Counting principle involving a specified arrangement89°FA certain train has 9 cars that are being lined up on a track. One of the cars is the engine, and another is the caboose. The engine will be the first car in line. Thecaboose will be the last car in line. In how many ways can the cars be lined up?0ExplanationI need help with this math problem.

Answers

Answer 1

Given:

\(\begin{gathered} Total(cars)=9 \\ Engine(car)=1 \\ Caboose(car)=1 \end{gathered}\)

To Determine: The many ways the cars can be lined up

Solution

Since we have 9 cars, the first must be engine car. The number of ways of that is 1!

The last must be caboose, then the number of ways of that is 1!.

In between will be remaining 7 ways to arrange the ways. This can be done in 7! ways

Therefore, the number of ways to arrange the 9 cars would be

\(\begin{gathered} Ways=1!\times7!\times1! \\ Ways=1\times7\times6\times5\times4\times3\times2\times1\times1 \\ Ways=5040 \end{gathered}\)

Hence, the number of ways the cars can be lined up is 5040 ways


Related Questions

Absolute value equation x=14,2

Answers

Answer:

X

Step-by-step explanation:

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used.
Find the endpoints of the t-distribution with 2.5% beyond them in each tail if the samples have sizes n1=16 and n2=21.
Enter the exact answer for the degrees of freedom and round your answer for the endpoints to two decimal places.

Answers

Answer:

Don't go on that link its a virus

Step-by-step explanation:

Express the graphed inequality in interval notation:012345678910

Answers

Looking at the graph

we have that

The shaded area is all real numbers less than six

so

x < 6

interval notation

(-infinite, 6)

Sammy wants to spend no more than $35 at the arcade. If he is playing games at the arcade that each cost $0.75, which inequality can be used to find g, the number of games that Sammy can play and stay within his goal

Answers

Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35

Please answer this It would mean alot to me.

Please answer this It would mean alot to me.

Answers

The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

How to find equivalent expression?

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Luis bought 8 2/5 pounds of oranges for his soccer team. The team ate 4 5/8 ponds of oranges. About how many oranges are left

Answers

Answer:

3.775

Step-by-step explanation:

Answer:

3.775 OR 151/40 OR 3 31/40

Step-By-Step Explanation:

Subtract 8 2/5 by 4 5/8

S vi) The temperature in Gulmerg in Kashmir was-10°C in January and it rose by 44°c to reach the maximum temperature during summer. The maximum temperature during summer in that year was​

Answers

The maximum temperature during summer in that year was 34°C.

It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.

A temperature rise of that magnitude would be extremely unusual and potentially dangerous.

However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.

The minimum temperature in January was -10°C, and if we add 44°C to it, we get:

-10°C + 44°C = 34°C

Therefore, the maximum temperature during summer in that year was 34°C.

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Where does 1/6 land on a number line

Answers

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

Complete the following sentence.

When two numbers are not equal, an ___________ is a sentence that uses the symbols >, <, ≥, ≤, or ≠ to show a relationship.

Answers

When two numbers are not equal, an inequality is a sentence that uses the symbols >, <, ≥, ≤, or ≠ to show a relationship between the two numbers.

Answer: The answer is E, or ≠.

Step-by-step explanation:

The symbol (≠) indicates that a number does not equal the other number. The correct option is E.

I hope this helped! A brainilist is appreciated and helpful! <3

Question 4
Which term in the sequence given by n th term formula 7n - 50 has a value of 41?
th term

Answers

Answer:

13th term

Step-by-step explanation:

41 = 7n - 50

41 + 50 = 7n

91 = 7n

7n = 91

n = 91/7

n = 13

13th term has value 41

Answer:

n = 13

Step-by-step explanation:

7n - 50 = 41

Add 50 to both sides

7n = 41 + 50

7n = 91

Divide both sides by 7

n = 91/7

n = 13

what happened to the U.S dollar when president Nixon closed the gold window?

Answers

The Nixon Shock effectively led to the end of the Bretton Woods Agreement and the convertibility of U.S. dollars into gold. The Nixon Shock was the catalyst for the stagflation of the 1970s as the U.S. dollar devalued.

What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13

Answers

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

20% of a full tank is 80 liters.

Answers

Step-by-step explanation:

you have to multiply 20 by 80

Answer:

How many liters are in a full tank? ----- Answer:

Step-by-step explanation:

20 % of 80 = 16

(I really don't know what your asking for, your missing pieces to the question.)

Sorry, :(

What is the distance, rounded to the nearest tenth, between the points (-2,4) and (6,-4)?

