Answers
In this case, n = 7 and r = 3
Plug those values into the formula below and evaluate
n C r = (n!)/(r!*(n-r)!)
7 C 3 = (7!)/(3!*(7-3)!)
7 C 3 = (7!)/(3!*4!)
7 C 3 = (7*6*5*4!)/(3!*4!)
7 C 3 = (7*6*5)/(3!)
7 C 3 = (7*6*5)/(3*2*1)
7 C 3 = 210/6
7 C 3 = 35
Note: the exclamation marks refer to factorial notation.
Therefore, the answer is choice D) 35
Related Questions
find a1 for the geometric series with r=3 and s6=364
Answers
Determine the solution set of x^2-80=0.
Answers
x^2 = 80 ...take the square root of both sides, eliminating the ^2
x = (+-) sqrt 80
x = (+-) sqrt 16 * 5
x = (+-) 4 sqrt 5
so x = 4 sqrt 5 or x = -4 sqrt 5
Answer: The required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]
Step-by-step explanation: We are given to determine the solution set of the following quadratic equation :
[tex]x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.
The solution of equation (i) is as follows :
[tex]x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm\sqrt{80}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm\sqrt{16\times5}\\\\\Rightarrow x=\pm4\sqrt5.[/tex]
Thus, the required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]
The cycling tour has 340 bottles of water for each week. There are ten people on the tour. How many bottles of water is that for each person per week?
Answers
WILL GIVE BRAINLIEST!!!
Which of the following equations represents an inverse variation?
A.
6y = x
B.
1/2y = 1/x
C.
–x = y + 8
D.
y = 1/4x
Answers
An equation typically used to represent inverse variation is y = k/x, where k is the "constant of proportionality for inverse variation."
6y = x does not represent inverse variation, since y increases when x increases or x increases when y increases. This is an example of direct proportion and is thus not an answer.
1/2y = 1/x should be written as (1/2)y = 1/x, to emphasize that (1/2) is a coefficient of y. Let's solve for y to see what form the resulting equation has:
(1/2)y = 1/x => y = 2/x. This has the form y = k/x, and thus represents inverse variation. y decreases when x increases.
–x = y + 8 is a linear equation and thus could not possibly represent inverse proportion. The "offset," +8, also makes it impossible for –x = y + 8 to represent direct variation. Reject this answer choice.
y = 1/4x has the form y = (1/4)x, which resembles a rule for direct variation.
Note, however, that if you really meant y = 1 / (4x), or y = (1/4)(1/x), then this would be a case of inverse variation.
The only answer choice in this problem that clearly represents indirect variation is (1/2)y = 1/x (as I have already said, above).
Answer:5
Step-by-step explanation:
1/2y=1/x
y=2/x
Annie found that 57 students in her school knew French and 23 of those students knew Spanish, as well. There were 11 students who did not know French but knew Spanish. There were 4 students who knew neither French nor Spanish. Which table best summarizes the data collected by Annie?
Knew Spanish Did not know Spanish Total
Knew French 57 34 91
Did not know French 11 4 15
Total 68 38 106
Knew Spanish Did not know Spanish Total
Knew French 12 34 46
Did not know French 11 4 15
Total 23 38 61
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 4 11 15
Total 27 45 72
Answers
Answer:
Table C is the correct option.
Step-by-step explanation:
We are given,
Number of students which knew French = 57
Number of students which knew both French and Spanish = 23
Number of students which knew Spanish but not French = 11
Number of students which knew neither French nor Spanish = 4
So, we get that,
Number of students not knowing French = 57 - 23 = 34
Hence, the table for the given situation is,
Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72
Thus, option C is correct.
option C is correct-
what are the domain and range for each of the following functions? write your answer using inequality symbols of possible PLEASE HELP :) ( on both graphs)
Answers
The Domain is the set of all first coordinates, the x'es.
The Range is the set of all the second coordinates, the y's.
1.
We can see the points (-2, 0), (-1, 1) and (2, -1)
Domain={-2, -1, 2} Range={-1, 0, 1}
2.
We see that x can be any value such that -1<x≤1
and y can be any value such that -1≤y<2
so
Domain: x, such that -1<x≤1
Range: y, such that -1≤y<2
Point C is the center of the circle. The measure of angle ACB is 12x – 7. Arc AB measures 10x + 7. Find the value of x.
