The number of different strings that can be made from the letters in ORONO using some or all of the letters is 63
What is the number of permutations in which n things can be arranged such that some groups are identical?Suppose there are n items.
Suppose we have
[tex]i_1, i_2, ..., i_k[/tex]
sized groups of identical items.
Then the permutations of their arrangements is given as
[tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}[/tex]
We're given the word ORONO.
Case 1: One letter string:3 ways: O, R, or N
Case 2: Two letter string:Subcase: Consists O:
5 ways: OR, RO, ON, NO, OO
Subcase: Doesn't consist O:
2 way: RN, NR
Total permutation under this case = 5+2 = 7
Case 3: Three letter string:Subcase: Consists 3 'O':
1 way: OOO
Subcase: Consists 2 'O':
6 ways: OOR, ROO, ORO, OON, NOO, ONO
Subcase: Consists 1 'O':
6 ways: ORN, ONR, RNO, RON, NOR, NRO (or that there are 3 distinct letters to be arranged, which can be done in 3! = 6 ways)
Subcase: Doesn't consist O:
0 ways as only R and N cannot form three letter string.
Total permutation under this case = 1+6+6= 13
Case 4: 4 letter string:Subcase: Consists 3 'O':
So, we've got {O,O,O,R,N}
3 'O's are mandatory, so fourth letter is either R or N:
O, O, O, R can arrange themselves in : [tex]4!/3! = 4 \: \rm ways[/tex] (as total 4 words but 3 are identical)
Similarly, O, O, O, N can arrange themselves in 4 ways,
So when 4 letter string from ORONO consists of 3 'O's, then total 4+4=8 distinct strings can be made.
Subcase: Consists 2 'O':
So, we've got {O,O,R,N}
The total permuations of these 4 letters, of which 2 are identital is:
[tex]\dfrac{4!}{2!} = 12[/tex]
Subcase: Consists 1 'O':
0 ways: Single 'O' and one-one R and N cannot form four letter string.
Subcase: Doesn't consist O:
0 ways as only R and N cannot form four letter string.
Total permutation under this case = 8+12 = 20
Case 5: Five lettered string:All 5 letters of ORONO would be used.
There are 3 identical objects, so total number of their permutation is:
5!/3! = 20
Thus, from all these cases, we conclude that:
Total permutations of string letters using some or all letters of ORONO is:
3+7+13+20+20 = 63
Thus, the number of different strings that can be made from the letters in ORONO using some or all of the letters is 63
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Use the three functions shown. 1. f(x)=x² II. f(x)=√x III. f(x) = ln x For which of the functions, if any, is a trapezoidal approximation for the area under the curve y = f(x) over the interval [1, 4] with 3 equal subintervals less than the midpoint approximation? none of the functions O I only II and III only all of the functions
II and III only
We split up the integration interval [1, 4] into 3 equally-spaced subintervals of length (4 - 1)/3 = 1 :
[1, 2], [2, 3], [3, 4]
The area over each subinterval [L, R] is either approximated by a trapezoid, whose area will be
1 • (f(L) + f(R))/2
or by a rectangle with height f((L + R)/2) and hence area
1 • f((L + R)/2)
For f(x) = x², the area under f(x) over [1, 4] is approximated by
• using trapezoids (T) :
[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}{2\times3} (1^2 + 2\times2^2 + 2\times3^2 + 4^2) = \frac{43}2 = \frac{86}4[/tex]
• using midpoints (M) :
[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}3 \left(\left(\frac32\right)^2 + \left(\frac52\right)^2 + \left(\frac72\right)^2\right) = \frac{83}4[/tex]
so T > M. (This eliminates "I only" and "all of the functions".)
For f(x) = √x, the area is approximated by
• T :
[tex]\displaystyle \int_1^4 \sqrt x \, dx \approx \frac{4-1}{2\times3} (\sqrt1 + 2\sqrt2 + 2\sqrt3 + \sqrt4) \approx 4.646[/tex]
• M :
[tex]\displaystyle \int_1^4 \sqrt x\, dx \approx \frac{4-1}3 \left(\sqrt{\frac32} + \sqrt{\frac52} + \sqrt{\frac72}\right) \approx 4.677[/tex]
so T < M. (This eliminates "none of the functions".)
Which of the following rational functions is graphed below?
Answer:
The answer should be C.
Step-by-step explanation:
It is C because you need to do first is to find is just the vertical asymptote of the function and to plug in the x values behind the vertical asymptote.
Find the area of a sector of a circle whose central angle measures π/4 radians and whose radius is 4 cm. Express In terms of π and as a decimal.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =\frac{\pi }{4} \end{cases}\implies A=\cfrac{ ~~ \frac{\pi }{4} ~~ (4)^2}{2}\implies A=2\pi \implies A\approx 6.28[/tex]
When 12 is multiplied by a fraction less than one, which of the following is true about the product.
(I don't know what are the answer choices, but I'm sure this should be one of the choices:)
Answer:
The product of 12 multiplied with a fraction less than 1 will be less than 12 itself.
