How many ways can a jury of four men and three women be selected from twelve men and ten women

Answers

Answer 1

There are 59,400 ways this jury can be selected.

Since the events are independent of each other (choosing one does not influence the chance of choosing the others) we multiply the combinations.

The first combination is [tex]_1_2C_4[/tex], because we are selecting 4 men from a possible 12.

The second combination is [tex]_1_0C_3[/tex], because we are selecting 3 women from a possible 10.

Multiplying these we have: [tex]_1_2C_4 \times _1_0C_3 \\ \\=\frac{12!}{4!8!} \times \frac{10!}{3!7!} \\ \\=\frac{479001600}{967680} \times \frac{3628800}{30240} \\ \\=495 \times 120 \\ = 59400[/tex]

Answer 2

Final answer:

The number of ways to choose the jury is 59,400.

Explanation:

The question is concerned with a combinatorial problem of selecting a jury from a larger pool of people, which is a classic example of the use of combinations in probability and statistics.

To find out how many ways we can select a jury of four men from twelve men, and three women from ten women, we use the combination formula which is C(n, k) = n! / (k! * (n-k)!), where '!' represents factorial, 'n' is the total number of people, and 'k' is the number of people to choose.

To select the men, we calculate the combinations as follows:

C(12, 4) = 12! / (4! * (12-4)!) = 495 ways

To select the women, we calculate the combinations as follows:

C(10, 3) = 10! / (3! * (10-3)!) = 120 ways

To find the total number of ways to select the jury of four men and three women, we multiply the number of ways to choose the men by the number of ways to choose the women:

495 ways (to choose men) * 120 ways (to choose women) = 59,400 different ways to select the jury.

Related Questions

what is eleven less than 7 times a number is at least 2 what is the inequality

Answers

----------------------------------------------------------
Define x.
----------------------------------------------------------
Let the number be x.

----------------------------------------------------------
Construct inequality
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7x - 11 ≥ 2

----------------------------------------------------------
Add 11 to both sides.
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7x ≥ 13

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Divide by 7 on both sides.
----------------------------------------------------------
[tex]x \geq \dfrac{13}{7} [/tex]

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[tex]\bf \text{ Answer: } x \geq \dfrac{13}{7} [/tex]
----------------------------------------------------------

Hence, the inequality is [tex]x\geq \frac{13}{7}[/tex].

What is an inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Here given that,

Eleven less than [tex]7[/tex] times a number is at least [tex]2[/tex].

Let the number be [tex]x[/tex]. Construct the inequality

[tex]7x - 11 \geq 2[/tex]

Now add [tex]11[/tex] to both sides.

[tex]7x\geq 2+11\\7x\geq 13[/tex]

Now, divide by [tex]7[/tex] both sides, we get

[tex]x\geq \frac{13}{7}[/tex].

Hence, the inequality is [tex]x\geq \frac{13}{7}[/tex].

To know more about inequality

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9. A model of a building is made using a scale of 1 inch = 25 feet. What is the height of the actual building, in feet, if the height of the model is 12.5 inches?

*PLZ HELP* *DUE IN 1 HOUR* *EMERGENCY* *17 POINTS* *YOU WILL GET A COOKIE*

Answers

You can use the ratio to find the height of the actual building, 1 inch:25 feet.
We have to find y which is the actual height, 12.5 inches: y.
To find y, you have to multiply 12.5 by 25 to find the actual height.
12.5×25= 312.5
So the actual height of the building is 312.5 feet.

Answer:

312.5

Step-by-step explanation:

i wil get my cookie

A parallelogram is symmetric with respect to either diagonal. true or false?

Answers

it is true as parallelograms are symmetrical on all edges

Not all parallelogram is symmetric with respect to either diagonal, therefore the answer is False.

A parallelogram is known as a quadrilateral (having four sides) with two pairs of parallel-lateral lines. A parallelogram has no line of symmetry but there are some exceptions to specific types of parallelograms. For example:

Rhombus is a special type of parallelogram and it has two lines of symmetry along its diagonals.

