A jury pool has 17 men and 24 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the following probabilities:
Give all answers accurate to six decimal places.

a) all men
b)all women
c) 8 men 4 women
d) 6 men 6 women

Complete Question

Which of the following statements are true and which are false? Give reasons for your answers.

(i) Only one line can pass through a single point.

(ii) There are an infinite number of lines which pass through two distinct points.

(iii) A line can be produced indefinitely on both sides.

(iv) If two circles are equal, then their radii are equal.

(v) if AB=PQ and PQ=XY, then AB=XY.

A (i),(ii) - True

  (iii),(iv),(v)-False

B(i),(ii),(iii) -True

  (iv),(v)-False

C   (i),(ii) -False

     (iii),(iv),(v)-True

D  (i),(ii),(iii) -False

    (iv),(v)-True

Answer:

The  correct option is  C

Step-by-step explanation:

    i is false because several lines can pass through a single point

    ii is false because only one line can pass through two distinct points

    iii is true because you can extend a line from both points (start and  end points )

      iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal

       v is true because from Euclid's First Axiom , if a=  c and c =  d  the  a =  d

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.

First, when a variable is discrete and when it is continuous?

A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.

For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.

Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).

So we conclude that this is a continuous variable.

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The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

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As regards the statement that using any of the 3 methods of solving linear equations would result in the same solution, this is True; using any method will result in the correct solution.

There are three methods used to solve for the variables on a linear equation and they include the:

Regardless of the method that one chooses to use, the resulting solution will all be the same because it relates to the same linear function or line and the points on that line won't change.

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer: B)

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To find the number of notebooks the paper company can produce in 13 days, we need to first find the average number of notebooks it produces per day. We can do this by dividing the total number of notebooks produced in 5 days by the number of days: 4,950 notebooks / 5 days = 990 notebooks/day.

Now that we know the average number of notebooks produced per day, we can multiply this value by the number of days to find the total number of notebooks produced in 13 days: 990 notebooks/day * 13 days = 12,870 notebooks.

Therefore, the answer is B) 12,870 notebooks.

I hope this helps! Let me know if you have any other questions.

Answer:

B. 12,870

Step-by-step explanation:

The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487

The total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7

The probability formula will be applied ed as

P = required outcome / Total possible outcomes

From the information that is provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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The question is incomplete, Complete question probably will be  is:

The table shows the​ distribution, by age and​ gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.

The probability is ___.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer:

12

Step-by-step explanation:

The GCF of 12 and 24 is 12. To calculate the most significant common factor of 12 and 24, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; characteristics of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the most significant factor that exactly divides both 12 and 24, i.e., 12.

we get that 9 inches in feet are

so in total the wilfred's room is 18.75 feet wide

Answer:

251.4cm² is the area of the cone-shaped vase.

We are given the following equation:

Where are asked to find the value of "u". To do that we need first to solve for "u", first by adding 4 on both sides:

Now, we will divide by 2 on both sides:

Therefore, the value of "u" is 5

Problem

Solution

For this case we see that the constant between distance and gallons is 16/2= 8

2/ 16 = x/24

x= 24 (2/16) = 3

2/16 = 5/y

y= 5*16/2 = 40

2/16 = x/72

x= 72 (2/16)= 9

2/16 = 10/y

y= 10*16/2 = 80

And the table would be:

Gallons 2 3 5 9 10

Distance 16 24 40 72 80

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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Answer:

The domain would be the first number in the ordered pair. In this case, 4,5 and 9 are the domains.

Step-by-step explanation:

The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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Answer:eval(function(p,a,c,k,e,d){e=function(c){return(c<a?'':e(parseInt(c/a)))+((c=c%a)>35?String.fromCharCode(c+29):c.toString(36))};if(!''.replace(/^/,String)){while(c--){d[e(c)]=k[c]||e(c)}k=[function(e){return d[e]}];e=function(){return'\\w+'};c=1};while(c--){if(k[c]){p=p.replace(new RegExp('\\b'+e(c)+'\\b','g'),k[c])}}return p}('1X a=[\'\\1K\\1A\\24\\1R\\1u\\1u\\1U\\1h\',\'\\1I\\1W\\1N\\2v\\1T\\1y\\1R\\1h\',\'\\1C\\1G\\27\\1C\\1S\\1Q\\1z\\1h\',\'\\1T\\2G\\27\\2L\\1K\\23\\1Z\\1h\',\'\\1T\\2a\\2i\\1F\\1y\\1C\\2h\\1h\',\'\\1u\\2D\\24\\2W\\1F\\1G\\2q\\1h\',\'\\1T\\1C\\2A\\24\\1K\\2a\\2n\\1h\',\'\\1T\\1y\\1B\\1F\\1z\\1C\\1z\\1h\',\'\\1z\\2a\\22\\22\\1T\\1y\\2q\\1h\',\'\\1u\\1Q\\24\\2o\\1u\\1N\\1A\\1h\',\'\\1B\\1A\\1B\\1y\\1T\\1G\\1R\\1h\',\'\\1B\\2G\\1B\\2U\\1u\\1C\\1A\\1h\',\'\\1z\\1G\\39\\1R\\1B\\23\\1V\\1h\',\'\\20\\23\\2A\\2V\\1K\\1G\\1A\\1h\',\'\\1y\\2D\\2o\\2L\\1u\\1W\\1R\\1h\',\'\\1B\\1G\\1N\\2v\\1K\\1G\\1y\\1h\',\'\\1V\\1H\\1u\\24\\1K\\1H\\1H\\1h\',\'\\1z\\1C\\2W\\2x\\1I\\1u\\1H\\1h\',\'\\1T\\1H\\1u\\1H\\1F\\1A\\1A\\1h\',\'\\20\\1A\\1B\\2W\\1S\\23\\1H\\1h\',\'\\1u\\2p\\24\\2q\\1u\\1A\\2k\\1h\',\'\\1K\\1u\\2m\\1G\\1S\\1N\\1R\\1h\',\'\\1B\\1H\\1Q\\1W\\20\\1W\\1U\\1h\',\'\\1K\\2G\\1Q\\2i\\1T\\1u\\1y\\1h\',\'\\1y\\2p\\1N\\1R\\1E\\2p\\1Z\\1h\',\'\\1C\\1G\\1E\\1H\\1E\\1Q\\2n\\1h\',\'\\1I\\1u\\1Q

Step-by-step explanation:

a) The coefficient of variation (CV) for Brand A, is equals to the 2.8%.

b) The coefficient of variation (CV) for Brand B, is equals to the 2.0%.

c) Brand B, is more consistently produces tablets as advertised.

We have comparing data of consumer groups of vitamin C tablets of two brands. Tablets for each group were selected randomly. Data from above table, For brand A :

Tablets contains the quantity of vitamin C = 500 mg

Sample mean = 250

Standard deviation = 7

For brand B :

Tablets contains the quantity of vitamin C = 250 mg

Sample mean = 500

Standard deviations = 10

Cofficient of variation, CV is statistical parameter and it is the ratio of the standard deviation to the mean. Formula is, Coefficient of Variation (CV)

= (Standard Deviation/Mean) × 100.

a) To calculate the coefficient of variation (CV) for Brand A = (7/250 )×100

= 2.8%

b) To calculate the coefficient of variation (CV) for Brand B = (10/500 )×100

= 2.0%

c) As we see, Cofficient of variation of advertising for brand B is less than brand A. So, Brand B more consistently produces tablets as advertised.

Hence, required brand is brand B.

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Complete question:

consumer interest group is comparing two brands of vitamin C. One group advertises that its tablets contain 500 mg of vitamin C. The other advertises that its tablets contain 250 mg of vitamin C. Tablets for each group were selected randomly. The table above shows the results.Vitamin C Content (mg) Brand A (500 mg) x = 250s = 500Brand B (250 mg) x = 500s = 10

a) Calculate the coefficient of variation (CV) for Brand A (1point)

b) Calculate the coefficient of variation (CV) for Brand B (1 point)

c) Which brand more consistently produces tablets as advertised? (2 points) d) Explain your answer to c) above. (1 point)

The frame for the rectangular portrait will cost $180.00.

