How many ways are there to arrange the first five letters of the alphabet?

Answers

Answer 1
In probability, problems involving arrangements are called combinations or permutations. The difference between both is the order or repetition. If you want to arrange the letters regardless of the order and that there must be no repetition, that is combination. Otherwise, it is permutation. Therefore, the problem of arrange A, B, C, D, and E is a combination problem.

In combination, the number of ways of arranging 'r' items out of 'n' items is determined using n!/r!(n-r)!. In this case, you want to arrange all 5 letters. So, r=n=5. Therefore, 5!/5!(505)! = 5!/0!=5!/1. It is simply equal to 5! or 120 ways.
Answer 2

Answer:

120 ways

Explanation:

Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.

I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.

I am happy to help with anything.


Related Questions

helpppppppppppppppppppppp

Answers

Slope = change in y/change in x.

-2-0/2-1
-2/1
-2

Final answer: -2

The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio

Answers

let [tex]a_n[/tex] be the n'th term of the sequence.

so [tex]a_1[/tex] is the first term, [tex]a_2[/tex] the second term and so on...

In a geometric sequence with [tex]a_1=c[/tex], and common ratio r, the terms are as follows:

[tex]a_1=c[/tex]
[tex]a_2=cr[/tex]
[tex]a_3=c r^{2} [/tex]
[tex]a_4=c r^{3} [/tex]
.
.
that is, each term is its previous term times the common ratio r.

In our example

[tex]a_2=cr=20[/tex] and [tex]a_4=c r^{3}=11.25 [/tex]

[tex] \frac{a_2}{a_4}= \frac{cr}{c r^{3}}= \frac{1}{ r^{2}}= \frac{20}{11.25}= 1.778 [/tex]

so [tex]r^{2} =1/1.778=0.56[/tex]

[tex]r= \sqrt{0.56}= 0.75[/tex]


Answer: r=0.75

There are 9 different positions on a baseball team. if a team has 18 players how many different line-ups can the team make?

Answers

Final answer:

To find the number of different line-ups a team can make, we use permutations. Using the formula for permutations, we arrive at the answer of 437,760 different line-ups.

Explanation:

To find the number of different line-ups a team can make, we need to use the concept of permutations. Since there are 9 positions on a baseball team and 18 players, we can arrange the players in a line-up using the formula for permutations:

P(n, r) = n! / (n-r)!

Where n is the total number of players (18) and r is the number of positions (9). Substituting the values, we get:

P(18, 9) = 18! / (18-9)! = 18!/9! = 437,760.

Therefore, there are 437,760 different line-ups that the team can make.

Which mathematical statement represents “17 more than a number is 26”?

Answers

17 + x = 26

17 +n = 26

n + 17 = 26


 something like those, you didn't give options to choose from.

Answer:

x + 17 = 26

Step-by-step explanation:

mathematical statement represents “17 more than a number is 26”

Let x be the unknown number

17 more means we add 17 with the unknown number x

so it becomes x+17

'is' represents an = sign

So the equation for the mathematical statement  “17 more than a number is 26” becomes  x + 17 = 26

When 23 is subtracted from 4 times a certain number the result is 4

Answers

If we say:
x = the 'certain number' we want to find
Then, we can formulate an equation:
4x - 23 = 4
Now, solve for x:
4x = 27
x = 27/4 = 6.25
Let the unknown number be x.

