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## A. about 60% of florida residents believe that florida is a nice place to live. suppose that six randomly selected florida residents are interviewed. what is the probability that at least one resident does not think that florida is a nice place to live?

At least 6, means: either 1 and 2 and 3 and 4 and 5 and 6

Probability(that Florida is a nice place to live) = 60% = 0.6
If  at least  6 randomly selected like Florida:
P(at lest 6 LIKE Florida) = (0.6)⁶ = 0.04665
P(at least 6 DON’T LIKE Florida) = 1-0.04665 = 0.9533

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## Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances?

chi square distribution with df = n-1

Step-by-step explanation:

Given that sample of size n=90  are randomly selected from the population of numbers (0 through 9) produced by a random-number generator

Since sample size is large and randomness is followed we can assume that the variable follows a normal distribution.

Hence the sample variance would follow a chi square distribution with degree of freedom = This is because we have is standard normal hence square will be a chisquare variate.  When we sum n variates we get chi square distribution with df n-1

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## Consider a political discussion group consisting of 9 ​Democrats, 7 ​Republicans, and 3 Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention. Find the probability of selecting no Democrats

Well, first you would add up how many objects you have to select from

9 democrats + 7 Republicans + 3 Independents = 19 total people
so then you would put how many people you can have over that number
so since we don’t want any Democrats it would be 10/19 (.52)
and that tells you the chances of not picking one the first time

then, since that person cannot be selected again, we remove them from the pool, making it only 18 people to pick from and 9 people you want picked so once again you put 9/18 (.50), then you take those, (in decimal form) and multiply them (.26) then convert it to a fraction by moving the decimal to the right two and have 26% chance of no Democrats

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## The body temperatures of adults are normally distributed with a mean of 98.6° f and a standard deviation of 0.60° f. if 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° f. 0.0228 0.8188 0.9360 0.9772

Here the population standard deviation is 0.60 degree F.  If a sample of 36 adults is randomly selected, that results in a sample standard deviation of 0.60 degree F divided by the square root of 36:  0.10 degree F.

The probability in question is the area under the standard normal probability distribution between 98.4 degree F and infinity, and intuitively you can detect that this will be more than 0.5 (corresponding to 50%).

Convert 98.4 degrees F to a z-score, using the sample standard deviation (0.10 degree F).  That z score is
98.4-98.6
z = ————–   =  -0.20/0.10 = -2
0.10

We need to determine the area under the standard normal curve to the right of z=-2.  Use a table of z-scores to do this, or use your calculator’s built-in probability functions.  My result is 98.21% (corresponding to an area of 0.9821).

With my calculator I can find this probability using the following command:

normalcdf(-2,100000,0.10).

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## If you have a bag that contains 24 marbles: 4 red, 12 blue, 6 black, 2 green. what is the probability of randomly picking one marble that is black?

Parallel lines…means ur equations will have the same slope and different y int’s.

x – 2y = 8….-2y = -x + 8….y = 1/2x – 4…slope is 1/2, y int is -4
2x + 4y = 12…4y = -2x + 12….y = -1/2x + 3…slope is – 1/2, y int is 3
not this one…different slopes

x – 2y = 8…slope is 1/2, y int is -4
2x – 4y = 12…-4y = -2x + 12…y = 1/2x – 3….slope is 1/2, y int is -3
same slope, different y int’s…..these are parallel lines..but this is not ur graph because the graph has a negative slope.

x + 2y = 8….2y = -x + 8….y = -1/2x + 4..slope is -1/2, y int is 4
2x + 4y = 12…4y = -2x + 12….y = -1/2x + 3…slope is -1/2, y int is 3
same slope, different y int’s…parallel lines…and ur y int’s match the graph…this is ur answer <===

x + 2y = 8…slope is -1/2, y int is 4
2x – 4y = 12..slope is 1/2, y int is 3
different slopes, different y int….this has 1 solution and ur lines are not parallel…not this one

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## A box contains 60 colored balls: 45 of the balls are purple, and 30 of the purple balls have stars on them. if a purple ball being randomly chosen and a ball with stars being randomly chosen are independent events, how many of the 60 colored balls have stars on them? use conditional probability to justify your answer.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## A box has 6 beads of the same size, but all are different colors. Tania draws a bead randomly from the box, notes its color, and then puts the bead back in the box. She repeats this 3 times. What is the probability that Tania would pick a yellow bead on the first draw, then a blue bead, and finally a yellow bead again?

Ahemmm having x-intercepts of -3 and -5.. ..well, that simply means, -3 and -5 are roots or solutions or zeros of the equation

it namely means x = -3 and x = -5, an x-intercept is when the graph touches the x-axis, at that point, the y-intercept is 0, so the point is (-3, 0) and (-5, 0)

if the roots are -3, and -5, then if you have the zeros/x-intercepts/solutions of the polynomial, all you have to do is, get the factors, as above, and get their product, to get the parent original polynomial.

