Using the combination formula, it is found that:
a) There are 8 students in the group.b) 165 teams of three can be selected from this group.---------------------------
The order in which the students are chosen is not important, which means that the combination formula is used to solve this question.
Combination formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
---------------------------
Question a:
3 students from a set of n, thus: [tex]C_{n,3}[/tex]2 students from a set of n, thus: [tex]C_{n,2}[/tex]Twice as many ways to choose the teams of 3 than the teams of 2, thus:
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 2\frac{n!}{2!(n-2)!}[/tex]
We have to solve for n, thus:
[tex]2!n!(n-2)! = 2(3!)(n!)(n-3)![/tex]
[tex](n-2)! = 3!(n-3)![/tex]
From the factorial concept: [tex](n-2)! = (n-2)(n-3)![/tex], thus:
[tex](n-2)! = 3!(n-3)![/tex]
[tex](n-2)(n-3)! = 3!(n-3)![/tex]
[tex]n - 2 = 3![/tex]
[tex]n - 2 = 6[/tex]
[tex]n = 8[/tex]
There are 8 students in the group.
---------------------------
Question b:
First we have to find the total number of students, using the same logic as item a.
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 3\frac{n!}{2!(n-2)!}[/tex]
[tex]2!n!(n-2)! = 3n!3!(n-3)![/tex]
[tex]2(n-2)(n-3)! = 18(n-3)![/tex]
[tex]n - 2 = 9[/tex]
[tex]n = 11[/tex]
---------------------------
The number of teams of three is:
[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
165 teams of three can be selected from this group.
A similar problem is given at https://brainly.com/question/23302762
Please solve both i will give brainliest!!! Love you in advance <3
how to Calculate the value of the angles indicated by small letters
Answer:
all you need to do is to follow steps . you can also use trigonometric ratios to get your unknown angle or using cosine rule and sine rule.
You plan to cut a board into 3 pieces to repair part of a railing. You are going to cut the two ends of the board off into two equal pieces that are 3.1 feet long, if the remaining piece needs to be 2.27 times longer than the each of the first two cuts what length board should you buy? Round to the nearest tenth
Answer:
the answer might be 20
Step-by-step explanation:
first you add 3.1 to 3.1 to get 6.2
then you multiply 6.2 by 2.27
then you add the answer you get from that to 3.1+3.1 to get the final length to be 20.274 and that would be 20 in the nearest tenth
Rey grew a tomato plant from seed. He measured its height
during the month of June. How much did it grow between
June 21 and June 28?
5 cm?
4 cm?
3 cm?
Answer:
3 cm
Step-by-step explanation:
Fimd the hcf of 144,384 and 432 by division method.
48..................
Please, someone help me with this task, I am stuck
Answer: the equation is y = -5x/6 - 2
Step-by-step explanation:
x1 = -6
y1 = 3
x2 = 6
y2 = -7
now
m(slope) = rise/run = (y2-y1)/(x2-x1)
= (-7-3)/(6-(-6))
= -10/12
= -5/6
now
y = mx+ b
-7 = m*6 + b
or, -7 = -5/6*6 + b
or, -7 = -5 + b
so, b = -2
now
y = mx +b
y = -5/6*x + (-2)
y = -5x/6 - 2
Answer:
y = -5/6 × x - 2 = -5x/6 - 2
Step-by-step explanation:
we have two marked points with seemingly integer coordinates for x and y.
the equation of a line is
y = a×x + b
now, we only need to put the x and y values pairs into this equation and calculate a and b.
P1 = (-6, 3)
P2 = (6, -7)
based on what I can see on the picture.
starting with P1
3 = a×-6 +b
b = 3 + a×6
then with P2
-7 = a×6 + b = a×6 + 3 + a×6 = a×12 + 3
-10 = a×12
a = -10/12 = -5/6
=>
b = 3 + a×6 = 3 + -5/6 × 6 = 3 - 5 = -2
so, the line equation is
y = -5/6 × x - 2 = -5x/6 - 2
What is the smallest integer greater than the square root of 325
Answer:
19
Step-by-step explanation:
√325 ≈ 18.02
The next greatest integer is 19.
If my answer is incorrect, pls correct me!