Answers

Answer: (11,3)




HOPE ITS HELP

Find the value of y.

Find the value of y.

Answers

The value of y is 4√3

What are similar triangles?

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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If a three-digit number is divided by 5 or by 6, remainder is 1 in each case. What is the least such three-digit number?

Answers

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Belle's dad lends her $10. Then Belle borrows another $15 from him. Write and evaluate an expression that shows the change in the amount of money Belle's dad has.

Answers

The expression that shows the change in the amount of money Belle's dad has is (x - 25) and this can be determined by forming the linear equation in one variable.

Given :

Belle's dad lends her $10. Then Belle borrows another $15 from him.

The following steps can be used to determine the expression that shows the change in the amount of money Belle's dad has:

Step 1 - Let the total amount of money Belle's dad have be 'x'.

Step 2 - Then it is given that Belle's dad lends her $10. So the expression becomes:

= x - 10b

Step 3 - Now, it is also given that Belle borrows another $15 from her dad. So, the above expression becomes:

= x - 10 - 15

Step 4 - Simplify the above expression.

= x - 25

So, the expression that shows the change in the amount of money Belle's dad has is (x - 25).

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4/8 - 3/10 pa answer ulii

Answers

Answer:

1/5

Step-by-step explanation:

4/8-3/10=1/5

So basically 4/8 -3/10 you first cross multiple the denominators so 8 multiplied by 10 and 3 and 10 multiplied by 8 and 4 so we have a total of 80 which is our denominator and 40-24 which will give us 16/80 then we simplify until we get 1/5 it’s a long way but very easy to understand
4/8 - 3/10 pa answer ulii

If a:b =1/2 :1/3 and b:c = 3:4 find a:c

Answers

Step-by-step explanation:

I've written the answer and steps to solve the question a piece of paper which is in the attached photo. Hope this helps!

If a:b =1/2 :1/3 and b:c = 3:4 find a:c

Answer:

a : c = 9 : 8

Step-by-step explanation:

Expressing the ratios in fractional form , then

\(\frac{a}{c}\) = \(\frac{a}{b}\) × \(\frac{b}{c}\)

Given a : b = \(\frac{1}{2}\) : \(\frac{1}{3}\) ( multiply both parts by 6 to clear the fractions )

a : b = 3 : 2 and b : c = 3 : 4 , then

\(\frac{a}{c}\) = \(\frac{3}{2}\) × \(\frac{3}{4}\) = \(\frac{3(3)}{2(4)}\) = \(\frac{9}{8}\)

That is a : c = 9 : 8

Here is a rectangle.
9 cm
7 cm
Work out the perimeter of the rectangle.

Answers

Answer:

P=32cm

Step-by-step explanation:

Here is a rectangle.9 cm7 cmWork out the perimeter of the rectangle.

Answer: 32

Step-by-step explanation: 9+9 =18

                                             7+7= 14

                                               14+18=32

find the sum of the values of a and b such that f(x)=2ax^2+bx+3 has a relative extremum at the point (-1,2)

Answers

the sum of the values of a and b such that f(x) = \(2ax^2 + bx + 3\) has a relative extremum at the point (-1,2) is 2.5.

If the function f(x) = \(2ax^2 + bx + 3\) has a relative extremum at the point (-1,2), then the derivative of the function must be zero at x = -1. This is because at a relative extremum, the slope of the tangent line is zero.

So, we need to find the derivative of f(x) and set it equal to zero at x = -1:

f'(x) = 4ax + b

f'(-1) = 4a(-1) + b = -4a + b = 0

Solving for b, we get:

b = 4a

Now, to find the sum of a and b, we just need to substitute b = 4a into the expression for f(x) and use the fact that f(-1) = 2:

f(x) = \(2ax^2 + bx + 3\)

f(-1) = \(2a(-1)^2 + b(-1) + 3 = 2\)

Substituting b = 4a, we get:

2a(1) - 4a + 3 = 2

2a - 4a + 3 = 2

-2a = -1

a = 1/2

Then, using b = 4a, we get:

b = 4(1/2) = 2

So, the sum of a and b is:

a + b = 1/2 + 2 = 2.5

Therefore, the sum of the values of a and b such that f(x) = \(2ax^2 + bx + 3\)has a relative extremum at the point (-1,2) is 2.5.

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This Venn diagram shows sports played by 10 students.
Karl
Jada
Gabby
PLAYS
BASKETBALL
O A=0.50
OB. 0.29
OC. =0.40
D.
=0.20
Fran
Juan
lan
Ella
Let event A = The student plays basketball.
Let event B = The student plays soccer.
What is P(AB)?
PLAYS
SOCCER
Mickey
Mai
Marcus

Answers

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

How to calculate a probability?

The parameters that are needed to calculate a probability are listed as follows:

Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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This Venn diagram shows sports played by 10 students.KarlJadaGabbyPLAYSBASKETBALLO A=0.50OB. 0.29OC.

Jamal is five years less than the age of his brother Alex and the product of their ages is 300. How old is Jamal?

Answers

Let's start by defining some variables:

Let's call Jamal's age "J".

Let's call Alex's age "A".

From the problem statement, we know that:

J = A - 5 (Jamal is 5 years younger than Alex)

J * A = 300 (the product of their ages is 300)

We can use the first equation to substitute J in the second equation:

(A - 5) * A = 300

Expanding the left-hand side:

A^2 - 5A = 300

Moving all terms to the left-hand side:

A^2 - 5A - 300 = 0

We can solve for A using the quadratic formula:

A = (-(-5) ± sqrt((-5)^2 - 41(-300))) / (2*1)

A = (5 ± sqrt(25 + 1200)) / 2

A = (5 ± sqrt(1225)) / 2

Since A is a positive integer, we take the positive solution:

A = (5 + 35) / 2 = 20

Now we can use the first equation to find J:

J = A - 5 = 20 - 5 = 15

Therefore, Jamal is 15 years old.

Write the difference of two algebraic expressions modeled by the algebra tiles. Let $x$ be the variable. Then use the algebra tiles to simplify the expression. Two groups of algebra tiles. The second is subtracted from the first. The first group has two positive variables tiles and seven positive unit tiles. The second group has two positive variable tiles and four negative unit tiles.

Answers

Answer:

3

Step-by-step explanation:

Who cares? just copy down the answer.

A total of 491 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 fewer student tickets than adult tickets. How many adult tickets were sold?

Answers

Answer:

Театр кассасында уш Кун ишинде  билет сатылды.биринши куни  билет сатылды,екинши куни  билет сатылды.ушинши куни неше билет сатылды?

The number of adults tickets that were sold is 275.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

Adults ticket = x

Student's tickets = y

Now,

x = y - 59  ____(1)

x + y = 491 _____(2)

Substituing (1) in (2)

y - 59 + y = 491

2y = 491 + 59

2y = 550

y = 275

Now,

x = 275 - 59

x = 216

Thus,

The number of adult tickets is 275.

The number of student tickets is 216.

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Calculate the height (in m) of a cliff if it takes 2.41 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.14 m/s. (Enter a number.)

How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)

Answers

The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s

What is motion under gravity?

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.

When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.

from equation of motion

H= ut-1/2gt^2( the object is moving upward)

where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity

(g=10ms^-2).

therefore h= 8.14×2.41-(1/2×10×2.41)

= 19.62-12.05

h= 7.57m

when the object is thrown Down,

V = u + gt

u will be 0 at top before coming down

V = gt

t= 8.14/10

= 0.814s

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the formula for converting celsius to fahrenheit is F = 9/5C+32.

a. The lowest temperature in Alaska, -62° C, was recorded on January 23, 1971 at Prospect Creek Camp. Use the formula to convert the recorded temperature to Fahrenheit

b. In February, the average high temperature in Puerto Vallarta, Mexico us 81° F. To the nearest whole number, what is this temperature in degrees Celsius?​

Answers

Answer:

a)-79.6

b)=27

Step-by-step explanation:

a) F=9/5(-62)+32

F=-79.6

b) 81=9/5C+32

81-32=9/5C

49=9/5C

C=27.222

Therefore C=27

Which linear function has the same y-intercept as the one that is represented by the graph?

On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.

Answers

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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During a trip, Amy had to take two different trains. Her first train traveled for 3 hours, and the second
train traveled for 4 hours. Combined, the trains traveled 625 miles.
If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this
equation?
Select two that apply.
The variable m in the equation represents the speed of the first train.
The variable m in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the first train.
The variable m in the equation represents the number of hours Amy traveled on the
first train.
The variable n in the equation represents the number of hours Amy traveled on the
second train.

Answers

Answer:

Let's solve for m.

3m + 4n = 625

Step 1: Add -4n to both sides.

3m + 4n + −4n = 625 + −4n

3m = −4n + 625

Step 2: Divide both sides by 3.

3m/3 = 4n + 625/3

m = -4/3 n + 625/3

C) The variable m in the equation represents the number of hours Amy traveled on the

first train.

D) The variable n in the equation represents the number of hours Amy traveled on the

second train.

What the meaning of statement this?

What the meaning of statement this?

Answers

The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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