Answer:
There are 220 choices
Step-by-step explanation:
Given
[tex]People = 12[/tex]
[tex]Selection =3[/tex] (President, Treasurer and Secretary)
Required
Determine number of selection (if no restriction)
This is calculated using the following combination formula:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where
[tex]n = 12[/tex]
[tex]r= 3[/tex]
So, we have:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
[tex]^{12}C_3 = \frac{12!}{(12 - 3)!3!}[/tex]
[tex]^{12}C_3 = \frac{12!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10*9!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3*2*1}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{6}[/tex]
[tex]^{12}C_3 = 2*11*10[/tex]
[tex]^{12}C_3 = 220\ ways[/tex]
There are 220 choices
For a school project, Max made a pyramid using 587 sugar cubes. On his way to school 34 of the sugar cubes fell off. When he got to school his friends took 18 more cubes off the pyramid to eat.
Estimate how many sugar cubes remain on Max's pyramid.
Answer:
535
Step-by-step explanation:
587-34-18=
535
Answer:
550
Step-by-step explanation:
just is the answer
. p−20=−30 .
i need your help
Answer:
p = -10
Step-by-step explanation:
-30 + 20 = -10
Two pounds of grapes cost $6.
Complete the table showing the price of different amounts of grapes at this rate
Answer:
2, 6
4, 12
8, 18
and so on
Step-by-step explanation:
multiply the number on the right by itself and do the same with the number on the left, this pattern could go on forever,
A 5-kilogram bag of cat food costs $18.90. What is the unit price?
$
per kilogram
Answer:
3.78
Step-by-step explanation:
A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Given:
Endpoints of a line segment AB are A(2,3) and B(8,11).
To find:
(1) Slope of AB.
(2) Length of AB.
(3) Midpoint of AB.
(4) Slope of a line perpendicular to AB.
Solution:
We have, endpoints of line segment AB, A(2,3) and B(8,11).
(1)
Slope of AB is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{11-3}{8-2}[/tex]
[tex]m=\dfrac{8}{6}[/tex]
[tex]m=\dfrac{4}{3}[/tex]
Therefore, the slope of AB is [tex]\dfrac{4}{3}[/tex].
(2)
Length of AB is
[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(8-2)^2+(11-3)^2}[/tex]
[tex]AB=\sqrt{(6)^2+(8)^2}[/tex]
[tex]AB=\sqrt{36+64}[/tex]
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the length of AB is 10 units.
(3) Midpoint of AB is
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{2+8}{2},\dfrac{3+11}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{10}{2},\dfrac{14}{2}\right)[/tex]
[tex]Midpoint=\left(5,7\right)[/tex]
Therefore, the midpoint of AB is (5,7).
(4)
Product of slopes of two perpendicular lines is -1.
Let the slope of line perpendicular to AB be m₁.
[tex]m_1\times \dfrac{4}{3}=-1[/tex]
[tex]m_1=-\dfrac{3}{4}[/tex]
So, slope of line perpendicular to AB is [tex]-\dfrac{3}{4}[/tex].
what is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2cm and a height of 9 1/2cm?
Answer:
8075.
Step-by-step explanation:
Volume of the prism
= 12 1/2 * 8 1/2 * 9 1/2
= 25/2 * 17 / 2 * 19/2
= 8075/8 cm^3
The volume of the small cubes = (1/2)^3 = 1/8 cm^3
So the number required = 8075 / 8 / 1/8
= 8075*8 / 8
= 8075.
A pair of jeans that originally costs $42 is 25% off. What is the sale price?
Answer:
$31.50
Step-by-step explanation:
42 x 0.25 = 10.5
42 - 10.50 = 31.50
$31.50
Explanation:
42 × 25% = 10.5
42 - 10.5 = 31.5
Helllllllpppppppppppppppp
Answer:
50x50=1000000
Step-by-step explanation:
What is the volume of the following rectangular prism pls help me I’m being timed
Answer:
ummmmm I guess I could add the dimensions in the text.
Step-by-step explanation:
The picture is a black screen.
Alex is ordering his girlfriend a bouquet of flowers for their anniversary. Roses cost $5 each and carnations cost $2 each. He would like to include at least 3 flowers in the bouquet. To stay in his budget, he must not spend more than $36. Write a system of inequalities to represent the situation. Let x represent the number of roses and y represent the number of carnations.
