How many different letter permutations, of any length, can be made using the letters M O T T O (For instance, there are 3 possible permutations of length 1.)
Answers
Answer:
89
Step-by-step explanation:
Given that
2 O, 2 T and 1 M
Now based on this, the following ways are there
1
Three ways i.e. {M,T,O}
2
XX or XY
XX in 2C1 = two ways i.e. {OO or TT}
XY in 3C2 × 2! = six ways
3
XXY or XYZ
XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve ways
XYZ in 3C3 × 3! = six ways
4
XXYY or XXYZ
XXYY = 4! ÷ (2! × 2!) = six ways
XXYZ in 2C1 × 4! ÷ 2! = twenty four ways
5
= 5! ÷ (2! ×2!)
= 120 ÷ 4
= 30
Therefore, the total is
= 3 + (2 +6)+ (12 +6) + (6 +24) + 30
= 89
There are 30 different letter permutations.
The word is given as:
MOTTO
From the given word, we have the following parameters:
\(n = 5\) --- the number of characters in the word\(T = 2\) --- the number of times letter T appears\(O = 2\) --- the number of times letter O appearsThe number of different (d) letter permutation is then calculated as:
\(d = \frac{n!}{T!O!}\)
This gives
\(d = \frac{5!}{2!2!}\)
Evaluate each factorial
\(d = \frac{120}{2 \times 2}\)
Evaluate the product of 2 and 2
\(d = \frac{120}{4}\)
Divide 120 by 4
\(d = 30\)
Hence, there are 30 different letter permutations.
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Related Questions
Help me out
Answer required
Answers
Answer:
a) True
b) False
c) True
d) False
e) True
f) False
g) True
h) False
i) True
j) False
plz mark me as brainliest
A decorative vase is on sale from $80 to $50. What is the
percent change of the price of the vase. Be sure to indicate
if it was a decrease or increase. Show the formula you use to
solve. Round to a whole number.
Answers
Since the result is negative, we can say that the price of the vase decreased by 37.5%. Rounding to a whole number, the percent change is 38% (since a 37.5% decrease is approximately equal to a 38% decrease).
What is percent?Percent (often symbolized as "%") is a way of expressing a fraction or a portion of something in terms of hundredths. It is used to describe the relationship between a part and a whole, with the whole being represented by 100%. Percentages are commonly used in many areas of life, such as finance, business, and statistics. They can be used to describe changes in values over time, to compare different quantities or amounts, or to express probabilities or frequencies.
Here,
The percent change in the price of the vase can be calculated using the formula:
percent change = (new price - old price) / old price x 100%
In this case, the old price of the vase was $80 and the new price is $50. Substituting these values into the formula, we get:
percent change = ($50 - $80) / $80 x 100%
percent change = -0.375 x 100%
percent change = -37.5%
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What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
StartFraction 10 Over 3 EndFraction divided by five-thirds
Five-thirds divided by StartFraction 10 Over 3 EndFraction
2 divided by five-thirds
2 divided by StartFraction 10 Over 3 EndFraction
Answers
Answer:
It's the first answer.
Step-by-step explanation:
Answer:
The Answer is A
Step-by-step explanation:
HELP MEEE!!!
Use the drawing below to answer the questions that follow.
What is the scale factor going from smaller to larger?
(reference photo please)
Answers
Step-by-step explanation:
Part A: Let see what number we can multiply by 3 to get 13.5
\(3x = 13.5\)
\(x = 4.5\)
so our answer is 4.5
Part B : Set up the proportion
3 and 13.5 correspond with each other and the question mark side corresponds with the 9 cm side.
let x = the side we are trying to find
\( \frac{3}{x} = \frac{13.5}{9} \)
Cross multiply
\(27 = 13.5x\)
\(x = 2\)
so our answer is 2.
Any positive integer greater than 6
Answers
7
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Answer:
8 9 10 11 12????????????????????
