How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?

Answers

Answer 1

If the letter z's are distinctly different, there are P(5,5) arrangements. That is
[tex]P\left(5,5\right)=5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120[/tex]

If the z's are interchangeable, the number of different arrangements is given by
[tex]\frac{5!}{2!}=5\cdot 4\cdot 3=60[/tex]

Answer 2

When each letter "z" is distinctly different, there are 60 possible arrangements.
When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

1. When each letter "z" is distinctly different from the others:
- The word "fuzzy" has 5 letters in total, including 2 "z" letters.
- To calculate the number of arrangements, we use the formula for permutations with repeated elements:
- The formula is: n! / (n1! n2! ... * nk!)
- n is the total number of letters in the word (5 in this case).
- n1, n2, ... are the number of repetitions of each distinct letter.
- Calculating: 5! / (1! 2! 1! * 1!) = 120 / 2 = 60 arrangements.

2. When the letter "z" is interchangeable with the other letters:
- In this case, there are 4 distinct letters in the word "fuzzy" (f, u, z, y).
- The total number of arrangements can be calculated using the formula for permutations of distinct items.
- Calculating: 4! = 24 arrangements.
In summary:
- When each letter "z" is distinctly different, there are 60 possible arrangements.
- When the letter "z" is interchangeable with the others, there are 24 possible arrangements.

Related Questions

If 7 is subtracted from the product of 3 and a number, the result is 5 more than the number.

Answers

If you subtract 3-7 and add 9 to it the result is 5. 3-7+9=5

Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town

Answers

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

HELP!!!!!!What is the equation of the graph below?

Answers

The answer to your question is y = sin(x + 90) as we have a sine graph phase shifted 90 units left

Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.

What is the volume of the cylinder rounded to the nearest cubic centimeter?

What is the total volume of the four balls rounded to the nearest cubic centimeter?

What percent of the volume of the container is occupied by the four balls?

Answers

Hello,
Please, see the attached files.
Thanks.

The frequency of F3 is 174.61 Hz. What is the frequency of the note that is a perfect fifth below f3?
A) 43.6525 Hz
B) 87.305 Hz
C) 116.407 Hz
D) 261.915 Hz

Answers

Notes separated by a perfect 5th have a frequency ratio of 3:2. The note a perfect 5th below f3 will have a frequency of
174.61 Hz × 2/3 = 116.407 Hz

The appropriate choice is ...
C) 116.407 Hz

Which of the following types of equations have you learned to solve using algebraic methods?
[]Quadratic[]Exponential[]Radical[]Linear[]Rational

Answers

The following types of equations have you learned to solve using algebraic methods is Linear.

Quadratic equations involve a variable raised to the power of 2, and algebraic methods like factoring or using the quadratic formula are used for solving.

Exponential equations involve variables in the exponent, and logarithmic methods are employed to solve them.

Radical equations involve roots, and solving them often involves isolating the radical and squaring both sides or other methods based on the root's degree.

Linear equations involve variables raised to the power of 1, and solving them uses standard algebraic techniques like isolating the variable.

Rational equations involve ratios of polynomials and are solved by methods such as clearing denominators and factoring.

In this triangle, side AT = 24. Please give the value for the sine, cosine, and tangent for this diagram (Which is the marked angle?). Give the value as a ratio ONLY. Make sure all ratios are in the lowest form.

Be sure to explain IN WRITING how you find sine, cosine, and tangent! If you are not sure, check the directions in this problem!

Question 1 options:

Answers

The value of the sine, cosine and tangent of the figure will be found as follows:
a] Sine
sin x=(opposite)/(hypotenuse)
opposite=7
hypotenuse=25
thus:
sin x= 7/25

b] Cosine
cos x=adjacent/hypotensue
adjacent=24
hypotenuse=25
cos x=24/25

Tangent
Tan x=opposite/adajcent
opposite=7
adjacent=24
thus
tan x=7/24

Factor the trinomial below.

