Your 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, I }, {J, K, L}), into a group assignment {{A, B, C},{D, E, F}, {G, H, 1},{J, K, L}}, this mapping is j-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?

Answer:

160°

Step-by-step explanation:

since it is a parallelogram it's opposite angles must be equal . So,

angle GHE = angle EFG

160 degree = angle EFG

Answer:

There are 42 dogs and 105 cats at the shelter. To find the number of rabbits, subtract these numbers from the total number of animals at the shelter. So there are 21 rabbits at the shelter.

Step-by-step explanation:

Because there are 168 animals at the shelter and \(\frac{1}{4}\) of the animals are dogs, you can infer that there are \(\frac{168}{4}\) or 42 dogs at the shelter. The question says that \(\frac{5}{6}\) of the remaining animals are cats, which you can get two things from this statement: #1, \(\frac{5}{6}\) of the remaining animals (not including dogs) are cats in the shelter. #2, \(\frac{1}{6}\) of the remaining animals (not including dogs) are rabbits in the shelter, since that is the remaining number of animals left that aren't cats or dogs. Using this, you can get the number of cats is the number of dogs subtracted by the total number of animals at the shelter and multiplied by \(\frac{5}{6}\), which would be  \(\frac{5}{6}\)(168 - 42) = \(\frac{5}{6}\)*126 = 5 * 21 = 105 cats at the animal shelter. Since the number of rabbits is \(\frac{1}{5}\) the number of cats in the shelter (\(\frac{5}{6}\) = \(\frac{1}{6}\) * 5), that means there are \(\frac{105}{5}\) or 21 rabbits at the animal shelter, and that we'd need to subtract the number of cats and dogs from the total number of animals at the shelter to find the number of rabbits.

Answer:

x=21°. :Angles subtended by the same arc

y=42°. :180-(117+21),angles subtended by the same arc

Answer:

Weight of apples = 1.72 kg

Step-by-step explanation:

Given:

Total mass of sale = 8.6 kg

Pears weight = 4/5 of total weight

Find:

Weight of apples

Computation:

Weight of apples = [1 - 4/5]Total mass of sale

Weight of apples = [1/5]8.6

Weight of apples = 1.72 kg

The 18th term of the arithmetic sequence -13, -9, -5, -1, 3,... is 55. Thus, the right answer is option A. which is A(18) = 55

Arithmetic Progression is a sequence of numbers in which the difference between two numbers in the series is a fixed definite value.

The specific number in the arithmetic progression is calculated by

\(a_n=a_1+(n-1)d\)

where \(a_n\) is the term in arithmetic progression at the nth term

\(a_1\) is the initial term in the arithmetic progression

d is the difference between two consecutive terms

In the given question, \(a_1\) = -13

d = -9 - (-13) = 4

Therefore, to calculate the 18th term,

\(a_{13}=a_1+(18-1)d\)

= -13 + (17) 4

= -13 + 68

= 55

Hence, the 18th term of the above AP is 55

Learn more about Arithmetic Progression:

https://brainly.com/question/18828482

#SPJ4

Answer:

6n + 24

Step-by-step explanation:

Answer:

The answer is B "by permitting Congress to pass any law seen as essential even if it has no link to an enumerated power"

Step-by-step explanation:

What does the Necessary and Proper Clause in the Constitution imply about the powers of Congress?

The Congress shall have Power... To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.

PLZ THANK GIVE FIVE STARS AND GIVE BRAINLIEST:)

Answer:

B, by permitting Congress to pass any law seen as essential even if it has no link to an enumerated power

Step-by-step explanation:

The necessary and Proper clause was created to limit the powers of the government and also for checks and balances so that no other branch has too much control over the others. Therefore the Congress has the power to make laws that are necessary and proper for carrying into execution de foregoing powers.

Answer: 8cm

Step-by-step explanation:

If the radius of the circle is 4 cm, then the diameter of the circle is 4 cm x 2, or 8 cm. If you know the circumference of the circle, divide it by π to get the diameter.

Answer:

Step-by-step explanation:

its B

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

Answer:

she will need 24 ounces of milk and 8 ounces of corn syrup

Step-by-step explanation:

let me know if im right good luck!