Find the difference between ¼ of #5.00 and 37/½% of #1.50
Answers
The difference between ¼ of 5.00 and 37/½% of 1.50 is 0.6875 because 1/4 of 5.00 is 1.25 and 37.5% of 1.50 is 0.5625.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
\(\rm \dfrac{1}{4} \ \ of \ 5.00\)
\(\rm = \dfrac{1}{4}\times 5.00\)
= 1.25
\(\rm 37 \dfrac{1}{2} \% \ of \ 1.50\)
= 37.5% of 1.50
= 0.5625
Difference between the numbers:
= 1.25 - 0.5625
= 0.6875
Thus, the difference between ¼ of 5.00 and 37/½% of 1.50 is 0.6875 because 1/4 of 5.00 is 1.25 and 37.5% of 1.50 is 0.5625.
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100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Answers
A. The distributions of the periods is that using the five number summary is that
The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher medianB. The box and whisker plot of the periods is attached
A. Comparing the distributions of the periodsFrom the question, we have the following parameters that can be used in our computation:
7th Period
66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96
3rd Period
52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97
The distributions of the periods will be compared using the five-number summaries
Using a graphing tool, the five-number summaries are:
7th Period
Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 963rd Period
Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97B. Creating a box and whisker plot of the periodsThe box and whisker plot of the periods is added as an attachment
From the box and whisker plot attached, we can see the five-number summaries of the periods
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Please help!!!! It’s urgent
Which of the following rational functions is graphed below?
-10
10-
-10
1
A. F(x) = 1/x(x+3)
B. F(x)= x/x+3
C. F(x)= 3/x
D. F(x)= 1/x(x-3)
Answers
Answer:
the answer is D. F(x) = 1/x(x-3)
Step-by-step explanation:
A dairy farmer wants to mix a 75% protein supplement and a standard 30% protein ration to make 1200 pounds of a high-grade 45% protein ration. How many pounds of each should he use?
Answers
The dairy farmer should use 400 pounds of the 75% protein supplement and 800 pounds of the 30% protein ration to make 1200 pounds of a high-grade 45% protein ration.
To determine how many pounds of each protein supplement the dairy farmer should use, we can set up a system of equations based on the given information.
Let's denote the following:
x = pounds of the 75% protein supplement
y = pounds of the 30% protein ration
The total weight of the mixture is 1200 pounds, so we have the equation:
x + y = 1200
The protein content in the mixture should be 45% of the total weight, so we have the equation:
0.75x + 0.30y = 0.45 * 1200
Now we can solve this system of equations.
First, let's rewrite the second equation in decimal form:
0.75x + 0.30y = 540
To make it easier to work with, we can eliminate the decimals by multiplying both sides of the equation by 100:
75x + 30y = 54000
Now we have a system of equations:
x + y = 1200
75x + 30y = 54000
We can solve this system using any appropriate method, such as substitution or elimination. In this case, let's use the substitution method:
Solve the first equation for x:
x = 1200 - y
Substitute the value of x into the second equation:
75(1200 - y) + 30y = 54000
Simplify and solve for y:
90000 - 75y + 30y = 54000
-45y = -36000
y = 800
Now we can substitute the value of y back into the first equation to find x:
x + 800 = 1200
x = 1200 - 800
x = 400
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Two pedestrians simultaneously left two villages 27 km apart and walked toward each other, meeting after 3 hours. The first pedestrian walked at a speed of 4 km per hour. At what speed (in km per h) did the second pedestrian walk?
Answers
The speed of the second pedestrian is 5 kilometers per hour.
At what speed did the second pedestrian walk?Let's say that the speed of the second pedestrian is S.
We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:
(4km/h + S)*3h = 27km
It says that both pedestrians work, together, a total of 27km in 3 hours.
Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.
4km/h + S = 27km/3h = 9 km/h
S = 9km/h - 4km/h = 5km/h
The speed of the second pedestrian is 5 kilometers per hour.
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26. My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CAN- NOT be the correct combination of my brother's lock? (A) 8560 (B) 3015 (C) 4906 (D) 1893 (E) 6348 0782 Activate Windows
Answers
Answer:
A
Step-by-step explanation:
The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.
In one season, a basketball player missed 50% of her free throws. How many free throws did she attempt if she made 183 free throws?
Answers
Answer:
Step-by-step explanation:
50% of 366 is 183, therefore your answer is 366.
