Answer:
(a) 1,902,231,808,400
(b) 84
(c) 20
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\cdot(n-k)!}[/tex]
(a)
Compute the number of ways to select 9 applicants from 100 as follows:
[tex]{100\choose 9}=\frac{100!}{9!\cdot(100-9)!}[/tex]
[tex]=\frac{100!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92}{9!}\\\\=1902231808400[/tex]
(b)
Compute the number of ways to select 6 people from 9 as follows:
[tex]{9\choose 6}=\frac{9!}{6!\cdot(9-6)!}[/tex]
[tex]=\frac{9!}{6!\times 3!}\\\\=\frac{9\times 8\times 7\times 6!}{6!\times 3!}\\\\=\frac{9\times 8\times 7}{3!}\\\\=84[/tex]
(c)
Compute the number of ways to select top 3 candidates from 6 as follows:
[tex]{6\choose 3}=\frac{6!}{3!\cdot(6-3)!}[/tex]
[tex]=\frac{6!}{3!\times 3!}\\\\=\frac{6\times 5\times 4\times 3!}{3!\times 3!}\\\\=\frac{6\times 5\times 4}{3!}\\\\=20[/tex]
Solve for x.
A)-6
B)-9
C)-15
D)-18
The line passing through the points (-2,12) and (3,-23) intersects the line passing through which of these pairs of points ? Select three that apply .
Answer:
The equation of the straight line passing through the points
7x +y +2=0
Step-by-step explanation:
Step(i):-
Given points are ( -2 , 12 ) and ( 3, -23)
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-23-12}{3-(-2)} = \frac{-35}{5} =-7[/tex]
Step(ii):-
The equation of the straight line passing through the points
[tex]y - y_{1} = m( x-x_{1} )[/tex]
[tex]y - 12 = -7( x-(-2) )[/tex]
y - 12 = - 7x -14
7 x + y - 12 + 14 =0
7x +y +2=0
pls help me i need help asap as possible
The first one is A and the second one is D.
what is 3/4. ÷ 1/6
Answer:
9/2
Step-by-step explanation:
Calculator
can you answer those 2 questions please?!thank you
Answer:
Question 1: Fraction
Question 2: Equal
Step-by-step explanation:
I know Q1 is right, I'm not so sure about Q2 so I'm sorry if that's wrong
"The Martin family's truck gets an average of 22 miles per gallon. Predict how many miles then can drive using 3 gallons of gas." I NEED THE ANSWER ASAP PLEASE
Answer: 66miles on 3 gallons of gas
Step-by-step explanation: multiply 22 by 3
Quadrilaterals and other polygons
Answer:
BD is a perpendicular bisector of AC
Find the whole.
40% of what number is 6?
40% ofis 6.
(Type a whole number.)
Answer:
2.4
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
it is 15 I think!!!!!
Find the slope of the line that passes through (33,47) and (9,53)
Answer:
-1/4
Step-by-step explanation:
y2-y1 / x2-x1 = 53-47 / 9-33 = 6/-24 = -1/4
Please help me answer these two questions!!!
Question 15 (5 points)
Solve |3x - 2| = |x + 1|
A) x = 3/2 or x= 1/4
B) x= 1/4
C) No solutions
D) x = 3 or x = -4
Answer:
A) x = 3/2 or x= 1/4
Step-by-step explanation:
Solve for x
|3x − 2| = |x + 1|
Rewrite the absolute value equation as four equations without absolute value bars.
3x − 2 = x + 1
3x − 2 = − (x + 1)
− (3x − 2) = x + 1
− (3x − 2) = − (x + 1)
After simplifying, there are only two unique equations to be solved.
3x − 2 = x + 1
3x − 2 = − (x + 1)
Solve 3x − 2 = x + 1 for x.
Move all terms containing x to the left side of the equation.
2x − 2 = 1
Move all terms not containing x to the right side of the equation.
2x = 3
Divide each term by 2 and simplify.
3
x = ------
2
Solve 3x − 2 = − (x + 1) for x.
Simplify − (x + 1).
3x − 2 = −x − 1
Move all terms containing x to the left side of the equation.
4x − 2 = −1
Move all terms not containing x to the right side of the equation.
4x = 1
Divide each term by 4 and simplify.
1
x = ------
4
can you do number one
Answer:
equally likely
Step-by-step explanation:
Hello! Does anyone know the answer for this question and how to work it out. I NEED HELP ASAP. I need the full workout out of it also
sorry i realy dont know sorrryy
If you ask the first 50 females who enter a restaurant to complete a survey about their experience, who is the sample?
Answer:
the first girl
Step-by-step explanation:
because the first girl to take the survey is a sample but the rest that follows are just extras(can i get brainliest pls)
The sample in this scenario would be the first 50 females who enter the restaurant and are asked to complete a survey about their experience. These 50 females form a subset of the entire population of females entering the restaurant during that specific period.
A sample is a smaller group selected from a larger population for the purpose of gathering information or conducting research. It is often used in situations where it is impractical or impossible to survey the entire population. By surveying this sample of 50 females, the restaurant may gain insights into the experiences and opinions of their female customers.
