in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies? ​

Answers

Answer 1

Answer:

5880 ways

Step-by-step explanation:

For selections like this, we solve using the combination theory. Recall that

nCr = n!/(n-r)!r!

Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,

= 10C6 * 8C4

= 10!/(10-6)!6! * 8!/(8-6)!6!

= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!

= 210 * 28

= 5880 ways

The arrangement can be done in 5880 ways


Related Questions

Kezang was 5 times as old as his son 10 years ago. After 8 years, Kezang will be twice as

old as his son. What are their present age​

Answers

Step-by-step explanation:

let father's age = x

son's age = y

Five years hence, age of father = x+5

age of son =y+5

So (x+5)= 3(y+5)

⇒x=3y+10

Five years ago, age of father = x-5

age of son = y-5

Sox-5=7(y-5)

⇒3y + 10-5=7y - 35

⇒ 4y = 40

⇒y=10 <<<<<<<
x = 3y +10= 40 <<<<<

Does this graph represent a function?

Answers

Answer:

I think it's a function

Step-by-step explanation:

as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.

Answer:

yes

Step-by-step explanation:

it's a cubic function having maximum and minimum turning points

it has a point of inflation, y - intercept and x-intercept

Find the missing side. Round your answer to the nearest tenth

Answers

Answer:

x = 24.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Sin theta = opp / hypotenuse

sin 75 = 24 /x

x sin 75 = 24

x = 24/ sin 75

x=24.84662

Rounding to the nearest tenth

x = 24.8

I think the missing side is 24.8

B
15x+7
6x+2y|
y +3
2y + 1
С
E
The triangles are congruent. Find the length of each hypotenuse.
A. 3
B. 5
C 17

Answers

Answer:

Hypothenus = 22

Step-by-step explanation:

From the question given above, we were told that the triangles are congruent (i.e same size). Thus,

AC = EF

BC = DE

To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:

For y:

AC = y + 3

EF = 2y + 1

AC = EF

y + 3 = 2y + 1

Collect like terms

3 – 1 = 2y – y

2 = y

y = 2

For x:

BC = 5x + 7

DE = 6x + 2y

y = 2

DE = 6x + 2(2)

DE = 6x + 4

BC = DE

5x + 7 = 6x + 4

Collect like terms

7 – 4 = 6x – 5x

3 = x

x = 3

Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:

Hypothenus = BC

Hypothenus = 5x + 7

x = 3

Hypothenus = 5x + 7

Hypothenus = 5(3) + 7

Hypothenus = 15 + 7

Hypothenus = 22

OR

Hypothenus = DE

DE = 6x + 2y

y = 2

x = 3

Hypothenus = 6(3) + 2(2)

Hypothenus = 18 + 4

Hypothenus = 22

he solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)

Answers

Answer:

The Answer Is Point B (2,0)

Step-by-step explanation:

This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Resou
Grade
A
B C D F
ајӘН
Frequency 5
10
15
3
Find the probability that a student earns a
grade of D or F.
p = [?]
Enter a decimal rounded to the nearest hundredth.
Eva nail

Answers

Answer:

14.29%

Step-by-step explanation:

Total observations that had grade D or F: 5

Total observations: 35

[tex]\frac{5}{35} =\frac{1}{7} =.1429[/tex]

Answer:

.14

without rounding it is .1492 , rounded to the nearest hundredth it is .14

Find the area of a rectangle whose length is 14cm and breadth is 6cm

Answers

Answer:

Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.

 

Traza 1

Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.

 

Traza 2

Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.

 

Traza 3

La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.

 

Traza 4

La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.

 

Traza 5

Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.

 

Traza 6

La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.

 

Traza 7

Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.

 

Traza 8

La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.

 

Traza 9

La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.

 

Traza 10

Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?

 

Traza 11

Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.

 

Traza 12

La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

 

Traza 13

La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo

 

Traza 14

La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.

 

Traza 15

El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.

 

Traza 16

El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.

 

Traza 17

Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.

 

Traza 18

Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?

 

Traza 19

Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.

 

Traza 20

Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.

 

Traza 21

La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.

 

Traza 22

Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.

 

Traza 23

En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.

 

Traza 24

Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.

 

Traza 25

Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.

 

Traza 26

Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.

 

Traza 27

Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.

 

Traza 28

Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.

 

Traza 29

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

 

Traza 30

Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:

 

Traza 31

Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.

 

Traza 32

Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.

 

Traza 33

Step-by-step explanation:

Answer:

A= 84cm

Step-by-step explanation:

length x width= area

plug in the given information.

14cm x 6cm = A

A=84

with a length of 14cm and a width of 6cm multiply them for an area of 84cm.

38)
A man completes a job in 5 days working 8 hours a day. How many days will he take to complete the same job working 2 hours overtime per day in addition?