Find the z-score separating the lowest 9% of scores from the highest score of 91%
Answers
Answer:
I'm not sure of my answer but try this:
Write and linear function f with f(0)=2 and f(5)=-3
Answers
Answer:
f(x) = -x + 2-----------------------------------
Slope-intercept form of a line:
f(x) = mx + b, where m-slope, b- y-interceptThe line has points:
(0, 2) and (5, - 3)The first point represents the y-intercept, b = 2.
The slope is:
m = (- 3 - 2)/(5 - 0) = - 5/5 = - 1The line is:
f(x) = - x + 2please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
please look at the image this is a homework problem I would appreciate help with!
Answers
ANSWER:
\(\sin (t+2\pi)-\cos (t+4\pi)+\tan (t+\pi)=c\)STEP-BY-STEP EXPLANATION:
We have the following expression:
\(\sin (t+2\pi)-\cos (t+4\pi)+\tan (t+\pi)\)Now, we apply the angle sum identities in each case, just like this:
\(\begin{gathered} \sin (t+2\pi)=\sin t\cdot\sin 2\pi+\cos t\cdot\cos 2\pi \\ \cos (t+4\pi)=\cos t\cdot\cos 4\pi+\sin t\cdot\sin 4\pi \\ \tan (t+\pi)=\frac{\tan t+\tan\pi}{1+\tan t\cdot\tan\pi} \end{gathered}\)We replace by the equivalences of a, b and c, like this:
\(\begin{gathered} \sin t\cdot\sin 2\pi+\cos t\cdot\cos 2\pi=a\cdot0+b\cdot1=b \\ \cos t\cdot\cos 4\pi+\sin t\cdot\sin 4\pi=b\cdot1+a\cdot0=b \\ \frac{\tan t+\tan\pi}{1+\tan t\cdot\tan\pi}=\frac{c+0}{1+c\cdot0}=\frac{c}{1}=c \\ \\ \text{ Replacing:} \\ b-b+c=c \end{gathered}\)what's 96.23 rounded to the nearest 10?
Answers
100 is the answer pls give me branliest (:
Step-by-step explanation:
If 4 quarts of organic grapes cost $20 how many quarts can you purchase for one dollar
Answers
Answer:
4/5 of a quart
Step-by-step explanation:
Set this up as a proportion. First of all we know that 4 quarts of organic grapes cost $20, so 4x = 20. Divide and you get that x = 5 meaning 1 quart equals 5 dollars. Now if we scale this down a bit and divide by 5, we end up with 4/5 of a quart = 1$.
Hope this helped (:
A television is discounted 20% in a sale. A shopper has a coupon for an additional 15% off the sale price. Which of the following is the total percent discount from the original price of the television?
Answers
Step by step explanation:
If the television is discounted by 20% in a sale and the shopper also has a coupon for an additional 15% of the sale price than you just add up the percentages and that’s the total percent of the discount.
I hope this helped you understand! :)
The total percent discount arises from the real price of the television is 32%.
Given that,
The television should be discounted at 20% in the sale i.e. price after discount should be 0.80 of the real price There is an additional 15% off the sale price. So, 15% of 80% i.e. 12%.So, the total percent discount should be
= 20% + 12%
= 32%
Therefore we can conclude that The total percent discount arises from the real price of the television is 32%.
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Akasha is covering her patio with stone tiles that are 1/2 yard by1/2 yard.The patio is 4 yards wide and 7 1/2 yards long.How many tilers will Akasha need to cover the patio?
Answers
The number of tiles needed by Akasha to cover the area of the patio is calculated as: 120 tiles.
How to Calculate the Area of a Rectangular Space?The patio is a rectangular space. Therefore, to determine the number of tiles Akasha will need to cover the patio, find the area of the patio and the area of one tile.
Area of the patio = area of rectangle = (length)(width).
Given the following:
Length of the patio = 7 1/2 = 15/2 yards
Width of the patio = 4 yards
Area of the rectangular patio = (15/2)(4)
Area of the rectangular patio = 30 yards²
Length of the tile = 1/2 yard
Width of the tile = 1/2 yard
Area of one tile = (1/2)(1/2)
Area of one tile = 0.25 yd²
Number of tiles needed to cover the patio = area of the patio/area of one tile
= 30/0.25
= 120 tiles
Thus, the number of tiles needed by Akasha to cover the area of the patio is calculated as: 120 tiles.
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I took a picture of the question
Answers
The transformation in the picture is option c Reflection.
Given,
Reflection transformation:
A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.
According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.
Here,
In the picture the transformation is reflection.
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Kevin and Randy Muise have a jar containing 100 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $15.00. How many of each type of coin do they have?
Answers
Answer:
what do we know?
we know that a quarter is $0.25 and a nickel is $0.05
4x$.25 = $1
20x$0.05 = $1
and we have 84 coin
n = the number of nickels
q = the number of quarters
(1) n + q = 84 and
(2) 5*n + 25*q = 100*11.80 (always work in cents)
(3) 5*n + 25*q = 1180
Now substitute n from equation (1) into equation (3) and get
5*(84 - q) + 25*q = 1180
420 - 5*q + 25*q = 1180
20*q = 1180 - 420
20*q = 760
q = 38
Then using equation (1), plug in q
n + 38 = 84
n = 46
now check these values.
Is (.05*38 + .25*46 = 11.80)?
Is (2.30 + 9.50 = 11.80)?
Is (11.80 = 11.80)? Yes
Step-by-step explanation:
Plz Mark me as brainliest
Answer: 7 quarters and 19 nickels
Step-by-step explanation:
Trying to find the equivalent ratio with lower terms
A. 30:36=20: ?
B. 21:35=? :20
Answers
The red thing at the top is a right angle. Find the missing side lengths and leave answers as radicals in simplest form ILL GIVE BRAINLIEST
Answers
Answer:
A. x = 13
y = (13√3)/3
Step-by-step explanation:
Reference angle = 30°
Hypotenuse = (26√3)/3
Adjacent = x
Opposite = y
✔️Apply CAH to find x:
Cos 30 = Adj/Hyp
Cos 30 = x/(26√3)/3
√3/2 = x*3/(26√3) (cos 30 = √3/2)
√3/2 = 3x/(26√3)
Cross multiply
2*3x = (26√3)*(√3)
6x = 26*3
6x = 78
x = 78/6
x = 13
✔️Apply SOH to find y:
Sin 30 = Opp/Hyp
Sin 30 = y/(26√3)/3
Sin 30 = y*3/(26√3)
½ = 3y/(26√3) (sin 30 = ½)
Cross multiply
2*3y = (26√3)*1
6y = 26√3
Divide both sides by 6
y = (26√3)/6
y = (13√3)/3
13) A rectangular garden has an area of 45 square meters. The garden will be 4 meters longer than its width Write and sowe an equation to find the dimensions in meters.
Answers
Answer:
9m ×5m
Step-by-step explanation:
Area of a rectangle= length ×width
Let the width be W meters and the length be L meters.
2 equations can be written from the given information:
45= WL -----(1)
L= W +4 -----(2)
Substitute (2) into (1):
45= W(W +4)
Expand:
45= W² +4W
-45 on both sides:
W² +4W -45= 0
Factorise:
(W +9)(W -5)= 0
W+9=0 or W-5=0
W= -9 or W= 5
(reject)
Substitute W= 5 into (2):
L= 5 +4
L= 9
∴ The dimensions of the garden is 9m ×5m.
4,0000000000×10,00000000
Answers
Answer:
yes 40
Step-by-step explanation:
she got it correct
I really do need help solving this equation
Answers
Answer:
D
Step-by-step explanation:
3/5 = 0.6
75% = .75
0.8, 0.75, 0.6, 0.56
(c) Problem 17:
How far will the baseball have dropped after
4.5 seconds?
(first taught in
lesson 90)
Afton
Answers
After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.
To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.
The terms involved in this calculation are:
Time (t): 4.5 seconds.
Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.
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One week, a farmer picked 388 pounds of apples. The next week, she
picked 301 pounds of apples. Which shows how many pounds of apples
she picked in all?
A 388 divided 301
B 388 + 301
388-301
D 388 x 301
HURRY
Answers
Answer:
388+301
Step-by-step explanation:
its saying in all so it walnts you to add bothe the total amounts of apples :))
Find an equation of a line with slope -4 and y-intercept 9. y =
Answers
Answer:
Y= -4X+9
Step-by-step explanation:
solve the equation by the help of the standard equation Y = MX + C
where M is the slope and C is the Y intercept