A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of 11? in how many ways can 3 men be selected from the 6 men? find the probability that the selected group will consist of all men.

Answers

Answer 1

Men = 6
Women = 5
Total number = 6+5 = 11

First question:
This is a question of combination.
Total number of selecting 3 people from the group = 11C3 = 11!/[3!(11-3)!]= 165 ways

Second question:
This is question of combination where only men are considered.
Total number of collecting 3 men from 6 men = 6C3 = 6!/[3!*(6-3)!]= 20 ways

Third question:
The probability that the 3 people selected will all be men is given by:
1st selection: 6/11
2nd selection: 5/10
3rd selection: 4/9
The probability = 6/11*5/10*4/9 = 4/33

Answer 2

[tex] \displaystyle
\binom{11}{3}=\dfrac{11!}{3!8!}=\dfrac{9\cdot10\cdot11}{2\cdot3}=165 [/tex]

[tex] \displaystyle\binom{6}{3}=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20 [/tex]

[tex] |\Omega|=165\\
|A|=20\\\\
P(A)=\dfrac{20}{165}=\dfrac{4}{33}\approx12\% [/tex]

Related Questions

When Mr. Peters drives from Boston to Worcester it takes him 30 minutes travelling at a speed of 60 miles per hour. Mrs. Peters drives from Boston to Worcester and leaves 5 minutes after Mr. Peters but travels at a speed of 90 miles per hour. Who will arrive first? By how many minutes?

Answers

Since the problem is requesting the answer in minutes, we are going to convert the speed of Mr. Peter to miles per minutes; to do that, we are going to multiply his speed by the multiplier [tex] \frac{60min}{1h} [/tex]:
[tex]60 \frac{miles}{h} * \frac{1h}{60min} =1 \frac{mile}{min} [/tex]

Now, to find the distance from Boston to Worcester, we are going to use the distance formula: [tex]d=vt[/tex]
where
[tex]d[/tex] is the distance
[tex]v[/tex] is the speed
[tex]t[/tex] is the time

We know that the speed of Mr. Peter is [tex]1 \frac{mile}{min}[/tex] and his time is 30 minutes. Lets replace those values in our formula:
[tex]d=1 \frac{mile}{min} *30min[/tex]
[tex]d=30miles[/tex]

Now, lets concentrate on Mr. Peter clone, Mr. P:
Lets convert the speed of Mr. P to miles per minute:
[tex] \frac{90miles}{h} * \frac{1h}{60min} =1.5 \frac{miles}{min} [/tex]
We also know that they will cover the same distance, 30 miles. Lets replace the values in our formula one more time to find t:
[tex]d=vt[/tex]
[tex]30miles= 1.5\frac{miles}{min} *t[/tex]
[tex]t= \frac{30miles}{1.5\frac{miles}{min}} [/tex]
[tex]t=20min[/tex]
But since Mr. P leaves 5 minutes after Mr. Peters, we need to add those 5 minutes to M. P's time:
[tex]t=20min+5min[/tex]
[tex]t=25min[/tex]

We can conclude that Mr. P will arrive first, 5 minutes before Mr. Peter.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

Mr. Peter takes [tex]\rm time=30 \; minutes \; and \;speed= 60 miles /hr[/tex]

Mrs. Peter takes [tex]\rm speed=90 miles/hr[/tex]

We will now calculate Mr. Peters speed,

[tex]\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}[/tex]

How to find distance from Boston to Worecester?

To find the distance, we will use distance formula

[tex]\rm Distance=speed\times time[/tex]

Here,given that the Mr Peters speed is [tex]\rm 60 miles /hr[/tex] and time is [tex]\rm 30 minutes[/tex]so by distance formula we will find distance of Mr. Peter

[tex]\rm Distance=\dfrac{mile}{min} \times 30 minutes[/tex]

[tex]\rm Distance= 30 miles[/tex]

Similarly, we will now calculate Mrs. Peters speed,

[tex]\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}[/tex]

by the given informations we know both covers the same distance

[tex]\rm ie. \;30 miles[/tex]

we will now find distance of Mrs. Peter

[tex]\rm Distance=speed\times time\\ 30miles=1.5\dfrac{miles}{min} \times time\\ time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\ time=20 minutes[/tex]

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

[tex]\rm time=20 minutes+ 5 minutes\\ time=25 minutes[/tex]

Therefore, it is clear that Mrs.Peter arrive before Mr Peter by 5minutes.