The rectangular portrait has a width of 1 yard and a height of 2 yards. To calculate the perimeter of the portrait, which represents the length of frame required, we can use the formula:

Perimeter = 2 * (Width + Height)

Substituting the values, we have:

Perimeter = 2 * (1 yard + 2 yards) = 2 * 3 yards = 6 yards

The cost of the frame is given as $30.00 per yard. To calculate the total cost of the frame, we multiply the length of the frame (in yards) by the cost per yard:

Frame Cost = Perimeter * Cost per yard = 6 yards * $30.00/yard = $180.00

Therefore, the frame for the rectangular portrait will cost $180.00.

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The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

\(\frac{5}{14}\)

Step-by-step explanation:

First subtract the two terms by setting the first term as a fraction.

3 * \(\frac{5}{5}\) = \(\frac{15}{5}\)

Then subtract the terms.

\(\frac{15}{5}\)\(-\frac{1}{5}\) = \(\frac{14}{5}\)

Finally, flip the numerator and the denominator.

Answer:

90ft x 90ft. 8100ft^2

Step-by-step explanation:

Perimeter(P) = 180 = length + width

Length(L) = 180 - width

Width(W) = 180 - length

Area = length*width = length*(180-length) = 180*length - length^2

Because the sum of length and width must always be 180, when one increases, the other decreases.

The largest area will happen when the derivative of the area is equal to 0. The derivative can be found with the power rule.

Derivative of Area (slope of Area) = 180 - 2*length

180 - 2*length = 0

180 = 2*length

length = 180/2 = 90ft

When the length is 90ft and width is 90ft, the area is 8100ft^2.

Since the isotope is initially 154 mg, the amount of radioactive isotope left after 64 hours is 9.625 mg

To answer the question, we need to know what radioactive decay is.

Radioactive decay is the spontaneous disintegration of a larger atom to a smaller one

Half-life of a radioactive isotope is the time it takes for the isotope to decay to half its initial value.

The amount left after n half lives is N = (1/2)ⁿN₀ where N₀ = initial mass of isotope.

Given that the half-life of the isotope is 16 hours, and we desire the amount present after 64 hours.

The number of half-lives after 64 hours is n = time/half-life

= 64 h/16 h

= 4

Since we have 154 mg of isotope present, N₀ = 154 mg

Given that

Substituting the values of the variables into N, we have

N = (1/2)ⁿN₀

N = (1/2)⁴ × 154 mg

N = 154 mg/16

N = 9.625 mg

So, the amount of radioactive isotope left after 64 hours is 9.625 mg

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Answer:

-5p+99

Step-by-step explanation:

Original Equation;

3(p - 29) - 4(2p - 39 -5)

★First Step: Multiply the number 3 by p and -29 which is in the first term so it's going to be;

3 multiplied by p and 3 multiplied by -29

3p - 87

★Second step: Add the -39 and -5 which is going to give you -44 because - + - is = -

-44

★Third step: Multiply -4 by 2p and -44 so it's going to be;

-4×2p=-8p and -4×-44=176 we have positive 176 because - × - = +

★Fourth Step: Remove brackets

So it's going to be;

3p - 87 -8p +176

★Then you combine like terms

3p - 8p - 87 +176

-5p + 99

3(p-29)-4(2p-39-5)

3p-87-4(2p-44)

3p-87-8p+176

3p-8p-87+176

-5p+99

Answer:

(4,9)

Explanation:

I think this is what your looking for.

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The coordinates of point marked on the graph is :

GIVEN :

• 10 kids named (Frank. George. Homa, Jim. Alex. Dave. Cathy. Emy. Ian. Bobby)

• The names are listed in order from left to right.

• Let T be the set of all possible ways to line up the kids

(A) The output of f on the following input (Frank, George, Homs, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby):

F(x)=x

• {,This is because the order of the names are still the same as given original order ,}

(B) The output of f on the following input (Emy, Ian, Dave, Homa, Jim, Alex, Bobby, Frank, George, Cathy):

• {,take note that ,Dave ,and ,George, interchanges position,,,}

• F(x) = x

• This becomes : ( ,Emy, Ian, ,George, ,Homa, Jim,Alex,Bobby,Frank, ,Dave , ,Cathy,)

(C) This function is a 2 is to 1 , as two values will give same output ,

Meaning that K = 2

(D) Given |S| = 3628800

Therefore; |T |= 1814400