9x2 + 6x + 1

A. (3x + 1)(3x – 1)
B. (9x + 1)(x – 1)
C. (9x + 1)(x + 1)
D. (3x + 1)(3x + 1)

Answers

Answer: D. (3x + 1)(3x+1)

Step-by-step explanation:

9x² + 6x + 1

find two factor of 9 such that its product gives 9 and its sum gives 6 (3 and 3, 3×3 = 9 , also 3+ 3=6)

we are going to replace 6x by 3x + 3x

9x² + 6x + 1

9x² + 3x +3x + 1

3x(3x + 1) + 1(3x+ 1)

(3x + 1)(3x+1)

The correct factorization of the trinomial 9x² + 6x + 1 is (3x + 1)(3x + 1) or (3x + 1)². option D.

How do we identify the correct option when the trinomial is factorized?

The trinomial 9x² + 6x + 1 is a perfect square trinomial, which can be factored as the square of a binomial.

Let's find the correct answer from your options:

(A) (3x + 1)(3x - 1): The difference of squares isn't the correct form for our trinomial.

(B) (9x + 1)(x - 1): Expanding this will not give us the original trinomial.

(D) (3x + 1)(3x + 1): When expanded, this gives us 9x^2 + 3x + 3x + 1, which simplifies to 9x² + 6x + 1.

Therefore option D (3x + 1)(3x + 1) is correct

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WILL GIVE BRAINLIEST PLZ HURRY!!!!!!!!Woodland High School recently won the state Academic Bowl Championship. The medal counts for the 7 members of the team are listed in the table. Which statement is true about the data shown in the table?
A) The range is less than the mode.
B) The mode is greater than the median.
C) The mean is greater than the median.
D) The median is greater than the mode.

Answers

Answer: B = The range is greater than the mean.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mean is greater than the median

What is 3 to the 100th power?

Answers

Final answer:

3 to the 100th power is a very large number with over 47 digits, symbolizing the potential of exponential growth.

Explanation:

The question is asking for the computation of the number 3 raised to the 100th power. In mathematics, exponents are used in expressions such as 'a to the power of n', written as an. Here, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself.

In our case, we have '3' as the base and '100' as the exponent. However, calculating 3100 directly is quite impractical due to the vast result it produces. However, we do know that it's a very large (over 47 digits!) number which could be useful for illustrating the power of exponential growth in mathematical or scientific contexts.

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Find the inverse function of h(x) = - 2/3x + 6.

h -1(x) = -3/2x + 9
h -1(x) = -3/2x - 6
h -1(x) = -2/3x + 9
h -1(x) = -2/3x - 6

Answers

let y=h-1(x) and lastly, find y

A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?
a. 36 ft
b. 108 ft
c. 42 ft
d. 126 ft

Answers

First Rectangle: P= 14; L= 4, W= ?
Second Rectangle: P= ?, L= ?, W= 9

STEP 1:
solve for the width in the first rectangle using perimeter formula

Perimeter= 2L + 2W
14= 2(4) + 2W

14= 8 + 2W
subtract 8 from both sides

6= 2W
divide both sides by 2

3= W

STEP 2:
Since the two rectangles are similar, they may be different sizes, but they have corresponding angles. We can set up a ratio to compare width and length.

First Rectangle: P= 14, L= 4, W= 3
Second Rectangle: L= ?, W= 9

length/width= length/width
4/3= L/9

cross multiply
4 * 9= 3 * L

36= 3L
divide both sides by 3

12= L

STEP 3:
find perimeter of second rectangle; use length from step 2

Perimeter= 2L + 2W
=2(12) + 2(9)
=24 + 18
=42 feet

ANSWER: (C) 42 feet

Hope this helps! :)

There are five red marbles eight blue marbles and 12 Green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble

Answers

you do add den you get30

Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?

Answers

So, the rate is 1 job / hours, so:
1/n + 1/1.5n = 1/6
We'll make the denominator 3n:
3/3n + 2/3n = 1/6
5/3n = 1/6
Cross multiply:
3n = 30
n = 10
It will take the slower person 10 hours to complete the room.

Which of the following is an undefined term?
Angle
Circle
Plane
Ray

Answers

I think it would be C.plane... I had this question a while ago and I think its right... plz tell me if I am wrong. Thanks.

Answer:

Plane is an undefined plane

Step-by-step explanation:

Hi, there are three undefined terms in geometry: point, line, and plane.

Point: has no size, only location . It can be named with a capital letter.