Answer:

\(48\) oz of milk

\(16\) oz of corn syrup

Step-by-step explanation:

\(3\times16=48\\1\times16=16\)

Answer:

The mean is 2.875 so its between 2 and 3

Step-by-step explanation:

If the coefficient of determination is 0.94, we can say that ninety-four percent of the total variation of the dependent variable is explained by the independent variable. The correct answer is: ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

This means that there is a strong positive relationship between the two variables. The coefficient of determination, represented as R², measures the proportion of the total variation in the dependent variable that is explained by the independent variable. In this case, an R² of 0.94 indicates that 94% of the total variation in the dependent variable can be explained by the independent variable. The coefficient of determination does not provide information about the direction or strength of the relationship. The correct answer therefore is ninety-four percent of the total variation of the dependent variable is explained by the independent variable.

More on coefficient of determination: https://brainly.com/question/28975079

#SPJ11

Answer:

Both of the equations are right because if you take s=4p, then reverse it, p=1/4 of s because 4 of p is equal to s so s/4 = p

Answer:

70

Step-by-step explanation:

using the Pythagorean theorem we see that the side length is 29, meaning the perimeter is 70

In degrees Celsius, the difference between Michigan's record low temperature and Colorado's record low temperature  to the nearest tenth if necessary is 5.50°C

The concept that wil be used here is temperature conversion. The degrees Celsius,  of Michigan's record low temperature can be calculated as

-51.7 °F we can convert to  °C,Using the equation below

F=1.8C+32

-51.7 ° = 1.8C+32

1.8C=-51.7 ° - 32

1.8C= -83.7

°C= -83.7/1.8

=-45.5°C

The degrees Celsius,  of Michigan's record low temperature can be calculated as -51. °C

The difference, in degrees Celsius, between colorado's record=( -45.5°C)  -(-51. °C) = 5.5°C

Learn more about temperature at:

https://brainly.com/question/25677592

#SPJ1

Answer:

slope = - 2, y- intercept = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x , that is

y = - 2x + 0 ← is in slope- intercept form

with slope m = - 2 and y- intercept c = 0 ( that is the origin )

The probability that less than or equal to 5 of the 10 independent customers will take more than 3 minutes to check out their groceries is approximately 0.9245.

To calculate this probability, we can use the binomial probability formula. Let's denote X as the number of customers taking more than 3 minutes to check out. We want to find P(X ≤ 5) when n = 10 (number of trials) and p (probability of success) is not given explicitly.

Step 1: Determine the probability of success (p).

Since the probability of each customer taking more than 3 minutes is not provided, we need to make an assumption or use historical data. Let's assume that the probability of a customer taking more than 3 minutes is 0.2.

Step 2: Calculate the probability of X ≤ 5.

Using the binomial probability formula, we can calculate the cumulative probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = C(10, 0) * p^0 * (1 - p)^(10 - 0) + C(10, 1) * p^1 * (1 - p)^(10 - 1) + C(10, 2) * p^2 * (1 - p)^(10 - 2) + C(10, 3) * p^3 * (1 - p)^(10 - 3) + C(10, 4) * p^4 * (1 - p)^(10 - 4) + C(10, 5) * p^5 * (1 - p)^(10 - 5)

Substituting p = 0.2 into the formula and performing the calculations:

P(X ≤ 5) ≈ 0.1074 + 0.2686 + 0.3020 + 0.2013 + 0.0889 + 0.0246

P(X ≤ 5) ≈ 0.9928

Rounding this probability to the nearest hundredth/second decimal place, we get approximately 0.99. However, the question asks for the probability that less than or equal to 5 customers take more than 3 minutes, so we subtract the probability of all 10 customers taking more than 3 minutes from 1:

P(X ≤ 5) = 1 - P(X = 10)

P(X ≤ 5) ≈ 1 - 0.9928

P(X ≤ 5) ≈ 0.0072

Therefore, the probability that less than or equal to 5 customers out of 10 will take more than 3 minutes to check out their groceries is approximately 0.0072 or 0.72%.