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David, Mike, and Anne are friends. As a hobby, the friends collect baseball cards. Mike owns 9 less than 9 times the number of cards that Anne owns. David owns 27 more than 3 times the number of cards that Anne owns. If David and Mike own the same number of baseball cards, how many baseball cards does Anne own?

Answers

Easy! Anne has 45 baseball cards!

Write an equation of te circle with the center (0,0) and radius square root of 15

Answers

Answer:
x² + y² = 15

Explanation:

The formula for the equation of a circle is (x - h)² + (y - k)² = r², where the center of the circle is ordered pair (h, k) and r represents the radius (in units).

Now, we plug the given information into the circle equation and simplify.
radius = √15
center (0, 0), h = 0, k = 0

(x - 0)² + (y - 0)² = (√15)²
(x)² + (y)² = (√15)²
x² + y² = 15

The equation of the circle is x² + y² = 15

The equation of the circle with a center at (0,0) and a radius of the square root of 15 is x² + y² = 15. The standard form of the circle equation, (x - h)² + (y - k)² = r², is used with h and k set to 0 to represent the origin.

To write an equation of a circle with the center at the origin (0,0) and a radius of the square root of 15, we use the standard form of the circle equation:

(x - h)² + (y - k)² = r²

Here, (h, k) represents the center of the circle and r is the radius. Since the center of the circle in question is at the origin, h = 0 and k = 0. The given radius is the square root of 15, so we have r = √15. Substituting these values into the standard form gives us the equation:

x² + y² = ( √15 )²

Which simplifies to:

x² + y² = 15

This is the equation for the desired circle centered at the origin with radius √15.

Write the equation of a line going through the point (-3,5) that is parallel to the line 2x+y=-8

Answers

2x + y = - 8
y = - 2x - 8

Since we are looking for a parallel line, we use the same slope of - 2x.

y = - 2x + b

Plug in your given point.

5 = - 2(- 3) + b
5 = 6 + b
5 - 6 = b
-1 = b

Your equation is y = - 2x - 1

What is the area of this polygon?
units²

5-sided polygon on a coordinate plane with vertices F, N, S, C, W. Point f is at (negative 4, negative 2), point N is at (2, 4), point s is at (5, negative 2), point c is at (5, negative 4), and point w is at (negative 4, negative 4)

Answers

Step 1) Draw a line from point F to point S. A rectangle forms (rectangle FSCW)

Step 2) Find the area of this rectangle. The area is 18 square units because it is 2 units high and 9 units across (9*2 = 18). You can count out the spaces or you can note how we go from x = -4 to x = 5 so subtracting the values gives -4-5 = -9 which has an absolute value of 9.

Step 3) Find the area of triangle FSN. The base is 9 units and the height is 6 units (count out the spaces or subtract y values). So the area is A = b*h/2 = 9*6/2 = 54/2 = 27

Step 4) Add up the area of the rectangle to the area of the triangle: 18+27 = 45

Final Answer: 45 square units

note: another way to find the answer is to find the area of rectangle WABC where point A is at (-4,4) and point B is at (5,4). Then subtract off the triangular areas of AFN and BNS

In this exercise we have to use the knowledge of polygon area to calculate the area of a trapezoid, in this way we find that:

[tex]45 units[/tex]

So find the area of this rectangle, this area will be:

[tex]9*2 = 18[/tex]

Find the area of triangle FSN, this area will be:

[tex]A = b*h/2 = 9*6/2 = 54/2 = 27[/tex]

Sum all the areas will be:

[tex] 18+27 = 45[/tex]

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What is the total surface area of the rectangular pyramid below?

(please see attached picture)

404 square feet
596 square feet
788 square feet
1,000 square feet

Answers

Answer:

596 square feet

Answer:

b I did the

Step-by-step explanation:

QS is the perpendicular bisector of PR solve for x

Answers

2x - 20 = 70 - x

3x - 20 = 70

3x = 90

x = 30

Final answer:

The term 'perpendicular bisector' means QS cuts PR into two equal parts at a 90-degree angle. If PR is '2x', then each half is 'x'. To solve for x, we would need data about the lengths of the line segments.

Explanation:

Given that QS is the perpendicular bisector of PR, it implies two things. Firstly, QS intersects PR at a 90-degree angle. Secondly, QS splits PR into two equal segments. So, if PR is represented as '2x', then PQ and QR are both 'x'.

