in how many ways can a principal choose 3 of their 30 teachers to attend a conference

need ko po ng explanation please.....​

Answers

Answer 1

Answer:

[tex]4,060[/tex]

Step-by-step explanation:

[tex]\binom{30}{3}=\boxed{4060}[/tex]

There are 30 teachers for the principal to choose from initially. After the principal chooses one, there will be 29, 28, 27, and so on.

Since the principal is only choosing 3, there are [tex]30\cdot 29\cdot 28=24,360[/tex] permutations. However, the order of which the principal chooses the teachers does not matter. In other words, without loss of generality, let the name of three of the teachers be Adam, Bernie, and Carla. Regardless of whether the principal chooses Adam then Bernie then Carla or Carla then Adam then Bernie, etcetera, the same three teachers are still being chosen.

Thus, we must divide by the number of ways you can rearrange three distinct teachers, which is [tex]3![/tex].

Therefore, the desired answer is [tex]\frac{24360}{3!}=\frac{24360}{6}=\boxed{4,060}[/tex]


Related Questions

if g(x) = 3x + 7 what is the value of g(-2)?

1- -1
2- 1
3- 8
4- 12

Answers

Answer:

12

Step-by-step explanation:

3x+7 = 12

Scientists found that a certain particle of dust doubles every 30 minutes. If the scientists tests this out with 21 grams of the specific dust, how many grams would they have after 2 days?

Answers

Answer: [tex]1.663\times 10^{30}\ gm[/tex]

Step-by-step explanation:

Given

Population of dust particle doubles every 30 minutes

If the initial sample is 21 grams

The model to predict the population will be

[tex]\Rightarrow P=21\cdot 2^{2t}[/tex]

Where t=time in hours

A day has 24 hours . So, for 2 days time is 48 hours

Population is given by

[tex]\Rightarrow P=21\cdot 2^{2\times 48}\\\\\Rightarrow P=21\times 2^{96}\\\\\Rightarrow P=1.663\times 10^{30}\ gm[/tex]

B
5
6
100° 5
A
Ta
60°
4 120°
W
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w = [? 1°

Answers

Answer:

I'm sorry but this is very wordy and hard for people to understand.

please reconsider fixing it and submitting it again for assistance.

The length of a rectangle is 3 yd less then twice the width, and the area of the rectangle is 27 yd^2. Find the dimensions of the rectangle.

Answers

Answer:

4.5yards and 6 yards is your rectangle measurement

(140-x)/(7)+70 = 120. Please answer correctly.

Answers

From question,
(140-x)/7+70=120
Or, (140-x)/7=120-70
Or,140-x=50X7
Or, -x=350-140
Or, -x=210
:• x = -210 answers

Put these numbers in order from least to greatest.
0.78
8.7
0.078

Answers

Answer:

Least:0.078

In between: 0.78

Greatest: 8.7

Step-by-step explanation:

What is the amplitude in the graph of y = 5sin(2x - 1) + 3?

Answers

Answer:

The amplitude is 5

Step-by-step explanation:

The function [tex]y=asin(bx-c)+d[/tex] has an amplitude of [tex]|a|[/tex]. Therefore the amplitude of the function [tex]y=5sin(2x-1)+3[/tex] is [tex]|a|=|5|=5[/tex].

If the farm has 10,000 spinach plants, Describe a method that would produce a random sample and how many in your sample study?

Answers

Answer:

Take an even number of random samples from the 10000 spinach plants

lets assume you take ; 100 random samples  each sample will contain = 10,000 / 100 = 100 spinach plants

Step-by-step explanation:

Given that the total number of spinach plants in the farm = 10,000

To obtain a random sample, take a census of the number of farms wherein the spinach plants are planted, determine the mean size and standard deviation of the farm that way you can apply the central limit theorem.

After determining these Take an even number of random sample from the 10000 spinach plants

lets assume you take ; 100 random samples  each sample will contain = 10,000 / 100 = 100

My mama got me doing freaking school work pls help me out

Answers

Answer:

x=50

Step-by-step explanation:

corresponding angles

Which choice is equivalent to the expression below when x 0?
√328 – 116x + 428 – 12x
O A. 3x12x
O B. 4x/2x
O c. 18x
O D. 32x

Answers

the answer is d hopes this helps you

Nadia is investigating rotations about the center of regular polygons that carry the regular polygon onto itself. She claims that there are rotations about the center that will carry both a regular hexagon and a regular nonagon (9-sided polygon) onto itself. Determine whether each angle of rotation below can be used to support Nadia's claim. Select Yes or No for each angle of rotation

Answers

Answer:

[tex]\theta_1 \ n\ \theta_2 = 120, 240[/tex]

Step-by-step explanation:

The question is incomplete, as the angles of rotation are not stated.

