Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD

Answers

Answer 1

Using the hypergeometic distribution, it is found that there is a 0.0175 = 1.75% probability that all three have a PhD.

The applicants are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

What is the hypergeometric distribution formula?

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

In this problem, the values of the parameters are as follows: N = 20, k = 6, n = 3.

The probability that all three have a PhD is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,20,3,6) = \frac{C_{6,3}C_{14,0}}{C_{20,3}} = 0.0175[/tex]

0.0175 = 1.75% probability that all three have a PhD.

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Related Questions

James has 3 blue candies and 3 green candies. 3 people come in and take 2 candies. What is the probability that they do not take 2 candies of the same color?
~ pls solve, i'm really confused

Answers

Answer:

33.3333333333

Step-by-step explanation:

we see that there are 6 candies in total

we also see that there is a 50% chance that someone will take out 3 candies of the same color,

50/3 = 16.66666666666667

so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333

I hope I could help

At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?

Answers

Answer:

-2

Step-by-step explanation:

25°-27°= -2°

At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?

= 25 - 27

= - 2°

what is 68% as a fraction

Answers

17/25 would be the fraction

The percentage 68% is converted into a fraction number as 17/25.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

The amount of any product is presented as though it were a percentage of a hundred. The ratio is one-quarter of one hundred.

The faction number is given in the form of a percentage. Then the percentage is converted into a decimal number by dividing 100.

⇒ 68%

⇒ 0.68 x 100 / 100

⇒ 68 / 100

⇒ 17 / 25

The percentage 68% is converted into a fraction number as 17/25.

More about the fraction number link is given below.

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Given h(r) = 5r-5,find h(2)

Answers

hello!

[tex]===================================[/tex]

let's find the value of h(2)

we know that

h(r)=5r-5

which means

h of r is 5 times r minus 5

hence

h of 2 is 5 times 2 minus 5

simplify:

h(2)=5(2)-5

h(2)=10-5

h(2)=5

[tex]==================================[/tex]

note:-Hope everything is clear; if you need any more explanation/clarification, kindly ask me, and I will comment and/or edit my answer :)

Answer:

5

Step-by-step explanation:

h(2)=5r-5

=5×2-5

=10-5

=5

A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?

Answers

Answer:

8

Step-by-step explanation:

For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.

So, by the triangle inequality theorem, 1+x>8, which means x>7.

So, the smallest possible whole number length is 8.

A circular concrete patio has a circumference of about 53 yards. The patio has a diameter of d yards. Which expression best represents the value of pi?

Answers

The expression that best represents the value of pi is 53/d.

What is the expression that represents pi?

Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD

53 = πD

π = 53/d

To learn more about how to determine the circumference of a circle, please check: https://brainly.com/question/14351152

The density of apple juice is 1. 04 grams per cm^3

Answers

Answer:

1,040kg/m³

Step-by-step explanation:

1g/cm³ =1,000kg/m³

1.04g/cm³=?

= 1.04×1000

Density =1,040kg/m³

someone help me please

Answers

Answer:

3x + 5y = 15

Find gradient:

coordinates taken: (5, 0), (0, 3)

[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\rightarrow \sf \dfrac{3-0}{0-5}[/tex]

[tex]\rightarrow \sf -\dfrac{3}{5}[/tex]

Here the y-intercept: 3gradient: -3/5

equation:

[tex]\sf \bold{ y = m(x) + b}[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + 3[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}[/tex]

[tex]\rightarrow \sf 5y =-3x+15[/tex]

[tex]\rightarrow \sf 3x+5y =15[/tex]

Take two points

(0,3)(5,0)x intercept=a=5y intercept=b=3

So

equation of line in intercept form

[tex]\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1[/tex]

Multiply each by 15

[tex]\\ \rm\rightarrowtail 3x+5y=15[/tex]

Ms. Lynch drove her new car
50000000 fast (12 miles in 6 mins.)
that she nearly scared Ms. Allen to
death; who was riding in the car.
What is her speed in miles per hour?

Answers

Answer:

120 miles/hour

Step-by-step explanation:

6 x 10= 60 min

12 x 10= 120 miles

Answer:

Definitely 120 miles per hour.

Step-by-step explanation:

First, if she drove 50,000,000 fast, you need to do 6 minutes x 10 because 10 can go into 50,000,000. So, yes, it's 60. But that isn't right... it's too short. Try the next one.

How about we do the miles. 12 miles x 10 will get you your answer; 120.

I honestly don't know what I'm doing. It most likely isn't 120, but I did the math, and it was hard.

please help with 1 or 2 i’ll mark brainly

Answers

Answer:

700 cubic centimetersDisagree. Volume does not depend on slant height.

Step-by-step explanation:

Cavalier's Principle tells you that the slant figures with the same base area and height have the same volume, regardless of the amount of offset.

__

1.

The volume of the oblique cylinder is the same as the volume of the right cylinder: 700 cubic centimeters.

