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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Please help as soon as possible
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]
what is the surface area of the a cylinder with base radius 3 and height 8.
Bonjour,
πr² *h
3,14 * 3² *8
= 3,14 *9 *8
=>226, 08 ....²
Answer:
66π square units
Step-by-step explanation:
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?
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=?
Step-by-step explanation:
a + 2 = 2
a = 2 - 2
a = 0
a² - b² = 8
0 - b² = 8
b² = -8
This question is impossible.
find the simple interest on $6000 invested for 8 years at 4%
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
Find the area of the unshaded region.
Answer: 21
Step-by-step explanation:
what is the answer please i need help asap
Answer: a third
Step-by-step explanation: im simply a genius
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
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
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
Answer:
C
Step-by-step explanation:
It's 50 cm for sure
Answer:
C
Step-by-step explanation:
It's 50 cm for sure
The density of apple juice is 1. 04 grams per cm^3
Answer:
1,040kg/m³
Step-by-step explanation:
1g/cm³ =1,000kg/m³
1.04g/cm³=?
= 1.04×1000
Density =1,040kg/m³
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
Answer:
Step-by-step explanation:
Given h(r) = 5r-5,find h(2)
[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
Please answer the question in the picture :) tysm
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 = 20The length of a square is 3x - 4 units. Find the area in terms of x.
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
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?
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
what is the answer for this?
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 mmUse 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.
Given QR || TU. Enter segments in the blanks provided that would result in a true
equation.
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
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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.
the sum of a minutes and b seconds, expressed in minutes, is:
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).
[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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What is the surface area? 5 cm 7 cm 4 cm square centimeters
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
A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?
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.
please help with 1 or 2 i’ll mark brainly
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.
Write down the irrational numbers from the following.
1/3, 0.65, square root 6, 2/5, cube root 8, pie
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..
someone help me please
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=3So
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]
Helppp meee please this one confuses me
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]
solve 2-6(1-x)=6-4(-x-2) for x
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
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?
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°
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?
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.
what is 68% as a 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.
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