A rectangle has two lines of symmetry going through the mid-point of the opposite sides.

A square has four lines of symmetry with two lines going through the diagonal and two lines going through the opposite sides.

Therefore, we can conclude that not all parallelogram is symmetric with respect to either diagonal.

Learn more about parallelogram here:

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How do u do #10? Plz show on paper

Answers

Reflection across the line y=x simply swaps the x and y coordinates.
K'(-2, -5), A'(1, -4), I'(-1, 0), J'(-4, -2)

A dairy mixes chocolate milk to sell in gallon containers. They mix 2,365 cups of skim milk with 108 cups of chocolate syrup. If each gallon container holds 16 cups of the chocolate milk, how many full containers will be filled?

Answers

So to solve this equation, you need to first figure out how many cups are going to be in all. You can do this by adding the cups of skin milk (2365) and the cups of chocolate syrup (108 cups), which leaves you with a total of 2473 cups.
Now, since each gallon is 16 cups and you are determining the amount of gallons, you take the total number of cups (2473) and divide it by the 16 cups. this then gets you the answer of 154.5635. BUT... Since it wants to know how many FULL containers... the real answer is simply 154 GALLONS

(2365 cups + 108 cups) ÷ 16 = 2473 ÷ 16
= 154.56
the quantity will fill a 16 containers

2a - 1 = 19
Solve the equation and show all work please show steps!!

Answers

Hello,

The answer is "x=10".

Reason:

First write the equation:

2a-1=19

Add one on both sides:

19+1=20

2a=19

Now divide 2 by 20:

20/2=10

a=10

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

Which describes the correct way to convert minutes to hours?

Answers

Every 60 minutes equals an hour.

60m = 1h

m = minutes | h =hour

60m + 60m = 120m = 2h

Hope this helped!

A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface too fast, he may suffer from a physical condition called "the bends." Suppose the diver started at 82 feet below the surface and rose in 5 steps of 15 feet each. Use an integer to describe his new position in relation to the water surface.

Answers

Start by multiplying 15 by 5, and you get 75. then subtract that from 82, and you get 7. Since you are below the surface, the number is negative. So you get -7.

Answer:

-7 feet

Step-by-step explanation:

The total distance the diver rose is 5*15 = 75 feet

If we take the zero at the water surface, then the initial position, that is, 82 feet below the surface has to be considered as -82. The 75 feet risen by the diver is a positive quantity, then his new position, in relation to the water surface, is -82 + 75 = -7 feet, i. e. 7 feet below the surface.

passing through (1,9),slope=2

Answers

Passes through (1, 9) with a slope of 2.

Assuming that we want this in slope intercept form, which is y=mx+b (m=slope, b=y-intercept) then we need to find the y-intercept! :)

To find the y-intercept (or b!!) you simply need to plug everything into slope intercept form using our given points.

y = mx + b

Plug everything in.

9 = 2(1) + b

Simplify.

9 = 2 + b

Subtract 2 from both sides.

9 - 2 = b

b = 7

Therefore, our y-intercept is 7! :)

Now that we have both the y-intercept and the slope, we can finally plug this into a new equation, using slope intercept form.

y = mx + b

y = 2x + 7

~Hope I helped!~

y = ax + b

Here the slope is 2.

Then, y = 2x + b

The line is passing through (1;9).

We just have to substitute that in the equation.

9 = 2*1+ b
b = 9 - 2
b = 7

That's the intercept.

Eventually, the equation is : y = 2x + 7

Hope this helps !

Photon

During a 5-year period, 32% of snowstorms in a certain city caused power outage Fifty-one of the snowstorms did not cause power outages. Find the total number of snowstorms in this city over the 5-year period.

Answers

To answer this question you will consider that if 32% of the storms did cause outages, then 100% (all of them)-32%= 68% did NOT produce a power outage. We can say that 68% of the total is 51.

