Given:
Total number of people = 10
To find:
The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.
Solution:
We know that the number of ways to select r items form n times is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].
The number of remaining people is [tex]10-2=8[/tex].
The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].
The number of remaining people is [tex]8-3=5[/tex].
The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].
Now, the total number of ways is:
[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]
[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]
[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]
[tex]Total=45\cdot 56\cdot 1[/tex]
[tex]Total=2520[/tex]
Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.
Martine grew at an average rate of 6cm/year for the first 18 years of her life. If Martine was 50 cm long when she was born, how tall was Martine when she turned 18?
Answer:
158cm
Step-by-step explanation:
Martine had the height of 50cm when born.
Every year she grows at an average rate of 6cm
So the the first 18 years will be 6cm × 18 = 108cm
She will be 108cm + 50cm = 158cm tall by the time she turns 18 years
50cm + (6 × 18)cm
50cm + (6 × 18)cm50cm + 108cm
50cm + (6 × 18)cm50cm + 108cm158cm
Andrea paid $9.99 to join an online music service. She purchases 12 songs each month at a cost of $0.79 per song Andrea thinks after six months she will have spent around $40 total is Andrea‘s estimate reasonable?
Answer:
không
Step-by-step explanation:
Answer:
I have no idea you can use the app paper.
Step-by-step explanation:
Hope it helps.
black pencils cost 75 naira each and colour pencils cost 105 naira each if 24 mixed pencils cost 2010 naira how many of them were black hint let there be x black pencils thus there are (24-x) coloured pencils.
Answer:
number of black pencils is 17
For the function
f
(
x
)
=
5
(
x
+
10
)
f(x)=5(x+10), find
f
−
1
(
x
)
f
−1
(x).
Answer:
45
Step-by-step explanation:
Given the preimage and image, find the dilation scale factor
Answer:
it should be 2 as your answer
(8-16) + (8 + 6)
If the parentheses are removed from the above
expression, how will the value of the expression
change?
A. no change
B. increase of 3
C. increase of 7
D. increase of 12
E. increase of 16
Step-by-step explanation:
Right now, we would solve everything within the parenthesis first.
(8 - 16) + (8 + 6)
(-8) + (14)
14 - 8
6
But if we remove the parenthesis, it doesn't matter what order we do things in.
8 - 16 + 8 + 6
8 + 8 - 16 + 6
16 - 16 + 6
6
The reason why both of these are the same, is because the only calculations we're doing are addition and subtraction, which don't care about parenthesis.
Answer:
A
Help needed ASAP rocky!
Answer:
C. {x | x < [tex]\frac{10}{7}[/tex]}
Step-by-step explanation:
x must be less than 10/7
I hope this helps!
Can anyone help me with this?
8.6
Answer:
Solution given:
[tex]\bold{\sqrt{74}=8.60232526704≈8.6}[/tex]
Answer:
[tex]8.6[/tex]
Step-by-step explanation:
Step 1: Find the approximate value of [tex]\sqrt{74}[/tex]
[tex]\sqrt{74}[/tex]
[tex]\sqrt{74}[/tex] ≈ [tex]8.6[/tex]
Answer: [tex]8.6[/tex]
A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3).
On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?
(–1, 2)
(1, 3)
(8, 11)
(9, 12)
i really dont get this at all can someone help me and explain
Answer:
(8,11)
Step-by-step explanation:
1st line
y = x+ 3
We need to find the equation of the other line
We have two points (3, 1) and (4, 3)
Slope
m = (y2-y1)/(x2-x1)
= ( 3-1)/(4-3)
= 2/1 = 2
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y =2x+b
Using the point (4,3)
3 = 2(4)+b
3 = 8+b
3-8=b
-5 =b
y = 2x-5
We have 2 lines
y =x+3 and y = 2x-5
Setting them equal to each other
x+3 = 2x-5
Subtract x from each side
x+3-x = 2x-5-x
3 = x-5
Add 5 to each side
3+5 =x-5+5
8=x
Now we can find y
y =x+3
y = 8+3
y=11
Answer:
c (8,11)
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Which is the solution to the inequality?
2 and three-fifths less-than b minus StartFraction 8 over 15 EndFraction
A. b less-than 2 and StartFraction 1 over 15 EndFraction
B. b greater-than 2 and StartFraction 1 over 15 EndFraction
C. b less-than 3 and StartFraction 2 over 15 EndFraction
D. b greater-than 3 and StartFraction 2 over 15 EndFraction
Answer: Choice D
b greater-than 3 and StartFraction 2 over 15 EndFraction
In other words,
b > 3 & 2/15
or
[tex]b > 3\frac{2}{15}\\\\[/tex]
========================================================
Explanation:
Let's convert the mixed number 2 & 3/5 into an improper fraction.
We'll use the rule
a & b/c = (a*c + b)/c
In this case, a = 2, b = 3, c = 5
So,
a & b/c = (a*c + b)/c
2 & 3/5 = (2*5 + 3)/5
2 & 3/5 = (10 + 3)/5
2 & 3/5 = 13/5
The inequality [tex]2 \frac{3}{5} < b - \frac{8}{15}\\\\[/tex] is the same as [tex]\frac{13}{5} < b - \frac{8}{15}\\\\[/tex]
---------------------
Let's multiply both sides by 15 to clear out the fractions
[tex]\frac{13}{5} < b - \frac{8}{15}\\\\15*\frac{13}{5} < 15*\left(b - \frac{8}{15}\right)\\\\39 < 15b-8\\\\[/tex]
---------------------
Now isolate the variable b
[tex]39 < 15b-8\\\\15b-8 > 39\\\\15b > 39+8\\\\15b > 47\\\\b > \frac{47}{15}\\\\b > \frac{45+2}{15}\\\\b > \frac{45}{15}+\frac{2}{15}\\\\b > 3+\frac{2}{15}\\\\b > 3\frac{2}{15}\\\\[/tex]
Side note: Another way to go from 47/15 to 3 & 2/15 is to notice how
47/15 = 3 remainder 2
The 3 is the whole part while 2 helps form the fractional part. The denominator stays at 15 the whole time.
ANSWER CORRECT AND GET BRAINLIEST
Answer:
answer 1
Step-by-step explanation:
x^2+4x+7
=(x^2+4X+4)+3
=(x+2)^2+3
Find the surface area of the composite solid.
A.
502 m2
B.
574 m2
C.
646 m2
D.
720 m2
Answer:
A is the answer I pretty sure
Answer:
i think the answer is 502 m2
Find the area and the circumference of a diameter 8yd Use the value 3.14 for π, and do not round answer
Answer:
circumference = 25.12 yards
area = 50.24 yards squared or yd^2
Step-by-step explanation:
circumference = pi * d
3.14 * 8 =
25.12
area = pi* r^2
r = 1/2 of d = 4
area = pi * 16
3.14 * 16 =
50.24
Answer:
Area: 50.24yds^2 Circumference: 25.12yds
Step-by-step explanation:
Area: The formula for area of a circle is a = πr^2.
The radius (r) of the circle is 4yds because it is half the length of the diameter. The equation would like like this:
A = (3.14)(4)^2
A = (3.14)(16)
A = 50.24yds
Circumference: The formula for circumference is 2πr. We already know all of the variables so we can plug them in.
C = 2(3.14)(4)
C = 25.12yds
Hope this helps
I will mark you as BRAINLIEST Please help me out here!!
Step-by-step explanation:
C1:
The pattern for this: you add 1/2 every time.
C2:
3, 3 1/2, 4, 4 1/2
C3:
5 1/2
C4:
The 14th
C5:
10
D1:
You add twice as more than you did before, starting at 3.
D2:
48, 96, 192, 384
D3:
192
D4:
The 9th
D5:
384
Hope this all helps.
Answer:
C)
1) As the sequence progresses, each term in the sequence increases by 1/2. 2) 3 ; 3 1/2 ; 4 ; 4 1/2
3) The 10th term in the sequence is 5 1/2.
4) 7 1/2 is the 14th term in the sequence.
5) The 17th term is 9.
D)
1) As the sequence progresses, each term multiplies by 2.
2) 48 ; 98 ; 192 ; 384
3) The 7th term in the sequence is 192.
4) 768 is the 9th term in the sequence.
5) The 8th term in the sequence is 384.
Step-by-step explanation:
FOR C : 1 + 1/2 = 1 1/2, 1 1/2 + 1/2 = 2, 2 + 1/2 = 2 1/2, and so on. This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.
FOR D: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24, and so on. This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.
What is the volume, in terms of cubic inches, of a cone with a diameter of 8 inches and a height of 6 inches?
Answer: [tex]100.544\ in.^3[/tex]
Step-by-step explanation:
Given
Diameter of the cone [tex]d=8\ in.[/tex]
Height of the cone [tex]h=6\ in.[/tex]
Volume of the Cone is given by
[tex]\Rightarrow V=\dfrac{1}{12}\pi d^2h[/tex]
[tex]\Rightarrow V=\dfrac{1}{12}\times \pi\times 8^2\times 6\\\\\Rightarrow V=16\pi \\\Rightarrow V=100.544\ in.^3[/tex]
The volume of the cone is [tex]100.544\ in.^3[/tex]
Choose the equation that represents the graph.
graph of a line passing through points negative 3 comma 0 and 0 comma 3
y = x − 3
y = −x + 3
y = −x − 3
y = x + 3
Answer:
Answer: Option D
Step-by-step explanation:
Hey there!
From the above question;
The line passes through (-3,0) and (0,3).
Use double point formula;
[tex]( y - y1) = \frac{(y2 - y1)}{(x2 - x1)} (x - x1)[/tex]
Keep all values;
[tex](y - 0) = \frac{(3 - 0)}{(0 - ( - 3))} (x + 3)[/tex]
Simplify it;
[tex]y = \frac{3}{3} (x + 3)[/tex]
Therefore, y = x+3.
Hope it helps!
Answer:
D
Step-by-step explanation:
Help Please !!
A right triangle pyramid has a height of 10 inches and a base of 41.57 square inches. What is the volume, in cubic inches, of the pyramid?
Answer:
Step-by-step explanation:
Volume of pyramid = Base area * height
= 41.57 * 10
= 415.7 cubic inches
Which graph represents a function?
Answer:
The last option
Step-by-step explanation:
In order for the graph to be a function it has to pass the vertical line test. If you draw a vertical line through the graph and it only intersects at one point then it is a function.
The following house is called an A-frame house because it looks like the letter A from the front.
Suppose that all edges of this A-frame house measure 6.5 yards, and the height of the house is 5.6 yards.
What is the area covered by the roof? [Type your answer as a number. Do not round.]
__ square yards
The area covered by the roof would be 84.5 square yards.
How to calculate the area covered by the roof of the house?To calculate the area covered by the roof the formula that should be used would be the formula for the area of a square;
That is ;
Area = 2(length×width)
= 2(6.5×6.5)
= 2(42.25)
= 84.5 yards²
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
5. For an acute angle 0, cos(0) = sin(33) is true. What is the value of 0?
Answer:
Value is 57
Step-by-step explanation:
sin 33
= sin (90-57)
= cos 57
Answered by GAUTHMATH
2) The cost of renting a boat for one or more
days is given by the function f(n)=12+20n,
where n = number of days and f(n) = total
cost in dollars.
What is the value of f(7-4)?=
Answer: 3f
Step-by-step explanation:
A game involves rolling a number cube. You get one point if you roll an even number and negative one point if you roll an odd number.
A 7-column table has 3 labeled rows. The first row is labeled Roll with entries 1, 2, 3, 4, 5, 6. The second row is labeled Probability with entries one-sixth, one-sixth, one-sixth, one-sixth, one-sixth, one-sixth. The third row is labeled Point(s) with entries negative 1, 1, negative 1, 1, negative 1, 1.
Which statements are true regarding this scenario? Check all that apply.
The sample space is {1, 2, 3, 4, 5, 6}.
The expected value for the game is 0.
The expected value for the game is One-half.
The game is fair because the expected value is equal to 0.
The game is unfair because the expected value does not equal 0.
Answer:
A. B. D.
Step-by-step explanation:
There are 6 possible values to roll. Since 3 values are even and 3 values are odd, the game should be 0.
Answer:
A, B, D
Step-by-step explanation:
EDG 2021
Brainliest?
For a line that contains the point (3, 4) and has a slope of 4, please name another point on this line. Show the work you did to find this answer.
Answer:
y = 4x - 8
Step-by-step explanation:
y = 4x + b
4 = 4(3) + b
4 = 12 + b
-8 = b
In the class interval 5-10, find the
(i) lower limit
(ii) upper limit
(iii) class mark
(iv) class size
Answer:
lower limit = 5
upper limit = 10
class mark = lower limit + upper limit ÷ 2 = 7.5
class size = upper limit - lower limit
= 10-5 = 5
Step-by-step explanation:
I hope this help you have an great day and safe health
Can someone help me out please
Answer:
CIRCUMFERENCE OF CIRCLE IS 2πr.
=2*3.14*6mi=results be the Answar
An 8 Foot ladder leans against a building. I'd the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? Also, how far from the building is the base of the ladder? round to the nearest 10th
9514 1404 393
Answer:
up the wall: 4√3 ft ≈ 6.9 ftalong the ground: 4 ftStep-by-step explanation:
The side ratios in a 30°-60°-90° triangle are 1 : √3 : 2. Since the hypotenuse of this triangle is 8 feet, the multiplier of these ratio values is (8 ft)/2 = 4 ft.
The triangle sides are ...
4 ft : 4√3 ft : 8 ft
The ladder reaches 4√3 ≈ 6.9 ft up the wall. Its base is 4 ft from the building.
If (x/3)-1 is twice as large as (x/4)-3, what is the value of x?
Answer:
30
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
The equation modelling the statement is
[tex]\frac{x}{3}[/tex] - 1 = 2 ( [tex]\frac{x}{4}[/tex] - 3 ) ← distribute parenthesis by 2
[tex]\frac{x}{3}[/tex] - 1 = [tex]\frac{x}{2}[/tex] - 6 ( multiply through by 6 to clear the fractions )
2x - 6 = 3x - 36 ( subtract 2x from both sides )
- 6 = x - 36 ( add 36 to both sides )
30 = x
If MO= 5x+3 and NO= 6x what is the length of MN
Answer:
MO= 5x +3
NO= 6x
MN= ( collect light terms) 5x+ 6x = 11x +3
ans= 11x+3
If points {M,N,O} are collinear, and N is between M and O, then this would allow us to use the segment addition postulate like this:
MO = MN + NO
MN = MO - NO
MN = (5x+3) - (6x)
MN = (5x-6x) + 3
MN = -x + 3
Answer: -x+3
ok so i have this question and it asks
josh has 30 keys and loses three when he bumped into someone then he finds 7 keys how much keys does he have?
Hey there!
At first, Josh has 30 keys.
Then, he loses 3 keys.
30 keys - 3 keys = 27 keys
After that, Josh finds 7 keys.
27 keys + 7 keys = 34 keys
Josh will have a total of 34 keys.
Hope this helps! Have a great day!
what percentage of 50kg is 65 kg?
Answer:
130
Step-by-step explanation:
65/50*100= 130
