Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there must be exactly 3 students on the committee b) there must be at least one teacher and at least one student on the committee (3 marks)

Answers

Answer 1

Answer:

a)[tex]X=3300[/tex]

b)[tex]Y=7770[/tex]

Step-by-step explanation:

From the question we are told that:

Number Teachers [tex]T=6[/tex]

Number Student [tex]S=12[/tex]

Number in committee [tex]n=5[/tex]

a) Generally the equation for exactly 3 students on the committee is mathematically given by

[tex]X=^{S}C_3*^{T}C_3[/tex]

[tex]X=^{12}C_3*^{6}C_3[/tex]

[tex]X=3300[/tex]

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

[tex]T=^{(6+12)}C_5[/tex]

[tex]T=8568[/tex]

Therefore

[tex]Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5[/tex]

[tex]Y=8568-798[/tex]

[tex]Y=7770[/tex]


Related Questions

Art class has 444 tables. There are 999 pencils at each table.
Ava multiplied 4\times94×94, times, 9 to find the total number of pencils.
Finn multiplied 9\times49×49, times, 4 to find the total number of pencils.
Who is correct?
Choose 1 answer:

Answers

Answer:

Both Ava and Finn are correct

Step-by-step explanation:

There are 4 tables and 9 pencils at each table

4 ( 9) = 36

9 * 4 = 36

Both Ava and Finn are correct

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST!!

Answers

Answer:

so the simplest way to find the volume of water is by dividing into different....objects

so when dividing you create a rectangular box that has length of 12 width of 14.5 and height of 5 and another rectangular box with length of 7 (19-12) width of 4 and height of 5

now calculate the volume of each box and add them up

v = length x width x height

box 1 = 12 x 14.5 x 5 = 870 ft^3

box 2 = 7x4x5 = 140

now smash them up together = 870+140=1010ft^3

hope that answers your question

CAN SOMEONE PLS TELL ME DOMAIN AND RANGE

Answers

Answers:

Domain is (-4, 3]Range is (-5, 5]

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

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that [tex]-4 < x \le 3[/tex]. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval [tex]-4 < x \le 3[/tex] then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

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

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is [tex]-5 < y \le 5[/tex]. This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

Answer:

Hello,

Step-by-step explanation:

Domain(f)= ]-4;3]={x€R | -4<x≤3}

Rang(f)=]-5;5]={y€R | -5< y ≤5}

[tex]\frac{\sqrt{x} +1}{x-\sqrt{x} +1}[/tex] Với x≥0. Tìm GTLN

Answers

Answer:

Step-by-step explanation:

[tex]\frac{\sqrt{x}+1 }{x-\sqrt{x}+1 }=\frac{\sqrt{x}+1}{(x+1)-\sqrt{x}}\\\\=\frac{(\sqrt{x}+1)([x+1]+\sqrt{x})}{([x+1]-\sqrt{x})+([x+1)+\sqrt{x}])}\\\\=\frac{\sqrt{x}*x+\sqrt{x}*1+\sqrt{x}*\sqrt{x}+1*x+1*1+1*\sqrt{x}}{(x+1)^{2}-(\sqrt{x})^{2}}\\\\\\=\frac{x\sqrt{x}+\sqrt{x}+x+1+x+\sqrt{x}}{x^{2}+2x+1-x}\\\\=\frac{x\sqrt{x}+2\sqrt{x}+2x+1}{x^{2}+x+1}\\\\[/tex]

(100 PTS!!) Match the following vocabulary

Answers

Answer:

Step-by-step explanation:

1. arc length

2. semicircle

3. minor arc

4. arc measure

5. circumference

6. radius

7. diameter

HOPE THIS HELPS

Answer:arc length

2. semicircle

3. minor arc

4. arc measure

5. circumference

6. radius

7. diameter

Step-by-step explanation:

$60 is shared between Ali, Ben and Carol in the ratio of 5 :3 : Z How much does Ben get?

Answers

Answer:

the answer is 100:60:40 hope it helps

WILL GIVE BRAINLEST!Two machines are printing shirts. The first machine can produce 2.400 shirts in 150 minutes. The second machine can produce 2.400 shirts in 120minutes. If the two work together, how long will it take them to produce 6,480 shirts? If necessary, round your answer to the nearest whole number.

Answers

Step-by-step explanation:

see the answer in attached picture

pls mark me as brainliest pls

Answer:

If two machine works together it takes 180 minute to complete 6480 shirts

Step-by-step explanation:

2400 ÷ 150 = 6

So here,

1st machine produces 20 shirts per minutes

let, x=minutes for shirt's production

Now,

(16+20)x=6480

36x=6480

x=6480/36

Therefor, x=180 minutes

30 points PLEASE HELP!!!!
Find the volume of the pyramid.
76.34 ft3
458.06 ft3
916.11 ft3
305.37 ft3

Answers

Answer:

916.11 ft³

Step-by-step explanation:

(9×6)×7.83/2×13/3

= 211.41×13/3

= 916.11 ft³

Answered by GAUTHMATH

Answer:

916.11 ft³

Step-by-step explanation:


(

2
,
2
)
(−2,2) under a translation is
(

3
,
5
)
(−3,5). Find the coordinates of the image of the point
(

3
,
1
)
(−3,1) under the same translation.