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-Chetan K
What is the difference between 34343 and 1212
Answer:
33131
Step-by-step explanation: 34343-1212= 33131
Hi! I'm happy to help!
To find the difference, means to use subtraction. So, to solve this, we need to subtract.
34343-1212=33131
The difference between 34343 and 1212 is 33131.
I hope this was helpful, keep learning! :D
can someone help me please?
Hi :)
15x^12/18x^2
Factor 3 out of 15 and 18
3(5x^12)/3(6x^2)
Divide
5x^10/6
Answer:
[tex] \frac{15 {x}^{12} }{18 {x}^{2} } \\ \frac{15}{18} \times \frac{ {x}^{12} }{ {x}^{2} } \\ \frac{5}{6} \times {x}^{12- 2} \\ \frac{5}{6} \times {x}^{10} \\ \frac{5 {x}^{10} }{6} [/tex]
An aircraft carrier left Hawaii traveling west seven hours before a container
ship. The container ship traveled in the opposite direction going 5 km/h slower
than the aircraft carrier for six hours after which time the ships were 540 km apart.
Find the aircraft carrier's speed.
Answer:
so speed of aircraft carrier is 30. thank you
The speed of an aircraft carrier is 30 km/h.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, An aircraft carrier left Hawaii traveling west seven hours before a container ship. The container ship traveled in the opposite direction going 5 km/h slower than the aircraft carrier.
Since,
Speed = distance/time
time is 13 hours, 7 hours before the container ship left then the 6 hours container traveled.
Let "s" be the speed of the aircraft carrier
=> d = 13s
Container ship:
time is 6 hours
speed is 5 km/h slower, so s-5
=> d = 6(s-5)
Since they are going in opposite directions, add up the distances to find how far apart they are
=> 13s + 6(s-5) = 540
Now solve for s-
=> 13s +6s -30 = 540
=> 19s = 570
=> s = 30
therefore, the Aircraft carrier was traveling at the speed of 30 km/h and the container ship at the speed of 25 km/h.
Learn more about speed here:
https://brainly.com/question/28224010
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What is the surface
area of a beach ball
with a diameter of 20
inches?
Step-by-step explanation:
diameter =20inches
radius =20/2=10 in
Surface area of sphere, A = 4πr²
π=3.14
area = 4×3.14×(10)²
area=1,256 in²
Divide 170 in the ratio 3.5 , 1.25 , 2.33 please show calculations.
Answer:
84.04, 30.14 and 55.95
Step-by-step explanation:
First you add the ratios together then divide by 170 and mutliply each answer by the answer of 170 divided by the sum of 3.5, 1.25 and 2.33
Answer:
84.04, 30.14 and 55.95
Step-by-step explanation:
→ Add the ratios together
3.5 + 1.25 + 2.33 = 7.08
→ Divide the answer by 170
170 ÷ 7.08 = 24.01129944
→ Multiply the answer by 3.5 , 1.25 , 2.33
3.5 × 24.01129944 = 84.04
1.25 × 24.01129944 = 30.14
2.33 × 24.01129944 = 55.95
URGENT!! Please help me
Draw the answer on and explain if you can please
Thanks a lot!!
I already filled in the 12345 but I need help on the top row.
Answer:
Step-by-step explanation:
Evaluate the expression, given functions f and h:
f(x) = 3x − 1,
h(x) = −2x2 + 3x − 2.
f
7
3
− h(−2)
Answer:
2.5 5 7.5 10 12.5
Step-by-step explanation:
b) 2.5*6=15
HELPPP MEE OUT PLZZZZZ
How do you find the slope of a line given the points ( -1 , -1 ) and ( 5 , -3 ) on the line?
Answer:
-1/3
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-3-(-1)/5-(-1)
-2/6
-1/3
Best of Luck!
Rewrite the following expressions as addition:
-25 + (-32) - 14
-14 - (-45) - 13
Answer:
-53
Step-by-step explanation:
-25-32-14-14+45-13
=53
Answer:
ANS IS -53
AS +45 &-45 WILL GET CANCELLED
AND -14-14-25 WILL GET ADDED
THAT IS -53
WHAT IS A COMPUTER??