Given,

4x - 23 = 4

4x = 27

x = [tex] \frac{27}{4} [/tex] = 6.75

Hence, the number is 6.75

A quadratic equation is shown below:

4x^2 − 12x + 10 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

A.
the radicand is b²-4ac
if it is in form ax²+bx+c

when it is
greater than 0, then 2 real roots
equal to 0, then 1 real root
less than 0, then no real roots

so
a=4
b=-12
c=10

b²-4ac=(-12)²-4(4)(10)=144-160<0
so 0 real roots



B.
using quadratic formula because it is easier
for
ax²+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]

so

for 2x²-13x+21
a=2
b=-13
c=21

[tex]x=\frac{-(-13)+/-\sqrt{(-13)^2-4(2)(21)}}{2(2)}[/tex]
[tex]x=\frac{13+/-\sqrt{169-168}}{4}[/tex]
[tex]x=\frac{13+/-\sqrt{1}}{4}[/tex]
[tex]x=\frac{13+/-1}{4}[/tex]
x=(13+1)/4 or (13-1)/4
x=14/4 or 12/4
x=7/2 or 3

Marisol receives total employee benefits that are 14.5% of her gross annual pay. If Marisol has a gross annual pay of $50,000, how much in total employee benefits does she receive?

Answers

7250! It is that because if you search up 14.5% of 50000 it gives you 7250! I hope this benifits you!

If Marisol has a gross annual pay of $50,000 and receives total employee benefits of 14.5% of her gross annual pay, then you can find how many benefits she receives, using proportion:

[tex] \$50,000 - 100\%,\\ \$x - 14,5\% [/tex].

Then

[tex] \dfrac{50000}{x} =\dfrac{100}{14.5} ,\\\\ x=\dfrac{50000\cdot 14.5}{100}=500\cdot 14.5=7250 [/tex].

In total she will receive $50,000+$7250=$57250.

Answer: $57250.


Write an appropriate direct variation equation if y = 27 when x = 9

Answers

y = kx where k is a constant

27 = k*9
k = 27/9 = 3

required variation is y = 3x

Answer:  y=3x

Step-by-step explanation:

Write the expression in standard form.
three divided by quantity three minus twelve i.

Answers

the answer would look like this 3 / (3 - 12i)

Answer:

What was the answer?!?!!?!? >-<

Suppose? 30% of the people in your town talk on their cell phones and drive at the same time. if you stood on a busy street corner and watched 50 people drive? by, about what proportion would you expect to see talking on their cell? phones?

Answers

30% of 50 = 15 people
15 people would be talking on there cell phones

What is the common ratio in the sequence -27, 9, -3, 1....?

A. 3

B. -3

C. 1/3

D. -1/3

Answers

the answer would be 3.hope that helped
find the common ratio, u divide the second term by the first term
9/-27 = -1/3

to find the next term in a geometric sequence, u multiply by the common ratio....
-27 * -1/3 = -27/3 = 9
9 * -1/3 = -9/3 = -3
-3 * -1/3 = -3/-3 = 1


Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4.

Answers

The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:

d + 4 = 0

d = -4

Evaluating when d = -4:

d^4 + 2 * d^2 + 5 * d − 10

= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10

= 256 + 2 * 16 – 20 – 10

= 256 + 32 – 30

= 258

 

Therefore basing on the remainder theorem, the remainder would then be:

Remainder = 258 / (d + 4)                             ---> Answer

Solve x2 – 4 = 5 by graphing the related function.

Answers

x2-4=5
    +4 +4
x2=9
square root both the x and 9
x=3


Answer:

Refer graph attached below

Step-by-step explanation:

Given equation  [tex]x^2-4=5[/tex]

We have to  Solve the given equation  [tex]x^2-4=5[/tex] graphically.

We first solve the given equation [tex]x^2-4=5[/tex]

Consider the given equation [tex]x^2-4=5[/tex]

Adding 4 both sides, we have

[tex]\Rightarrow x^2-4+4=5+4[/tex]

Simplify, we get,

[tex]\Rightarrow x^2=9[/tex]

[tex]\Rightarrow x^2-9=0[/tex]

To plot the graph let [tex]x^2-9=y[/tex] be the equation

It will be a parabola with vertex (0,9).

Refer graph attached below

How do you solve and graph a piece wise function and state the domain and range?