Unfortunately, missing information prevents a specific solution for x. We'd need additional data about the lengths of these line segments to solve the equation for x. For instance, if PR = 10, then '2x = 10' which gives us 'x = 5'.

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Jeanine baker makes floral arrangements. she has 18 different cut flowers and plans to use 7 of them. how many different selections of the 7 flowers are possible?

Answers

Final answer:

Jeanine can create 43758 different floral arrangements using 7 flowers out of the 18 available. This was calculated using the mathematical concept of combinations.

Explanation:

To find the number of different selections of 7 flowers Jeanine can make out of 18, we need to use the mathematical concept of combinations. In this context, the combination formula is used, which is: C(n, k) = n! / [k!(n-k)!]

Where n is the total number, k is the number chosen, and '!' stands for factorial, which is the product of all positive integers less than or equal to the number. Thus, the number of ways Jeanine can choose 7 flowers out of 18 is calculated as follows: C(18, 7) = 18! / [7!(18-7)!] = 43758. Therefore, there are 43758 different ways Jeanine can create floral arrangements using 7 flowers out of the 18 available.

It should be noted that the color of the flowers does not influence the number of combinations if she intends to select any 7 flowers irrespective of their color.

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This question is about finding the slope of the tangent line to an inverse function. I would love to know if my answer of 1/5 is correct.

g(1) = 2
g^-1(2) = 1

(g^-1(x))' = 1/(g'(g-1(x))
(g^-1(2))' = 1/g'(g-1(2))
(g^-1(2))' = 1/g'(1)

g(x) = x^3 + 2x - 1
g'(x) = 3x^2 + 2
g'(1) = 3+2=5
(g^-1(2))' = 1/5

Answers

Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.

Here's another way to look at it:

When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.

For any tangent on g(x), its slope is m = (dy)/(dx)

The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here.

So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.

Daniel is using logarithms to solve the equation 24x = 14. Which of the following equations would be equivalent to his original expression?

2 log 4x = log 14
4x log 2 = log 14
2 log 4 = x log 14
x log 4 = 2 log 14

Answers

The resulting expression of the given logarithmic function will be 4xlog2 = log14.

Given the logarithmic expression below:
[tex]2^{4x}=14[/tex]

We are to determine which of the equations would be equivalent to his original expression.

Taking the logarithm of both sides, we will have:

[tex]log2^{4x}=log14\\4xlog2=log14\\[/tex]

From the solution, we can see that the resulting expression will be 4xlog2 = log14.

The table shows the height, in feet, of the tide over time, in hours.

I know the answer is that it should be cosine instead of sine, but I don't how to determine that. I'd like to know so I could solve questions like these in the future.

Answers

For this case we have the following function:
f (x) = - 4sine ((pi / 6) x) + 5
We evaluate the function for x = 0
f (0) = - 4sine ((pi / 6) 0) + 5
f (0) = -4 * (0) + 5
f (0) = 5
We note that the result does not correspond to the table.
Let's rewrite the function:
f (x) = - 4cosine ((pi / 6) x) + 5
We evaluate the function for x = 0
f (0) = - 4cosine ((pi / 6) 0) + 5
f (0) = -4 * (1) + 5
f (0) = 1
The result corresponds to the table
Answer:
The student's mistake is to use the sine function instead of using the cosine function.
The correct function is:
f (x) = - 4cosine ((pi / 6) x) + 5

A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

Answers

For this case we have the following equation:
h = -16t ^ 2 + 184t + 20
Deriving we have:
h '= -32t + 184
We equal zero and clear t:
-32t + 184 = 0
32t = 184
t = 184/32
t = 5.75 s
Then, the maximum height is given by:
h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
h (5.75) = 549 feet
Answer:
It takes the boulder to reach its maximum height about:
t = 5.75 s
the boulder's maximum hieght is:
h (5.75) = 549 feet

Answer:

The answer should be C.

Solve by graphing y= -5/3x + 4 y= -5/3x + 3

Answers

For this case we have the following system of equations:
y = -5 / 3x + 4
y = -5 / 3x + 3
We note that the lines have the same slope:
m = -5 / 3
Therefore, the lines are parallel.
Thus, the system has no solution.
Answer:
It has no solution (parallel lines).
See attached image.

What is the sine value of pi?