Answers

Answer:

kslskd बोडलालामसूनिविवल

james cuts 2 of his neighbor's lawn the first is 1000 m long and 100 m wide what is the area

Answers

The formula for area is l(w). This stands for length and width, or long and wide in this problem. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000m.

Step-by-step explanation:

The formula for area is l x b. This stands for length and breadth. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000 m.

HOPE IT HELPS YOU

MARK ME BRAINLIEST

which of the following functions are an example of exponential decay???

Answers

Answer:

C. II only

Step-by-step explanation:

iyzgkxhldlufulduo

Consider the reflection of parallelogram PQRS across the line of reflection wy

Answers

Answer:

Consider the reflection of the parallelogram PQRS across the line of reflection wy if RR = 14 Then RZ= If SX=5 then = 5

Step-by-step explanation:

Simplify the expression.
7(5 +t) - 4(t + 4)
7(5 + t) - 4(t + 4) = [

Answers

7(5 + t) - 4(t + 4) =

= 35 + 7t - 4t - 16 =

= 7t - 4t + 35 - 16 = 3t + 19

please help me is for my homework​

Answers

Answer:

50%

Step-by-step explanation:

so 1 half is colored in so 1/2 is also 50%

Answer:

it's 50% because it's half the circle

X
( = [?]
DK
x Х
А AK
140°
B
HC
Angles are not drawn to scale

Answers

Answer:

40 degrees

Step-by-step explanation:

Supplementary angles are a pair of angles that add up to 180 degrees

Since ABD and DBC are supplementary, you can make the equation:

180=140+x

Simplify and you get x=40

When the sum of the measures of two angles is 180°, such angles are called supplementary angles.

[tex]\bf \large \implies \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]

[tex]\bf \large \implies \: \: x \: = \: 180 \degree - \: 140 \degree[/tex]

[tex]\bf \large \implies \: \: x \: = \: 40 \degree[/tex]

From the Rule y = -4x+1 fill in the following table

Answers

Answer:

y: 1, -3, -7, -11, -15

Step-by-step explanation:

Substitute the value of x in the chart for the formula given:

y = -4x + 1

For the first column in the x-row, do the following

y = -4(0) + 1

y = 1

And...

y = -4(1) + 1

y = -3

And so on.

A man was traveling by air is allowed a maximum of 20kg luggages .The man has four bags weighing 3.5kg ,15 kg ,2kg and 1.5kg .Find excess weight of his luggage. 2 . Express the excess weight as a percentage of his maximum weight allowed.

Answers

Answer:

See explanation

Step-by-step explanation:

Maximum weight = 20 kg

Bag 1 = 3.5kg

Bag 2 = 15 kg

Bag 3 = 2kg

Bag 4 = 1.5kg

Total weight of bags = 22 kg

Excess weight of his luggage = Total weight of bags - Maximum weight

= 22 kg - 20 kg

= 2 kg

Express the excess weight as a percentage of his maximum weight allowed = excess weight / maximum weight × 100

= 2/20 × 100

= 0.1 × 100

= 10%

Express the excess weight as a percentage of his maximum weight allowed = 10%

Solve the equation :
-3 • ( 2 - x ) + 4 = 2 • ( 1 - 2x) + 3
thanks :) ​

Answers

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  1

-6+3x+4=2-4x+3

-8+7x+1=0

7x=7

x=1

Answer:

x=1

Step-by-step explanation:

SEE IMAGE for Solution

Geometry, please answer question ASAP

Answers

Answer:

A

Step-by-step explanation:

The inscribed angle IJK is half the measure of its intercepted arc, so

arc IK = 2 × 75° = 150°

The 3 arcs sum to  360° , then

arc IJ = 360° - (150 + 110)° = 360° - 260° = 100° → A

40) what is the area of a rectangular porch measuring 8 ft x 12/f

45) Create a stem and leaf plot to represent this set of data.
30, 62, 32, 63, 43, 77, 48, 78, 49, 82, 51, 84, 60,


please make sure to answer both questions ​

Answers

40. 8 times 12. = 96 ft

Find the exact value of the indicated trigonometric function for the acute angle a:
Given: sin a=5/13, Find: cos a and tan a

Answers

Answer:

cos a = 12/13

tan a = 5/12

You use these properties to solve the question,

sin²a+cos²a=1

tana=sina/cosa

Show that 1.272727... = 1.27 can be expressed in the form , where p and q are integers and q not equal to 0.​

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]1.272727....=1.\overline{27}\\\\=1+\dfrac{27}{99} \\\\=1+\dfrac{3}{11} \\\\=\dfrac{11+3}{11} \\\\=\dfrac{14}{11} \\[/tex]

One other way:

Let say x=1.272727...

