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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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Study Solutions

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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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**Answer:**

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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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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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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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

therefore, ur answer is : 3rd answer choice

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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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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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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 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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**Answer:**

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.**

**So,** AD=AB=44.8 cm

DC=BC=72 cm

**The diagonals are perpendicular.**

**S**o, AC ⊥ BD

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

AC= AO+OC

AC= …….[1]

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

………[2]

**Applying Pythagorean theorem in ΔCOD**

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

**Subtract [2] and [3]**

……….[4]

**Add equation [1] and [4], to get values of x and y**

**Substitute x in [1]**

**Substitute value of x in equation [2], 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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To solve this problem, we should note that there are:

total questions = 100

questions answered correctly = 90

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:

Probability = (question 1 answered correctly) * (question 2 answered

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

consecutive needs additional clue, therefore:

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

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

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

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

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

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

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

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

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

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

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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)

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

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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?

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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
ANSWER)**

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[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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Option: B is the correct answer.

The window size that display all the points are:

** 0 ≤x ≤ 20 ; 0 ≤ y ≤ 60**

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**

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