Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are repeating elements, with the number of times given by [tex]n_1, n_2, \cdots, n_n[/tex], the number of arrangements is given by:
[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:
[tex]A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200[/tex]
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(2x+1)(x^2+8x-3)
help standard form
Answer:
[tex]2x^3+17x^2+2x-3[/tex]
Step-by-step explanation:
[tex]\left(2x+1\right)\left(x^2+8x-3\right)\\=2xx^2+2x\cdot \:8x+2x\left(-3\right)+1\cdot \:x^2+1\cdot \:8x+1\cdot \left(-3\right)\\=2x^3+17x^2+2x-3[/tex]
In this equation, the variables were isolated to simplify the problem, following the order of operations. Negative-three either became an exponent or positive integer, 3, subtracted by a byproduct of the previous equation.
Two independent random samples of size n1 = 50 and n2 = 75 are drawn from two very large populations: population 1 and population 2. both populations are right skewed. is the use of t procedures still valid?
Answer:
No
Step-by-step explanation:
You should only use t procedures when the sample sizes are less than 30, as that is when the Central Limit Theorem kicks in.
Essentially, t procedures are good for small samples while z procedures are better for larger samples.
2y=-x+9
3x - 6y=-15
pls helpppp
Answer:
Step-by-step explanation:
The given equations are:
1) 2y = -x + 9
⇒ x = 9-2y
2) 3x - 6y = -15
⇒3x = 6y - 15
x = 2y - 5
Equating the values of x, we get:
9 - 2y = 2y - 5
9 + 5 = 4y
14 = 4y
y = 3.5
Using this value of y in equation 1 we get:
x = 9 - 2(3.5) = 2
So, the solution set is (2, 3.5)
Find the equation of the lien shown.
Answer:
y = [tex]\frac{1}{2}[/tex] x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 3) ← 2 points on the line
m = [tex]\frac{3-0}{6-0}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x ← equation of line
g more than the quotient of b
and f
6^2-4(3-√25)^2/|4-8|
the answer is 5 but im not sure on the steps and how to get 5, please help tysm :)
I'm going to assume you start with
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|}[/tex]
Let's simplify some pieces of this:
[tex]6^2 = 6\times6 = 36[/tex]
[tex]\sqrt{25} = \sqrt{5^2} = 5[/tex]
[tex](3 - \sqrt{25})^2 = (3 - 5)^2 = (-2)^2 = (-2)\times(-2) = 4[/tex]
[tex]|4 - 8| = |-4| = 4[/tex]
So as a first step we can reduce this to
[tex]\dfrac{6^2 - 4 (3 - \sqrt{25})^2}{|4 - 8|} = \dfrac{36-4\times4}4[/tex]
Now,
[tex]36 = 9\times4[/tex]
so every term contains a factor of 4 that we can cancel:
[tex]\dfrac{36-4\times4}4 = \dfrac{9\times4-4\times4}4 = \dfrac{9-4}1 = 9-4 = \boxed{5}[/tex]
as expected.
[tex]-2\sqrt{15}(-8+10\sqrt{15}[/tex]
We simplify the expression -2√15(-8 + 10√15) = 150 + 16√15
To answer the question, we need to know what surds are
What are surds?Surds are square roots of positive integers.
Since we have -2√15(-8 + 10√15), we simplify the expression
So, -2√15(-8 + 10√15) = -2√15 × (-8) + 10√15 × √15 (expanding the bracket)
= -2× (-8) × √15 + 10 × √(15 × 15)
= 16 × √15 + 10 × √15²
= 16 × √15 + 10 × 15
= 16√15 + 150
= 150 + 16√15
So, we simplify the expression -2√15(-8 + 10√15) = 150 + 16√15
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Carlita has a swimming pool in her backyard that is rectangular with a length of 24 feet and a width of 14 feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck.
The required, expression for the perimeter of the wood deck is 4w + 76 + 8c.
The length of the rectangular region will be the original length of the pool plus twice the width of the walkway since the walkway will extend out from both sides of the pool:
Length of rectangular region = 24 + 2c
Similarly, the width of the rectangular region will be the original width of the pool plus twice the width of the walkway:
Width of rectangular region = 14 + 2c
Now, to find the perimeter of the wood deck, we need to add up the lengths of all four sides of the rectangular region. Each side will have a length of w, since the wood deck extends w feet on all sides:
Perimeter of wood deck = 2(w + Length of rectangular region) + 2(w + Width of rectangular region)
Substituting the expressions we found for the length and width of the rectangular region, we get:
Perimeter of wood deck = 2(w + 24 + 2c) + 2(w + 14 + 2c)
= 4w + 76 + 8c
Therefore, the expression for the perimeter of the wood deck is 4w + 76 + 8c.
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What is bigger 1.97x 1.97 × 0.11 inches or 1.89 x 5.42 x 5.2 inches
Answer:
1.89 x 5.42 x 5.2 inches
Step-by-step explanation:
Use your calculator or multiply it yourself, times all of them together.
If UW = 9x – 9, what is UW in units?
Answer
36 units
Step-by-step explanation:
UW = UV + VW
9x-9 = 2x - 4 + 4x + 10
9x - 9 = 6x + 6
3x = 15
x = 5
UW = 9(5) - 9 = 45 - 9 = 36
answer is 36 units
simplify the expression
4x(x + 1) (3x − 8) (x + 4)
Answer:
4×(x+1)(3x-8)(x+4)= (4x²+4)(3x-8)(x+4)= (12x³-32x²+12x²-32)(x+4)= (12x³-20x²-32)(x+4)= 12x⁴+48x³-20x³-80x²-32x²-128x= 12x⁴+28x³-112x²-128x
Find the solution
a2-b2=9
a.b=3
a+b=?
Answer:
a
2
=9a+b
2
Step-by-step explanation:
Answer:
Step-by-step explanation:
(a²+b²)²=(a²-b²)²+4a²b²=(a²-b²)²+4(ab)²=9²+4×3²=9²(1+4)
a²+b²=3√5
(a+b)²=a²+b²=2ab=3√5+2(3)=3(2+√5)
a+b=√3√(2+√5)
There is a pair of parallel sides in the following shape 6,4,8 what is the area of the shape?
The figure, polygon ABCD is dilated by a factor of 2 to produce A B C D with the origin as the center of dilation
In the polygon ABCD, the production of point A' and point D' is (-2,-2) and (4,-2) respectively.
What is the transformation rule?In coordinate planes, the rule of transformation involves interchanging the x and y values on the plane such that:
[tex]\mathbf{(x,y) \to (k_x, k_y)}[/tex]
where;
k = scale factorFrom the given information:
The scale factor = 2the origin as a center of dilation for image vertices = (0, 0)Now, using the coordinate vertices:
A = (-1, -1)D = (2, -1)The corresponding coordinate of the image vertices is as follows:
A(-1,-1) → A'(2 × (-1), 2 × (-1))
A' = (-2,-2)
D(2,-1) → A'(2 × (2), 2 × (-1))
D' = (4,-2)
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AABC is reflected across the x-axis and then dilated by a factor of 2 using the
point (-2, 1) as the center of dilation. What is the transformation of A(3, 1)?
6-
C(2,4)
4
B (5, 3)
2+
A (3.1)
4
-2-
OA. A(-6, 2)
B. A (6, -2)
C. A (8,-3)
D. A(3,-1)
-4
-2
N+
746
+00
8
10
The transformation of A is A' = (8, -3)
How to determine the transformation?From the graph, we have:
A = (3,1)
The scale factor and the center of dilation are given as:
k = 2
(a,b) = (-2,1)
The rule of reflection across the axis is:
(x,y) ⇒ (x,-y)
So, we have:
A' = (3,-1)
The rule of dilation is represented as:
(x,y) ⇒ (k(x - a) + a, k(y - b) + b)
So, we have:
A' = (2(3 + 2) - 2, 2(-1 - 1) + 1)
Evaluate
A' = (8, -3)
Hence, the transformation of A is A' = (8, -3)
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A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
(50, 22.5) is the solution of the system of equations, therefore, the true statement would be: Both plans cost the same when 50 texts are sent.
What is the Solution of a System of Linear Equations?A solution to the system of linear equations is the point of intersection where both line of each equation meet.
The solution to the system of linear equations given in the graph attached below is (50, 22.5).
(50, 22.5) implies that both plans will cost the total amount when 50 text are sent.
The true statement using the graph would be: Both plans cost the same when 50 texts are sent.
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Answer:
Both plans cost the same when 22 texts are sent
Step-by-step explanation:
on edge
Simplify the expression. Write your answer as a power.
((-3)²)⁴
The simplified expression is
Answer:
this is your answer
[tex] {9}^{4} [/tex]
[tex]\large{\sf \boxed{(\sf -3)^8}}[/tex]
Explanation:[tex]\rightarrow \sf ((-3)^2)^4[/tex]
apply exponent rule: [tex]\sf \bf \left(a^b\right)^c=a^{bc}[/tex]
[tex]\rightarrow \sf (-3)^8[/tex]
Which method correctly solves the equation using the multiplication property of equality and the reciprocal of one-third? one-third (x 9) = negative 12 one-third (x 9 = negative 12. one-third x 3 = negative 4. one-third x = negative 7. x = negative 27. one-third (x 9) = negative 12. x 9 = negative 4. x = negative 13. one-third (x 9) = negative 12. x 3 = negative 12. x = negative 15. one-third (x 9) = negative 12. x 9 = negative 36. x = negative 45.
The solution to the equation one-third (x + 9) = negative 12 is x = -45
How to solve the equation?The equation is given as:
one-third (x + 9) = negative 12
Rewrite properly as:
1/3 (x + 9) = -12
Multiply both sides by 3
x + 9 = -36
Subtract 9 from both sides
x = -45
Hence, the solution to the equation one-third (x + 9) = negative 12 is x = -45
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A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.
(A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs.
(B) Graph the total daily cost for 0≤x≤ 200.
(C) Interpret the slope and y intercept of the cost equation.
(A) C =
(Simplify your answer. Use integers or fractions for any numbers in the oxpropion
The function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A plant can manufacture 50 golf clubs per day at a total daily cost of $4671 and 70 golf clubs per day for a total cost of $5871.
Let's suppose x is the fixed cost and y is the variable cost.
4671 = 50y + x …(1)
5871 = 70y + x …(2)
1200 = 20y
y = 60
x = 1671
Total cost:
C(g) = 1671 + 60g
g is the number of golf per day.
Slope = 60
y- Intercept = 1671 (from the graph)
Thus, the function C(g) that represents the total daily cost, C, of producing x golf clubs is C = 1671 + 60g
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necesito esto resuelto porfa! en 20 minutos
Help which one is right?
Answer:
I think it is c
Step-by-step explanation:
I graphed it
if A squared plus B squared = C squared, what would it be if you timesd it by 2 waht would u get?
which expression gives the length of arc ab of the circumference of the circle is 40 cm
Answer:
110 / 360 * 40 pi
Step-by-step explanation:
Give circumference = 40 pi (NOT 40 cm as posted)
AB covers a fraction of 360 complete circle 110/360 ths
110/360 * 40 pi units
In a mathematic test 30 students obtained the following scores
3,4,7,2,9,5,2,1,8,2,3,6,9,3,4,3,4,1,5,3,3,1,7,7,7,5,6,4,6,5
a) Prepare a frequency table for the data
b) Draw a pictogram
c) Construct a barchart
Answer:
a) Prepare a frequency table for the data
Step-by-step explanation:
these box plots show daily low temeratures for a samle of days in two different towns
which statement is the most appropriate comparsion of the centers
The correct statement about the center of both box plots is the median for Town A, 30° is greater median for Town B, 25°
What is the correct statement?A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The whiskers represent the minimum and maximum numbers.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
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I kinda need help with this
Applying the leg rule, the value of x in the given right triangle is: A. 6.
What is the Leg Rule?The leg rule for solving a right triangle having an altitude is expressed as:
hypotenuse/leg = leg/part.
In the image given we have the following:
Hypotenuse = 4 + 5 = 9 units
Leg = x
Part = 4
Plug in the values into the leg rule formula:
9/x = x/4
(x)(x) = (9)(4)
x² = 36
x = √36
x = 6 units.
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The femur is the upper leg bone, and the tibia is one of the lower leg bones. the average length of the fumer is 50.5 cm,and the average length of the tibia is 43.03 cm. estimate the total length of the leg if the bones were placed end to end
what is the mean of each question?
Formula for finding mean:
Mean = (a1 + a2 + ... + an) / n
Mean is another word for average; average number of a data set.
Problems with steps:
---------------------------------------------------------------------------------------
1) 9, 3, 6
Average = Sum/Count
Sum = 18/6
Count = 3
2) 14, 12, 17, 9
52/4
Mean = 13
3) 15,8,10,5,7
= 45/5
Mean = 9
4) 18,19,11
= 48/3
Mean = 16
5) 4,20,16,4
= 44/4
Mean = 11
6) 12,11,12,20,15
= 70/5
Mean= 14
7) 19,8,3
= 30/3
Mean = 10
8) 7,13,6,2
= 28/4
Mean = 7
9) 12,15,17,2,14
60/5
Mean = 12
10) 10,18,8
= 36/3
Mean = 12
11) 5,2 ,0,1
= 8/4
= 2
12) 3,9,5,16,7
= 40/5
Mean = 8
SOLVED !
Hope this helps!
- ROR
Given that (a+b√3)(2-√3)= 5√3-4, find the values of a and b
Answer:
a=π-3/5,B =π-2/5
Step-by-step explanation:
product of roots
sum of roots
answer asap, thanks:)
Answer: Answer is In the step-by-step EXPLANATION.
Step-by-step explanation: Let's Begin,
Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198.
6t + 12d = 198
Ndiba sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127.
7t + 6d = 127
So when you find, the cost of each package of tulips bulbs and one bag of daffodil bulbs.
Use elimination here, multiply the 2nd equation by 2, subtract the 1st equation
14t + 12d = 254
Then, 6t + 12d = 198 -subtraction eliminates d, find t
8t + 0 = 56
t = 56/8
t = $7 for tulips
Find d using the 1st equation, t=7
6(7) + 12d = 198
42 + 12 d = 198
12d = 198 - 42
d = 156/12
d = $13 for daffodils
And I think that's it.