Answer:
See explanation
Step-by-step explanation:
Total number of letters = n! = 10
Permutation for 10 letters = n!
= 10!
= 10*9*8*7*6*5*4*3*2*1
= 3628800
From n letters:
Number of A = 2
Number of C = 2
Number of L = 2
A₁, A₂, C₁, C₂, L₁, L₂, O, R, T, U
Out of 3628800 permutations the word calculator can be spelled as:
C₁ A₁ L₁ C₂ U L₂ A₂ T O R
C₂ A₂ L₂ C₁ U L₁ A₁ T O R
and so on
So total number of different permutations are
(permutation of number of letters) / permutation of (number of As * number of Cs * number of Ls)
= 10! / (2! 2! 2 !)
= 10*9*8*7*6*5*4*3*2*1 / (2*1) (2*1) (2*1)
= 3628800 / 2 * 2 * 2
= 3628800 / 8
= 453600
Hence probability that a randomly selected permutation of the letters A, A, C, C, L, L, O, R, T, U would spell "calculator" is:
1 / total number of different permutations
= 1 / 10! / (2! 2! 2 !)
= 1/453600
= 0.000002
someone tell me the answers tho these please. Part A: Factor 3x2y2 − 2xy2 − 8y2. Show your work. (4 points) Part B: Factor x2 + 10x + 25. Show your work. (3 points) Part C: Factor x2 − 36. Show your work. (3 points)
Step-by-step explanation:
x2 + 10x + 25
x2 + 5x + 5x + 25
x(x + 5) + 5(x + 5)
(x + 5)(x+ 5) are the factors
x2 - 36
Both are squares so
x2 - (4)2
i need help with this page
Answer:
<abc=14
Step-by-step explanation:
<abc= 14 ; because if the whole thing is 90 and <CBD is already 76 then you subtract 90-76 to get the rest of the angle which is 14 degrees
Solve -4(x + 1) – 3 = -3(x - 4).
Answer:
x =-19
Step-by-step explanation:
[tex]-4(x + 1) - 3 = -3(x - 4).\\\\\mathrm{Expand\:}-4\left(x+1\right)-3:\quad -4x-7\\\\\mathrm{Expand\:}-3\left(x-4\right):\quad -3x+12\\-4x-7=-3x+12\\\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\-4x-7+7=-3x+12+7\\\\Simplify\\-4x=-3x+19\\\\\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}\\-4x+3x=-3x+19+3x\\\\Simplify\\-x=19\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{19}{-1}\\\\Simplify\\x=-19[/tex]
Answer:
We have this equation:
-4(x+1) - 3 = -3(x-4)
First of all, we solve the paretheses:
-4x - 4*1 - 3 = -3x - (-3*4)
-4x - 4 - 3 = -3x + 12
-4x -7 = -3x + 12
We sum 7 on both sides and 3x on both too:
-4x - 7 + 7 + 3x = -3x + 12 + 3x + 7
-4x + 3x = 12 + 7
-x = 19
x = -19
Now we can verify:
-4(-19+1) - 3 = -3(-19-4);
-4(-18) - 3 = -3(-23);
72 - 3 = 69 (TRUE)
(4x5 - 13x2 - 10) - (2x5 - 9x2 + 15)
2x5 - 11x2 + 5
2x5 - 4x2 - 25
2x5 - 4x2 + 5
-27x7
Next QuestionNext
Answer:
2x5-4x2-25
Step-by-step explanation:
First you distribute the negative sign to the second equation which makes each number it's opposite
Which would result in 4x5-13x2-10-2x5+9x2-15
Then you combine like terms and get 2x5-4x2-25
Answer:
-23
Step-by-step explanation:
Use the Distance Formula to answer the following questions. Round all of your answers to the nearest tenth (one decimal place). 2) Find the distance between the points (-3, 1) and (5,-2). Round your answer to the nearest teeth.