However, I will list the angles less than 360 degrees that will carry the hexagon and the nonagon onto itself

We have:

[tex]Nonagon = 9\ sides[/tex]

[tex]Hexagon = 6\ sides[/tex]

Divide 360 degrees by the number of sides in each angle, then find the multiples.

Nonagon

[tex]\theta = \frac{360}{9} =40[/tex]

List the multiples of 40

[tex]\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320[/tex]

Hexagon

[tex]\theta = \frac{360}{6} =60[/tex]

List the multiples of 60

[tex]\theta_2 = 60, 120, 180, 240, 300[/tex]

List out the common angles

[tex]\theta_1 = 40, 80, 120, 160, 200, 240, 280, 320[/tex]

[tex]\theta_2 = 60, 120, 180, 240, 300[/tex]

[tex]\theta_1 \ n\ \theta_2 = 120, 240[/tex]

This means that, only a rotation of [tex]120, 240[/tex] will lift both shapes onto themselves, when applied to both shapes.

The other angles will only work on one of the shapes, but not both at the same time.

what property 8 + 43 = 43 + 8

Answers

Answer:

commutative property

Step-by-step explanation:

It's basically just changing the order of the equation.

4. Multiply the following fractions and reduce to the lowest form.
(a)9/4 8/81
(b)20 x 4/5​

Answers

a) 2/9
b) 104/5 or 20 4/5
A) 2/9

B) 16

I wrote all the solution you need in this pic so good luck and best of wishes ;)

Find WX. Assume that segments which appear to be tangent are tangent.

Answers

Answer:

Step-by-step explanation:

Tangent from the point outside the circle are equal

WX  = XY

7x - 29 = 2x + 16 {Add 29 to both sides}

7x  = 2x + 16 +29

7x = 2x + 45 {Subtract 2x from both sides}

7x - 2x = 45

5x = 45     {Divide both sides by 5}

x = 45/5

x = 9

WX = 7x - 29

       = 7*9 - 29

        = 63 - 29

WX = 34

Analyze the diagram below and complete the instructions that follow.

Find the exact value of sin(O)

Answers

Answer:  C) 12/13

=====================================================

Explanation:

Use the pythagorean theorem

a^2+b^2 = c^2

to find that c = 13 when a = 12 and b = 5.

So that makes the hypotenuse MO = 13 units long.

The opposite side is MN = 12 units long as this side is furthest we can get from angle O.

The sine ratio involves opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(O) = MN/MO

sin(O) = 12/13

Answer:

C.    12/13

Step-by-step explanation:

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 =  c²

c = 13

------------

sin = opp/hyp

sinO = 12/13

PLEASE PLEASE PLEASE SOMEONE HELP ME THIS IS DUE TODAY

EXPLAINING YOUR ANSWER = BRAINLIEST

What is m∠E?

Answers

Answer:

try 144

Step-by-step explanation:

m<E is basically just ot asking you to find the angle of E, i think :').

And since all angles equal to 180, 180-36=144

(hope ots right)

There are 3 red, 1 blue and 2 yellow marbles in a bag. Once a marble is selected it is not replaced.Find P(red then yellow). *

A.1/6

B.1/5

C.5/6

D.2/5

Answers

Answer:

B)  1/5

Step-by-step explanation:

P(R then Y) = 3/6 · 2/5 = 6/30 or 1/5 simplified

Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?

Answers

Answer:

So , 41 years ago, Mothers age is 3 times of Sally's age. When Sally's age was 13 , and her mom age was 39 (

help......................​

Answers

Answer:

17.

[tex] 7 \times {10}^{ - 6} [/tex]

18. 8 sides (and 8 corners)

19. the chance is 50% or 0.5, and yes, both colors have the same chance.

20. on a coordinate grid make a point at x=1 and y=5. and then simply draw a line through that point.

Step-by-step explanation:

17. the defining digit is 7. and it is at the the 6th position after the decimal point. that is how you write this.

18. the more corners or sides a polygon has, the closer it gets to a circle. that means that the outside angles always add up to 360 degrees.

so, with the inside angles being 135 degrees, the outside angles are 180-135 = 45 degrees.

his many such outside angles can we add together until we reach 360 degrees ?

360/45 = 8 (just imagine : 2×45 = 90, and 90×4 = 360)

so, this polygon has 8 corners and therefore 8 sides.

19. 12 balls are in the bag. the chance for a single ball to be pulled is therefore 1/12.

but there are 6 red balls. we don't care which specific ball we pull, as long as it's red. so, we have 6/12 chances to achieve that.

and yes, for exactly the same reason, black balls have the same chance.