Step-by-step explanation:
This is true because if you multiply 12 by (for example) 1/2, then your answer is going to be 6 since 12x1=12 itself, and 12x0=0. So that's why, if it's less than 1, then the product is going to be less than 12 itself.
Hence, one of the answer choices can be something like: The product will be less than 12 itselfPLEASEE HELPPPPPPP QUICKLY
Answer:
A
Step-by-step explanation:
A. 23÷49
Using this method from Internet, it occurs to be the least fraction is A which meaning least likely to happen.
claire is considering in a new business
Why is a recipe a good example of procedural writing? Check all that apply.
options:
A. Making a recipe requires materials.
B. Recipes have a method, or a sequence of steps.
C. Making a recipe requires experience.
D. All recipes have a goal.
E. Recipes are fun to make.
F. Users can determine whether the recipe was successful.
Answer: A, B, D, F
Explanation:
Edge 2022
Answer:
A, B , D, F
Step-by-step explanation:
These are a good example of procedural writing
Hope it helped ! Mark me as Brainliest pls !
help i need a answer asap!!
Answer: One angle measures more than 90 degrees
Step-by-step explanation:
PLEASE HELP ME !!!!
Answer:
D
Step-by-step explanation:
Exterior means outside which means it has to be one of the angles outside the triangle.
Options A, B, and C have angles inside the triangle.
Option D is the only angle outside the triangle
Please help me solve this trig problem!
Answer:
the awnser I got is 279
Step-by-step explanation:
if it's wrong I'm so sorry I'm not the best at math >-<
Answer: 105.66 ft
Step-by-step explanation:
Please help the distance formula
Answer:
7.8
Step-by-step explanation:
distance formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where the x and y values are derived from the given points
here the given points are (11,3) and (6,9)
assigning variables
(x1,y1) = (11,3) so x1 = 11 and y1 = 3
(x2,y2) = (6,9) so x2 = 6 and y2 = 9
plugging in values into formula
recall formula [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
==> plug in x1 = 11 , y1 = 3 , x2 = 6 and y2 = 9
[tex]d=\sqrt{(6-11)^2+(9-3)^2}[/tex]
==> subtract values in parenthesis
[tex]d=\sqrt{(-5)^2+(6)^2}[/tex]
==> evaluate exponents
[tex]d=\sqrt{25+36}[/tex]
==> add 25 and 36
[tex]d=\sqrt{61}=7.8[/tex] ( approximately )
What is the value of the expression below when a = 4?
6a + 7
A. 31
B. 41
C. 53
D. 71
Mrs. Smith gave a math test. The following stem and leaf plot shows the scores of all of her students.
How many students took Mrs.Smiths math test?
The number of students that took Mrs. Smith's Math test as dshown in the stem-and-leaf plot is: 20.
What is a Stem-and-Leaf Plot?A stem-and-leaf plot displays a data distrubution as follows, i.e., if 56, 57 are data points, 5 would be the stem while 6, 7 will be the leaf (5 | 6, 7).
The data points in the stem-and-leaf plot shown represents the score of each of the student. There are 20 data points.
Therefore, the number of students that took the test is: 20.
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what is the y intercept of F(x) = 1000(2)[tex]x^{2}[/tex]
Answer:
The y-intercept is 0
Step-by-step explanation:
y = mx + b
b is y-intercept
There are no constants in this equation
What is the solution of the system of equations shown in the following graph? Please help
Answer:
aedi on
Step-by-step explanation:
Suppose a random sample of biweekly snowfalls in the pacific northwest has a sample mean of x¯=22.2 inches, with a sample standard deviation of s=3.5 inches. Since snowfall amounts in this area are generally symmetric and bell-shaped, we can apply the Empirical Rule.
Between what two amounts are approximate 99.7% of the data?
Using the Empirical Rule, it is found that 99.7% of the data will be between 11.7 and 32.7 inches.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering the mean and the standard deviation of the data-set, the bounds between which 99.7% of the data-set are given by:
22.2 - 3 x 3.5 = 11.7 inches.22.2 + 3 x 3.5 = 32.7 inches.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Answer: 11.7 & 32.7
Step-by-step explanation:
Approximately $99.7\%$ of the snowfall amounts are between 1$$ inches and 2$$ inches.
Correct answers:
1: 11.7 2: 32.7
The Empirical Rule states that approximately 99.7% of the data is within 3 standard deviations of the mean. In terms of the sample mean x¯ and sample standard deviation s, that is between x¯−3s and x¯+3s.
The value 3 standard deviations below the mean is
x¯−3s=22.2−3(3.5)=11.7.
The value 3 standard deviations above the mean is
x¯+3s=22.2+3(3.5)=32.7.
So by the Empirical Rule, we can say that approximately 99.7% of the snowfall amounts are between 11.7 and 32.7 inches.
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Bluegrass was develope from tradition
Simple / repetitive cuord proggression the
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the country Acoustic instrumen
7. What wast the social significance of cover songs in early
What was the significance of cover songs in early rock music
Joe can paint 2 yards of fence for $48.60. What is the price per foot.