Plane: a flat surface that has no thickness, that extends infinitely n every direction. Is named by a single letter or by three coplanar, but non-collinear, points.

Line: Set of points extending in either direction infinitely.

Angle, circle, and ray are not undefined terms. are not Plane.

Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle

Answers

6. C=67
AC=23.
BA=55.2

Please help me, if you'd be so kind.

A right rectangular prism is shown.

What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?

Drag and drop the answer into the box.

Answers

[tex]\overline{DH}=\sqrt{3^2+1.5^2+1^2}=\sqrt{9+2.25+1}=\sqrt{12.25}=\boxed{3.5}[/tex]

what is the value of the expression?

Answers

To solve this we are going to use the unitary circle and the fact that [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex]

From our circle we can infer that [tex]sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2} [/tex] and [tex]cos\frac{5 \pi }{3}= \frac{1}{2} [/tex].

Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]

We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].

What is the value of b?

Answers

Look at the picture.

d° + c° = 2 · 68° = 136°

b° = 360° - (136° + 104°) = 360° - 240° = 120°

Please help me I’m about to cry

Answers

The reflections will be as shown in the attached figure:
A-Blue
B-Green
C=yellow
D=Grey
E=maroon
Triangle E is not the same as triangle C. This means she was wrong.

Please refer to the attached figure for the drawings, the colors represent the triangles in the order above.

Find the surface area of the cylinder in terms of π.

See picture

a) 1008π in.2

b) 522π in.2

c) 360π in.2

d) 396π in.2

Answers

[tex]\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=9\\ h=20 \end{cases}\implies SA=2\pi (9)(20+9) \\\\\\ SA=18\pi (29)\implies SA=522\pi [/tex]

Help needed soon. please

Answers

For this case we first define variables:
x = daisies flowers
y = roses flowers
We write the system of equations:
x + 2y = 33
x = y + 3
Solving the system we have:
x = 13
y = 10
Therefore, the cost of roses is:
2 * y = 2 * 10 = 20 $
Answer:
Roses = $ 20

Calculate the total cost of the order: Veggiburger with cola and soup, sales tax 4%, tip 15.

Veggiburger: $3.25
Cola: $1.50
Soup: $2.25

A $8.33
B $7.28
C $7.00
D $5.50

Answers

Add the prices of the food together to get $7. Then you calculate the sales tax, which is 1.04 * $7 = $7.28. The tip is 15% I am assuming, and not 15, so it would be $7 * 0.15 = $1.05. Add $1.05 with $7.28 to get $8.33, so the answer is A.

Final answer:

The cost of the order, including the sales tax of 4%, comes out to be $7.28. However, the tip is unclear in the question. If it's 15%, the cost rises to $8.37, but none of the provided options match this result.

Explanation:

The first step is to calculate the total cost of the Veggiburger, cola, and soup by adding them together. So, $3.25 (Veggiburger) + $1.50 (cola) + $2.25 (soup) = $7.00. Next, apply the 4% sales tax on this amount which is $7.00 * 4/100 = $0.28. So the subtotal now is $7.28 ($7.00 + $0.28). Finally, the tip mentioned in the problem is not clear whether it is a percentage or a fixed amount. If it is a 15% tip, then calculate 15% of the subtotal, i.e $7.28 * 15/100 = $1.09 (Approx). Adding this to the subtotal we get $8.37 which is not an option in the given answers. If $15 is a fixed tip amount, the total cost would be substantially larger. Please ensure the tip amount is correct.

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Circle J has center J (4,-3) and radius 5 What is the measure, in degrees, of the arc with endpoints A (9,-3) and B (4,2)?
Explain the process you used (in words) and include the work you did to find this answer.

Answers

This would be a 90° arc.

To find this, we can find the measure of the central angle that intercepts the arc.

The endpoints of the arc are at (9, -3) and (4, 2).
The slope of the line that passes through the endpoint (9, -3) and the center (4, -3) is given by
m=(-3--3)/(9-4) = 0/5 = 0.

Since the slope is 0, this tells us it is a horizontal line.

The line that passes through the endpoint (4, 2) and the center (4, -3) has a slope that is undefined; it is a vertical line at x=4. Numerically the slope is given by
m=(2--3)/(4-4) = 5/0, which is undefined.