For more questions like Probability click the link below:

https://brainly.com/question/11234923

#SPJ11

If person c must always sit on the right of person a, then there are two possible seating arrangements for them: either a is at the top of the table and c is to their right, or c is at the top of the table and a is to their left.

In either case, we can consider person c as fixed in place and count the number of ways to seat the remaining three people around the table.
If we seat person a first, there are four choices for their seat. Then person b can be seated in any of the remaining three seats. Finally, person d can be seated in one of the two remaining seats. So, there are 4 x 3 x 2 = 24 ways to seat the remaining three people around the table. Therefore, there are 2 x 24 = 48 different seatings possible overall.
To draw the possibilities, we can start by drawing a circle to represent the circular table. Then, we can label the top of the circle as either person a or person c (depending on which one we choose to fix in place). From there, we can draw arrows to represent the possible positions for person b and person d, making sure to avoid any duplicates due to rotations of the table. By doing this, we can visualize all 48 possible seatings for the four people around the circular table.

To know more about Circular table visit:

https://brainly.com/question/15953753

#SPJ11

Answer:

no it does not show a fucntion

Answer:

4/5 or 1 1/3

Step-by-step explanation:

4 over 5, or 1 and then 1 over 3

Answer:

QT = 45

Step-by-step explanation:

ST = 65

SP = 26

RQ = 30

QT = 4x - 3

Given that ∆STR is similar to ∆PTQ, therefore:

\( \frac{ST}{PT} = \frac{RT}{QT} \)

Plug in the values

\( \frac{65}{65 - 26} = \frac{30 + (4x - 3)}{4x - 3} \)

Solve for x

\( \frac{65}{39} = \frac{30 + 4x - 3)}{4x - 3} \)

\( \frac{5}{3} = \frac{27 + 4x}{4x - 3} \)

Cross multiply

\( 5(4x - 3) = 3(27 + 4x) \)

\( 20x - 15 = 81 + 12x \)

Collect like terms

\( 20x - 12x = 81 + 15 \)

\( 8x = 96 \)

Divide both sides by 8

\( x = \frac{96}{8} \)

\( x = 12 \)

✅QT = 4x - 3

Plug in the value of x

QT = 4(12) - 3 = 48 - 3

QT = 45

The sample space are:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

The favorable outcomes care:

{RS, RT, SR, ST, TR, TS}

The probability is  0.3 or 30%

Part A:

The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.

The sample space can be represented as follows:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

Part B:

The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.

The favorable outcomes can be represented as follows:

{RS, RT, SR, ST, TR, TS}

Part C:

To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.

The number of favorable outcomes is 6, and the size of the sample space is 20.

Therefore, the probability of selecting 2 cards that are consonants is:

P(consonants) = favorable outcomes / sample space

P(consonants) = 6 / 20

P(consonants) = 0.3 or 30%

Learn more about sample space at

https://brainly.com/question/10558496

#SPJ1

Answer:

8

Step-by-step explanation:

20.00 divided 2.50 = 8.

Answer:

8

Step-by-step explanation:

$20.00/$2.50 = 8

Answer:

length= 6x

width= x

AREA= 135

solution

AREA = length times width

135 = 6x multiplied by x

135=6x^2

x^2 as subject of formula

x^2=135/6

x^2=22.5

square root both sides

x=4.74

width = 4.74

Answer:

9

Step-by-step explanation:

Answer:

2.3 equals 230%

Step-by-step explanation:

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 2.3 × 100 = 230% (answer).

➥ The ease way:

1) Move the decimal point two places to the right: 2.3 → 23 → 230.

2) Add a % sign: 230%

Answer: 230%

Explanation:

The first set {x | x < -3} means we're talking about numbers smaller than -3. This includes -4, -5, -6, etc

The second set {x | x > 5} means we're talking about numbers larger than 5. So things like 6,7,8,...

Combining both at the same time, we want to find a number that is both smaller than -3 and larger than 5. This is impossible as no such number exists. You can pick one or the other, but not both.

There are no solutions. Since there are no solutions, the solution set is the empty set.

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

For more such information on volume of triangular prism, visit:
https://brainly.com/question/31637705

#SPJ8