Answer:
Choice C. [tex]3,\! 780[/tex].
Step-by-step explanation:
The word "[tex]\verb!TENNESSEE![/tex]" contains nine letters:
Four [tex]\verb!E![/tex]'s, Two [tex]\verb!N![/tex]'s, Two [tex]\verb!S![/tex]'s, andOne [tex]\verb!T![/tex].If all these nine letters are unique, the number of possible arrangements would be:
[tex]P(9, 9) = 9! = 362,\! 880[/tex].
However, because some of these letters were not unique, a large number of that [tex]362,\!880[/tex] arrangements would be duplicates. What would be the exact number of duplicates? Start by considering giving each of the duplicate letters an index number. For example, consider the duplicates due to the letter "[tex]\verb!E![/tex]". There are four [tex]\verb!E![/tex]'s in [tex]\verb!TENNESSEE![/tex]. Label them as [tex]\verb!E!_1[/tex], [tex]\verb!E!_2[/tex], [tex]\verb!E!_3[/tex], and [tex]\verb!E!_4[/tex]:
[tex]\begin{array}{ccccccccc}\verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ & \uparrow & & & \uparrow & & & \uparrow & \uparrow \\ & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\end{array}[/tex].
These four [tex]\verb!E![/tex] can be shuffled and rearranged to give a large number of duplicates:
[tex]\begin{array}{r|ccccccccc}& \verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ &&\uparrow&&&\uparrow&&&\uparrow &\uparrow\\ 1 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\\ 2 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_4 & \verb!E!_3 \\ 3 & & \verb!E!_1 & & & \verb!E!_4 & & & \verb!E!_3 & \verb!E!_2 \\\ \vdots & & \vdots & & & \vdots & & & \vdots&\vdots \\4! = 24&&\verb!E!_4 & & & \verb!E!_3 & & & \verb!E!_2 & \verb!E!_1 \end{array}[/tex].
Each of these duplicate corresponds to a unique way for arranging four unique item in a row. There are [tex]4! = 24[/tex] ways to arrange four unique items in a row. Therefore, for each arrangement that is truly unique, the letter "[tex]\verb!E![/tex]" alone would have caused the arrangement to be counted [tex]4! = 24[/tex] times if the nine letters were assumed to be unique.
At the same time, letters "[tex]\verb!N![/tex]" and "[tex]\verb!S![/tex]" would further exaggerate the count by a factor of [tex]2[/tex] each. On the other hand, the letter [tex]\verb!T![/tex] appeared only once and would not create duplicates.
Overall, if the nine letters were assumed to be unique, each arrangement that is truly unique would have been counted:
[tex]4! \times 2! \times 2! \times 1! = 96\; \text{times}[/tex].
The count based on the incorrect assumption (that the nine letters are all distinct) is [tex]362,\!880[/tex]. Divide that count by the factor of exaggeration ([tex]4! \times 2! \times 2! \times 1! = 96[/tex]) to find the number of arrangements that are truly unique:
[tex]\begin{aligned} & 362,\!880 \times \frac{1}{4! \times 2! \times 2! \times 1!} = 3,\!780\end{aligned}[/tex].
Data was collected for 221 randomly selected 10 minute intervals. For each ten-minute interval, the number of people entering the atrium of a large mall were recorded. The data is summarized in the table below. Number of Guests Frequency 100 – 119 45 120 – 139 76 140 – 159 56 160 – 179 17 180 – 199 27 What is the class width for this GFDT?
Answer:
20
Step-by-step explanation:
From the above question, we were given the following information:
Number of Guests = Frequency
100 – 119 = 45
120 – 139 = 76
140 – 159 = 56
160 – 179 = 17
180 – 199 = 27
Class width can be defined as :
The difference between the upper limits of two consecutive classes, or the difference between the lower limits of two consecutive classes.
The class width for this GFDT : 139 - 119
= 20
20 - 10y - 7y + 9
please need help
ASAP
.................,...........................................,...,................
Suppose you want to equate an expression to zero:
[tex]\[\begin{array}{l}20 - 10y - 7y + 9 = 0\\29 - 17y = 0\\17y = 29\\y = \frac{{29}}{{17}}\end{array}\][/tex]
Work your brain today y'all!!
I had $3.00.
My Mom gave me $10.00.
My Dad Gave me $30.00.
My Aunt & Uncle gave me $100.00.
I had another $7.00.
How much did I have?
Right answer will get deleted.
I won against: I stole this post or sure the answer...
Answer:
We need to add to the $3.00 we have at the start, what they gave him:
He started with $3.00 and received $10.00:
3.00 + 10.00 = $13.00
Then (when having $13.00) received $30.00:
13.00 + 30.00 = $43.00
Then (when having $43.00) received $100.00:
43.00 + 100.00 = $143.00
Then (when having $143.00) he had another $7.00:
143.00 + 7.00 = $150.00
The answer is $150
I initially had $3
My mom gave me $10
= $10+$3
= $13
My dad gave me $30, my aunt and uncle also gave me $100
= $100+$13+$30
= $143
I had another $7
= $7 + $143
= $150
This makes it a total of $150
Hence the amount i have is $150
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A child walks due east on the deck of a ship at 3 miles perhour.
The ship is moving north at a speed of 16 miles per hour.
Find the speed and direction of the child relative to thesurface of the water.
Speed = mph
The angle of the direction from the north = (radians)
Answer:
16.28 mph ; 79.38°
Step-by-step explanation:
Given the following :
Speed of child due east = 3mph
Speed of ship due North = 16mph
Relative speed of th child is obtained by using Pythagoras rule to find the hypotenus
Relative Speed = Sqrt(3² + 16²)
Relative Speed = sqrt(9 + 256)
= sqrt(265)
= 16.2788 mph
= 16.28 mph
From trigonometry ;
Tanθ = opposite / Adjacent
Tanθ = (16 / 3)
Tanθ = 5.333
θ = tan^-1(5.333)
θ = 79.379°
θ = 79.38°
1. Write the ratio 2/3 to 8 as a fraction in simplest form.
Answer:
2/3 +8/3=10/3
Step-by-step explanation:
What is the factored from of the polynomial. x^2 + 9x + 20
Answer:
Step-by-step explanation:
Hello, the sum of the roots is -9=-4-5 and the product is 20=(-4)*(-5) so we can write
[tex]x^2+9x+20=(x+4)(x+5)[/tex]
thanks
Answer:
( x + 4 ) ( x + 5 )
Step-by-step explanation:
For this polynomial, we will factor the coefficient of the x^2 term and the constant.
The coefficient of x^2 is 1, which just factors to 1.
The constant 20 factors into 2 * 2 * 5.
Note, that our middle term coefficient is 9 and thus we want a pairing of 1 with either 2, 4, or 5 to make 9. 4 + 5 = 9, so we will choose that.
Using the standard binomials, we will factor the polynomial:
( x^2 + 9x + 20 )
= ( x + 4 ) ( x + 5)
We can check by performing foil:
= ( x + 4 ) ( x + 5 )
= ( x * x + x * 5) + ( 4 * x + 4 * 5)
= ( x^2 + 5x ) + ( 4x + 20 )
= ( x^2 + 9x + 20 )
Thus, we have successfully factored our polynomial.
Cheers.
The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends preparing for the test. If a student receives 72 points on a test for which she spent 3 hours preparing, what score would she receive on the next test if she spent 4 hours preparing?
Answer:
The teacher woll award the student 96 points for studying for 4 hours
Step-by-step explanation:
The student receives 72 point for preparing a test as long as 3 hours.
If she prepares for another test for 4 hours.
3 hours= 72 points
4 hours=( 72*4)/3
4 hours=72/3 *4
4 hours = 24*4
4 hours= 96 points
The teacher woll award the student 96 points for studying for 4 hours
Is 63 greater than 48.1 or less than
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
63 is greater than 48.1 ...
63 > 48.1
Step-by-step explanation:
63 is greater than 48 remember. So you need to remove the [.1] and focus on the 63 and 48.
Hope it helps!!Please mark me as the brainliest!!!Thanks!!!!❤❣❤
:)angel buys a 12-pack of granola bars for $9. What is the unit price?
Answer:
If 12 granola bars are nine dollars,
(12/9)
We divide the amount by the price!
Twelve divided by nine is about $1.33.
The image is rounded to the nearest thousandth
Find the slope of the line that passes through each pair of points. Express as a fraction in simplest form.
(-9,-11), (6,3)
6/8 skkssbjsjdsdhdhbddbd dhhdhshshs
Answer:
14/15
Step-by-step explanation:
To find the slope
m= ( y2-y1)/(x2-x1)
= ( 3 - -11)/( 6 - -9)
= ( 3+11)/( 6+9)
= 14/15
Help me please thank you
Answer:
y = 120º
Step-by-step explanation:
180 - (33 + 87) = 60
x = 60
180 - 60 = 120
y = 120º
or y = 33 + 87, because the outer angle of one angle equals the other two inner angles.
Answer: 120°
Step-by-step explanation:
If you add up all the triangles angles, it always is 180. So, when you add 33+87, you get 120. This means that x=60 because 120+60 =180.
Then, you also know that x and y together, make a 180° also because it is a straight line. So, y is equal to 120° because 60+120 = 180°.
Hope this helps! :)
The ______ can be used to determine whether the graph a relation is a function.
Answer:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
Step-by-step explanation:
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1, 4
Answer:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
Step-by-step explanation:
For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.
If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.
Where;
cos α = [tex]\frac{a . i}{|a| . |i|}[/tex] ---------------------(i)
cos β = [tex]\frac{a.j}{|a||j|}[/tex] ---------------------(ii)
cos γ = [tex]\frac{a.k}{|a|.|k|}[/tex] ----------------------(iii)
And from these we can get the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
Now to the question:
Let the given vector be
a = 5i + j + 4k
a . i = (5i + j + 4k) . (i)
a . i = 5 [a.i is just the x component of the vector]
a . j = 1 [the y component of the vector]
a . k = 4 [the z component of the vector]
Also
|a|. |i| = |a|. |j| = |a|. |k| = |a| [since |i| = |j| = |k| = 1]
|a| = [tex]\sqrt{5^2 + 1^2 + 4^2}[/tex]
|a| = [tex]\sqrt{25 + 1 + 16}[/tex]
|a| = [tex]\sqrt{42}[/tex]
Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e
cos α = [tex]\frac{5}{\sqrt{42} }[/tex]
cos β = [tex]\frac{1}{\sqrt{42} }[/tex]
cos γ = [tex]\frac{4}{\sqrt{42} }[/tex]
From the value, now find the direction angles as follows;
α = cos⁻¹ ( [tex]\frac{a . i}{|a| . |i|}[/tex] )
α = cos⁻¹ ( [tex]\frac{5}{\sqrt{42} }[/tex] )
α = cos⁻¹ ([tex]\frac{5}{6.481}[/tex] )
α = cos⁻¹ (0.7715)
α = 39.51
α = 40°
β = cos⁻¹ ( [tex]\frac{a.j}{|a||j|}[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{\sqrt{42} }[/tex] )
β = cos⁻¹ ( [tex]\frac{1}{6.481 }[/tex] )
β = cos⁻¹ ( 0.1543 )
β = 81.12
β = 81°
γ = cos⁻¹ ( [tex]\frac{a.k}{|a|.|k|}[/tex] )
γ = cos⁻¹ ([tex]\frac{4}{\sqrt{42} }[/tex])
γ = cos⁻¹ ([tex]\frac{4}{6.481}[/tex])
γ = cos⁻¹ (0.6172)
γ = 51.89
γ = 52°
Conclusion:
The direction cosines are:
[tex]\frac{5}{\sqrt{42} }[/tex], [tex]\frac{1}{\sqrt{42} }[/tex] and [tex]\frac{4}{\sqrt{42} }[/tex] with respect to the x, y and z axes respectively.
The direction angles are:
40°, 81° and 52° with respect to the x, y and z axes respectively.
Simplify the expression 5^3•5^-5
Answer:
5^8Step-by-step explanation:
[tex]5^3\times\:5^5\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times\:a^c=a^{b+c}\\5^3\times\:5^5=5^{3+5}\\\\=5^8=390625[/tex]
The solution of the expression will be 5⁻².
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 5³ x 5⁻⁵. The expression will be solved as below,
E = 5³ x 5⁻⁵
E = 5³⁻⁵
E = 5⁻²
Hence, the expression will be E = 5⁻².
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10 pts
Point K (-2,-3) is translated (x + 5, y-7). What are the coordinates K?
Answer: (3,-10)
Step-by-step explanation:
Using the translated rule that x is increase by 5 and y is decreased by 7 put it into the equation and solve for the coordinates of k.
(-2 +5 ) = 3
(-3 -7) = -10
So now the coordinates will be (3,-10)
206 MAI
ALEKS Probabilities of draws with replacement
Toples
? SAMPLE QUESTION
A fair die is rolled 6 times. What is the probability of having no 4 and no 5 among
places.
(If necessary, consult a list of formulas.)
3
Step-by-step explanation:
Two of the sides are 4 and 5. The other four sides are 1, 2, 3, and 6.
The probability of rolling a number other than 4 or 5 on any roll is 4/6, or 2/3.
The probability of rolling no 4s or 5s six times is:
P = (2/3)⁶
P ≈ 0.088
Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday. What fraction of the fliers did she give out on Wednesday? Use a diagonal fraction bar in your answer. Explain how you found the answer
Answer:
0.66
Step-by-step explanation:
Rosalia passed out fliers that say, “Vote for Rosalia!” She gave out 85 fliers on Monday, 66 fliers on Tuesday, and 99 fliers on Wednesday.
Total fliers shared= 85+66+99
Total fliers shared= 250 fliers
Fraction of the fliers she gave out on Wednesday= fliers on Wednesday/total fliers
=99/150
= 33/50
= 3.3/5
= 0.66
Answer:
0.66
Step-by-step explanation:
The graph below represents which of the following functions?
Answer:I believe the answer is C
Step-by-step explanation:
The y-intercept is 2
Is 93.43 an integer or not
Answer:
The answer is no
To which set of numbers does -15 belong to? Select all apply.
Answer:
Integer
Step-by-step explanation:
On every number line we have both negative and positive numbers. So negative 15 is an integer
Write a real world situation the would represent -5 + -2 +3 = -4
mean of 7
observations was calculated as 40. It was detected on rechecking that the value 63 was
wrongly copied as 36. Find the correct mean?
Answer:
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Because 63 is a multiple of 7
So.... 63/7
=9
So this shows us 9 is the mean
HOPE IT HELPS YOU!
PLEASE MARK ME AS BRAIN LIST IF MY ANSWER IS HELP FUL
Sam had 225 dollars to spend on 8 books. After buying them he had 17 dollars. How much did each book cost?
Answer:
Each book costs 26 dollars
Step-by-step explanation:
Let b be the price of each book
8*b +17 = 225
Subtract 17 from each side
8b+17-17 = 225-17
8b =208
Divide by 8
8b/8 = 208/8
b =26
Each book costs 26 dollars
which of the following must describe an irrational number
Answer:
An Irrational number is a number that cannot be expressed as the ratio of two integers.
Example: [tex]\pi[/tex]
its numbers are infinite
5) Determine o conjunto solução da equação: x² + 12x - 189 = 01 ponto{ - 21, 9}{ 21, -9 }{ 21 }{ - 9 }
Answer:
x = 9 or x = -21
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 12 x - 189 = 0
The left hand side factors into a product with two terms:
(x - 9) (x + 21) = 0
Split into two equations:
x - 9 = 0 or x + 21 = 0
Add 9 to both sides:
x = 9 or x + 21 = 0
Subtract 21 from both sides:
Answer: x = 9 or x = -21
2. Find the solution to the following system of eguations using the addition method
4x - 5y = 13
X + 5y = -3
Answer: (2, -1)
Explanation: Since one equation has a -5y and the other equation
has a +5y, when we add the equations together, the y's will cancel out.
So we have 5x = 10 and x = 2.
To find y, plug 2 back in for x in either of the two original equations.
I have chosen to plug 2 into the second equation to get (2) + 5y = -3.
Solving from here, y = -1.
So our final answer is the ordered pair (2, -1).
Now, check your answer.
Change 64 hours to minutes
Answer:
3840 minutes
Step-by-step explanation:
60x64= 3840
can i have the brainliest, please????
Answer:3840 minutes
Step-by-step explanation:
there is 60 min in an 1 hr so there for you can multiple 64x60 which equals 3840
( -7v 4 - 5v ) - ( -5v 3 - 2v ) + ( -7v - 6v 4 - 4v 3 ) simplified
Answer:
-13v^4 + v^3 - 10v (if simplified)
Step-by-step explanation:
combine like terms
(-7v^4 - 5v) - (-5v^3 - 2v)+ ( - 7v - 6v^4 - 4v^3)
-7v^4 + -6v^4 = -13v^4
-5v^3 + -4v^3 = v^3 (the five becomes positive because of the negative sign infront of the parenthesis) Example: -(-5v^3) = +5v^3
-13v^4 + v^3 -5v -(-2v) -7v (now we have the -2 left alone in the parenthesis which means it becomes positive too) Example: -(-2v) = +2v
-5v +2v - 7v = -3v -7v = -10v
Answer: -13v^4 + v^3 - 10v
here is a histogram of the yearly number of unprovoked attacks by alligators. what is the overall distributions
Answer:
Hello your question has some missing parts attached is the missing part
answer : slightly skewed to the right ( B )
Step-by-step explanation:
From the attached histogram related to the question above, it can be seen that the the right tail is longer than the left tail and this can help us draw the conclusion that the overall shape of the distribution is slightly skewed to the right
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $775 per week. How much did she earn last week if she sold $4,300 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Answer:
$1108.25
Step-by-step explanation:
Danielle's commission on $4300 in sales is ...
0.0775 × $4300 = $333.25
That, added to her base salary, gave her weekly earnings of ...
$333.25 +775 = $1108.25 . . . . Danielle's pay last week