Answers
bear in mind that, arcs get their angle measurement from their central angle. Thus, those two are equal.
Answer:
x=7
Step-by-step explanation:
Subtract 10x
from both sides of the equation.
12x−7−10x=7
Subtract 10x
from 12x
2x−7=7
Add 7
to both sides of the equation.
2x=7+7
Add 7 and 7
2x=14
Divide each term by 2 and simplify.
x=7
The ages of 3 brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the younger brother?
A. 14
B. 18
C. 22
D. 26
Answers
3n=n+4+48
3n=n+52
2n=52
n=26
So the youngest brother is 26 years old.
Put these substances in order of density with the most dense first and the least dense last.
air
pumpkin pie
whipped cream
steel
Answers
Answer: Hello there!
We know that:
[tex]density = \frac{mass}{volume}[/tex]
This means that two of two objects whit the same size ( volume) the heaviest one is the more dense object.
The 4 that we have here are:
Air, Pumpkin pie, Whipped cream, and Steel
It is easy to assume that the steel is the more dense object.
The pumpkin pie comes second
third is the whipped cream, which is cream with a lot of tiny air bubbles inside
the less dense object is the air.
then the order is:
Steel, pumpkin pie, whipped cream, air.
help
The coordinate grid shows the graph of four equations:
A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.
Which set of equations has (5, 0) as its solution?
A and B
C and D
B and D
A and D
Answers
for line A, we have (-3,4) and (9, -2)
y - y1 = m(x - x1)
y - 4 = (-2 - 4/9 -(-3))(x - (-3))
y - 4 = -(1/2)(x+3)
2y - 8 = -x - 3
2y = -x + 5
substitute (5,0)
2(0) = -5 + 5
0 = 0
What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?
Answers
The easy way to see this is to divide all terms by the highest order variable...
(x^2/x^3 +x/x^3-6/x^3)/(x^3/x^3-1/x^3) and all of that mess boils down to
0/1 or just 0 as x approaches ±oo
So the horizontal asymptote is the horizontal line y=0
The vertical asymptote will occur when there is division by zero, which is undefined because it is not a real value.
x^3-1=0
(x-1)(x^2+x+1)=0
So this only occurs as x approaches -1, so the vertical asymptote is the vertical line x=-1.
Answer:
Hence, x=1 is the vertical asymptote
Hence, y=0 is the horizontal asymptote
Step-by-step explanation:
We have been given an expression
[tex]\frac{x^2+x-6}{x^3-1}[/tex]
For vertical asymptote we equate the denominator to zero that means
[tex]x^3-1=0[/tex]
[tex]\Rightarrow x^3=1[/tex]
[tex]\Rightarrow x=1[/tex]
Hence, x=1 is the vertical asymptote.
Now, for horizontal asymptote we compare the degree of numerator and denominator
Here degree of numerator is 2 and degree of denominator is 3
When degree of denominator is greater than degree of numerator y=0 is the horizontal asymptote
Hence, y=0 is the horizontal asymptote.
kelvin to fahrenheit f= 9/5(k-273.15) +32
Answers
How many ways can a librarian arrange 15 books on a top shelf if she has 20 books from which to pick?
Answers
Answer: 20!/5!
Step-by-step explanation:
I NEED HELP ASAP! PLS HELP ME!
Answers
2.11*7 = 14.77
2.11*9 = 18.99
the answer is y=2.11x
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answers
time rent
hours $
3 43
8 113
Assume a linear relation, this is r(t)= Ax + C
=> [r - 43] / [ x - 3] = [113 - 43] / 8 - 3]
=> [r - 43] / [x - 3] = 70 / 5
=> [r - 43] / [x - 3] = 14
=> r - 43 = 14 [x - 3]
=> r - 43 = 14x - 14*3
=> r - 43 = 14x - 42
=> r - 14x - 1 = 0 <----- standard form
Part B: Write the equation obtained in Part A using function notation. (2 points)
r - 14x - 1 = 0 => r(x) = 14x + 1 <------------- function notation, r(x)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
1) Horizontal axis = x
2) Vertical axis = y
3) Domain x > 0 = [0, ∞)
4) Range r > 0 = [0, ∞)
5) r-intercept=> x = 0 => r = 14(0) + 1 = 1 => (0,1)
6) slope: 14
7) x-intercept => r = 0 => 0 = 14x + 1 => x = -1/14 => (-1/14, 0)
Find Y of the polygon
Answers
If you look at the large triangle on the left where the corner angles are 35 and 80 and 20+an unknown angle. We can work out the missing angle by doing 180-80-35-20= 45.