Answer:
A computer is an electronic device for storing and processing data, typically in binary form, according to instructions given to it in a variable program.
Answer:
a computer ia an electronic device which process raw data and gives meaningful information to the user
Pls help me sry for asking so much..
Answer:
Z = 3/2
Hope it helps!! :)
please help angles on a Cartesian plane
Answer:
a) 16/25
b)3/2
Step-by-step explanation:
all explaination is in picturw below
Sketch the graph of y=-4(x+4)^2+4 and identify the axis of symmetry.
Answer: (-4,4) is the vertex. The graph is symmetrical to the x = -4 line.
Step-by-step explanation:
Graph the equation using DESMOS.
Half a watermelon and a half pound of cherries cost $3.09. A whole watermelon and two pounds of cherries cost $8.16. Find the cost of each type of fruit. (Find the cost of cherries per pound)
Answer:
each watermelon=$1.98, each pound of cherry=$4.2
Step-by-step explanation:
all step by step explaination is in picture.
Determine the vertical distance and horizontal distance of P(-2,1) and Q(8,7).
Answer:
5.830952 should be the answer
Step-by-step explanation:
Plz help with these 2 questions WILL GIVE BRAINLIEST!!
Answer:
<ALS - <2 = <1
< LDA + <ADE = 180 degrees
Step-by-step explanation:
<ALS = <1+<2
<ALS - <2 = <1
< LDA + <ADE = 180 degrees since it forms a straight line
Eighth grade
>
A.2 Divisibility rules
Is 932,920 divisible by 4?
Yes or no
Answer:
Yes.
Brainliest, please!
Step-by-step explanation:
If we try to divide 932,920 by 4, we get 233,230, which is a whole number.
Answer:
Step-by-step explanation:
Yes!
Done without a calculator. Just look at the last 2 digits. 20 is divisible by 4 so the whole number is. Now you can check it with your calculator.
932920 / 4 = 233230
ASAP PLS
1. Using the figure below to answer the question. If the sector (APB) has an area of 7pi and m<APB = 44°, find the radius length for circle P. (answer choices are 6.35, 9.27, 7.57, and 9.7)
Answer:
7.57
Step-by-step explanation:
the area = 44/360 × π × r²
7 π = 44/360 × π× r²
eliminate π
7 = 44/360 x r²
r² = 7× 360/44
r² = 57.27
r =√57.27 = 7.57
13 x − y 13 x - y given that x = 11 x = 11 and y = 18 y = 18
Answer:
125
Brainliest, please!
Step-by-step explanation:
13x - y
x = 11, y = 18
13(11) - 18
143 - 18
125
Answer:
125
Step-by-step explanation:
13x - y
Substituting x = 11 and y = 18,
=> 13(11) - 18
=> 143 - 18
=> 125
How would you write the expression "6 is less than a number tripled?"
Answer:
3q
Step-by-step explanation:
i think
Answer:
6< 3x
[where 3x = a number tripled]
What is 6 tenths, 2 hundredths, 8 thousandths in standard form?
A.0.0628 B.0.628 C.6.28 D.628
Answer:
B: 0.628
Step-by-step explanation:
Place value rules.
The value of each digit in a number is known as the place value. The number that has 6 tenths, 2 hundredths, and 8 thousandths can be written in the standard form as 0.628. The correct option is B.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of the place value of a digit in a number:
The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10Given 6 tenths, 2 hundredths, 8 thousandths, this can be written in the standard form as,
Standard form = 0.6 + 0.02 + 0.008 = 0.628
Hence, the number that has 6 tenths, 2 hundredths, and 8 thousandths can be written in the standard form as 0.628.
Learn more about the Place Value here:
https://brainly.com/question/27734142
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What is 0.278 rounded to the nearest tenth?
Answer:
0.3
Step-by-step explanation:
If you like to round 0.278 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post
Therefore the answer is 0.3
Hope you got it
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Look at photo for question ?
Answer:
1/3n - 3<6
n < 27
Step-by-step explanation:
1/3n - 3<6
Add 3 to each side
1/3n -3+3<6+3
1/3 n <9
Multiply by 3
1/3n *3 < 9*3
n < 27