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## Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## A librarian randomly selects 25 returned books one day and finds that three of them were returned late. based on this sample, how many of the 410 returned books that day are likely to be late returns?

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 numbers. there are 26,000 possible codes. what is the probability that you will be assigned the code a123?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC= …….

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z  ………

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z  …………

Subtract  and    ……….

Add equation  and , to get values of x and y   Substitute x in   Substitute value of x in equation , to get z     We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## In a quiz contest, Mary answers 90% of the questions correctly without any additional clues from the quiz coordinator. The randomly generated numbers below simulate this situation. The numbers 0 to 8 represent questions answered correctly without additional clues, and the number 9 represents questions that needed additional clues.

To solve this problem, we should note that there are:

total questions = 100

questions that needed additional clues = 10

1. The first question is to find the probability that in the
third question, Mary would need additional clue. Therefore this implies that in
the first and second questions, Mary would answer it correctly. Therefore:

correctly) * (question 3 needed clue)

Probability = (90/100)*(89/99)*(10/98)

Probability = 0.08256 = 8.26%

2. The second question finds for the probability that two

Probability = (question 1 needed clue) * (question 2 needed
clue)

Probability = (10/100)*(9/99)

Probability = 9.1*10^-3 = 0.91%

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## URGENT A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women? A. 5/143 B. 7/143 C. 28/143 D. 30/143

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## A new surgery is successful 75% of the time. if the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by Therefore, the distance between the points A(8, 9) and B(x, y) is given by Since, distance between A and B is 10 units, so

d = 10.

Therefore, Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## Among the contestants in a competition are 3636 women and 2525 men. if 5 winners are randomly? selected, find the probability that they are all? men? round to five decimal places.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## Researchers want to test the effectiveness of a new anti-anxiety medication. three hundred eighty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. in clinical testing, 64 out of 200 people taking the medication reported symptoms of anxiety. of the other 180 people receiving a placebo, 88 reported symptoms of anxiety. do you think if the patients in the two groups performed significantly different with respect to symptoms of anxiety? please use 0.05 as the level of significance. (hint: use 1.96 and -196 as the critical z-values).

The Contribution Margin per unit (CM) can be calculated
from the difference of Selling Price per unit (SP) and Total Expenses per unit
(TE).

First, let’s calculate the value of SP:

SP = Sales / Units sold

SP = \$1,043,400 / 22,200 units sold

SP = \$47

Second, calculate all expenses:

Direct materials per unit = \$234,948 / 27,970 units
manufactured = \$8.4

Direct labor per unit = \$131,459 / 27,970 units
manufactured = \$4.7

Variable manufacturing overhead per unit = \$240,542 / 27,970
units manufactured = \$8.6

Variable selling expenses per unit = \$113,220 / 22,200
units sold = \$5.1

TE = \$26.8

Therefore the CM is:

CM = SP – TE

CM = \$47 – \$26.8

CM = \$20.2 per unit

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## A tour boat operator wants to know the average age of all the people in her tour group. She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34. What is the best estimate of the average age of all the people in the tour group? Round to the nearest whole number.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl??

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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## Your parents are always complaining that you do not do enough housework. they say that you should be helping them out because you are only a student and you have a lot more spare time than them. the number of hours per week that your parents work has a mean of 48.69 hours and a standard deviation of 2.90 hours. you believe that the number of hours per week that you have to study for university has a mean of 48.17 hours and a standard deviation of 2.60 hours. you plan to record the number of hours that you study each week over 15 randomly selected weeks throughout the year. calculate the probability that the mean of your sample is greater than the mean number of hours per week worked by your parents. assume that the population of study hours per week is normally distributed. give your answer as a decimal to 4 decimal places. probability

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## You want to make five-letter codes that use the letters A, F, E, R, and M without repeating any letter. What is the probability that a randomly chosen code starts with A? 0.10 0.15 0.20 0.25

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

————————————

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn’t listed as an answer choice. Let’s try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

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## A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light. Which element of experiment design is known to be a part of this study? A. blinding B. replication C. randomization

A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light. Which element of experiment design is known to be a part of this study? A. blinding B. replication C. randomization

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## A box contains ten cards labeled J, K, L, M, N, O, P, Q, R, and S. One card will be randomly chosen. What is the probability of choosing a letter from L to Q?

A box contains ten cards labeled J, K, L, M, N, O, P, Q, R, and S. One card will be randomly chosen. What is the probability of choosing a letter from L to Q?