__

2.

Disagree. Both the volume formula for the pyramid and Cavalier's Principle tell you that the volume is not a function of the slant height.

Find the area of the unshaded region.

Answers

Answer: 21

Step-by-step explanation:

what is the answer for this?

Answers

Answer:

0.729 cubic millimeters

Step-by-step explanation:

Here,

Length ( l ) = 0.9 mm

Base ( b ) = 0.9 mm

Height ( h ) = 0.9 mm

l = b = h = 0.9 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 0.9³

= 0.9 x 0.9 x 0.9

= 0.729 cubic milimeters

Answer:

Formula for volume of cube;

V = [tex]s^{3}[/tex]

Where 's' represents one side of a cube which is being cubed.

or

V = w · l · h

Where 'w' stands for the width, 'l' is the length, and 'h' represents the height.

For this, I'll be using the formula [tex]s^{3}[/tex].

What we know:

Width = 0.9 mmLength = 0.9 mmHeight = 0.9 mm

Use one of these sides to substitute for 's';

V = [tex]s^{3}[/tex]

V = 0.9^3 ← (The " ^ " symbol is another way of showing to the power of.)

V = (0.9 · 0.9 · 0.9)

V = 0.729 mm, the volume of this cube is 0.729 cubic millimetres.

what is the surface area of the a cylinder with base radius 3 and height 8.​

Answers

Bonjour,

πr² *h

3,14 * 3² *8

= 3,14 *9 *8

=>226, 08 ....²

Answer:

66π square units

Step-by-step explanation:

Helppp meee please this one confuses me

Answers

Step-by-step explanation:

=[tex] =(3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

Bro really?? Anyway it's

[tex]anyway \: its \: 3x { }^{2} + 3x + 2x + 2[/tex]

A map shows a scale of 5cm = 40 miles. The distance from Los Angeles,
CA to San Francisco, CA is 400 miles. How far apart will the two cities be
on the map?
OA) 0.5 cm
OB) 5 cm
O C) 50 cm
OD 500 cm

Answers

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

What is the surface area? 5 cm 7 cm 4 cm square centimeters ​

Answers

Answer: 166 feet^2

Step-by-step explanation:

The equation for surface area is 2(wl+hl+hw). So that would be:
Surface Area = 2×(5×7 + 5×4 + 7×4) = 166 feet^2

Answer:16 square cm

Step-by-step explanation: Surface area = base, height (Side 1 + Side 2+ Side 3) H = Side 1 = 5 cm

Side 2 = 7cm

Side 3 = 4cm (add all these numbers ) = 16 Square cm

Given QR || TU. Enter segments in the blanks provided that would result in a true
equation.

Answers

The similar Triangle OPN and triangle LMN are similar have the ratio LM / MN = OP / NP

What are similar figures?

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle OPN and triangle LMN are similar, hence:

LM / MN = OP / NP

The similar Triangle OPN and triangle LMN are similar have the ratio LM / MN = OP / NP

Find out more on similar figures at: https://brainly.com/question/2644832

find the simple interest on $6000 invested for 8 years at 4%

Answers

Answer:

$1920.00

Step-by-step explanation:

You want to calculate the interest on $6000 at 4% interest per year after 8

year(s).

The formula we'll use for this is the simple interest formula, or:

I= P * r * t

Where:

• P is the principal amount, $6000.00.

• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.

• t is the time involved, 8.…..year(s) time periods

So, t is 8...year time periods.

To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:

The interest is: $1920.00

what is the answer please i need help asap

Answers

Answer: a third

Step-by-step explanation: im simply a genius

Omar thinks his pet goldfish, Finn, might be lonely. So, Omar buys another goldfish to keep Finn company. He also buys a large 10-gallon tank so the two fish can swim together. If Finn currently lives in a 2-quart fish bowl, how many times bigger is his new tank than his old bowl?

Answers

Answer:

i think 20 times bigger  

Step-by-step explanation:

Answer:

times 20

Step-by-step explanation:

2 quart to 10 gallon

4 quarts= 1 gallon

So 2quarts x 20 quarts= 40 quarts= 10 gallons

help, asap, explain, thx
a^2-b^2=8
a+2=2
then a-b=?

Answers

Step-by-step explanation:

a + 2 = 2

a = 2 - 2

a = 0

a² - b² = 8

0 - b² = 8

b² = -8

This question is impossible.

