A class is attended by n sophomores, n juniors, and n seniors. In how many ways can these students form n groups of three people each if each group is to contain a sophomore, a junior, and a senior

Answers

Answer 1

Answer:

n!² ways

Step-by-step explanation:

The number of ways in which the students can form "n" groups of three people each provided that each group has to contain a sophomore, a junior, and a senior inclusive.

The first step to take is to line up the sophmores in any and no particular way. After doing that, we proceed to lining up the juniors across from the sophmores in any one of n! ways. Finally, we get to line up the seniors across from the juniors in any one of n! ways.

After all these we get a result that is a total of n!² ways.

Answer 2

The number of ways should be \(n!^2 ways\)

The following information should be considered:

To see why this is, each group must contain one of each student, which is \((n!)\times (n!)\times (n!)\)ways to sort the students into groups. But, the order of the groups doesn't matter, so we have to divide by (n!), which is the number of ways to order the groups, leaving \((n!)^2\) as the number of ways.  

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Related Questions

7) Monday's temperature at 6pm was 11 degrees Fahrenheit. By 10pm, thetemperature dropped 6 degrees. By Tuesday early morning, the temperature haddropped another 7 degrees. What was the temperature on Tuesday morning?

Answers

Monday :

6pm= 11 F

10pm = dropped 6 F

Tuesday

Morning= Dropped another 7 degrees

temperature dropped is negative.

So, we have to add the temperatures:

11 + (-6) + (-7)

11-6-7

-2

what integer is equivialnt to 25 3/2

Answers

Answer: There is none.

Step-by-step explanation:

Fractions and decimals can't be integers.

what is a square of 1.5cm ​

Answers

Answer:

a square with 1.5 cm width and height

Answer:

2.25

Step-by-step explanation:

1.5 * 1.5 = 2.25.

its asking me 7th geade questions

its asking me 7th geade questions

Answers

Amy spent $21 on school supplies.

The correct answer is option C, $21.

To determine how much Amy spent on school supplies, we first need to calculate the fraction of her total money that was spent on school supplies. It is given that Amy spent 1/6 of her money on school supplies.

We are also given that Amy spent a total of $126 at the store. So, to find the amount spent on school supplies, we need to find 1/6 of $126.

To calculate 1/6 of a value, we can multiply the value by the fraction 1/6. In this case, we have:

(1/6) x $126 = $21

Therefore, Amy spent $21 on school supplies.

The correct answer is option C, $21. This means that out of the total $126 spent, $21 was allocated to school supplies.

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What does negative 3 over 5 > −2 indicate about the position of negative 3 over 5 and −2 on the number line?
A. negative 3 over 5 is located on the right of −2
B.negative 3 over 5 is located on the left of −2
C.negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 D.negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
Will mark Brainliest!

Answers

Answer: A. negative 3 over 5 is located on the right of −2

Step-by-step explanation:

On a number line, the greater numbers are to the right and the smaller numbers are to the left.

d - 41 = 19

Choose the answer that shows what to do in the process step, and what the solution (answer is).

Question Options:

add 41; d = 60

subtract 41; d = 60

multiply by 41; d = 60

divide by 41; d = 60

Answers

Answer:

see explanation

Step-by-step explanation:

add 41; d = 60

The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?

Answers

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Hey guys, Why people use the word hairline to roast so much. Mine looks like the mcdonalds sign :/

Answers

Answer:

Step-by-step explanation:

Became they most likely have nothing else to roast about.

the opposite sides of a parallelogram are ? congruent
A: always
b: sometimes
c: never

Answers

Opposite sides are always congruent
A: always

A family of 3 goes to a fair. Tickets cost $5 each, but
each person has a coupon. They pay $7 altogether.
How much money does each person save on buying
their ticket?

5x - 7 = 3

7 = 3(5 + x)

3x + 5 = -7

x + 7 = 3 x 5

Answers

Answer: $105

Step-by-step explanation:

Answer:

$2.66

Step-by-step explanation:

Step 1: Multiply the $5 to the family of 3

\(5 \times 3 = 15\)

That's what they would have paid if they did not have a coupon. Now they have a coupon and only pay $7.

Step 2: Subtract what they paid from the result

\(15 - 7 = 8\)

Now we have found how much they save altogether. To find how much they saved each;

Step 3: Divide the result found in step 2 by the family of 3

\(8 \div 3 = 2.66666\dots\)

Each person saves approximately $2.66

Give me a long sum using bodmas which equals 6​

Answers

Answer:

Step-by-step explanation:

2 x 12 - (9 - 3) x 2 / 2

Evaluate the following expression when x = -2, y = 5, and t= 8.
[x]+3t-9y

Answers

Answer:

the answer is -23 let me if you have questions

The supply and demand for a product are related to price by the following​ equations, where y is the​ price, in​ dollars, and x is the number of​ units, in thousands. Find the equilibrium point for this product. yequals​S(x)equals300plus40x yequals​D(x)equals4300minus40x

Answers

Answer:

The equilibrium point for the product (x,y) = (50,2300)

Step-by-step explanation:

The equilibrium point refers to the point in the demand and supply curves where we have the quantity demanded equals the quantity supplied at a particular price.

From the question, we can identify the following;

S(x) = 300 + 40x

D(x) = 4300 - 40x

Now, at the equilibrium point, S(x) = D(x)

This means that;

300 + 40x = 4300 -40x

80x = 4300-300

80x = 4000

x = 4000/80 = 50

Now, we input the value of x into any of the equation of the demand and supply to get the quantity.

Let’s use S(x) = 300 + 40x = 300 + 40(50) = 300 + 2000 = 2,300

The equilibrium point for the product (x,y) = (50,2300)

I am a solid figure with two congruent
polygons that are bases, connected
with lateral faces that are rectangles.

Answers

PRISM! a solid figure with two congruent polygons that are bases, connected with lateral faces that are rectangles. A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices.

THE ANSWER IS PRISM

In recent years, Sheffield Transportation purchased three used buses. Because of the frequent turnover in the accounting department, a different accountant was in charge of selecting the depreciation method for each bus, and various methods have been used. Information concerning the buses is summarized in the table below. Bus 1, Bus 2, Bus 3, For the declining-balance method, the company uses the declining method rate. For units-of-activity method, total miles are expected to be 125,000. Actual miles of use in the first 3 years were 2021, 27,000; 2022, 35,000; and 2023, 33,000.

(a1) For Bus #3, calculate depreciation expense per mile under units-of-activity method.

Answers

Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

How is the depreciation expense per mile determined?

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Question Completion:

Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

select the option for "?" that continues the pattern in each question

3,-6, 12, 4, 20

13
14
6
16

Answers

Answer:

The next number in the sequence is: 13

Step-by-step explanation:

So we start with 3, then the pattern is:

subtract 9, add 18, subtract 8, add 16, subtract 7, add 14...

If we apply this to the pattern we can see that it works. You should be able to continue the pattern if needed.

Megan saves $42 every 6 days. How much does she save in 1 day?

Answers

Answer:

7

Step-by-step explanation:

6x7=42

Step-by-step explanation:

$42 divided by 6 = 7 so Megan makes $7 each day.

PLEASE HURRY~ CHOOSING BRAINLIEST
Write the equation of the line with x-intercept 3 and y-intercept 2.
A) y = 2/3 x + 2
B) y = 3/2 x + 2
C) y = − 2/3 x + 2
D) y = − 3/2 x + 2
(the numbers with / between them are fractions)

Answers

Answer:

Step-by-step explanation:

Because the y intercept is two our y=mx+b equation looks like this

y=mx+2

We then need to find a slope that gives us an x intercept of 3 or satisfies the coordinates of (3,0)

We can plug this in and solve

0=3m+2

-2=3m

-2/3=m

which means our final equation is

-2/3x+2

C

C because y=mxb so plug in the numbers

a teacher randomly selects one student from a group of students where 12 are wearing a black shirt 8 are wearing a red shirt and 12 are wearing a blue shirt what is the probability that the selected student is wearing a blue shirt

Answers

Answer:

12/32 or 3/8 or 37.5%

Step-by-step explanation:

Select whether the pair of lines is parallel, perpendicular, or neither. y−4=3(x+5), y+3=−13(x+1)

Answers

Answer:

neither

Step-by-step explanation:

parallel lines will have the same number next to the x

perpendicular lines will have the negative reciprocal number next to the x

(for example 2 and -1/2 are negative reciprocals)

y−4=3(x+5)

parenthesis first

y−4=3x+15

y=3x+19

y+3= −13(x+1)

y+3= −13x−13

y= −13x−16

3x and −13x are neither the same nor negative reciprocals of each other so

the answer is neither

10 in. 6 in. l Find l. l = √[?] in. Enter​

10 in. 6 in. l Find l. l = [?] in. Enter

Answers

Answer:

l = √109 in.

Step-by-step explanation:

We see that the 10. in. apothem connecting the top of the cone and the circular base and a radius of the circle creates a right triangle.

Step 1:  First we need to find the radius of the circle.

Since 6 is the diameter of the circle and the diameter is 2 * the radius, the radius is 3 in. since 2 * 3 = 6 and 6/2 = 3.

Step 2:  Because we're working with a right triangle, we can now find l using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

a and b are the shorter sides called legs,and c is the longest side called the hypotenuse.

We can plug in 10 for and 3 for b, allowing us to solve for c (aka l since l is the hypotenuse in the right triangle).

10^2 + 3^2 = c^2

100 + 9 = c^2

√109 = c

Thus, the measure of l is √109 in.

Two consecutive integers are such that 7 times the biggest and then added to the smallest equals
495, what are they?

Answers

Answer:

61,62

Step-by-step explanation:

Let the smallest  number be x

Hence, the biggest number = x+1 [as it consecutive]

Hence,

7(x+1)+x=495

7x+7+x+495

8x=495-7

8x=488

x=61

Hence, smaller number=61, bigger number=62

The volume of a cylinder is 637 cm³. If the radius is 3 cm, what is the height
of the cylinder?

The volume of a cylinder is 637 cm. If the radius is 3 cm, what is the heightof the cylinder?

Answers

If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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EASY POINTS!

Which is the BEST definition of the term mirror line?
A mirror line is the line over which an object in the coordinate plane is reflected.
A mirror line is a line in the plane that is units away from the y-axis.
A mirror line is another name for the line of translation.
A mirror line is always a diagonal line in the plane that divides it into eight sections.

Answers

The best definition of the term mirror line is "A mirror line is the line over which an object in the coordinate plane is reflected". So option A is correct.

What is mirror line ?

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

Given options,

A. A mirror line is the line over which an object in the coordinate plane is reflected.

Yes this statement is according to definition of mirror line.

B. A mirror line is a line in the plane that is units away from the y-axis.

no its is not like that so it is incorrect option.

C. A mirror line is another name for the line of translation. no translation is a different concept so it also incorrect.

D. A mirror line is always a diagonal line in the plane that divides it into eight sections. it is also not correct.

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Kate kicked 25 goal shots at soccer practice and scored on 13 of them. What percent of shots did she make

Answers

She made 52% of the shots.

Answer:

52%

Step-by-step explanation:

If 25% is the 100% only multiply 13 by 4 and thats it

what is the surface area means​

Answers

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.

Answer:

that is the outsider part.of something

the sum of the areas of all the faces of a three dimension figure or in 3-D shapes

Can someone help me with this one

Can someone help me with this one

Answers

Answer:

A

Step-by-step explanation:

I think because I just had this similar problem if I'm wrong I'm sorry not a 100%sure just trying to help

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?

Answers

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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An object attached to a coiled spring is pulled down 5 centimeters from its rest position and released. If the motion is simple harmonic in nature, with a period of pi seconds, answer the following questions.
A. what is the maximum displacement form equilibrium of the object?
B. what is the time required for one oscillation?
C. what is the frequency?
D.write an equation to model the motion of the object.

Answers

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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How many feet are in 5 yards 1 foot?

Answers

Answer:

welp-_- in 1 yard theres 3 so..........in 5 yards there 15 feet + 1 is 16 your welcome

Step-by-step explanation:

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*take the space out*

There are 16 feet in 5 yards
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