Answers

for 3)  check the picture, on the right-hand-side

now for 4) check the picture on the left-hand-side

if you notice the intervals, it goes from -∞ and stops at -2, then goes from 2 over to 3, then from 3 onwards, so the domain will also be (-∞ , +∞).

Now, the range...

the 1st subfunction 3-x is just a line coming down form -∞....

the 2nd subfunction is just 2x, also a line going up, now once you get to

the 3rd subfunction is just 5, meaning y = 5, or f(x) = 5, which is just a horizontal line at y = 5.

since the 3rd subfunction goes from x > 3 onwards to +∞, and is just a horizontal line, it doesn't go below 5, so one would think the range is -∞, 5.

however, from the 2nd subfunction if we use say x = -1.9999, 2x ---> 2(-1.9999) = -3.9998 , that's lower than 5, and that's the lowest the piece-wise goes, thus, the range comes from -∞ and goes as low as -3.9998,  (-∞ ,-3.9998]

notice, we didn't use -2, because the 2nd subfunction 2x, doesn't include it in its range -2 < x ⩽ 3.

now, for 4) I used -1.9999 but your teacher might be expecting something like -1 or thereabouts, just an integer amount.  But the idea being, the 2nd subfunction, does not include the -2.

A new truck that sells for 29,000 depreciates 12% each year. What is the decay factor b?

Answers

[tex]\bf y=a(b)^t\qquad or\qquad A=I(1-r)^t\qquad \textit{let's check}\\\\ -------------------------------\\\\ \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &29000\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=29000(1-0.12)^t\implies \begin{array}{llll} A=&29000(0.88)^t\\ &\uparrow \qquad\quad \uparrow \\ &a\qquad\quad b \end{array}[/tex]

Exit Felix was given $125 for his birthday from his grandmother. He plans to put this money toward the purchase of a $250 skateboard. The remainder of the money he plans to earn mowing lawns for the rate of $35 each. What is the least number of lawns Felix will have to mow in order to have enough to buy the skateboard?

Answers

Hi!

First let's set up an inequality.

35x ≥ 125

Now solve for x
125/35 = 3.6 (round up to nearest whole number)
x = 4

The answer is 4

Hope this helps! :)

What is the sum of?

A. S=1.5
B.S=2
C.S=4.5
D.=8

Answers

8.  You can graph this or use the summation function on the TI computer. 

∑4(0.5)ⁿ⁻¹
n=1
For n = 1 → 4(0.5)¹⁻¹ = 4(0.5)⁰ = 4(1) = 4
For n = 2 → 4(0.5)²⁻¹ = 4(0.5)¹ = 4(0.5) = 4(0.5)
For n = 3 → 4(0.5)³⁻¹ = 4(0.5)² 
For n = 4 → 4(0.5)⁴⁻¹ = 4(0.5)³ 
We notice this is a geometric series with first term:
a=4 & r= 0.5
Since r<1, then the formula of the sum when n→∞ is:

Sum= a(1/1-r)
Sum = 4/(1-0.5)
Sum = 4/(1/2) = 4 x 2

 ∞
∑4(0.5)ⁿ⁻¹ = 8 (answer D)
n=1

Determine whether the forces are pulling at right angles to each other. Explain. 3.5 lb, 6.2 lb, resultant force 9.1 lb
A. yes; 3.52 + 6.22 = 9.12
B. no; a + b > c
C. no; 3.52 + 6.22 ≠ 9.12
D. yes; a + b > c

Answers

The resultant force in this item, is that which connects the heads of the magnitude of the given vectors. The magnitude of the resultant force can be calculated through the Pythagorean theorem which states that the square of the resultant force should be equal to the sum of the squares of the smaller forces. That is,
          A² + B² = C²

Investigating the vector values, 
 A² + B² = (3.5 lb)² + (6.2 lb)² = 50.69 lb²
C² = (9.1 lb)² = 82.81 lb²

Since the Pythagorean theorem is not satisfied by the given set of forces then, the forces are not in right angle. 