And so if we use the fact that alternate angle must be equal then y= 45 degrees (I think!)
65° - 20° = 45°
y = 45° (alt. ∠s)
Doug entered a canoe race. he rowed 3 1/2 miles in 1/2 hours what is his average speed in miles per hour
Answers
7miles/1hour
7mph
.
One angle in a pair of complementary angles is 4/5th of the other . Find the measure of the two angles
Answers
complementary angles equal 90 degrees
angle 1 = x
angle 2 = 4/5x
x + 4/5x = 90
9/5x = 90
x = 90 / 9/5 = 50
angle 1 = 50 degrees
angle 2 = 4/5 x 50 = 40 degrees
You invest $300 in an account that has an interest rate of 1.3%, compounded monthly. How much money is in the account after 20 years? Round your answer to the nearest whole number.
Answers
A=p (1+r/k)^kt
A future value?
P present value 300
R interest rate 0.013
k compounded monthly 12
T time 20 years
A=300×(1+0.013÷12)^(12×20)
A=389.02
Answer:
$389
Step-by-step explanation:
The formula for final value of compound interest is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here, we have
P = $300
r = 0.013
t = 20 years
n = 12
Substituting these values and find A
[tex]A=300(1+\frac{0.013}{12})^{12\cdot20}\\\\A\approx389[/tex]
Therefore, in 20 years, the account will have $389.
A function is given. f(x) = 5x − 7; x = 2, x = 3 (a) determine the net change between the given values of the variable.
Answers
A convex polyhedron has 30 edges and 8 fewer vertices than faces. How many faces does the polyhedron have? Euler’s formula: V + F = E + 2 12 18 20 24
Answers
Answer:
C or 20
Step-by-step explanation:
Just got the answer on Edge :)
Answer:
c
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y= -1/2x +5?
A(-2
B(- 1/2
C( 1/2
D( 2
Answers
B. -1/2
Explanation:
The equation is in y= mx + b form, which means that m= slope and b= y-intercept. You can see that the slope is -1/2.
A puzzle contains a triangular piece with a base of 3 in. and a height of 4 in. A manufacturer wants to make 80 puzzles. Find the amount of wood used if each puzzle contains 20 triangular pieces.
Answers
I believe this question asks for the total amount of area of wood that is needed to make 80 puzzles.
The formula for area of triangle is given as:
A = (1 / 2) b h
where,
b = is the base of the triangle = 3 in
h = height of the triangle = 4 in
So calculating for area of 1 on triangle (A1):
A1 = (1 / 2) (3 in) (4 in)
A1 = (1 / 2) 12 in^2
A1 = 6 in^2
We are given that we are to make 80 puzzles and each puzzle has 20 triangles, therefore the total amount of triangles we need to make is:
n = 80 * 20
n = 1600
Therefore the total area needed (A) is:
A = A1 * n
A = 6 in^2 * 1600
A = 9,600 in^2
Can anyone PLEASE help geometry is my worst subject!
Answers
Which of these is not an example of a geometric shape or form?
Answers
Please help ill give brainiest to who helps
Joey intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is divisible by 3? A. Each roll has a 0.117 probability of being divisible by 3. B. Each roll has a 0.333 probability of being divisible by 3. C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.
Answers
there are 2 numbers that could be divisible by 3, either 3 or 6
so there is a 2/6 probability
2/6 = 0.333
so the answer is B
Segment RT is a mid-segment of triangle CDE. What is the length of segment CE?
A) 38 in.
B) 32 in.
C) 24 in.
D) 9.5 in.
Answers
so CE = 2(RT) = 2(19) = 38
answer
A. 38
can someone please help
Answers
Answer both please !
Answers
36) the equation would be: 44 x 0.63 =
37) 6.1% = 0.061
59150 x 0.061 = 3608.15 increase
HELP If f(x)=2x-12, then f^-1(x)=?