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## The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 26 different days and records the number of calls. the sample yields a mean of 258.4 calls with a standard deviation of 32.7 calls per day. the 95% confidence interval for the mean number of calls per day has an upper bound of ________. (round your answer to 1 decimal place.)

First we calculate for the total number of possibilities
(permutation) to select 4 disks from the container:

Total number of possibilities = 10 * 9 * 8 * 7

Total number of possibilities = 5040

Now let us find the 4 disks that will result in a range of 7.

Range = highest number – lowest number

The pair of highest and lowest number that will result in
range of 7 is: (1 & 8), (2 & 9), (3 & 10)

As a basis of calculation, let us use the pair 1 & 8.

There are four possible ways to select 1 and three for 8.

Arrangements of maximum and minimum pair = 4 * 3

Arrangements of maximum and minimum pair=12

Now we need to calculate for the remaining 2 disk. There
are 6 numbers between 1 & 8. The total possibilities for selecting 2 disk
from the remaining 6 is:

Possibilities of selecting 2 disk from remaining 6 = 6 *
5

Possibilities of selecting 2 disk from remaining 6 = 30

Therefore, the total possibility to get a range of 7 from
a pair of 1 & 8 is:

Total possibility for a pair = 12 * 30

Total possibility for a pair = 360

Since there are a total of three pairs (1 & 8), (2
& 9), (3 & 10):

Total possibilities of the 3 pairs = 360 * 3

Total possibilities of the 3 pairs = 1080

Therefore:

Probability = Total possibilities of the 3 pairs / Total
number of possibilities

Probability
= 1080 / 5040 = 3 / 14                      (FINAL

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## The probability that a randomly selected 55?-year-old male garter snakegarter snake will live to be 66 years old is 0.932080.93208. ?(a) what is the probability that two randomly selected 55?-year-old male garter snakegarter snakes will live to be 66 years? old

[Incomplete question. I found a table in other source –
see attachment]

I made a graph and it looks like a line (see attachment).

If the proportion is exactly linear, you have to use this
kind of equations:

y=mx+b

where:

y are the sales

x is the number of months since the beginning of the year
(for example, January is 1, February is 2, etc)

m is the proportion (how much it increases every month)

b is how much it was sold in month 0 (if January is 1, 0
would be December of last year)

But it’s not exactly linear – you have to round a little
to make it straight. So now we need to know the equation of the line that fits
best with these data. The most accurate way to know that is the method of least
squares – no one actually calculates that, not even university professors: we
just put data in Excel, click “add trendline”, and Excel does all the work ☺ Or you can just eyeball
it and draw
a line that looks right – in this case, make dY/dX to find m and the
intersection with y-axis to find b.

This is what Excel told me:
y = 1.2727x + 30.54

So if you want to know how much will be sold in November,
assuming the rate goes on like this, you have to replace 11 in the equation:

y = 1.2727*11 + 30.54=44.539

So that would mean  44,539 gallons

And 12 for Dezember:

y = 1.2727*12 + 30.54=45.812

So that would mean 45,812 gallons

So you will not exceed 50,000 until next year.

Let’s find in which month of next year:

1.2727x + 30.54 = 50

1.2727x = 50 – 30.54

x = (50 – 30.54)/1.2727=12.147

So this means it will be in month 13 (you
have to round it up)

which would be January (you have to substract
12)

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## The probabilities of the orphaned pets in six cities’ animal shelters being different types of animals are given in the table. If a randomly selected orphaned pet in a St. Louis animal shelter is a dog, what is the probability that it is a mastiff? City Cat Dog−Lhasa Apso Dog−Mastiff Dog−Chihuahua Dog−Collie Austin 24.5% 2.76% 2.86% 3.44% 2.65% Baltimore 19.9% 3.37% 3.22% 3.31% 2.85% Charlotte 33.7% 3.25% 3.17% 2.89% 3.33% St. Louis 43.8% 2.65% 2.46% 3.67% 2.91% Salt Lake City 28.9% 2.85% 2.78% 2.96% 2.46% Orlando 37.6% 3.33% 3.41% 3.45% 2.78% Total 22.9% 2.91% 2.68% 3.09% 2.58% 15.30% 18.15% 21.04% 21.84%

Option: B is the correct answer.

The window size that display all the points are:

0 ≤x ≤ 20  ;   0 ≤ y ≤ 60

## Step-by-step explanation:

We are given a table of values as:

x                       y

2                      5

5                      16

6                      20

10                     29

12                     36

17                     53

Clearly from the set of given x and y values we could observe that the minimum value attained by x is 2 and maximum value attained by x is 17.

Hence, the all the x-values lie in the interval:

0 ≤ x ≤ 20

Similarly,  we could observe that the minimum value attained by y is 5 and maximum value attained by y is 53.

Hence, the all the y-values lie in the interval:

0 ≤ y ≤ 60