The answer to the question is letter C. 

△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″.△DEF is reflected in the y-axis. Then it is translated along the vector ⟨3,−5⟩. Enter your answers as points using parenthesis and commas. Do not use any spaces.

Answers

Reflecting DEF on the y-axis gives the following coordinates of D'E'F' as follows

the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)

Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows

the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)

The diagram below shows the transformation of triangle DEF

Write an algebraic equation for the following. The product of three and a squared number is twice the sum of the number and four.

Answers

3*x^2 = 2*(x+4)

x is the unknown number

Using the given zero, 2 - 4i, find one other zero of f(x) = x4 - 4x3 + 21x2 - 4x + 20

Answers

The conjugate of the given zero 2 - 4i is 2 + 4i, which must also be a zero of the polynomial f(x) due to the Complex Conjugate Root Theorem.

Given the zero 2 - 4i of the polynomial function f(x) = [tex]x^4 - 4x^3 + 21x^2 - 4x + 20,[/tex] we know by the Complex Conjugate Root Theorem that if a polynomial has real coefficients, then any complex zeros must occur in conjugate pairs. Therefore, the conjugate of 2 - 4i, which is 2 + 4i, must also be a zero of the polynomial function.

As a result, the polynomial can be factored to include the factors (x - (2 - 4i)) and (x - (2 + 4i)). When these factors are multiplied out, they will give you a quadratic factor of the polynomial, which when multiplied with the remaining factors, will result in the original polynomial f(x). The two factors, when multiplied together, yield a quadratic with real coefficients, which means any remaining zeros must also satisfy this quadratic equation.

If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?

Answers

f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x

(f + g)(x) = –x2 + 3x + 5 + x2 + 2x 
(f + g)(x) =   5x + 5  

Answer:

Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]

Now, calculate first [tex](f+g)(x)[/tex] ;

[tex](f+g)(x) = f(x) + g(x)[/tex]

Substitute the given values we have;

[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]

Combine like terms;

[tex](f+g)(x) =5x+5[/tex]

Let y = [tex](f+g)(x)[/tex]

Then, we have y = 5x+5

Now, Graph the equation of the line y =5x +5

Using slope intercept form: An equation of line is given by :

y = mx +b ; where m is the slope of the line and b is the y-intercept.

On comparing we get;

m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)

Now, find the intercepts of the equation: y=5x+5;

x-intercepts: The graph or line crosses the x-axis i.,e

Substitute y = 0 and solve for x;

0 = 5x +5

Subtract 5 on both sides we get;

-5 = 5x

Divide both sides by 5 we get;

x = -1

x-intercepts= = (-1, 0)

Similarly for y-intercept:

Substitute the value of x= 0 and solve for y;

y = 5(0)+5

y = 5

y-intercepts = (0, 5)

Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.



An investment of $200 increases at a rate of 9.5% per year. What is the growth factor, b?

Answers

The standard form for rate equation is:

F = P (1 + r)^n

or

F = P b^n

So b = 1 + r

In this case, r is given as 9.5% or 0.095. Therefore:

b = 1 + 0.095

b = 1.095

The growth factor is 1.095.

A rectangular prism has a length of 8 feet, a width of 3 feet, and a height of 5 feet. What is the surface area of the rectangular prism?

Answers

surface area = 2(wl +hl+hw)

w=3

l=8

h=5

wl=3*8 =24

hl=5*8 =40

hw=5*3 =15

24+40+15 = 79

2*79 = 158 feet^2

The surface area of the rectangular prism is 158 square feet.

What is surface area?

The surface area of any given object is the area or region occupied by the surface of the object.

Formula for finding the surface area of rectangular prism:

Surface Area = 2{(h × l) + (h × w) +(l × w)]

Where,

l is the length of the rectangular prism

h is the  height of the rectangular prism

w is the width of the rectangular prism

According to the given question

Length of the rectangular prism = 8 feet

width of the rectangular prism = 3feet

height of the rectangular prism = 5 feet.