100x=127.272727...

x=1.272727...

99x=126

x=126/99

x=14/11

pls helppppppp it’s due in 20 minutes

Answers

Answer:

hope this helps you

havea great dayy

Answer:

39

Step-by-step explanation:

3(6m-17)

3(30-17)

3(13)

39

Find the surface area of the
rectangular prism.
2 cm
6 cm
3 cm
[?] sq cm
Enter

Answers

Answer:

72 sq cm

Step-by-step explanation:

Surface area of the cuboid is 2*(lb+bh+lh)=2*(12+18+6)=2*36=72

Answer:

36 sq cm

Step-by-step explanation:

This prism is formed by rectangles, and to find the area of a rectangle you have to multiply its sides. So, to find the surface area, you find the area of each rectangle and after add it all:

3×2 = 6 sq cm, and your have two of this rectangles

6×2 = 12 sq cm, and you also have two of this

3×6 = 18 sq cm, and also have two of this

6 + 12 + 18 = 36 sq cm

Please help me!!!!!
What are the answers

Answers

Answer:

y=3x

Step-by-step explanation:

The equation of the line is y=3x

— 12 — бр – (-2)
HELP ASAP

Answers

Answer:

-10 - 6p

Step-by-step explanation:

-12 - 6р - (-2)

~Combine like terms

-10 - 6p

Best of Luck!

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{-12 - 6p - (-2)}\\\\\huge\text{COMBINE the LIKE TERMS}\\\huge\textsf{\underline{\underline{-12 - (-2)}} + \underline{\underline{\underline{(-6p)}}}}\\\\\\\huge\text{\underline{\underline{-12 - (-2)}}}\\\huge\textsf{= -12 + 2}\\\huge\textsf{= \bf -10}\\\\\\\huge\textsf{-6p \text{does not have any like terms so it}}\\\huge\textsf{stays the same}\\\\\\\huge\textsf{= \bf -6p - 10}\\\\\boxed{\boxed{\huge\text{Answer: \bf -6p - 10}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\boxed{\huge\boxed{\frak{Amphitrite1040:)}}}[/tex]

3000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. Meanwhile, 20000 dollars is invested in a bank account at an interest rate of 5 percent compounded annually.

To the nearest year, when will the two accounts have the same balance?

Answers

9514 1404 393

Answer:

  after 89 years

Step-by-step explanation:

For principal p, interest rate r, and number of years t, the two account balances are ...

  a = p·e^(rt) . . . . continuous compounding

  a = p(1+r)^t . . . . annual compounding

Using the given values, we have

  3000·e^(0.07t) . . . . . compounded continuously

  20000·1.05^t . . . . . . compounded annually

We want to find t so these are equal.

  3000·e^(0.07t) = 20000·1.05^t

  0.15e^(0.07t) = 1.05^t . . . . divide by 20,000

  ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms

  ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t

  t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t

  t ≈ 89.4 ≈ 89

The two accounts will have the same balance after 89 years.

Frank can type a report in 2 hours and James takes 7 hours. How long will it take the
two of them typing together?

Answers

Answer: x = 1 hour and 33 minutes

Step-by-step explanation:

Let x = time (hours) it takes typing together

then

x(1/2 + 1/7) = 1

 multiplying both sides by 14:

x(7 + 2) = 14

x(9) = 14

x = 14/9

x = 1.56 hours

or

x = 1 hour and 33 minutes

Hope tjis help you!:)

Answer: 14/9 hr

Step-by-step explanation:

If you divide Frank's ability to write 1 report by 2 hours, he could write half a report in an hour. James could write one seventh of the report in a hour after dividing his ability to write 1 report in 7 hours. Find the least common denominator between 2 and 7, which is 14 convert 1/2 to that, which would be 7/14 and 2/14. Add That together and you'd get the amount of report they can write in an hour. If you multiply this by a number equalvilent to flipping 9/14, you'd get 1. This number is 14/9 hours.

A hemispherical tank is filled with water and has a diameter of 16 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

Answers

Answer: 133,827 lb/ft^3

Step-by-step explanation:

V = (4/3) (3.14)(8^3) = 133,827

The inequalities x < -5 and -X > -5 are the same.
True
False

Answers

QUESTION-:

The inequalities x < -5 and -X > -5 are the same.

True

False

ANSWER-:

FALSE

!! HOPE ITS HELP U !!

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