Question 5 options:
x+y≥35x+2y≤36
5x+2y≥3x+y≤36
x+y≤35x+2y≥36
5x+2y≤3x+y≥36
0 of 5 questi
Answer:
32
Step-by-step explanation:
32=y
5=x
5x2
Is the equivalent to 32
Answer:
5x+2y≥3x+y≤36
Step-by-step explanation:
Could some help with this problem it is due in about 20 mins and I am really stuck I will give a brainlist to the best answer :)
Answer:
Step-by-step explanation:
29.
2x+4+x+2x-9=180
5x-5=180
5x=180
x=36
Q=76°
P=63°
R=36°
30.
C=90° (Given)
4x+7+8x-1+90=180
12x+96=180
12x=84
x=7
B=55°
A=35°
-6 + (-3) - (-2) =
A. 11
B. 7
C. -7
D. -11
Answer:
C. -7
Step-by-step explanation:
find the value of w(u(-4)) i need some help lol
Answer:
The functions u and w are defined as follows. u(x) =-2x+2 w(x) = 2x2 +1 Find the value of w (u (4)). w (u (4)) = 05Step-by-step explanation:
what is 42/18 written as a mixed number?
Step-by-step explanation: 2 1/3
50 POINTS PLZ HELP MEEEE
Answer:
Step-by-step explanation:
It’s c
Answer:
c
Step-by-step explanation:
I have a box of crackers that weighs 5.25 oz. if one serving of crackers is .15 ounces. How many servings are in the box?
Answer:
0.15÷5.25 should give u the answer
What is the length of segment DA?
Answer:
Step-by-step explanation:
The length of this line segment is the distance between its endpoints A and B. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
Answer: DA = 6
====================================================
Explanation:
The triangles are similar, allowing us to make the proportion below
DB/DA = DA/DC
Plug in the given values. Cross multiply and solve for x
DB/DA = DA/DC
9/DA = DA/4
9*4 = (DA)*(DA)
36 = (DA)^2
(DA)^2 = 36
DA = sqrt(36)
DA = 6
The length of DA is exactly the geometric mean of the lengths BD and DC
geometric mean of x and y = sqrt(x*y)
If we divide 2 and 6 by 2 what is our new simplified ratio?
Answer:
Step-by-step explanation:
help
graph
i understand it but will it be to the right or left
Answer:I believe left
Step-by-step explanation:
Which diagram represents the type of solution to this system of equations?
7x − 12y + z = -1
8x − 10y = 5
21x − 36y + 3z = -3
A.
B.
C.
D.
Answer: The answer should be A.
Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.
The correct diagram represents the type of solution to this system of equations is shown in Option A.
We have to given that,
System of equations are,
7x - 12y + z = -1 .. (i)
8x - 10y = 5 .. (ii)
21x - 36y + 3z = -3 .. (iii)
Now, From equation (i);
Multiply by 3;
3( 7x - 12y + z) = -1 × 3
21x - 36y + 3z = - 3
Which is same as equation (iii).
Hence, Equation (i) and (ii) are parallel to each other.
And, It's a triple relationship.
Thus, Only option A has parallel planes.
So, Option A is true.
Learn more about systems of equations at:
brainly.com/question/14323743
#SPJ2
Jkgdgdkhhgkdksytsktsykkusutskfkxh
Answer:
39% , 0.39 , 39/100
Step-by-step explanation:
I thought your randomness of letters was your question lol. Hope this helps though!
Jacob has several wood dowel remnants. He needs
several pieces that are at least 2 1/4 feet long to use for
4.
a project. Select ALL of the lengths that would be
useable.
(Select all that apply.)
2
feet
16
2.3 feet
2.25 feet
2 feet
Answer:
2 feet, 2.3 feet, 2.25 feet, and 16 feet
solve for x (x-2)(x+1)=3x-2 what is x and x
in the picture will explain the explanation
PLEASE HELP MEE!!!!!!!!Joshua is 11 years old, and his dad is 33
years old. What is the ratio of Joshua's
age to his dad's age?
Answer:
11:33 or in simplified terms 1:3
Step-by-step explanation:
Hope this helps!:)
PLZ HELP ME! 1ST GETS BRAINIEST! THIS IS DUE TODAY!
