There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?
Answers
[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]
Question :-
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?Answer :-
The coach can choose 3 of the 10 students in 120 ways.[tex] \rule{200pt}{3pt}[/tex]
Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].
Solution :-
As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.
To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-
[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]
Substitute the given values into the above formula and solve for C:
[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]
[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]
Therefore :-
The coach can choose 3 of the 10 students in 120 ways.[tex]\\[/tex]
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Related Questions
Evaluate if x =3 and y = -2
x2+2xy−4y
Answers
Answer:
5
Step-by-step explanation:
With the equation [tex]x^2 + 2xy - 4y[/tex], we can substitute the values of x = 3 and y = -2 into the equation to find its result.
[tex](3^2) + (2\cdot3\cdot-2) - (4\cdot-2)\\\\9 + (6\cdot-2) - (-8)\\9 - 12 + 8\\5[/tex]
Hope this helped!
Find the perimeter of this figure. (Image down below)
Answers
Answer:
The answer is
44 ftStep-by-step explanation:
The figure above is a rectangle
To find the perimeter of a rectangle we use the formula
Perimeter of a rectangle = 2l + 2w
where
l is the length of the rectangle
w is the width of the rectangle
From the question
length = 14 ft
width = 8ft
Substituting the values into the above formula we have
Perimeter = 2(14) + 2(8)
= 28 + 16
We have the final answer as
Perimeter = 44 ftHope this helps you
Increase 150 by 120%
O A. 330
OB. 180
O c. 300
OD. 200
Answers
Answer:
C
Step-by-step explanation:
Find 120% of 150
1.2 x 150 = 180
Increase to 150
180 + 150 = 330
Hope that helped!!! k
Apply
48. Think About a Plan A lumberjack cuts 7 pieces of equal length
from a log, as shown at the right. What is the change in the log's
length after 7 cuts?
• What operation can you use to find the answer?
• Will your answer be a positive value or a negative
value? How do you know?
49. Farmer's Market A farmer has 120 bushels of beans for sale at a farmer's market.
dau what is the change in the
Answers
Answer:
you can use a median method of counting and eliminating each side being each cut but the difference would it would be an equal number as the central off number cut divides one piece of wood into an even number.
Another operation is subtracting the cuts from the pieces you have 7 - 6 = 1 whole. Meaning the answer is correct if you are left with 1
If the cuts were even then you would have an a number of pieces that amount to an odd number.
So with 7 they are even and positive.
With counter checking they are positive as you always start with one piece of wood.
67) Interest on a Loan: Jeff Hubbard borrowed $800 from his brother for 2 years. At the end of 2 years, he repaid
the $800 plus $128 in interest. What simple interest rate did he pay?
Answers
Answer:
0.08%
Step-by-step explanation:
2 years,
the $800 plus $128 in interest. What simple interest rate did he pay?
128/2
$64 a year
64/800=0.08
so 0.08%
Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4
Answers
Answer:
Step-by-step explanation:
[tex]9^{-4}[/tex]
=[tex]\frac{1}{9^{4} }[/tex] ∴ [tex]x^{-n} = \frac{1}{x^{n} }[/tex]
=[tex]\frac{1}{9*9*9*9}[/tex]
=[tex]\frac{1}{6561}[/tex]
A rectangle has a perimeter of 26 feet. Twice its length is one foot more than three times its width (w). What is
the length of the rectangle, in Thet?
Answers
Answer:
The length of the rectangle is 13
Step-by-step explanation:
13 times 2 its equal 26
PLEASE HELP! WHOEVER ANSWERS BEST WITH EXPLANATION BECOMES BRAINLIEST! Maria is conducting a survey to determine the ages of 100 dogs in an animal shelter. Which of the following questions is an appropriate statistical question for this survey? What is the number of dogs in the shelter that are more than 5 years old? What is the average number of years a dog stays at the shelter? How old is the youngest dog in the animal shelter? How old is each dog in the animal shelter?
Answers
Answer:
The answer is either A or B. Answer D is not appropriate for a survey of 100 dogs. Answer C, is also not correct, because it doesn't exactly matter out of 100 dogs. Answer A, is more accurate, then Answer B, because it is more of a statistical question, as in surveys, we want statistics. Thus, I must go with A) - What is the number of dogs in the shelter that are more than 5 years old?
Step-by-step explanation:
Answer:
the average
Step-by-step explanation:
option1: will help you get a population of those above five only therefore frequency for a large group of above five years which you can't analyse
2: you are able to see e.g average is 25yrs so your classes can start from e.g 0 to at most 26yrs therefore clearly defined classes
3 and 4: help you either get upper and lower limits but the other respective limits are infinite
Is △FHK similar to △GHJ? If so, which postulate or theorem proves these two triangles are similar? △FHK is similar to △GHJ by the SSS Similarity Theorem. △FHK is similar to △GHJ by the SSA Similarity Theorem. △FHK is similar to △GHJ by the SAS Similarity Theorem. △FHK is not similar to △GHJ.
Answers
Answer:
ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Step-by-step explanation:
Picture for the given question is missing; find the picture attached.