Please help as soon as possible

Answers

Answer:

[tex]9 \times 3 = 27 \\ 15 \times 6 = 90 \\ = 30.255 \\ 49 \times 3.14 = 153.86 \\ 153.86 + 30.255 + 27 = 211.115[/tex]

FIND THE VOLUME OF EACH SNOWBALL)

Joshua and Isabella are having a snowball fight. Joshua has a snowball, shaped as a sphere, with a radius of 6 cm. Isabella also has a spherical snowball that is 6cm across the center of the sphere find the volume of each snowball use 3.14 for pi

Answers

Answer:

Step-by-step explanation:

solve 2-6(1-x)=6-4(-x-2) for x

Answers

Answer:

x = 9

Step-by-step explanation:

Simplifying

2 + -6(1 + -1x) = 6 + -4(-1x + -2)

2 + (1 * -6 + -1x * -6) = 6 + -4(-1x + -2)

2 + (-6 + 6x) = 6 + -4(-1x + -2)

Combine like terms: 2 + -6 = -4

-4 + 6x = 6 + -4(-1x + -2)

Reorder the terms:

-4 + 6x = 6 + -4(-2 + -1x)

-4 + 6x = 6 + (-2 * -4 + -1x * -4)

-4 + 6x = 6 + (8 + 4x)

Combine like terms: 6 + 8 = 14

-4 + 6x = 14 + 4x

Solving

-4 + 6x = 14 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

-4 + 6x + -4x = 14 + 4x + -4x

Combine like terms: 6x + -4x = 2x

-4 + 2x = 14 + 4x + -4x

Combine like terms: 4x + -4x = 0

-4 + 2x = 14 + 0

-4 + 2x = 14

Add '4' to each side of the equation.

-4 + 4 + 2x = 14 + 4

Combine like terms: -4 + 4 = 0

0 + 2x = 14 + 4

2x = 14 + 4

Combine like terms: 14 + 4 = 18

2x = 18

Divide each side by '2'.

x = 9

Simplifying

x = 9

Write down the irrational numbers from the following.

1/3, 0.65, square root 6, 2/5, cube root 8, pie​

Answers

As we can see the value of root 6 does not terminate after 3 decimal places. It can still be extended further. Hence, this makes √6 an irrational number.

hope it will help you..

A survey stopped men and women at random to ask them where they purchased
groceries, at a local grocery store or online.


How many men surveyed shop at a local grocery store.

Answers

35 men because it says 35 men shop at a grocery store

Please answer the question in the picture :) tysm

Answers

Answer:

a= 50

b=50

c=110

d=20

Answer:

Step-by-step explanation:

This is a kite. So the two triangles formed by the longest diagonal being drawn in form 2 congruent triangles.

Therefore c = 110 degrees.

d = 20 degrees.

a and b are found by noting that every triangle has 180 degrees.

110 + 20 + a = 180           Combine the left.

130 + a = 180                   Subtract 130 from both sides

a = 180 - 130

a = 50 degrees

b also equals 50 degrees.  Congruent triangles

Answer

a = 50b = 50c =  110d = 20

the sum of a minutes and b seconds, expressed in minutes, is:​

Answers

Answer:

(1+b/60) minutes

Step-by-step explanation:

A minute = 1minute

b seconds = b/60minutes =b/60 minutes

sum of a minute and b seconds= (1+ b/60) minutes

ab" that goes through points (0,9)
Write an exponential function in the form y
and (10,9216).

Answers

[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{0}~~,~~\stackrel{y}{9})\qquad \implies 9=ab^0\implies 9=a(1)\implies 9=a~\hfill \underline{y=9b^x} \\\\\\ (\stackrel{x}{10}~~,~~\stackrel{y}{9216})\qquad \implies 9216 = 9b^{10}\implies \cfrac{9216}{9}=b^{10}\implies 1024=b^{10} \\\\\\ \sqrt[10]{1024}=b\implies 2=b~\hfill \underline{y=9(2)^x}[/tex]

The Exponential function is [tex]y = 9(2^{x} )[/tex]

What is Exponential function?

The mathematical expression for an exponential function is f (x) = aˣ where “x” denotes a variable and “a” denotes a constant that is the base of the function and ought to be greater than 0. The most regularly utilized remarkable capability base is the supernatural number e, which is roughly equivalent to 2.71828.

Given function

y = abˣ

and coordinates (0, 9) and (10, 9216)

when x = 0,  y = 9

[tex]y = ab^{x}[/tex]

substitute values

9 = ab⁰

9 = a

and [tex]y = ab^{x}[/tex]

when x= 10 and y = 9216

9216 = 9(b)¹⁰

1024 = b¹⁰

[tex]\sqrt[10]{1024}[/tex] = b

b = 2

[tex]y = 9(2^{x} )[/tex]

Hence equation is [tex]y = 9(2^{x} )[/tex].

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The length of a square is 3x - 4 units. Find the area in terms of x.

Answers

Answer:

9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true

Step-by-step explanation:

L * W =  area  length = width on a sqare so L * L = area too

(3x - 4) * (3x - 4)

use foil method

9x^2 - 24x + 16

Answer:

9x^2 − 24x + 16

Step-by-step explanation:

To find the area of a square, you use the formula

A = x^2

So we plug in 3x-4 for x

A = (3x-4)^2

A = 9x^2 − 24x + 16

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