Pretend a classmate missed the lesson today. What would you tell them about how to make a table to represent a rate? How would you tell them how to use the table to make a graph?
Answer:
You would tell them by labeling the x and y and the titles of the graph and what corresponds to it
Step-by-step explanation:
Benjamin colors 40% of total grids on his paper he colors 8 grids enter the total number of grids on Benjamin's paper
Answer:
320%
Step-by-step explanation:
You collect data on the color of cars driven by students in your statistics class, and want to display this information graphically. Which is the better choice for this data, a bar graph or a histogram?
Answer:
bar graph
Step-by-step explanation:
The best choice for this scenario would be a bar graph. This is because a histogram is used to represent data ranges or data in a specifically given time interval. For example, age ranges, time ranges, and income ranges are all common examples of data that is represented using histograms. Bar graphs on the other hand tend to represent the quantity of specific pieces of data in a large set of data, such as the number of specific color cars that appear out of a wide set of colors.
The probability that a vehicle will change lanes while making a turn is 45%. Suppose a random sample of 7 vehicles are observed making turns at a busy intersection. Find the probability that a least 5 vehicles will change lanes while making the turn.
Answer:
0.1529
Step-by-step explanation:
Given that:
Probability of changing lane ; p = 45% = 0.45
Sample size (number of trials) = n = 7
Probability that atleast 5 vehicles will change lane :
Using the binomial probability formula :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
(1 - p) = 1 - 0.45 = 0.55
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x = 5) = 7C5 * 0.45^5 * 0.55^2
P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221
P(x = 6) = 7C6 * 0.45^6 * 0.55^1
P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969
P(x = 7) = 7C7 * 0.45^7 * 0.55^0
P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736
P(x ≥ 5) = 0.152926
P(x ≥ 5) = 0.1529
Using the binomial distribution, it is found that there is a 0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
For each vehicle, there are only two possible outcomes, either they change lanes while making a turn, or they do not. The probability of a vehicle changing lanes while making a turn is independent of any other vehicle, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The probability that a vehicle will change lanes while making a turn is 45%, hence [tex]p = 0.45[/tex].A sample of 7 vehicles is taken, hence [tex]n = 7[/tex].The probability that at least 5 vehicles will change lanes while making the turn is:
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.45)^{5}.(0.55)^{2} = 0.1172[/tex]
[tex]P(X = 6) = C_{7,6}.(0.45)^{6}.(0.55)^{1} = 0.0320[/tex]
[tex]P(X = 7) = C_{7,7}.(0.45)^{7}.(0.55)^{0} = 0.0037[/tex]
Then
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1172 + 0.0320 + 0.0037 = 0.1529[/tex]
0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
Select all of the fractions that are equivalent to -2/3 ( SELECT ALL THAT APPLY)
Options
A)3/-2
B)-2/-3
C)- 2/3
D)-3/-2
E)2/-3
F)-3/2
Answer:
- 2/3, 2/-3
Step-by-step explanation:
none of the rest work 3/2 is a completely different number and having two negatives in a fraction make it a positive
Let f be a continuous function on the interval [a, b]. Determine if the following statement is true or false. The expression lim f(xi") ax may lead to different limits if we choose the x * to be the left endpoints instead of midpoints. ni=1 Choose the correct answer below. O A. The statement is true. Each sum will be smaller when picking a left endpoint, so the limit will be smaller. OB. The statement is false. Any sample point can be chosen within the interval without affecting the limit. O C. The statement is true. The value of the function at the left endpoint is not the same as the value at the midpoint of the interval D. The statement is false. The value of the function at the left endpoint is the same as the value at the midpoint of the interval. w Click to select your answer
Answer:
The correct answer is B.
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}f(x_i\, ^\star)\Delta x[/tex]
In this case, B is the correct answer.
B states that any sample point can be chosen without affecting the limit.
This is a true statement. Regardless of which point we choose for our sample point, since n approaches infinity, we will have infinite partitions.
Hence, this will not affect the sum of our expression.
A and C are false because we have infinite partitions, so the statements cannot be true. D is not true simply because the left-hand values do not have to be the same as the midpoint-values depending on the behavior of the function for [a, b].