This can be written as 0.68 x = 51 where x is the total number of snowstorms. Divide both sides by 0.68 to solve for x. X = 75 snowstorms. Another way to do this is to use Ratios. See the attached page for the strategy.

Answer:
Total number of snowstorms = 75 storms

Explanation:
We are given that:
32% of the snowstorms caused power outage
This means that we can get the percentages of the snowstorms that did not cause power outage as follows:
% of storms not causing outage = 100% - 32% = 68%

Now, we are given that the number of snowstorms that did not cause power outage is 51
Assuming that the total number of storms is x, the equation would be as follows:
68% * x = 51
0.68x = 51
x = 51 / 0.68
x = 75 storms

Hope this helps :)

Malik drinks 1\2 liter of water and 1\3 liter of liter of juice.did malik drink more water or juice?

Answers

malik drank more water than juice

I don’t know how to find the missing angles

Answers

Actually those 4 angles are equal to 110 because those are vertical angles

you have to divide because 2 change a smaller number two a larger number divide

Kerry cut an 8 foot long board into 6 pieces that are equal in length. Represent this problem as a fraction

Answers

The answer is 8/6. Hope this helped! God bless :)

8/6 which is simplified to 4/3

50% of babies are born female. Olive wants to find the probability that 20 or more of the 50 babies born today were female. Use the simulation data to find the probability. Round to the nearest percent.

Answers

It is 94%. Add everything from 20-21 all the way onwards and divide by 200. Then multiply by 100.

find the measure of the missing angle in the triangle shown 49° 57°

Answers

Ok, we know that there are 270 degrees in a triangle, so just add 49+57, the you'll get 106, 270-106=164. ANSWER: 164

In a triangle everything must add up to 270 degrees meaning that if there is already 49 and 57 you must add them both together so 49+57 is 106 so you would now have to subtract 106 from the total number of the triangle, being 270.
So the equation would have to be 270-106= 164. The missing angle that you are missing is 164 degrees

Which relation is a function of x?

Answers

The correct awnset to that question would be D

Answer:

last option is correct.

Step-by-step explanation:

A relation is a function if each x value has a unique y value.

We'll use this concept to check whether the relation is a function or not.

For the first relation,

the x value 2 has two different values -9 and 8 . Hence, it is not a function.

For the second relation,

the x values -8 and 1 has different y values . Hence, it is not a function.

For the third relation

The x value -5 has different y values. Hence, it is not a function.

For the fourth relation

All the x values have unique y values. Hence, from the definition it is a function.

Therefore, last option is correct.

You have $85 in your bank account. Each week you plan to deposit $7 from your allowance and $25 from your paycheck. The equation bequals85plus(25plus7)w gives the amount b in your account after w weeks. How many weeks from now will you have $275 in your bank account?

Answers

Answer:
number of weeks = 6 weeks

Explanation:
You initially have $85
Each week (w), you will deposit $7 in addition to $25

This means that the equation representing the amount (b) in the account will be:
b = 85 + (7+25) w
b = 85 + 32w

Now, we want to know in how many weeks will the amount saved be equal to $275.
To get the number of weeks, we will simply substitute with b = $275 in the above equation and solve for w as follows:
b = 85 + 32w
275 = 85 + 32w
275 - 85 = 32w
190 = 32w
w = 5.9 which is approximately 6 weeks.

Hope this helps :)

PLS HURRY FIRST ANSWER IS MATKED BRAINLEST!!!

What is the volume of the piles of hay??

Answers

6 x 4 x 3 = 72

1 x 2 x 4 = 8

72 -8 = 64 cubic feet

the pyramid arena in memphis tennessee is a square pyamid that is 321 feet tall. the base has 600 foot sides. find the volume of the pyramid

Answers

38,520,000 [tex] ft^{3} [/tex]

The volume of a pyramid is represented by

V = [tex] \frac{l * w* h}{3} [/tex]

The sides are 600 and the height is 321 so by filling in the values in the formula, you can get to your final answer. This is represented in the attached image.