A sculptor needs to lift a piece of marble it’s a cuboid with dimensions 1 by 0.2 by 0.5 marble has a density of 2.7 what’s the mass in kg

Answers

Answer:

Mass of piece of marble  = 0.27 kilogram

Step-by-step explanation:

Given:

Dimensions of cuboid = 1 x 0.2 x 0.5

Density of marble = 2.7

Find:

Mass of piece of marble

Computation:

Volume of cuboid = (l)(b)(h)

Volume of marble = 1 x 0.2 x 0.5

Volume of marble = 0.1

Mass = Density x Volume

Mass of piece of marble  = Density of marble x Volume of marble

Mass of piece of marble  = 2.7 x 0.1

Mass of piece of marble  = 0.27 kilogram

area of the triangle ABC ​

Answers

Answer:

180

Step-by-step explanation:

hope this answer be right :)

The following table shows the probability of rolling the numbers 1 through 7
on a fair 7-sided die.
х
1
2
3
4
5
6
7
P(X) 1/71/71/71/71/71/71/7
What is the standard deviation of the random variable X, "the number that
comes up on the die"?
A. 1.708
OB. 3.745
O C. 2.917
Оооо
D. 3.5
E. 2.0

Answers

Answer:

2.0

Step-by-step explanation:

Couldn't really understnd what you wrote but I'll assume it's the standard deviation of a fair, 7-sided die

The standard deviation is just the square root of the variance (which is just the second moment minus the first moment squared)

The first moment (AKA the average is..)

[tex]\frac{1+2+3+4+5+6+7}{7}=4[/tex]

The second moment is..

[tex]\frac{1^2+2^2+3^2+4^2+5^2+6^2+7^2}{7}=20[/tex]

[tex]\sqrt{20-4^2}=2[/tex]

A rectangular park is 260 m by 480 m. Danny usually trains by running 5 circuits around the edge of
the park. After heavy rain, two adjacent sides are too muddy to run along, so he runs a triangular path
along the other two sides and the diagonal. Danny does 5 circuits of this path for training. Show that
Danny runs about 970 metres less than his usual training session

Answers

Answer:

971 m to nearest metre

Step-by-step explanation:

training distance = 5*2*(260 + 480) m  

Diagonal distance = √(2602 + 4802) m

Heavy rain training distance = 5*(260 + 480 + √(2602 + 4802)) m

Difference between these:

 

5 × 2  × ( 260 + 480 ) - 5 ×( 260 + 480  + √ 260 ^ 2 + 480 ^ 2 )

   = 970 . 5311872087638744

 

difference = 971 m to nearest metre

Hope this answer helps you :)

Have a great day

Mark brainliest

Https://imgur.com/a/n3PRcMY

Answers

1: Those angles are equal. That means 3x + 10 = 5x - 10.
20 = 2x.
That means x = 10

2. Easy now that u have x. Angle 1 is 3x + 10, which means its 3(10) + 10 which is 40

Any of you guys know this answer?

Answers

The answer would be 10

write an equation of the line in slope intercept form

Answers

Answer:

[tex]y=-2x+2[/tex]

Step-by-step explanation:

[tex]y=mx+b[/tex] is the slope intercept

[tex]m[/tex] is the slope

[tex]b[/tex] is the y-intercept

The slope in the graph is 4/2 or 2 simplified. From point (-2,6), you have to go down 4 and right 2 to get to the point (0,2)

The y-intercept is 2 because the line crosses the y axis at exactly 2.

Hope this helps

Two lines are intersecting. What is the value of X? And to your answer in the box

Answers

X= 51 is the answer you need to remember that since they share a straight line you add the together to get 180 which is half a circle

Answer:

x = 51

Step-by-step explanation:

The two angles form a straight line

Angles that form a straight line add up to equal 180

Hence, 2x + 4 + x + 23 = 180

( note that we just created an equation that we can use to solve for x )

we now solve for x using the equation we created

2x + 4 + x + 23 = 180

step 1 combine like terms

2x + x = 3x

4 + 23 = 27

we now have 180 = 27 + 3x

step 2 subtract 27 from each side

180 - 27 = 153

27 - 27 cancels out

we now have 153 = 3x

step 3 divide each side by 3

153 / 3 = 51

3x / 3 = x

we're left with x = 51

A company bought a piece of machinery for $16 200. In the first it depreciated 15%, and in the second year 10%. How much was it worth when two years old?

Answers

It’s is 69% because I know that I’m going to help you

pls help middle school math

Answers

Given ,

5<x<10 and 8<y<19

For y-x,

8-5<y-x<19-10

3<y-x<9

Please help me i would give more points but i dont have much (Giving brainlest)

Answers

5.3x - 8.14 + 3.6x + 9.8

Rearrange to make it easier!

5.3x + 3.6x + 9.8 - 8.14

8.9x + 1.66

B is the answer.

Answer:

Step-by-step explanation:

First, put them in order.

5.3x+3.6x+9.8-8.14

Add 5.3x and 3.6x

8.9x

Subtract 8.14 from 9.8

1.66

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