A. -1/2

B. 1/2

C. 0

D. 1

Answers

Answer: C) 0

You can use a calculator to get this answer, a reference table, or the unit circle. The angle pi radians is equivalent to 180 degrees. Note how the point on the unit circle corresponding to 180 degrees is (1,0). This point has a y coordinate of zero. More broadly, y = sin(theta) where theta is the angle.

plz help in the picture below

Answers

= 4 (3/4 -2/4) + 18
= 4(1/4) + 18
= 1 + 18
= 19

answer
A) 19

Miriam bought a bushel of apples from the apple orchard to bake apple pies for a bake sale. She started with 126 apples. After the first day of baking, she had 108 apples left. After the second day, she had 90 apples. After the third day, she had 72 apples left.If she continues this pattern, how many apples will she have left after 7 days of baking?

Answers

Miriam will have no apples left after the 7th day of baking.

Here is the number of apples she will have after each day starting with after the 1st day of baking.

126, 108(1st day), 90(2nd day), 72(3rd day), 54(4th day), 36(5th day), 18(6th day), 0(7th day).

Each day the number of apples decreases by 18.

Arithmetic, because the sequence has a common difference. answer on edgenui......

How do u find the median of 4 numbers?

Answers

The median of a set of numbers is found by lining them up least to greatest. Then find the two that are in the middle. I like to cross off first and last and circle what is last. This helps when you are doing a long string of numbers. After you have your circled numbers, add them together and divide them by two. This works for all even sets.

What are the solutions of the equation 4x2 + 3x = 24 – x?
a.)–3, 2, or 4
b.)–3 or 2
c.)–2, 3, or 4
d.)–2 or 3

Answers

Its option B:-3 or 2(just did this question on e2020) :D

Answer:

Its B

Step-by-step explanation:

area of the parrelogram pls 25 points

Answers

To find the area if a parallelogram, you do:

Area = base * height

The area of parralellogram is base x height. Note that you'll have to change it into a rectangle by "moving" the triangle to the other side (see attached picture)

hope this helps

Harry was given an assignment. He had 42 days to get 336 tasks done at work.Which operation would he use to figure out how many tasks he needs to complete each day

Answers

42divided by 336 that is it

He would use division to divide his tasks by the days to realize he has to do 8 assignments a day.

Hope this Helped :D

The frequency of the musical not B3 is about 246.94 Hz. What is the frequency of the note a perfect fifth below B3

370.42 Hz
246.94 Hz
241.94 Hz
164.63 Hz

Answers

Notes separated by a perfect fifth have a frequency ratio of 3:2.
The frequency of the note a perfect fifth below B3 will be
246.94×2/3 = 164.62667

The appropriate choice is ...
164.63 Hz

164.63Hz is the correct answer

HELP PLEASE!!!
Base your answer to the question on the diagram shown below.

Fernando is going to draw a marble from the bag, replace it, and then draw another marble. What is the probability that Fernando will get a green or blue marble on the first draw and a pink on the second draw?

(3 green, 4 yellow, 5 blue, 8 pink)

1.) 4/5
2.) 4/25
3.) 3/100

Answers

The answer is actually the second choice 4/25 hope this helps...

Answer: The correct option is (2) [tex]\dfrac{4}{25}.[/tex]

Step-by-step explanation: Given that there are 3 green, 4 yellow, 5 blue and 8 pink marbles in a bag. Fernando is going to draw a marble from the bag, replace it, and then draw another marble.

We are to find the probability that Fernando will get a green or blue marble on the first draw and a pink on the second draw.

Let, S be the sample space for the experiment of drawing a marble from the bag.

Then, n(S) = 3 + 4 + 5 + 8 = 20.

Let E denotes the event of drawing a green or blue marble and F denote the event of drawing a pink marble.

Then, we have

n(E) = 3 + 5 = 8 and n(F) = 8.

Since the second marble is drawn after replacing the first marble,

so the required probability of Drawing a green or blue marble on the first draw and a pink marble on the second draw is

[tex]P\\\\=P(E)\times P(F)\\\\\\=\dfrac{n(E)}{n(S)}\times \dfrac{n(F)}{n(S)}\\\\\\=\dfrac{8}{20}\times\dfrac{8}{20}\\\\\\=\dfrac{4}{25}.[/tex]

Thus, the required probability is [tex]\dfrac{4}{25}.[/tex]

Option (2) is CORRECT.

Is the following relation a function ? Yes or no

Answers

yes it is a function

Kill bought items costing $3.45,$1.99,$6.59 ,and $12.98. She used a coupon worth $2.50 .if Jill had $50.00 when she went into the store,how much did she have when she left?