PLZ!!! HELP!!!!!!!!!

This figure is 14 of a circle.

What is the best approximation for the perimeter of the figure?

Use 3.14 to approximate pi.

A.7.85 in.
B.12.9 in.
C. 17.9 in.
D. 31.4 in.

The file is the picture of the quarter or 1/4 circle

Answers

The answer is c with a side of bacon hope that helps. :)

Answer:

C. 17.9

Step-by-step explanation:

Formula: 1/4 π x d

d = diameter

d = 2r

1/4 π x 10 = 10/4 π

Add the 2 non-curve sides

5 + 5 = 10

10/4 x (3.14 = π) x 10

= 17.9

I hope this helps! :)

a square has the sides of 2 yards. plastic cues with sides of 8 inches are placed on the rug. if the cubes cost $2 each, how much money is needed to completely cover the rug with the cubes

Answers

The square is 6 by 6 feet or 72 by 72 inches.
The area of the square is 5184 inches squared.
Divide the area by 64 (area of cube) to equal 81 cubes.
Multiply 81 by 2 to find cost.
Cost = $162

Hope this helps!! :)

A mini-cube measures 1.5 in. wide. A mega-cube is 5 times as wide. What is the volume of the mega-cube, rounded to the nearest tenth?

Answers

my guess is it is round to 7.5

Answer:

the answer is 421.9 in³

Hurry I'm TIMED!!!! The following graph shows the low temperatures for the past six nights. What was the range of temperatures for the six nights?

34°F
22°F
12°F
8°F

Answers

Organize by number.

8, 12, 22, 34

Range is the difference between the highest number and lowest number in a set of data. To find the range for this data you take 34 and subtract 8 which gives you 28.

Answer:

the answer above is incorrect! So you take 22 which is the lowest on the graph and you take 34 which is the highest on the graph and 8 is not on the graph so 34-22=12

Step-by-step explanation:

SOYOUR ANSWER IS: 12YOU ARE WELCOME MY DEAREST FRIEND!

After taking core samples all over a cone-shaped mountain, you have determined that for every 1,000,000 yd3 there is about 2 lbs of gold to be mined. If the mountain has a base that is 2,000 yards wide and a height that is 3,000 yards tall, about how much gold is it expected to hold?

Answers

Final answer:

To find the expected amount of gold in the mountain, calculate the volume of the cone and multiply it by the gold density.

Explanation:

To determine the amount of gold expected to be held in the mountain:

Calculate the volume of the cone using the formula V = (1/3)πr²h.

Convert the volume to cubic yards since the gold density is given in lbs per 1,000,000 yd³.

Multiply the volume by the gold density to find the total amount of gold expected in lbs.

What are three two dimensional shapes that could result from slicing a cube

Answers

Any 3 of ...
triangle, square, rectangle, trapezoid, parallelogram, pentagon, hexagon.

How do you solve 9x+2=8x+9

Answers

Try solving for the variable and get everything to one side

start by moving all whole numbers to one side and all x values to the other so you would subtract 2 from each side first and be left with 9x=8x+7 and then you would subtract 8x from both sides and you would have 1x=7 and lastly you would divide each side by 1 and be left with your answer x=7
Hope this helps and have a wonderful day :)

What is the median of the following data set? {6, 3, 9, 1, 7} 3 6 8 9

Answers

The median of a data set is the number in the very middle.
Your answer would be 9.

Answer:

Step-by-step explanation:

translate the verbal phrase into a algebraic expression pls

Answers

2 × (x + 3) < 5
...................................................................

Find x. Round to the nearest hundredth.

Answers

X = 11 x tan(64)

x = 22.55

Justin drank 1 liter of water during soccer practice. He drank 2000 milliliters of water during the soccer game. How many milliliters of water did he drink during the practice and the game?

Answers

1 liter = 1000 mL
2000 + 1000 = 3000 mL
He drank 3000 mL during practice and the game.

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