Answers

Answer:

dbcjchdiskcnbcksksnnckdkxnn

Original measure work: 1 man x 5 days x 8 hours per day = Total Work Content = 40 hours.
Revised Work Schedule: = 40 Hours Work
Answer: 10 hours per day x 4 days x 1 man.
The Balancing Ratio on Time, an 20% uplift in daily labour input with 10 hours worked instead of 8 hours per day.
= 20% reduction in Total Length of Time from 5 days to 4 days)

state the hundred thousands place for 7,832,906,215

Answers

Answer:

Step-by-step explanation:

6 is the thousands place

0 (right next to it) is the 10 thousands place

9 is the hundred thousands place. There is only 1 nine present so the answer is unique.

!!! HELP ASAP !!! I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!

Answers

Hi!
The question is asking you to round to the nearest hundredth. That means that if it’s asking you to round 2.03, it would round down to 2.00.

what is the image of ( 4, -8 ) after a dilation by a scale factor of 1/4 centered at the origin ?

Answers

what we know?:

* scale factor of 1/4

* the point (4, -8)

all we have to do is put 4/4 (because we are dilating by 1/4)

4/4= 1

same for the other one: -8/4= -2

FINAL ANSWER: (1, -2)

A store has clearance items that have been marked down by 55%. They are having a sale advertising an additional 40% off Clarence items what percentage of the original price do you end up paying?

Answers

9514 1404 393

Answer:

  27%

Step-by-step explanation:

The price multiplier for the first discount is (1 -55%) = 0.45.

The price multiplier for the second discount is (1 -40%) = 0.60.

Then the price multiplier for the two discounts together is ...

  (0.45)(0.60) = 0.27

You end up paying 27% of the original price.

Does anyone know how to take the fuzzy stuff off

Answers

Answer:

???

Step-by-step explanation:

PLEASE ANSWER!!
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39

Answers

A: 25.

Explanation: Check the attached image.

For synthetic division, you just need to multiply the 1st number of the polynomial by the divisior, and then, add it up to the next number; then, the coefficient will be multiplied by the divisor, and so on and so forth until you reach the last number... that last coefficient at the end is the reminder that you've been asked for

Is the following shape a square? How do you know?
.8
C.
A
0
O A. No, the opposite sides are not parallel.
B. Yes, the opposite sides are parallel, and all sides are the same
length
O C. No, the sides are not congruent.
D. Yes, the adjacent sides are perpendicular, and all sides are the
same length

Answers

The answer is C because although the sides are parallel, they are not congruent


• The difference between a polynomial or rational equation and polynomial or rational inequality

Answers

Answer:

An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.

If the number of observations for each sample is 150 units, what is the 3-sigma upper control limit of the process

Answers

Complete Question

Complete Question is attached below

Answer:

[tex]UCL= 0.25[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size[tex]n=150[/tex]

Sample Variants [tex]s=7[/tex]

Sigma control limits  [tex]Z = 3[/tex]

Therefore

Total number of observations is Given as

[tex]T_o=n*s[/tex]

[tex]T_o=150 *7[/tex]

[tex]T_0=1050[/tex]

Generally

Summation of defectivee

[tex]\sum np=23+34+15+30+25+22+18[/tex]

[tex]\sum np= 167[/tex]

Generally the equation for P-bar is mathematically given by

[tex]P-bar=\frac{\sum np}{T_o}[/tex]

[tex]P-bar=\frac{167}{1050}[/tex]

[tex]P-bar=0.16[/tex]

Therefore

[tex]Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}[/tex]

[tex]Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}[/tex]

[tex]Sp=0.03[/tex]

Generally the equation for 3-sigma upper control limit of the process is mathematically given by

[tex]UCL = P-bar + Z*Sp[/tex]

[tex]UCL= 0.16 + 3*0.03[/tex]

[tex]UCL= 0.25[/tex]

Question 5 of 25
Find the common ratio for this geometric sequence.
0.7, 2.1, 6.3, 18.9,...
O A. 1.4
O B. 3
O C.-3
D. 0.33
SUBMIT

Answers

Answer:

3

Step-by-step explanation:

common ratio

2.1/0.7=3

6.3/2.1=3

18.9/6.3=3

therefore common ratio is equal to 3

PLEASEEEE HELPPPPPPP!!!!!

Answers

To find S or T add them together:

3/5 + 1/3

Rewrite the fractions to have a common denominator

9/15 + 5/15 = 14/15

Answer: 14/15

Step-by-step explanation:

Here is your answer . Hope it helps.

Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?

Answers

Answer:

[tex]\displaystyle 64[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Rule [Variable Direct Substitution Exponential]:                                         [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]

Step 2: Solve

Rewrite [Limit Property - Multiplied Constant]:                                           [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:       [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer: C. 64

Step-by-step explanation:

Edge 100%

Hey!!! Plz help the question is below in a image

Answers

Answer:

desculpa não consigo responder pq esta td inglês ou espanhol prá mim se vc me dizer como posso fazer para voltar a ser português possa te ajudar em algo

Answer:

2.72 [tex]cm^2[/tex]

Step-by-step explanation:

You first find the area of the whole rectangle.