Answers

first you add up all the items and the coupon then you will get $24.51. then subtract $50.00 take away $24.51 then you will get $25.49. So when she left the store she had $25.49

ASAP

A central angle θ in a circle with a radius of 3.5 centimeters intercepts an arc with a length of 6.3 centimeters.

What is the radian measure of θ ? Enter your answer, as a decimal, in the box.

Answers

By definition, the arc length is given by:
S = r * θ
Where,
r: radio
θ: central angle
Clearing θ we have:
θ = S / r
Substituting the values we have:
θ = 6.3 / 3.5
θ = 1.8 radians
Answer:
the radian measure of θ is:
θ = 1.8 radians

1.) How is the graph of y equals negative 2 x squared minus 5 different from the graph of y equals negative 2 x squared?

2.)

Answers

-2x^2 - 5 is same shape as -2x^2 except that the whole graph is translated verticall downwards 5 units

The transformation on the graph of y = -2x²- 5 is described as 5 units downward.

What is transformation on the graphs?

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

As per the given information:

The graphs are let f(x) = y = -2x²- 5 and g(x) = y = -2x².

As per the definition, the transformation on the graph can be described as,

-5 < 0.

The graph shifts downward.

Therefore, the graph of y = -2x²- 5 is 5 units down than y = -2x².

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What is the surface area of a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches? 150 square inches 150 cubic inches 170 square inches 170 cubic inches

HELPPPP

Answers

the surface area is 170 square inches

Answer:

Option (3) is correct.

The surface area of a rectangular prism of given dimension is 170 square inches.

Step-by-step explanation:

Given : a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches.

We have to find the surface area of a rectangular prism of given dimension.

Since a rectangular prism whose base is 5 inches by 6 inches

That is length (l)= 5 inches

Width (w) = 6 inches

and height (h) = 5 inches.

Also . [tex]\text{surface area of a rectangular prism}=2(lw+wh+hl)[/tex]

Substitute, we have,

[tex]\text{surface area of a rectangular prism}=2(5\cdot 6+5\cdot 5+5\cdot 6)[/tex]

simplify , we have,

surface area of a rectangular prism = 170 inches²

Thus, the surface area of a rectangular prism of given dimension is 170 square inches

a construction company is replacing a window in a house. the window is currently 3 feet wide by 4 feet tall. The homeowner wants to add 4 1/2 inches to each side of the window. What is the new perimeter of the window in feet? Justify your reasoning.

Answers

For this case, the first thing you should do is take into account the following unit conversion:
1 foot = 12 inches
Therefore, the perimeter of the new window is given by:
p = 2w + 2l
Where,
w: width
l: long
Substituting values:
p = 2 * (3 + ((4 1/2) / 12)) + 2 * (4 + ((4 1/2) / 12))
p = 15.5 feet
Answer:
The new perimeter of the window in feet is:
p = 15.5 feet

A certain number of bacteria are in a petri dish. If the growth rate is 2.7 percent per hour, how many hours will it take the bacteria to double in number?

Answers

Final answer:

Using the rule of 70, which states that the doubling time in hours is equal to 70 divided by the growth rate percentage, it will take approximately 25.93 hours for the bacteria to double in number at a growth rate of 2.7 percent per hour.

Explanation:

To calculate the time it will take for the bacteria to double in number with a growth rate of 2.7 percent per hour, we can use the rule of 70. The rule of 70 states that we can find the doubling time by dividing 70 by the percentage growth rate.

Doubling time = 70 ÷ growth rate percentage = 70 ÷ 2.7 ≈ 25.93

Therefore, it will take approximately 25.93 hours for the bacteria to double in number.

What is the value of y?
Please enter your answer, as an exact value

Answers

tan (60) = y/ 5
y = tan(60) * 5
and you know tan(60) = √3
so
y = 5√3

answer
5√3 (exact value)

Answer: 8.66

So to Solve this we are going to be using Tangent.

Tangent: opposite/adjacent

Tan60 = y/5

Tan60 * 5 = y/5 *5

Tan60 * 5 = y

8.66 = y

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A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of​ 11? in how many ways can 3 men be selected from the 6​ men? find the probability that the selected group will consist of all men.

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A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of 11? in how many ways can 3 men be selected from the 6 men? find the probability that the selected group will consist of all men.