If [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H
Then ΔFHK ~ ΔGHJ
[tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex]
[tex]\frac{(12+10)}{10}=\frac{(15+18)}{15}[/tex]
[tex]\frac{22}{10}=\frac{33}{15}[/tex]
[tex]\frac{11}{5}=\frac{11}{5}[/tex]
Since, [tex]\frac{\text{FH}}{\text{GH}}=\frac{\text{HK}}{\text{HJ}}[/tex] and ∠H ≅ ∠H [By reflexive property]
Therefore, ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Option (3) will be the answer.
Answer:
ΔFHK and ΔGHJ are similar triangles by the SAS similarity theorem.
Step-by-step explanation:
Verified correct with test results.
what is the angle taken in anticlockwise direction between (1) North-east and south- west
Answers
Answer:
Step-by-step explanation:
North-east has a bearing of 45 degrees
South-west has a bearing of 225 degrees.
Taken anticlockwise,
angle = south-west - north-east
= (225-45)
= 180 degrees
answer
hope this helps....
Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 35 and, in a separate drawing, you must also select the correct single number between 1 and 45. Find the probability of winning the jackpot.
Answers
Answer:
1 / 14608440
Step-by-step explanation:
Given the following :
Winner has to select the five correct numbers between 1 and 35
Then, a single correct number between 1 and 45
Step1:
Number of ways to select 5 corre t numbers between 1 and 35; selecting 5 things from a total of 35 = 35C5
nCr = n! ÷ (n-r)!r!
35C5 = 35! ÷ (35-5)!5!
35C5 = 35! ÷ (30)!5!
= (35 * 34 * 33 * 32 * 31) / (5 * 4 * 3 * 2 * 1) = 324632 ways
Then find number of ways of selecting 1 correct number between 1 and 45:
45C1
45C1 = 45! ÷ (45-1)!1!
45C1 = 45! ÷ (44)!1!
45C1 = 45 ÷ 1 = 45
35C5 * 45C1 = 324632 * 45 = 14608440
Therefore, probability of winning the jackpot :
Required outcome / Total possible outcomes
= 1 / 14608440
Convert 5280 vodas to pivos. Show three significant figures for your answer.
1 pivo = 3.1416 molokos
1 moloko = 2.71828 vodas
Answers
(5280 vodas) * (1/2.71828 moloko/voda) * (1/3.1416 pivo/moloko) ≈ 618 pivos
(because 5280 has 3 significant digits)
Basic math for 20 points + brainliest!
Answers
Answer:
Look at photo
Step-by-step explanation:
In Exercise 4, find the surface area of the solid
formed by the net.
Answers
Answer:
535.2 cm²
Step-by-step explanation:
The surface area the solid formed by the net in exercise 4 can be calculated by finding the area of each part that makes up the net.
The net consists of 2 triangles and 3 rectangles.
Each triangle has a base (b) of 8 cm and a height (h) of = √(8² - 4²) (using Pythagorean theorem)
height = 6.9cm
Each rectangle has length (l) of 20cm, and width (w) of 8cm
Therefore, Surface Area (S.A) = area of 3 rectangles + area of 2 triangles
S.A = 3(l*b) + 2(½*b*h)
S.A = 3(20*8) + 2(½*8*6.9)
S.A = 3(160) + (1*8*6.9)
S.A = 480 + 55.2 = 535.2 cm²
Please help
A) y< 2x+4
B) y< 1/2x+3
C)y> 1/2x+3
D) y> 2x+3
Answers
Answer:
B
Step-by-step explanation:
if it is shaded under than it is <
the slope is 1/2x so that is the answer
Which transformation shows a reflection across the y-axis? A) A B) B C) C D) D
Answers
Answer:
The answer is A
Step-by-step explanation:
This shows a mirroring effect over the vertical y axis.
Choices B and C are a translation (aka shifting)
Choice D is a reflection but over the horizontal x axis.
Multiply the input by 2. Then add 4 to the result to get the output.
Answers
Answer:
2x +4
Step-by-step explanation:
The Expression for "Multiply the input by 2 and then add 4 to the result to get the output" is 2x+ 4.
What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Multiply the input by 2.
let the input be x.
So, 2x
Now, add the result to 4
Then, 2x+ 4
Hence, the expression is 2x+ 4.
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determine if the following set of ordered pairs represents a quadratic function explain (5,7),(7,11),(9,14),(11,18)
Answers
Answer:the pairs are not a quadratic eqation
Step-by-step explanation:
The differences between the differences of the y value are not consistent
The set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
What is a function?A relation is a function if it has only One y-value for each x-value.
Given,
The set of ordered pairs
(5,7),(7,11),(9,14),(11,18)
We have to determine whether the (5,7),(7,11),(9,14),(11,18) is quadratic function or not.
Start by representing the function as an x-y table
x:- 5 || 7 || 9 || 11
y:- 7 || 11 || 14 || 18
The difference between the y values is not same
11-7=4
14-11=3
18-14=4
For the function to be quadratic, the above difference must be the same and since they are not, then the function does not represent a quadratic function.
