 37, 40\\41, 43, 46, 47, 49, 52, 53, 55, 58, 59, \\61, 64, 65, 67, 70, 71, 73, 76, 77, 79, \\82, 83, 85, 88, 89, 91, 94, 95, 97, 100[/tex]

Clue C: Start at 5. The rule is: Add 12.

The numbers are: 5,17,29,...

We have left:

[tex]1, 4, 7, 10, 11, 13, 16, 19, \\22, 23, 25, 28, 31, 34, 35, 37, 40\\ 43, 46, 47, 49, 52, 55, 58, 59, \\61, 64, 67, 70, 71, 73, 76, 79, \\82, 83, 85, 88, 91, 94, 95, 97, 100[/tex]

Clue D: Start at 83. The rule is: Subtract 12.

The numbers are 83,71,59,...

We have left:

[tex]1, 4, 7, 10, 13, 16, 19, \\22, 25, 28, 31, 34, 37, 40\\ 43, 46, 49, 52, 55, 58, \\61, 64, 67, 70, 73, 76, 79, \\82, 85, 88, 91, 94, 95, 97, 100[/tex]

Clue E: Start at 1. The rule is: Add 3.

The numbers are 1,4,7,...

We are left with:

[tex]95[/tex]

The treasure is hidden under 95.

Answer:1968ft^2

Step-by-step explanation:

Perimeter(p)=178feet

P=2L+2w

178=2L+2w

178=2(L+w)

L+w=178 ➗ 2

L+w=89.............(1)

W+7=L

L-w=7...................(11)

L+w=89... ..........(1)

L-w=7...................(11)

Subtract (11) from (1)

2w=89-7

2w=82

w=82 ➗ 2

w=41 width=41feet

Substitute w=41 in (11)

L-w=7

L-41=7

L=7+41

L=48feet

Area= length x width

Area=48 x 41

Area=1968ft^2

The area of the garden is 1968 square feet by setting up and solving equations based on the information about the garden's length, width, and perimeter.

The problem is asking for the area of a rectangular garden where the length is 7 feet longer than its width. We also know the perimeter of the garden is 178 feet. Normally in a rectangle, the formula for the perimeter is P = 2(length + width).

Since the length is 7 feet longer, let's denote the width as 'w' and therefore the length as 'w+7'. Substituting in the perimeter formula we get: 178 = 2(w + w + 7).

By simplifying and solving the equation we find that the width, w = 41 feet. Therefore, the length is w+7 = 48 feet.

Lastly, the area of a rectangle is calculated as length * width, so substituting the values we found we get the area = 48 feet * 41 feet = 1968 square feet.

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Answer:

r = 12.6, j = 16.6, n = 37.8

Step-by-step explanation:

Set up your system of equations:

j = 4 +r

n = 3r

67 = j + n + r

Plug in the first two to get down to just r so that you can solve:

67 = (4 + r) + 3r + r

67 = 5r + 4

63 = 5r

12.6 = r

Plug in r value into the other two equations above to get j and n:

j = 4 + 12.6 = 16.6

n = 3(12.6) = 37.8

Hope this helps!

Answer:

160°

Step-by-step explanation:

∠C and ∠D are both inscribed angles of arc AB.  Therefore, they are equal.

5w + 20 = 7w − 4

24 = 2w

w = 12

Therefore, ∠C = ∠D = 80°.

Inscribed angles are half the central angle, so mAB = 2 × 80° = 160°.

Answer:

a) y-intercept = 2.59

b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Step-by-step explanation:

(a) What is the y-intercept of the regression line? (Use 2 decimal places)

The given regression equation is

y = 2.59 + 0.0126x

The standard form of the regression equation is given by

y = a + bx

Where a is the y-intercept of the regression line and b is the slope of the regression line.

Comparing the given equation with the standard form,

y-intercept = 2.59

(b) What is the correct interpretation of the y-intercept?

The y-intercept is the value we get when x = 0

y = 2.59 + 0.0126(0)

y = 2.59 + 0

y = 2.59 minutes

Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.

Answer:

Step-by-step explanation:

Hello!

You have the information about the number of red lights a commuter pass on her way to work and the probability of them stoping her:

Be x: number of red lights

X: 0,         1,        2,       3,      4,      5

hi: 0.05, 0.25, 0.30, 0.20, 0.15, 0.05

a. What is the expected number of red lights at which she will stop on her way to work?