Therefore,

the surface area of the rectangular prism = 2[(8 × 5)+ ( 5 × 3) + ( 8 × 3)]

surface area of rectangular prism = 2[ 40 +15 +24} = 158 square feet.

Hence, the surface area of the rectangular prism is 158 square feet.

Learn more about the surface area of rectangular prism here:

https://brainly.com/question/14987814

#SPJ2

Given 5n² + 6n + 7 = n² - 4n : a. Find the value of the discriminant. b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]

Answers

[tex]\bf 5n^2+6n+7=n^2-4n\implies 5n^2+6n+7-n^2+4n=0 \\\\\\ 4n^2+10n+7=0\\\\ -------------------------------\\\\ \begin{array}{llccll} &{{ 4}}x^2&{{ +10}}x&{{ +7}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \\\\\\ discriminant\implies b^2-4ac= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

if you get a positive value, that means 2 real solutions
if you get 0, means 1 real solution only
if you get a negative value, is an imaginary root solution, same as saying no solution.

Solve the inequality. 4(p – 4) > 12

Answers

Hello there!

4(p - 4) > 12

First, we need to apply the Distributive Property to the left side of the inequality.
To apply the Distributive Property, we need to multiply the number/variable outside of the parenthesis by all inside numbers/variables inside of the parenthesis.

4(p - 4)
4(p) + 4(-4)
4p - 16 is what we're left with on the left side of the inequality.

Now, our inequality is this:
4p - 16 > 12
Add 16 to both sides.
4p > 28
Divide both sides by 4.
p > 7

p > 7 is your solution.

I  hope this helps!
p>7 is your answer
plz rate

If f(x) = -2[x] + 8, what is f(-1.8) (PLS HELP ASAP)

Answers

the function is least integer function, not greatest integer function.
in this the output is the closest right side integral value.
-2[-1.8]+8
=-2×-1+8
=2+8
=10

Answer:

option c)10

Step-by-step explanation:

Given is a least integer function as

[tex]f(x) =-2[x]+8[/tex]

We are to find out the function value when x = -1.8

Substitute for x the value -1.8

we have

[tex]f(x) =-2[-1.8]+8\\[/tex]

-1.8 has the integer -1 to the left of it.

Hence we get

[tex]f(x) =-2[-1]+8=10[/tex]

Hence answer is option c)10

The highest temperature recorded in the town of Westgate this summer was 180°F. Last winter, the lowest temperature recorded was -15°F.

Find the difference between these two extreme temperatures.

Answers

195 degrees
Good luck and have nice day.

Terry earns $22,500 annually. What is the total amount of each paycheck if she is paid biweekly?

Answers

52 weeks per year

 biweekly means she gets paid every 2 weeks

 so 52/2 = 27

22500/27 = 833.33 each paycheck

The point $(r,\theta)$ in polar coordinates is $(7,5)$ in rectangular coordinates. what is the point $\left( 2r, \theta + \frac{\pi}{2} \right)$ in rectangular coordinates?

Answers

Final Answer:

The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).

Step-by-step explanation:

In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).

Given that the point [tex]$(r, \theta)$[/tex]  in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:

[tex]\[ x = r \cos(\theta) \][/tex]

[tex]\[ y = r \sin(\theta) \][/tex]

For the given point $(7, 5)$, we have:

[tex]\[ x = 7 \cos(5) \][/tex]

[tex]\[ y = 7 \sin(5) \][/tex]

Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:

[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]

[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]

We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:

[tex]\[ x' = -2r \sin(\theta) \][/tex]

[tex]\[ y' = 2r \cos(\theta) \][/tex]

Now, if we substitute the values of [tex]$r$[/tex]  and [tex]$\theta$[/tex] from the given point (7, 5):

[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]

[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]

Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.

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