These slopes are negative reciprocals of one another; 5/0 and 0/5 (0 has no sign). This means that these two lines would form a right angle, so the central angle of the circle is a right angle.

The intercepted arc has a measure equal to that of the central angle, so the arc is also 90°.

A license plate has 3 letters and 3 digits in that order. a witness to a hit-and-run accident saw the first 2 letters and the last digit. if the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit?

Answers

26×10×10=2600

Hope this helped!

The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.

To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.

Calculating the number of possible combinations:

First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilities

Therefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:

26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.

I really need help

What is the equation of a circle with its center at(10,−4) and a radius of 4?

(x−10)2+(y+4)2=4

(x+10)2+(y−4)2=16

(x−10)2+(y+4)2=16

(x+10)2+(y−4)2=2

(x−10)2+(y+4)2=2

(x−10)2+(y+4)2=8

(x+10)2+(y−4)2=8

(x+10)2+(y−4)2=4

Answers

The answer should be
(x-10)²+(y+4)²=16

The equation of any circle is
(x – h)² + (y – k)² = r²

(h,k) is the center point and r is the radius

A train travels at a constant speed. What is the train's speed between checkpoints, expressed as a unit rate? Use the information given in the picture to help you.

Answers

Remember that the speed is the rate of change of the position with respect to time, so to solve this we are going to use the kinematic equation: [tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
where
[tex]S[/tex] is the speed of the train
[tex]d_{i}[/tex] is the initial distance
[tex]d_{f}[/tex] is the final distance
[tex]t_{i}[/tex] is the initial time
[tex]t_{f}[/tex] is the final time

Since checkpoint A is the initial checkpoint, we can infer that [tex]d_{i}=105[/tex] and [tex]t_{i}=2[/tex]. Similarly, since checkpoint B is the final checkpoint, we can infer that [tex]d_{f}=285[/tex] and [tex]t_{f}=5[/tex]. Lets replace the values in our kinematic euation:
[tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
[tex]S= \frac{285-105}{5-2} [/tex]
[tex]S= \frac{180}{3} [/tex]
[tex]S=60[/tex] mph

We can conclude that the train's speed between checkpoints is 60 mph.

the checkpoints is 60 mph if you have any questions just ask:)

which transformation can verify congruence by flipping a triangle over the y-axis?

A. Dilation
B. Translation
C. Reflection
D. Rotation

Answers

Reflection. Reflection is when you flip an object over an axis. Flipping the triangle over axis wouldn't change the triangles properties.

Answer: C. Reflection

Step-by-step explanation:

There are three rigid transformations which create congruent figures :

a)reflections, b) rotations, c) translations

A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.

A translation moves a shapes by a particular distance.

A rotation rotates a shape around a fix point by an angle .

Therefore, the transformation can verify congruence by flipping a triangle over the y-axis is reflection.

Multiply: (2x2 − 5x)(4x2 − 12x + 10)

Answers

The answer is 60x^2 - 138x + 72

Hope this helps!

Answer:

[tex]8x^4-44x^3+80x^2-50x[/tex]

Step-by-step explanation:

The given expression is

[tex](2x^2-5x)(4x^2-12x+10)[/tex]

Using distributive property we get

[tex]2x^2(4x^2-12x+10)-5x(4x^2-12x+10)[/tex]

[tex]2x^2(4x^2)+2x^2(-12x)+2x^2(10)-5x(4x^2)-5x(-12x)-5x(10)[/tex]

On simplification we get

[tex]8x^4-24x^3+20x^2-20x^3+60x^2-50x[/tex]

On combine like terms.

[tex]8x^4+(-24x^3-20x^3)+(20x^2+60x^2)-50x[/tex]

[tex]8x^4-44x^3+80x^2-50x[/tex]

Therefore the product of two polynomials is [tex]8x^4-44x^3+80x^2-50x[/tex].

What is the slip of the line given by the equation y=-1/3 x

Answers

the slip? I don't think it has any slip, but as far as the slope goes, well, the equation is in slope-intercept form, thus

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{3}}x~~\stackrel{y-intercept}{+0}[/tex]

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