The expected number of red lights is the sample mean, you can calculate it using the following formula:

[tex]X[bar]= sum Xi*hi= (0*0.05)+(1*0.25)+(2*0.30)+(3*0.20)+*(4*0.15)+(5*0.05)=2.3[/tex]

She's expected to be stopped by 2.3 red lights on the way to work.

b. Suppose each red light delays the commuter 1.8min. What is the standard deviation od the number of minutes that she is delayed by red lights?

If each light delays the commuter 1.8 min then you can determine a new variable of interest:

Be Y: the time a commuter is delayed by red lights on the way work, then Y= X*1.8min

Meaning if X= 0, then Y=0 (the commuter will be delayed 0 min), if X=1, then Y= 1.8min, if X=2, then Y= 3.6min and to on....

The properties of variance state that if

Y= X*k (Where K= constant)

Then the sample variance of Y will be

V(Y)= V(X*k)= k²*V(X)

Then the standard deviation of Y will be the constant k by the standard deviation of X:

Sy= k*Sx= 1.8 * 1.27= 2.286

I hope it helps!

Answer:

D

Step-by-step explanation:

hope I was correct

To get the average he should add the three numbers and divide by 3.

The mean of a group of numbers is the average of the numbers. It is given by:

Average = (sum of all numbers) / total number of numbers

From the dot plot:

Average = (1 * 0 + 1 * 0.5 + 1 * 4) / 3 = 1.5

To get the average he should add the three numbers and divide by 3.

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OK, let's try with no figure.  We have an isosceles triangle sides s,s, and b.

Opposite b is angle t.

Draw the altitude h to bisect t.  We have two right triangles, legs b/2 and h, hypotenuse s.  The angle opposite b/2 is t/2 so

sin(t/2) = (b/2)/s = b/2s

So we arrived at the first part,

b = 2s sin(t/2)

The area of a triangle with sides s,s and included angle t is

A = (1/2) s² sin t

Answer:

Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is a feasible solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c^Tx and a dual problem of minimizing b^Ty (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c^Tx > b^Ty, then y must be dual infeasible. (i.e not a feasible solution for the dual problem). (f) [1pt] In a two player zero sum game, there exists at least one Nash equilibrium.

Step-by-step explanation:

a. true

Because two basic feasible solution stands to be adjacent in case they possess basic variable in common. Two distinct basic solutions with respect to set related with linear constraint under is considered to be adjacent.

b.False.

If a linear problem has no solution it may have null feasible region not important to have unbounded feasible region.

c.True.

If Shadow price is feasible for standard form of LP then it will be feasible solution of dual problem of this LP.

d. False.

As there will be 'n' variables 'm' constraints having nCm feasible solutions.

e.True.

As stated in weak duality theorem

f.True

For every zero-sum 2-player normal-form game, a Nash equilibrium exists. Moreover, a pair of mixed strategies (p,q)(p,q) for the two players is a Nash equilibrium if and only if each strategy is a maximin strategy.

Answer:

The correct option is (a).

Step-by-step explanation:

According to the Centers for Disease Control and Prevention, 0.22 or 22% of US adults of 25 years or older smoke.

But a researcher suspects that this percentage is lower if the US adults of 25 years or older have a bachelor's degree or higher education level.

So, the researcher needs to test whether the proportion of US adults  of 25 years or older who smoke is less in case the adults have bachelor's degree or higher.

To test his suspicion the researcher can use a one-proportion z-test.

The hypothesis of the test can be defined as:

H₀: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is 0.22, i.e. p = 0.22.

Hₐ: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is less than 0.22, i.e. p < 0.22.

Thus, the correct option is (a).

Final answer:

The alternative hypothesis for the scenario where a researcher suspects a lower smoking rate among U.S. adults with higher education is that the proportion of smokers in this group is less than .22.

Explanation:

The alternative hypothesis in this research scenario is that the proportion of U.S. adults age 25 or older who have a bachelor's degree or higher education level and smoke is lower than .22. The alternative hypothesis translates the researcher's suspicion into a testable statement and is essential for conducting a hypothesis test. The correct alternative hypothesis based on the research question would be: 'The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22.'