Answer:
the price per foot = $8,1
Step-by-step explanation:
Note : 2 yards = 2 × 3 = 6 foot
Then
Joe can paint 6 foots of fence for $48.60
Then
Joe can paint 1 foot of fence for 48.60 ÷ 6 = $8,1
Number 31 please help
Step-by-step explanation:
you should respond : "you are right" !
1. The area of Alabama is 51,718 square miles and its population is 4,779,736. The area of Missoun is 69,709 square miles and its population is 5,988,927. The average state population density is 87,4 people per square mile. How do the population densities of Alabama and Missouri compare to the national average?
Answer:
Alabama is greater than the national average Missouri is less than national average
Step-by-step explanation:
Find the pop densityof each state = people / mi^2
Alabama 4779736 / 51718 = 92.4 people per square mile
Missouri 5988927 / 69709 = 85.9 people per square mile
The dot plots below show the weights of the players of two teams:
Team C
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
Weight (pounds)
Team D
120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
Weight (pounds)
Based on visual inspection of the dot plots, which team appears to have the larger
mean weight? (5 points)
1. Not enough information is available to draw a conclusion
2. Both groups are similar
3. Team C
4. Team D
The value of the mean of team C and team D will be equal. Then the correct option is B.
What is Mean?The average of a group of numbers is simply defined as the mean. In statistics, the mean is regarded as one of the indicators of central tendency. Arithmetic mean is a term used to describe the average. It's the percentage of the actual number of observations to the sum of the observations.
The dot plots below show the weights of the players of the two teams:
Team C
120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140. Weight (pounds)
Team D
120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140. Weight (pounds)
Then the mean of team C will be
[tex]\mu _c = \dfrac{120 +121 +122 +123 +124 +.....+139 +140}{21}\\\\\mu _c = \dfrac{2730}{21}\\\\\mu _c = 130[/tex]
Then the mean of team D will be
[tex]\mu _d = \dfrac{120 +121 +122 +123 +124 +.....+139 +140}{21}\\\\\mu _d = \dfrac{2730}{21}\\\\\mu _d = 130[/tex]
Then the value of the mean of team C and team D will be equal.
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please help me im stuck
Answer: The mean is 6, mean also means the constence.
Step-by-step explanation:
6 is able to go into 10,20,30,40. But I maybe wrong, sorry if I am.
Fred bought 3 shirts and a tie. He remembers each shirt was $25, and the total cost was $85. How much was the tie?
Answer:
The tie is $10
Step-by-step explanation:
3 shirts were bought, so 25*3 is 75. The total cost is $85, you take 85 and subtract 75 from it and you get the cost of the tie, $10.
need help fast! 100 POINTS
Answer:
100 points ??? I see 5 points :]
What is the area of the base of the cone below? A cone with height 12 feet and volume 90 feet cubed. 2.5 feet squared 4 feet squared 22.5 feet squared 26 feet squared
Answer:
its C or 22.5
Step-by-step explanation:
Im doing the test right now
Answer:
22.5
Step-by-step explanation:
When Lance goes jogging, his heart rate increases to pump blood faster and
supply his muscles with more
oxygen to move quicker. Which two interaction
of body systems would help lance go back to homeostasis?
Select one:
•
muscular and circulatory
•
digestive and circulatory
•
excretory and circulatory
•
respiratory and digestive
The correct answer is option A
5sq km95 ha8,994sq m+11sq km11 ha9,010sq m
type english is the answer ok just learn HOW TO TYPE ENGLISH
Answer:
iou213 hr2938ru 298rh243 ru23y
Step-by-step explanation:
po2iu4jrt 2r 23r9p23 r,
r24lon24 f23 r293hr,
dgngo34 9,
Therefore, iou213 hr2938ru 298rh243 ru23y
Elijah’s home is 1.1km from the library
His journey from his home to the library, including a 2 minute stop on the way, is shown on the
graph below.
How much faster was Elijah travelling before his stop than afterwards?
Give your answer in km/h.
Elijah was travelling before his stop than afterwards with speed of 0.5 km/h.
What is formula to calculate speed or velocity?To solve for distance use the formula for distance d = vt, or distance equals speed times time. Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour.
Before his stop, the velocity =[tex]\frac{0.4km}{0.1 h}[/tex]
= 4 km/h
After his stop, the velocity =[tex]\frac{2.7km}{2.2 h}[/tex]
= 3.5 km/h
So, 4-3.5 km/h= 0.5 km/h
Elijah was travelling before his stop than afterwards with speed of 0.5 km/h
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find the value of p and x
Answer:
see photo for detailed analysis
Step-by-step explanation:
Find the area of the figure below, formed from a triangle and a rectangle, in square centimeters.
Answer:
44 square cm
Step-by-step explanation:
Total Area = Area of triangle + Area of rectangle
= (1/2 * base * height) + (Length*Width)
= (1/2 × 8 × 6) + ( 10 × 2)
= 24 + 20
= 44 square cm