Answer:
distance= 9 units to the nearest
Step-by-step explanation:
using the formula
√(∆x)^2+(∆y)^2
√73
= 8.5
= 9 units
===========================================
Work Shown:
d = distance between (-3,1) and (5,-2)
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-5)^2 + (1-(-2))^2}\\\\d = \sqrt{(-3-5)^2 + (1+2)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.5440037\\\\d \approx 8.5\\\\[/tex]
Alternatively, you can plot the two points on the same xy grid. Then form a right triangle with the two points as the endpoints of the hypotenuse. Use of the pythagorean theorem will result in getting the same approximate distance. The distance formula is effectively the same as the pythagorean theorem, but just in a different form.
Name the Reflection Rule that results in the following transformation
A(1,4), B(2, 7), C(9, 3) to
A'(1,-4), B'(2, -7), C'(9, -3)
The function h(x)=4/3x-1 represents the composite h(x)=f(g(x)).if f(x)=2x-1,what is g(x)
Answer:
[tex]g( x) = \frac{2}{3}x[/tex]
Step-by-step explanation:
Given:
Composite Function:
[tex]h( x)=f( g( x))[/tex]
Also,
[tex]h( x)=\frac{4}{3}x-1[/tex]
To find:
[tex]g( x ) = ?[/tex]
Solution:
First of all, let us learn about a composite function.
Composite function [tex]f( g( x))[/tex] means to write [tex]g( x)[/tex] in place of [tex]x[/tex] in the function [tex]f( x)[/tex].
Let [tex]g( x) = y[/tex]
So, [tex]f( g( x))[/tex] = [tex]f( y )[/tex].
Therefore,
[tex]h( x) =f( g( x)) = f( y)[/tex]
So, [tex]f( y) = 2y-1[/tex]
We have to solve for [tex]y[/tex] in terms of [tex]x[/tex] to find the value of [tex]g(x)[/tex]:
[tex]\Rightarrow \frac{4}{3}x-1 = 2y-1\\\Rightarrow 2y=\frac{4}{3}x\\\Rightarrow y = \frac{2}{3}x[/tex]
Hence, the answer is [tex]g( x ) = \frac{2}{3}x[/tex].
Checking whether the answer is correct or not:
[tex]f( g( x)) = f( \frac{2}{3}x) = 2\times \frac{2}{3}x -1 = \frac{4}{3}x-1[/tex]
which is [tex]h( x)[/tex].
Hence, our answer [tex]g( x ) = \frac{2}{3}x[/tex] is correct.
The g(x) of the function is:
g(x) = (2/3)x
How to find what g(x) is?A function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
We have:
h(x) = (4/3)x - 1
h(x) = f(g(x))
f(x) = 2x - 1.
Thus, we can say:
h(x) = f(g(x)) = 2*g(x) - 1
(4/3)x - 1 = 2g(x) - 1
(4/3)x - 1 + 1= 2g(x)
(4/3)x = 2g(x)
(4/3)x * 1/2 = g(x)
(2/3)x = g(x)
g(x) = (2/3)x
Therefore, g(x) = (2/3)x.
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3(x + 5) = 2(4x + 9)
Answer:
x=-3/5
Step-by-step explanation:
3(x + 5) = 2(4x + 9)
First, distribute:
3(x)+3(5)=2(4x)+2(9)
3x+15=8x+18
-5x= 3
x= -3/5
On James’s MP3 player, he has 12 sad songs and 40 upbeat songs that he wants to put into playlists. He wants to have the same number of sad songs and upbeat songs in each playlist. What is the maximum number of playlists that he can create?
Answer:
4 playlists
:)
Which is the mode of this data set?
55, 78, 43, 39, 78, 61, 75, 50, 43, 78
Answer:
78
Step-by-step explanation:
Mode = number that appears most in a set of numbers
The number that appears the most in this set is 78. So, the mode is 78. Hope it helps!
Answer:
Step-by-step explanation:
arrange in ascending order
39,43,43,50,55,61,75,78,78,78
mode=78
Evaluate the expression: 6:3+2x7
Answer:
15.41
Step-by-step explanation:
8 gal to 9 1/3 gal write ratio in lowest form with whole numbers in numerator and denominator
Answer:
[tex]\bold{\dfrac{6}{7}}[/tex]
Step-by-step explanation:
Given ratio is:
8 gal to [tex]9\frac{1}3[/tex] gal
To find:
Ratio in Lowest form with whole numbers in numerator and denominator.
Solution:
First of all, let us convert [tex]9\frac{1}3[/tex] to simple [tex]\frac{p}{q}[/tex] form:
Formula:
[tex]a\dfrac{b}{c} = \dfrac{a\times c+b}c[/tex]
Using the formula, we get:
[tex]9\dfrac{1}{3} = \dfrac{9\times 3+1}{3} = \dfrac{28}{3}[/tex]
Now, let us have a look at the ratio:
[tex]8 : \dfrac{28}{3}[/tex]
Any ratio, [tex]p:q[/tex] can be written as [tex]\frac{p}{q}[/tex].
Writing given ratio as per above:
[tex]\dfrac{8}{\dfrac{28}{3}}\\\Rightarrow \dfrac{8 \times 3}{28}\\\Rightarrow \dfrac{2\times 3}{7}\\\Rightarrow \bold{\dfrac{6}{7}}[/tex]
Therefore, the answer is
[tex]\bold{\dfrac{6}{7}}[/tex]
solve for x and y please
Answer:
Y=40
X=67
Step-by-step explanation:
In a cross line problem, one part of the cross, (such as 63°) is always the same on the other side. (like y+23° and 63°. This means Y=40 because 40+23 is 63.
To find x, you must know that 360° is all the way around in degrees. you know that 126° (63 +63) is already taken up. So you subtract 126 from 360 and then multiply the answer by 1/2 because you trying to find the bottom total.(360-126)=234(1/2)= 117 Lastly, you find X in the equation 2x-17=117.
x=67
A rectangular pool is twice as
long as it is wide. What are the
dimensions of the pool if the
perimeter is 48 yd?
Step-by-step explanation:
L=2B
P=2(L+B)
48=2(2B+B)
48=2(3B)
48=6B
B=8yd
L=2*8
=16yd
Answer:
length * width = 16 yd * 8 yd
or
length = 16 yd
width = 8 yd
Step-by-step explanation:
take the rectangular pool to have sides a (length) and 2a (width).
we are told that the length is as twice as its width, therefore,
Perimeter is given by (a + 2a) × 2 = 48 yd
Divide both sides by 2 ⇒ [tex]\frac{((a + 2a) * 2)}{2} = \frac{48 yd}{2}[/tex] ⇒ a + 2a = 24 yd
⇒3a = 24 yd
Divide both sides by 3 ⇒ [tex]\frac{3a}{3} = \frac{24 yd}{3}[/tex] ⇒ a = 8 yd
therefore, the width of the pool is 8 yd and its length is 16 yd (Twice as long as it is wide)
please answer and give reasoning. might give brainliest.
Answer:
A
Step-by-step explanation:
A contains √3 --> irrational number because 3 is not a square number
For other choices:
- All numbers in the form a/b (a,b are integer numbers) are rational numbers
- √36, √9, √4, √25, √49, √100 are integer numbers because (36, 9, 4,....) are square numbers
- All given decimal numbers can be written in the fraction form
0.5 = 1/2
39.77 = 39 + 77/100 = 3977/100
0.15151578 and 0.00010001 are finite decimals, 0.303030... is infinite repeating decimal, so technically they are rational numbers.
Simplify the expression where possible. (6 3 ) -3
the first half of food+the last quarter of door
Answer:
For
Step-by-step explanation:
the first half of food + the last quarter of door
= F o o d + d o o r
= Fo + r
= For
HELP PLEASE! I dont know what to do now! 10 points!
Answer:
It would be losing 300.
Step-by-step explanation:
The opposite of gaining is losing the integer would be -300
Answer:
-300
Step-by-step explanation:
A recipe that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needs to make 195 cookies for his party. How many cups of oats will he need?
A garden hose faucet is able to fill a gallon conainer in 20 seconds. A homeowner accidentally left his hose on for a full day. How many gallons per day can a hose release?
One day is equivalent to 86400 seconds.
So 86400÷20=4320 gallons
Find the sum: 3.85 + 6.29 =
Answer:
3.85 + 6.29 = 10.14
Hoped I helped
Step-by-step explanation:
3.85+6.29= 10.14
thank
A large western state consists of 3129 million acres of land. Approximately 55% of this land is federally owned. Find the number of acres that are not federally owned
Answer:
1408.5 acres
Step-by-step explanation:
If 55% of the land is federally owned, then 100 - 55 = 45% of the land is not federally owned.
We need to find how many acres are not federally owned, in other words, we need to find how many acres represent 45% of the total 3129 acres. So, to do this we can apply a rule of three:
3129 acres ---- 100%
x acres ------ 45%
[tex]x=\frac{(3129)(45)}{100} =3129(0.45)= 1408.05[/tex]
Therefore, the total of acres that are not federally owned are 1408.5 acres.
Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay?
Answer:
0.85x - $50
Step-by-step explanation:
Given that :
Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay
Discount on price = 15%
Amount parents agreed to pay = $50
Cost of bike = x
Discount on bike = 0.15x
Cost after discount is removed = (x - 0.15x) = 0.85x
Parent pays $50 of cost price, amount Brandon will have to pay equals :
(0.85x - $50)
Answer:
0.85x - $50
Step-by-step explanation:
Can someone help me with this problem please??? If ƒ( x ) = x 2 + 1 and g( x ) = 3 x + 1, find 2 · ƒ(4). A. 18 B.34 C.65
Answer: B
Step-by-step explanation:
They've given you two functions f(x) = x^2 + 1 and g(x) = 3x +1 And they are you to find 2 * f(4) then g(x) is not needed so input in 4 for the function f(x) and multiply the output by 2.
F(4) = 4^2 + 1
F(4) = 16 +1
f(4) = 17
17 * 2 = 34
Answer:
B.34Step-by-step explanation:
[tex]f( x ) = x^ 2 + 1 \\ g( x ) = 3 x + 1\\\\f(4) \times 2 = ?\\f(4) = 4^2 +1\\\\=( 16+1) \times 2\\\\= 17\times 2\\\\= 34[/tex]
add r to q, then add s to the result
Answer:
(r+q)+s
Step-by-step explanation:
The parentheses make it clear that r and q need to be added first.
5. Which of the following is a multiple of 8?
A 4
C 20
B 8
D 100
Answer:
8
Step-by-step explanation:
8 can be divisible by 8. Therefore, it would be a multiple of 8.
The first multiple of a number is always that number.
All other options given are not multiples of 8.
Hope this helps.
AB is a straight line
Work out the size of angle x
Hi May I know how to solve this?
Answer:
k = 3/4
Step-by-step explanation:
Parallel lines have the same slope so first, we need to find the slope of 8x + 6 = 2y. To do so, we can do the following:
8x + 6 = 2y
2y = 8x + 6
y = 4x + 3 (This is now in slope intercept form - y = mx + b where m = slope and b = y-int.)
Therefore, the slope is 4. Now, we can do:
3x = ky - 10
3x - 10 = ky
(3x / k) - (10 / k) = y
y = (3x / k) - (10 / k) (where k ≠ 0)
Now that the second line is in slope-intercept form, we can set the two x terms equal to each other, therefore:
3x / k = 4x
3x = 4x * k
3x / 4x = k
k = 3/4
There are nine teddy bears in the diagram below. How many TOTAL squares are
there?
Answer: 14
Step-by-step explanation: 9 small squares with one teddy bear in each, 4 medium squares with 4 bears in each medium square, and 1 big square for the entire thing.
The total number of square is 14
What is figure counting?In the counting of figures, you have a shape or a figure. From the given shape you will have to identify a given known shape and count the number of times it is present in the given shape.
According to the question
9 small squares with one teddy bear in each,
4 medium squares with 4 bears in each medium square.
1 big square for the entire thing.
Total square = 9 + 4 + 1
= 14
Hence, the total number of square is 14
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Solving Quadratics
Solve for all values of x by factoring. x² + 4x + 5 = -6x + 5
Answer: x=5 and x=-1
Step-by-step explanation:
X^2-4x-5=0
(X-5) (x+1)=0
X-5=0. And. X+1=0