Hence, the set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
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There are a total of two hundred students and chaperones going on a
field trip. Each bus can hold 60 passengers. How many buses will be
used for the field trip? Explain why your answer is reasonable.
Answers
Answer:
4 bus is required for field trip to carry 200 passengers.
Step-by-step explanation:
Total no . of passengers = 200
let the be x bus required to carry 200 passengers
capacity of 1 bus = 60 passengers
capacity of x bus = 60*x passengers = 60x passengers
Thus,
60x = 200
x = 200/60 = 3 2/3
thus, 3.66 bus is required , but no. of bus cannot be in fraction hence we take integral value greater than 3.66 which is 4
Thus, 4 bus is required for field trip to carry 200 passenger.
Which expression is equivalent 6+7n+4+8n?
Answers
Answer: 5(2+3n)
Step-by-step explanation:
Answer:
15n + 10 should be your answer.
Step-by-step explanation:
The table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day. What is P(took a vitamin | got the flu)? (Note: If your fraction will reduce, you need to reduce it.)
Answers
Answer:
1/4
Step-by-step explanation:
25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4
The P(took a vitamin | got the flu) will be 1/4.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.
We need to find the P(took a vitamin | got the flu).
Now, 25 people took a vitamin and still got the flu.
The total number is 100.
So, the fraction is 25/100 which can be reduce to 1/4.
P(took a vitamin | got the flu) = 25/100
P(took a vitamin | got the flu) = 1/4
Therefore, the P(took a vitamin | got the flu) will be 1/4.
Learn more about the unitary method;
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is the measure of how much the values in a data set vary, or deviate, from the mean; it tells us how spread out the data is from the mean.
Answers
Answer:
Standard deviation
Step-by-step explanation:
The standard deviation provides a measure of the overall variation in a data set. The standard deviation is always positive or zero. The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread.
in scientific notation
1.6 x 10^3/ 8 x 10^7
Answers
Answer:
Step-by-step explanation:
[tex]\frac{1.6*10^{3}}{8*10^{7}}=\frac{1.6}{8}*10^{3-7}\\\\\\=0.2*10^{-4}\\\\\\=2.0*10^{-5}[/tex]
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
What is the the product of (-1 - 3i) and it’s conjugate?
Answers
Answer:
10
Step-by-step explanation:
(-1 - 3i)(-1 + 3i) = 1 - 3i + 3i -9i²
1 - 9i²; i² = -1, therefore 1 - 9(-1) = 1 + 9 = 10
HELP! answer if you can !!
Answers
You can find the area of a triangle by using this formula. A=bh/2.
Basically what you do is you multiply the base by the height, and then divide that by 2 to get your area.
Answer:
The formula for ABC Triangle
(AB×AC)/2
= (4.7×2.4)/
= 11,28/2
= 5,64 in²
Special right triangles
Answers
what should we do??? the question isn't there!
Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis
(Choice B)
B
(b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis
(Choice C)
C
2(b)+2(3c)2(b)+2(3c)2,
Answers
Answer:
B. (b+3c)+(b+3c) C. 2(b)+2(3c)Step-by-step explanation:
Given this expression 2(b+3c), its equivalent expression is derived by simply opening up the bracket as shown below;
Open the parenthesis by multiplying the constant outside the bracket with all the variables in parenthesis.
= 2(b+3c)
= 2(b)+ 2(3c)
= 2b +2*3*c
= 2b +6c
It can also be written as sum of b+3c in 2 places i.e (b+3c)+(b+3c) because multiplying the function b+3c by 2 means we are to add the function by itself in two places.
Hence the equivalent expression are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c
HELP PLS Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass?
Answers
Answer:
⅓litres
Step-by-step explanation:
1²/5+1³/5 =(1+1)+(²/5+³/5)
=2+ 1 = 3
3÷9=³/9.
simplify. ³/9= ⅓
Kelly pours 1/3 liter of fruit punch into each glass at a party for her chess team.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
For example 4/2 = 2
She combined 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice which are given in the question.
As per the above situation, the required solution would be
⇒ 1 2/5 + 1 3/5
Convert mixed numbers to fractions,
⇒ 7/5 + 8/5
Take the LCM in the above equation,
⇒ (7 + 8)/5
⇒ 15/5
⇒ 3
Then, she split the fruit punch evenly among 9 glasses.
Now, we have to divide 3 liters of fruit punch into 9 glasses
So 3/9 = 1/3 liters of fruit punch
Therefore, she pours 1/3 liter of fruit punch into each glass.
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If P = (3,4), Find: Rx=1 (P)
Answers
Answer:
-1, 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer is (-1,4)
MP Find the Error Katrina states that
3.5 X 104 is greater than 2.1 x 106 because
3.5 > 2.1. Explain her mistake and correct it.
Answers
Answer:
3.5 X 10^4 < 2.1 x 10^6
Step-by-step explanation:
3.5 X 10^4 < 2.1 x 10^6
The first thing we look at is the exponent
10 ^4 is less than 10^6
10000 < 1000000
If the exponents are the same, then we look at the numbers out front