Then you have to find the area of the circle. The area of a circle is [tex]2\pi r[/tex].

The radius is 1 so it will be 2[tex]\pi[/tex].

[tex]\pi[/tex] equals 3.14 so you have to do 3.14*2 that equals 6.28.

Finally subtract 9-6.28=2.72

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X > 3), n = 5, p = 0.2

Answers

Answer:

0.0064

0.00032

Step-by-step explanation:

Given the details:

P(X > 3), n = 5, p = 0.2

The binomial distribution is related using the formula:

P(x = x) = nCx * p^x * q^(n-x)

q = 1 - p = 1 - 0.2 = 0.8

P(X > 3) = p(x = 4) + p(x = 5)

P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064

P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032


Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12
h
slower than the other. If they meet in 3 hours, what is the rate of each bus?
km
Rate of the slower bus:

Rate of the faster bus:

Answers

Answer:

Rate of slower bus; 90 km/h

Rate of faster bus; 102 km/b

Step-by-step explanation:

We know that formula do distance is;

Distance = speed/time

We are told that One bus travels 12h slower than the other.

Let speed of slower bus be x.

Thus;

Speed of faster bus = x + 12

Speed of slower bus = x

After 3 hours, distance by faster bus = 3(x + 12)

Speed of slower bus = 3x

Since the towns are 576 km apart, then;

3(x + 12) + 3x = 576

Divide through by 3 to get;

x + 12 + x = 192

2x + 12 = 192

2x = 192 - 12

2x = 180

x = 180/2

x = 90 km/h

Faster bus speed = 90 + 12 = 102 km/h

PLEASE HELP!! MIGHT GIVE BRAINLIEST!!!!!

Graph a line with x - intercept of -2 and has a slope of 3

Answers

Answer:

The answer must be between 20 and 5000 characters

Evaluate the following expressions using the chip method. SHOW ALL WORK!!!

Answers

Answer:

a. -7 b. -20c. 7

Step-by-step explanation:

a. -9+2, in this case, it is -7 because you take the bigger number and subtract it by the lower number. If the bigger number is negative your answer will be negative, if the bigger number is positive it will be positive it is just really a basic subtraction problem just add the sign.b. In multiplication +++=+ ++-=- and a -+-=+ do your problem without thinking about the signs and then add the signs with the formula I showed you.c. ---=+

Hope this helps :)!

write the greatest and least number by using the following digits with out repeating any of the digits. 2,5,1,6,3,0,8,7 ​

Answers

Answer:

87653210=highest

01235678=least

Answer:

Least number: 10235678

Greatest number: 87653210

1. Define the following: Odds ratio Relative risk 2. Describe how to calculate the Odds ratio and provde the formula. 3. Describe how to calculate the Relative Risk and provide the formula.

Answers

Answer and Explanation:

Odds ratio is the odds that an outcome would happen given a level of exposure in comparison to the occurrence of that outcome without exposure. Odds ratio is calculated by dividing odds of event occurring with exposure(the first group) by odds of event(usually disease) occurring without exposure. Odds is different from probability(denoted p/1-p). While probability is the number of favorable events divided by total number of events, odds is number of favorable events/number of unfavorable events.

Relative risk, also measuring relationship between exposure and outcome, is the ratio of the probability that an outcome would occur without exposure and probability that an outcome would occur with exposure.

What is the length of segment AC?

Answers

Answer:

10 units

Step-by-step explanation:

Point A (3,-1)

Point B (-5,5)

Distance between them,

√{(-5-3)²+(5-(-1))²}

= √{(-8)²+6²}

= √(64+36)

= √100

= 10 units

Find all the zeros of f(x).
f(x) = 2x3 + 7x2 - 28x + 12
Arrange your answers from smallest to largest. If
there is a double root, list it twice.

Plz help!

Answers

Answer:

The zeroes are -6, 1/2 and 2.

Step-by-step explanation:

f(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one guess for a zero is x = 2.

So substituting x = 2:

f(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient

       2x3  - 4x2

                 11x2 - 28x

                 11x2 - 22x

                          - 6x + 12

                           -6x + 12

                            .............

Now we solve

2x2 + 11x - 6 = 0

(2x - 1)(x + 6) = 0

2x - 1 = 0 or x + 6 = 0, so:

x = 1/2,  x = -6.

Answer: -6, 1/2, 2.

Step-by-step explanation:

{(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one

guess for a zero is x=2.

So substituting x=2:

{(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <

Quotient

Sam can mow a lawn in 40 minutes. Melissa can mow the same lawn in 80 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?

Answers

Answer:

It will take them both 24 minutes to mow the lawn if they are working together.

Step-by-step explanation:

Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:

1/40 + 1/60 = 1 / X

3X + 2X = 120

X = 120/5

X = 24

Thus, it will take them both 24 minutes to mow the lawn if they are working together.

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