It's important to note that the sample should ideally be randomly selected to ensure that it represents the population fairly. In this case, if the first 50 females entering the restaurant are chosen randomly, they can provide valuable feedback on their overall experience, which may help the restaurant make improvements or gain valuable insights into their customer base.
To know more about a sample:
https://brainly.com/question/32907665?
#SPJ2
Daren draws a scale model of the Statue of Liberty
that is 15 inches tall. If the Statue of Liberty is 305
feet tall, what is the scale of the model?
Answer: 1525
Step-by-step explanation:
Explanation:
One way we can do this is to divide the hight of the Statue by the model height:
305ft 1525ft
20in = 1 in
And so for every inch of the model, it represents 15.25 feet.
Select the graph that correctly represents the cost, y, in dollars, to buy x grapefruit that cost $1.50 each.
Answer:
The first graph
Step-by-step explanation:
find the percent increase. round to the nearest percent from 85 books to 134 books. the percent increase is *blank*
Answer:
57.65%
Step-by-step explanation:
((y2 - y1) / y1)*100 = your percentage change
(where y1=start value and y2=end value)
((134 - 85) / 85) * 100 = 57.65 %
BRAINLLEST HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
1200cm
Step-by-step explanation: this is the suface area:)
Answer:
face 1. 5, 8 - area = 40
face 2. bottom, 3, 8 = 24
face 3. Back ,4, 8 = 32
triangular faces, 3 , 4, A=6
Step-by-step explanation:
Surface area should be 108 if i'm not mistaken.
I'll GIVE YOU BRAINLIEST ANSWER!!! If someone can help me with this problem???
The sum of two numbers is 15. One number is 3 less than the other number. Find the
smaller number
Answer:
6+9 I think so 6
Step-by-step explanation:
I think this is right, hope it helped!
Answer:
6
Step-by-step explanation:
First make an equation where x symbolises the bigger number.x-3 is the smaller one. Solve for x.
x+(x-3)=15
x+x-3=15
x+x=15+3
2x=18/:2
x=6
Jayson reads the first 48 pages of a 480-page book in 3 days. Marcus reads the first 50 pages of a 400-page book in 4 days. Nina reads the first 120 pages of a 600-page book in 5 days. If they continue to read at these rates, who will finish first?
Answer:
Nina will finish first.
Step-by-step explanation:
Let's calculate how many pages each person reads in one day:
Jayson ⇒ 48 pages / 3 days = 16 pages/dayMarcus ⇒ 50 pages / 4 days = 12.5 pages/dayNina ⇒ 120 pages / 5 days = 24 pages/dayThen we divide the number of pages of each book by reading speed of the respective person:
Jayson ⇒ 480 pages ÷ 16 pages/day = 30 days Marcus ⇒ 400 pages ÷ 12.5 pages/day = 32 days Nina ⇒ 600 pages ÷ 24 pages/day = 25 daysThus Nina will take the shortest time finishing her book.
Answer:
Step-by-step explanation:
the amswer is nina
What is the quotient and the remainder of 21÷6
Answer:
The quotient is 3, and the remainder is 0.5. So the answer is 3.5!!!
Step-by-step explanation:
Answer: = 3 R 3
21 divided by 6 equals = 3 with a remainder of 3
Step-by-step explanation:
0 3
6 2 1
− 0
2 1
− 1 8
3
sorry bit hard to explain on this note pad thing uwu
please help me answer this...
Answer: 1.9375
Step-by-step explanation: i tried man gimme brainliest if i got it wrong or right
Which is not equivalent to Ax + By=C?
С
y =
В.
y =
C-Az
B
O y=-4
Oy=
C-A
2
B
Answer: c-a
Step-by-step explanation:
GUESS WHO IMA RIDE ALLLLL NIGHTTTT
duh spirit the stallion u nasty
Answer:
no guess what I'm going to be riding all night is your mom
Which of the following options have the same value as 30%, percent of 81? Choose 3 answers: A 30/100⋅81 B 0.3⋅81 C .03⋅81 D 3/10⋅81 E 30⋅81
Answer:
A, B, and D
Step-by-step explanation:
What is the greatest common factor of 10, 20, and 50?
Answer:
10
Step-by-step explanation:
first you need to find the prime factors of the three numbers
ex:
prime factor of 18= [tex]2*3*3[/tex]
prime of 24=[tex]2*2*2*3[/tex]
there is one 2 and one 3 in common
greatest common multiple 2*3=6
so the greatest common multiple is ten because it is the only one that can divide between all three evenly.
[tex]10=10/10=1\\20=20/10=2\\50=50/10=5[/tex]
so 10 is your answer
Level: Standard
2) Given: -2(x - 4) = 3(x + 12); Prove: x = -5.6
Statements
Reasons
Answer:
comments r full
Step-by-step explanation:
Answer:
hsishisnsidhidhdidjjxnxindidhdinsixhxkxjosjskxijxhsishodjdixjishs
Please help me ASAP I’ll mark Brainly
Answer:
-2.3 repeating
Step-by-step explanation:
help me with this please! asap, thank you
Answer:
i cant see it
Step-by-step explanation: