our class tutorial has 12 students, who are supposed to break up into 4 groups of 3 students each. Your Teaching Assistant (TA) has observed that the students waste too much time trying to form balanced groups, so he decided to pre-assign students to groups and email the group assignments to his students. (a) Your TA has a list of the 12 students in front of him, so he divides the list into consecutive groups of 3. For example, if the list is ABCDEFGHIJKL, the TA would define a sequence of four groups to be {A,B,C),{D, E, F},{G, H, 1}, {J, K, L}). This way of forming groups defines a mapping from a list of twelve students to a sequence of four groups. This is a k-to-1 mapping for what k? (b) A group assignment specifies which students are in the same group, but not any order in which the groups should be listed. If we map a sequence of 4 groups, ({A, B, C),{D, E, F),{G, H, 1},{J, K, L}), into a group assignment {{A, B,C),{D, E, F),{G, H, 1), (J, K, L}}, this mapping is ;-to-1 for what j? (c) How many group assignments are possible? (d) In how many ways can 3n students be broken up into n groups of 3?
(a) The mapping from a list of twelve students to a sequence of four groups is a k-to-1 mapping, where k is equal to 3.
Each group consists of 3 students, so when the list is divided into consecutive groups of 3, we have 4 groups in total. Therefore, each group assignment is determined by 3 students from the list, resulting in a 3-to-1 mapping.
The mapping is a 3-to-1 mapping because it assigns 3 students to each group.
(b) The mapping from a sequence of 4 groups to a group assignment is a 1-to-1 mapping.
In a group assignment, the order of the groups does not matter. As long as the students are assigned to the same groups, the assignment is considered the same. Therefore, the mapping is a 1-to-1 mapping, as there is only one possible group assignment for a given sequence of groups.
The mapping is a 1-to-1 mapping because each sequence of groups corresponds to a unique group assignment.
(c) The number of group assignments possible can be calculated by multiplying the number of ways to select 3 students from 12 for the first group, then the number of ways to select 3 students from the remaining 9 for the second group, and so on.
The number of ways to select 3 students from a group of 12 can be calculated using the combination formula "nCr," where n is the total number of students and r is the number of students to be selected. In this case, the formula becomes C(12, 3) for the first group, C(9, 3) for the second group, C(6, 3) for the third group, and C(3, 3) for the fourth group.
The total number of group assignments possible can be calculated as C(12, 3) * C(9, 3) * C(6, 3) * C(3, 3).
(d) The number of ways to break 3n students into n groups of 3 can be calculated using the multinomial coefficient formula.
The multinomial coefficient formula is used to calculate the number of ways to distribute objects into distinct groups, where the number of objects can vary in each group. In this case, we have 3n students to be distributed into n groups of 3, so the formula becomes (3n)! / (3!)^n.
The number of ways to break 3n students into n groups of 3 is (3n)! / (3!)^n.
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how many 5-digit passwords can I make out of the English alphabet. lowercase only
Answer:
7,893,600 different combinations
Step-by-step explanation:
Answer:
We have a total.of 26 alphabets in the english language and numbers 0 to 9 will be 10.
Since there are no other limitations, we have to arrange 8 places with the 36 options we have.
It will simply be 36c8.
The answer will be 3,02,60,340.
Bobby purchased a brand new car for $23,000 every year the car depreciates 20%. The function f(x)=23,000 × 0.8^x models this situation. How much will the car be worth after 6 years?
Answer:
that earns 3% interest compounded annually. He ... Is the equation A = 21000(1 – 0.12)'a model of ... (1+0.03)= 1.03 ... The value of a car purchased for $20,000 decreases ... Kathy plans to purchase a car that depreciates. ... B) P= 10,000(0.8) ... YEARS. Wolves d is less than 1! d is more than 11. 1 Growth f(x) = 80(0.1165).
Step-by-step explanation:
PLz help
how would you represent this situation( Write the equation or inequality.)
On a carnival ride you must be at least 42 inches tall to ride
Answer:
x≥k y for you y≥42 inches tall
Step-by-step explanation:
can i have brainliest if right
TB
05-75 2/10,n/30 is interpreted as
The term "TB 05-75 2/10, n/30" represents the payment terms for a transaction.
The term "TB 05-75 2/10, n/30" provides specific information regarding the payment terms for a transaction. Here's a breakdown of its components:
1. "TB": This stands for "Trade Discount" and signifies that the terms are related to a discount offered for the transaction.
2. "05-75": The numbers indicate a cash discount percentage and a payment period. In this case, "05" represents a cash discount of 5%, and "75" indicates a payment period of 75 days.
3. "2/10, n/30": These terms further elaborate on the payment conditions. "2/10" means that a 2% cash discount can be taken if the payment is made within 10 days. The "n/30" portion implies that the net payment is due within 30 days from the date of the transaction.
In summary, "TB 05-75 2/10, n/30" signifies that a trade discount is offered, a cash discount of 5% is available if payment is made within 10 days, and the net payment is due within 30 days. It provides clear guidelines for the payment terms and discounts associated with the transaction.
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Suppose Y varies directly with X and Y equals 10 when X equals -3 what direct variation equation relates XNY what is the value of Y when X equals -1
Answer:
Expression: Y = -10/3 X
Y = 10/3
Step-by-step explanation:
If Y varies directly as X, then;
Y∝X
Y = kX
k is the constant of variation
If Y = 10 and X = -3
10 = -3k
k = -10/3
Substitute k = -10/3 into the expression Y = kX
Y = -10/3 X
This gives the required expression
To get the value of Y when X = -1
Recall that Y = kX
Y = -10/3 (-1)
Y = 10/3
Hence the value of Y is 10/3
A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, round to the nearest tenth?
Answer: 2035.8
Step-by-step explanation:
The volume of the cylinder is 2034.72 cubic ft
What is the volume of the cylinder?The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold or we can say the volume of a cylinder is the number of unit cubes that can be fit into it. The formula for volume of cylinder is V = A × h
Assuming the given cylinder is Right Circular Cylinder
Then the formula is V = πr²h
From the question radius (r)= 6ft
height (h)=18ft
volume (V)= π× 6² × 18
=2034.72 cubic ft
Thus the volume of the cylinder is 2034.72 cubic ft
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a string runs up and to the left in the x-y plane, making an angle of 29◦ to the vertical. determine each component of the unit vector that points along the string, beginning with ˆrx.
To determine the components of the unit vector that points along the string, we need to break down the vector into its x and y components.
Given that the string makes an angle of 29 degrees to the vertical, we can define the unit vector as follows:
ˆr = ˆrx + ˆry
To find the x-component (ˆrx) of the unit vector, we can use the cosine of the angle:
cos(29°) = ˆrx
To find the y-component (ˆry) of the unit vector, we can use the sine of the angle:
sin(29°) = ˆry
Let's calculate the values:
ˆrx = cos(29°)
ˆry = sin(29°)
Using a calculator or mathematical software, we can find the numerical values of ˆrx and ˆry:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
Therefore, the components of the unit vector that points along the string are approximately:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
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Ahmad throws dice find the probability that it is:not a 2
yah it's not probably it's not 2 mmmm
2+2x+x2 but x=5 need help
Answer:
22
Step-by-step explanation:
Answer:
6x
Step-by-step explanation:
because i said so 2+2+2=6 and x=5 but two x=10
Given the data set, calculate the mean
{9, 3, 1, 8, 3, 6}
Please help!!!
Answer:
mean: 5
Step-by-step explanation:
(9 + 3 + 1 + 8 + 3 + 6) / 6 = 5
For the linear operator 2x х T := [ х y on R2, find the matrix representation B'[T]b relative to the ordered bases B' B s={1} -(0) [-1.0]
The matrix [T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] represents the linear operator T with respect to the bases B′ and B.
The matrix representation [tex][T]\left \{ {{B} \atop {B'} \right.[/tex] of the linear operator T relative to the ordered bases B' and B, we need to determine how the basis vectors of B' are transformed under the linear operator T and express them as linear combinations of the basis vectors of B.
B′={1} and B={(0),[−1.0]} we can represent the basis vectors as column matrices
[1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1]
[0][tex]\left \{ \atop {B'}} \right.[/tex] = [tex]\left[\begin{array}{ccc}0\\0\\\end{array}\right][/tex]
[-1.0][tex]\left \{ \atop B' \right.[/tex] = [tex]\left[\begin{array}{ccc}-1\\0\\\end{array}\right][/tex]
Now, we can apply the linear operator T to the basis vectors of B' and express the results in terms of the basis vectors of B.
T([1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1][tex]\left \{ {\atop {B'}} \right.[/tex] = [1] = 1.[0][tex]\left \{ \atop {B'}} \right.[/tex] + 0.[-1.0][tex]\left \{ \atop B' \right.[/tex]
Therefore, we have
[T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex]
The matrix [T][tex]\left \{ {{B} \atop {B'}} \right.[/tex] represents the linear operator T with respect to the bases B′ and B.
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Sasha had to run 1/3 of a mile. She decided to walk, jog, and run the 1/3 mile, in equal parts. What fraction of the mile will she run?
A.9
B.3/9
C.1/9
D.3/3
(Need help asap pls)
Answer:
C 1/9
Step-by-step explanation:
She needs to run 1/3 of a mile and is going to run/jog/walk that 1/3 mile
So she must do 1/9 of a mile running, 1/9 walking, and 1/9 jogging because 1/3 is equivalent to 3/9.
Since she is going to run/jog/walk the same amount of the 1/3 she is going to run 1/9 of the 1/3
Let me know if I'm wrong
Hope I helped :]
f(x)=x^2. what is g(x)?
please help asap!!
The equation of the red graph, g(x) is g(x) =1/3x²
How to calculate the equation of the red graphFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
In the graph, we can see that
The blue graph passes through the vertex (0, 0)The red graph passes through the vertex (0, 0) but it is 3 times widerThis means that
g(x) = 1/3f(x)
Recall that
f(x) = x²
This means that
g(x) =1/3x²
This means that the equation of the red graph is g(x) =1/3x²
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please answer ASAP AFAP PLEASE PLEASE ANSWER RIGHT OR I'LL REPORT YOU TO BRAINLY . but on the other hand if you answer correctly I'll just give you brainliest, and go to your profile and thank you and give you a 5 star rating!
Answer:
The answer is B. 4.4 oz.
Step-by-step explanation:
What do we know? We have the 6-pack of 12-ounce bottles and they cost $2.99, we also know that the other bottle 67.6 ounces that also costs $2.99.
Forgot the money, we're just going to be looking at the ounces.
First, we take the 6-pack and multiply by 12 because we want the size as one, rather than seperate. 6 x 12 = 72
The question is asking how many more ounces are you getting if you purchase the 6-pack. In order to do this, we take the 72 ounces that we got and subtract that 67.6 ounces of the other drink. 72 - 67.6 = 4.4
The ounces saved are 4.4 ounces.
what two steps are necessary to put this equation into standard form?
x^2-3 x 27=8 x-3x 2 −3x 27=8x−3
A. Add 3 to both sides and substract 8x from both sides
B. The equation is already in standard from
C. Substract 3 from sides and substract 8x from both sides
D. Add 3 to both sides and add 8x from both sides
The two necessary steps to put this equation into standard form is A) Add 3 to both sides and subtract 8x from both sides.
To put the equation x² - 3x + 27 = 8x - 3 into standard form, the two necessary steps are:
A. Add 3x to both sides: By adding 3 to both sides of the equation, we eliminate the constant term -3 on the right side and move it to the left side.
x² - 3x + 3x + 27 = 8x - 3 + 3x
x² + 27 = 11x
B. Subtract 11x from both sides: By subtracting 8x from both sides of the equation, we eliminate the term 8x on the right side and move it to the left side.
x² + 27 - 11x = 11x - 11x
x² - 11x + 27 = 0
Therefore, the equation in standard form is x² - 11x + 27 = 0. Therefore, the correct answer is option A.
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determine whether the following equations are second-order linear differential equations.(a)y'' = −3x(y')2
To determine whether the equation y'' = −3x([tex]y')^2[/tex]is a second-order linear differential equation, we need to examine its form.
A second-order linear differential equation has the general form:
[tex]y'' + p(x)y' + q(x)y = r(x)[/tex]
where y is the dependent variable, x is the independent variable, and p(x), q(x), and r(x) are functions of x.
In the given equation, [tex]y'' = -3x(y')^2,[/tex]we can observe that the dependent variable y only appears in the squared term [tex](y')^2.[/tex]This indicates that the equation is not linear in y or its derivatives. It contains a non-linear term [tex](y')^2[/tex]multiplied by the function -3x.
Therefore, the equation [tex]y'' = -3x(y')^2 i[/tex] is not a second-order linear differential equation.
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The length of a rectangle is five more than three time its width. The perimeter of a rectangle is 234. What is the width of the rectangle
Answer:
28 units
Step-by-step explanation:
Given data
Let the width be x
The length is =3x+5
Perimeeter= 234
The expression for the perimeter is
P=2L+2W
Substitute
234= 2*x+2(3x+5)
234= 2x+6x+10
Collect like terms
234= 8x+10
234-10= 8x
224=8x
x= 224/8
x=28
Hence the width is 28 units
100 - x2 + 15, cuando x = 9
Use the spinner below for each of the following
questions. Place an "x" along the number line to
represent how likely the event is to occur.
How likely is it for the spinner to land on a 5?
Please help ASAP I’ll give u brilliant
Answer: I’m sorry I meant B
Step-by-step explanation: 9.6/3=3.2
3.2•8=25.6
If ab=8 and a^2+b^2=16 then what is the valué of (a+b)^2 PLSS HELP NOW
I think that i got it but at the same time not sure but the value of a+b should be 14+20
G(x)= x^2 + 5x
g(-3)=
Answer: The answer is g=x/16
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
g(-3) = (-3)^2 + 5(-3) [Take x value as -3]
= 9 -15
= -6
b) A cubical water tank has 1.5m as the length of its each side. Find the volume of the tank.
Answer:
3.375
Step-by-step explanation:
To get the volume of a cube you need to multiply length width and height since the cube is similar in length width and height you need to multiply 1.5 by itself three times.
V=l×w×h
V=1.5×1.5×1.5
V=3.375
Note:you need to multiply it to itself three times not to the number three.
Also it is only used if one number is given if three numbers are given multiply those three numbers hope this helps have a good day
Please help me!! No files allowed. I need the answer and an explanation!
Answer:
I belive the answer is 1/324
how do i solve 60=2b+20 also show me how u did ur work please
Answer: b=20
Step-by-step explanation:
First for the equation 60=2b+20
We will subtract 20 from both sides to start isolating b
40=2b
Divide both sides by 2
and you get b=20
Answer:
b = 20
Hope This Helps!
Step-by-step explanation:
60 = 2b + 20
-20 -20
--------------------
40 = 2b
40/2 = 2b/2
20 = b
b = 20
Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by
T(x) = 7-9(x-2)2-3(x-2)3
a. find f(2) and f '' (2).
b. Is there enough information given to determine wheather fhas a critical point at x = 2?
If not, explain why not.
If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.
c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?
If not, explain why not.
If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.
d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.
Solution :
Given : [tex]$T(x)=7-9(x-2)^2-3(x-2)^3$[/tex]
a). f(2) = T(2) = 7
[tex]$\frac{f""(2)}{2!} =-9$[/tex] , so f''(2) = [tex]$-18$[/tex]
b). Yes, since f'(2) = T'(2) [tex]$=$[/tex] 0, [tex]$f$[/tex] does have the critical point at [tex]$x=2.$[/tex]
Since f''(2) = [tex]$-18$[/tex] < 0, [tex]$f(2)$[/tex] is relative maximum value.
c). [tex]$f(0)=T(0)=-5$[/tex]
It is also not possible for determining if [tex]$f$[/tex] has a critical point at x = 0 because [tex]$T(x)$[/tex] gives exact information only at [tex]$x=2.$[/tex]
d). The Lagrange [tex]$\text{error}$[/tex] bound [tex]$=\frac{6}{4!}|0-2|^4= 4$[/tex]
[tex]$f(0) \leq T(0)+4 = -1$[/tex]
Therefore, [tex]$f(0)$[/tex] is negative.
(450) + (28.75x) = 967.50
solve for x
Answer:
x=18
Step-by-step explanation:
Answer:
x= 18
Step-by-step explanation:
To solve this equation you have to work backwards
Start by dealing with the numbers that we know:
450 + (28.75 × x) = 967.5
-450 -450
28.75x = 967.5
(when a number and a letter in mathematics are next to each other they are multiplying)
Now divide to find the value of x:
967.5 ÷ 28.75 = 18
18 is the value of x
Solve for x and then answer
Answer:
Value of x = 70'
Step-by-step explanation:
Given:
Given quadrilateral is a cyclic quadrilateral, in a cyclic quadrilateral sum of opposite angle is 180' .
Find:
Value of x
Computation:
x' + 110' = 180'
x' = 180' - 110'
Value of x = 70'
The equations y = 5x and y = –1∕5x + 4 represent what types of lines?
Answer:
It might be perpendicular lines
Step-by-step explanation: