Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?

Answers

Answer 1

Answer:

(a) 720 ways

(b) 120 ways

(c) 24 ways

Step-by-step explanation:

Given

[tex]Word = DANCER[/tex]

[tex]n =6[/tex] --- number of letters

Solving (a): Number of arrangements.

We have:

[tex]n =6[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =6![/tex]

This gives:

[tex]Total =6*5*4*3*2*1[/tex]

[tex]Total =720[/tex]

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

[tex]n = 5[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =5![/tex]

This gives:

[tex]Total =5*4*3*2*1[/tex]

[tex]Total =120[/tex]

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

[tex]n = 4[/tex]

So, the number of arrangements is calculated as:

[tex]Total =n![/tex]

This gives:

[tex]Total =4![/tex]

This gives:

[tex]Total =4*3*2*1[/tex]

[tex]Total =24[/tex]


Related Questions

Ana is baking cookies for her family reunion. Her recipe uses 3/4 cup sugar and has a yield of 24 cookies. How many cups of sugar will Ana need if she wants to bring 10 dozen cookies? (1 dozen = 12).

Answers

9514 1404 393

Answer:

  3 3/4 cups

Step-by-step explanation:

The yield from 3/4 cup of sugar is 2 dozen cookies. Multiply that by 5 and you get: the yield from 15/4 cups of sugar is 10 dozen cookies.

As a mixed number 15/4 = 3 3/4.

Ana will need 3 3/4 cups of sugar for 10 dozen cookies.

Answer:

Solution given:

recipe use 3/4 cup of sugar for 24 or 2 dozen Cooke's

now

we have

2 dozen=3/4 cup of sugar

10dozen=3/4×10/2=15/2 cup of sugar is needed

Please help I’ll mark you as brainliest if correct!

Answers

Answer:

half of 11:

5.5^2 x 3.14

30.25 x 3.14 = 94.985

round

94.99

NO LINKS! NO FILES

please :)

Answers

Answer:

the answer is 40 because you count all the squares that are in the shape

Step-by-step explanation:

The answer is 40 from what I see

The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Answers

Answer:

[tex] \huge \purple{ \boxed{ y = \frac{2}{3} }}[/tex]

Step-by-step explanation:

Since, the variables x and y are inversely proportional.

[tex] \therefore \: y \: \: \alpha \: \: \frac{1}{x} \\ \implies \: y = \frac{k}{x} \\ (k = constant) \\ \implies \: xy = k ...(1)\\ plug \: y = 2, \: \: x = 3 \: in \: equation \: (1) \\ we \: find \\ 2 \times 3 = k \\ k = 6 \\ plug \:k = 6 \: in \: equation \: (1) \\ xy = 6 \\ (this \: is \: the \: equation \: of \: variation) \\ when \: x = 9 \: \: y =? \\ \\ 9y = 6 \\ y = \frac{6}{9} \\ \huge \red{ \boxed{ y = \frac{2}{3} }}[/tex]

A 30-ounce box of cereal contains 12 servings.
Which value represents the unit rate in this scenario?
O A. 0.4 ounces/serving
O B. 2.5 ounces/serving
O c. 6 ounces/serving
O D. 18 ounces/serving

Answers

Answer:

tha answer is B

Step-by-step explanation:

Sami made $23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year. What is his hourly and weekly pay rate

Answers

Answer:

$15 / hr

$450 / week

Step-by-step explanation:

30 h x 52 w = 1560 hrs

$23400 / 1560 = $15 / hr

$15 * 30 hrs = $450 / week

Find the area of a circle with diameter = 42 cm. Use 3.14​

Answers

Area of circle = pi * r^2
42/2 = radius, radius = 21
3.14 * 21^2 = radius
3.14 * 441 = 1,384.74

Solution: 1,384.74 cm^2

1
From the graph Y =
shown below, what happens to the y-values as the positive x- values get closer to zero?
.
4
s
-
-3
2
1
w
2
C.
d.
They stay the same
cannot be determined
a.
They increase
b. They decrease

Answers

Answer:

a

Step-by-step explanation:

a.

They increase

V22 + V2
+
why can you NOT add these?

Answers

Answer:

The Bell Boeing V-22 Osprey is an American multi-mission, tiltrotor military aircraft ... However, the V-22 is generally not capable of hovering on one engine.

2. If it costs $0.12 Per Cubic inch
for the Juice, What is the Cost for the
original Container ?

Answers

what was the original container?

What is the slope of the line shown below? (Enter your answer as a decimal if
necessary.)
(-2, 4)

(4,-5)

Answers

Answer:

- 1.5

Step-by-step explanation:

Given points

( x1 , y1 ) = ( 4 , - 5 )

( x2 , y2 ) = ( - 2 , 4 )

Now

Slope (m)

= ( y2 - y1 ) / ( x2 - x1 )

= ( 4 + 5 ) / ( - 2 - 4 )

= 9 / - 6

= -1.5

Hope it will help :)❤

solve the equation 10x-6+18x-6(2x-4)=2

Answers

Answer:

x=-1

Step-by-step explanation:

multiplique el paréntesis por -6

10x-6+18x-12x+24=2

agripe los términos semejantes

16x-6+24=2  ......   16x+18=2

mueva la constante al lado derecho y cambie su signo

16x=2-18

calcula la diferencia

16x=-16

divida ambos lados de la ecuación entre 16

x=-1

may someone please help me? I’m having trouble finding G and H. It would be okay if you only found G for me. I will give the first answer a brainliest if it is reasonable or correct! Thanks you

Answers

g would be 125 degrees

h would be 62 degrees

Answer:

g = 118°

Step-by-step explanation:

b = 180 - 62 = 118 because b is supplementary to the 62° angle

g = 118 because b and g are alternate interior angles

PLEASE HELP
WHAT ARE THE coordinates for the center of the hyperbola??

Answers

Answer:

The coordinates of the center of the hyperbola are (1,-3)

Step-by-step explanation:

Equation of a hyperbola:

The equation of a hyperbola with center [tex](x_0,y_0)[/tex] is given by:

[tex]\frac{(x - x_0)^2}{a^2} - \frac{(y - y_0)^2}{b^2} = 1[/tex]

In this question, we have that:

[tex]-x_0 = -1 \rightarrow x_0 = 1[/tex]

[tex]-y_0 = 3 \rightarrow y_0 = -3[/tex]

The coordinates of the center of the hyperbola are (1,-3)

find inverse of f(x)= 5x+ln(x-2)​

Answers

Answer:

y = 5 x + ln ( x − 2 )

The radius of a circle is 4 feet. What is the area of a sector bounded by a 45 degree arc

Answers

45/360 * 4^2 pi = 6.283
ANSWER IS 6.283 (3 decimal places)

Answer:

2π ft²

Step-by-step explanation:

Circle Area:

A = πr²

A = π × (4 ft)²

A = 16π ft²

Sector Area:

A = (45°)/(360°) × 16π ft²

A = 2π ft²

NORD PROBLEMS
23
Landon has 48 books. He can fit 7
books in a box. How many boxes does he need?
How many books will be in
the last box?

Answers

Answer: He will need 7 boxes and there will be 6 in the last box

Step-by-step explanation:

I did division and solved it lol

Answer:

he needs 7 boxes

there will be just one book in the last box

Math please help!!!!

Answers

Answer:

6.3 years

Step-by-step explanation:

Given

[tex]P = 22400[/tex] --- initial value

[tex]r = 12\%[/tex] -- rate

[tex]A = P(0.88)^t[/tex] --- function

Required

Find t when [tex]A = 10000[/tex]

We have: [tex]A = P(0.88)^t[/tex]

Substitute: [tex]A = 10000[/tex] and [tex]P = 22400[/tex]

[tex]10000 = 22400 * 0.88^t[/tex]

Divide both sides by 22400

[tex]0.4464 = 0.88^t[/tex]

Take log of both sides

[tex]\log(0.4464) = \log(0.88^t)[/tex]

Apply law of logarithm

[tex]\log(0.4464) = t\log(0.88)[/tex]

Solve for t

[tex]t = \frac{\log(0.4464)}{\log(0.88)}[/tex]

[tex]t = \frac{-0.3503}{-0.0555}[/tex]

[tex]t = 6.31[/tex]

[tex]t \approx 6.3[/tex]

Find the exact value of x .

x = ?

Do the side lenghts form a Pythagorean triple?

Answers

Answer:

x = 14

Yes, the form a Pythagorean triple.

Step-by-step explanation:

50^2 - 48^2 = x^2

196 = x^2

x=14

According to the table below, what is the probability that a student chosen at random will be 16 or older?
Age. 13 14. 15. 16. 17. 18
Probability 0.01 0.25 0.30 0.28 0.15 0.01
A. 0.46 B. 0.83 C. 0.41 D. 0.44​

Answers

Answer:

probability: 0.44

The probability that a student chosen at random will be 16 or older is 0.44 or 44%.

What is probability?

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability that a student chosen at random will be 16 or older is the sum of the probabilities of selecting a 16-year-old or older student.

P(16 or older) = P(16) + P(17) + P(18)

P(16 or older) = 0.28 + 0.15 + 0.01

P(16 or older) = 0.44

Therefore, the probability that a student chosen at random will be 16 or older is 0.44 or 44%.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ7

15 POINTS!
7. Which of the following systems of inequalities describes the shaded region in the graph below?

Answers

Answer:

Step-by-step explanation:

the 2nd choice looks good Emily

y > x

y > x+2

y>x and y>x+2 is the  systems of inequalities describes the shaded region in the graph below.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade.

If the symbol ≥ or > is used, shade above the line.

If the symbol ≤ or < is used shade below the line.

y>x and y>x+2 is the inequality describes the shaded region in the graph below as it is greater.

Hence, y>x and y>x+2 is the  systems of inequalities describes the shaded region in the graph below.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ2

Joe ate twice as many pieces of Halloween candy as Ed. Together they ate 48 pieces.

How many pieces of candy did Ed eat?

A. 12
B. 16
C. 24
D. 32​

Answers

Answer: 16

Step-by-step explanation:

Let the number of candy Ed took be denoted as "x"

Since Joe ate twice the amount of candy Ed ate, then the number of candies joe ate will be denoted as "2x"

Since all together they ate a total of 48 candies, then the sum of the candies eaten by Joe and Ed is what gives a total of 48

This means:

2x + x = 48

3x = 48

X = 16.

Please help I’ll mark you as brainliest if correct!

Answers

Answer:

D. 50.24

Step-by-step explanation:

The circumference based on the diameter of 16 is 50.27. Since its asking for the closest I would believe its D.  :) hope this helps  

What is 729 in a exponent
Pls help quickly

Answers

Answer:

27×27=729

729^6..........

729 as in a exponent is 9

a. 75.5 meters in 20 seconds

Answers

What are you asking ????

What is the center of the circle?
A.(-1,-6)
B.(3,−1)
C.(−1,3)
D.(−6,1)

Answers

(3,-1) hope this helped

Answer:

B

Step-by-step explanation:

The x component must be positive (3)

What is the product of (6x^2 + 8)(3x^2 – 5x + 7)?

Answers

Answer:

x = 14 /3

Step-by-step explanation:

Answer: 18x^4 - 30x^3 + 66x^2 - 40x + 56

Area 15 cm 12 cm 19 cm triangle

Answers

Answer:

not clear

Step-by-step explanation:

what is the height and base? need an image

Use 3.14 for PI( π )

Diameter: 5 ft
Formula: A= πr2

Answers

Answer:

[tex]\boxed {\boxed {\sf 19.625 \ ft^2}}[/tex]

Step-by-step explanation:

The area of a circle is found using this formula:

[tex]a= \pi r^2[/tex]

We know the circle's diameter is 5 feet, but we don't know the radius. Remember the diameter passes through the center from one side to the other, while the radius connects the center and the side. Therefore, the radius is half the diameter.

r=d/2r= 5 ft/2r= 2.5 ft

We know the radius is 2.5 feet and we are using 3.14 for pi. Substitute the values into the formula.

[tex]a= (3.14)* (2.5 \ ft)^2[/tex]

Solve the exponent.

(2.5 ft)²= 2.5 ft *2.5 ft=6.25 ft²

[tex]a= (3.14)*(6.25 \ ft^2)[/tex]

Multiply.

[tex]a=19.625 \ ft^2[/tex]

The area of the circle is 19.625 square feet.

If y=1/4x and x=-12, find y.

Answers

Answer:

-3 I believe

Step-by-step explanation:

why dose the answer have to be 20+ letters

Answer:

-3

Step-by-step explanation:

To find y, plug in -12 for x in the y=1/4x equation. Multiply -12 by 1/4 (or divide -12 by 4) and you get -3.

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