![[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/5pKwNW1qN0qsSwLrjpPKodTl0pJvkl4S.jpeg)
Answers
(A) (m,n) = g(n,m) for all positive integers m,n,
(B) (m,n + 1) = g(m + 1,n) for all positive integers m,n,
(D) (2m,2n) = (g(m,n))2 for all positive integers m,n
Explanation[tex] \rm f(m,n,p) = \sum \limits_{i = 0}^{p} {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + i} C_{p} \: \: {}^{p + n} C_{p - i}[/tex]
[tex]\rm {}^{m} C_{i} \dfrac{(n + i)!}{p!(n - p + i)!} \times \dfrac{(n + p)!}{(p - i)!(n + i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!} \times \dfrac{1!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \times \dfrac{(n + p)!}{p!n!} \times \dfrac{n!}{(n -p + i)!(p - i)!} [/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex]\rm {}^{m} C_{i} \: \: {}^{n + p} C_{p} \: \: {}^{n} C_{p - i} \: \: \{{}^{m} C_{i} \: \: {}^{n } C_{p - i} = {}^{m + n} C_{p } \}[/tex]
[tex] \rm f(m,n,p) = {}^{n + p} C_{p}{}^{m + n} C_{p}[/tex]
[tex] \rm \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} = {}^{m + n} C_{p}[/tex]
Now,
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} \dfrac{f(m,n,p)}{{}^{n + p} C_{p}} [/tex]
[tex] \rm g(m,n) = \sum \limits_{p = 0}^{m + n} {}^{m + n} C_{p}[/tex]
[tex] \rm g (m,n) = {2}^{m + n} [/tex]
[tex] \rm(A) \: g(m,n) = q(n,m)[/tex]
[tex] \rm(B) \: g(m,n + 1) = {2}^{m + n + 1} [/tex]
[tex] \rm g(m + n,n ) = {2}^{m + 1 + n} [/tex]
[tex] \rm(D) \: g(2m,2n) = {2}^{2m + 2n} [/tex]
[tex] = \rm( {2}^{m + n} {)}^{2} [/tex]
[tex] = \rm(g(m,n)) {}^{2} [/tex]
Related Questions
32 - (4 x s) = 12
What does the s stand for?
PLEASEEE HELPPPP
ASAP 20 POINTS!!!!!
Answers
Answer:
5.
Step-by-step explanation:
32-20-12.
In 2002, a school population was 1655. By 2008 the population had grown to 2711.
1) How much did the population grow between the year 2002 and 2008?
Answers
2002 School Population-1655
2008 School Population-2711
The Growth of Population between the years 2002 and 2008
= 1056 students
Therefore, the population grew by 1056 students between the years of 2002 and 2008.
Car A is rated at 36 mi/gal (miles per gallon) for city driving and 28mi/gal for highway driving. Car B is rated at 29 mi/gal city and 37 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving?
(a) 300 mi of city driving plus 100 mi of highway driving
(b) 100 mi of city driving plus 300 mi of highway driving
Question content area bottom
Part 1
(a) Car A consumes
enter your response here gallons; Car B consumes
enter your response here gallons.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
(b) Car A consumes
enter your response here gallons; Car B consumes
enter your response here gallons.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
Car A consumes 11.9 gallons.
Car B consumes 13 gallons
Car A consumes 16.3 gallons
Car B consumes 11.6 gallons
How many gallons would be used?In order to determine the required values, the mathematical operation that would be used is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
Gallons that would be consumed when driving 300 mi of city driving plus 100 mi of highway driving:
For Car A = (300 / 36) + (100 / 28) = 11.9 gallons
For Car B: (300 / 29) + (100 / 37) = 13 gallons
Gallons that would be consumed when driving 100 mi of city driving plus 300 mi of highway driving:
For Car A = (100 / 36) + (300 / 28) = 16.3 gallons
For Car B: (100 / 29) + (300 / 37) = 11.6 gallons
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QUESTION 8 Nigel received a student loan for $9467. If his tuition was $4997.94, textbook costs $854.84, student fees $702.88, and school supplies $80.41, how much did Nigel have left after paying all his school related expenses? Round your answer to the nearest cent. 3 poin
Answers
4997.94
+ 854.84
——————
5852.78
+ 702.88
—————-
6555.66
+ 80.41
—————
6636.07
2. Subtract
9467.00
-6636.07
——————
2,830.93
What are the degree and leading coefficient of the polynomial? 18u - 8u^2 -9 + u^7
Answers
The leading coefficient and degree of the polynomial 18u - 8u^2 -9 + u^7 are 1 and 7 respectively.
According to the given question.
We have a polynomial 18u - 8u^2 -9 + u^7.
As we know that the leading coefficient of a polynomial is the coefficient of the leading term.
And the highest and the greatest power of a variable in a polynomial equation is called degree of a polynomial.
Here, the leading term of the given polynomial is u^7. Therefore, the leading coefficient of a polynomial is 1.
And the degree of the polynomial is 7.
Hence, the leading coefficient and degree of the polynomial 18u - 8u^2 -9 + u^7 are 1 and 7 respectively.
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Alesha went to the movies. A popcorn is $3 more than a soda. She purchased 1 popcorn and 2 sodas. She spent $21. How much is a popcorn?
Answers
Answer: a popcorn is $9
Step-by-step explanation:
soda is $6
Zoey needs to order some new supplies for the restaurant where she works. The restaurant needs at least 711 glasses. There are currently 281 glasses. If each set on sale contains 10 glasses, use the drop-down menu below to write an inequality representing
s
s, the number of sets of glasses Zoey should buy
Answers
The inequality that represents the number of sets of glasses Zoey should buy is s ≥ 43
What is the inequality?The first step is to determine the number of glasses needed.
The number of glasses needed = 711 - 281 = 430
The second step is to determine the number of sets Zoey needs to buy.
Number of sets needed = 430 / 10 = 43 sets
The third step is to determine the appropriate inequality sign to use
Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe ≥ (greater than or equal to ) would be used since the number of sets can either be equal to or greater.
s ≥ 43
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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mpb? What is always true about the product speed x time?
Answers
The times associated with each speed are:
20 h10 h6.667 h5 h4 hIt is always true that the speed is inversely proportional to time.
How to analyze the motion of a bicycle at constant speed
In this case we find the situation of bicycle moving at constant speed, where the traveled distance (s), in miles, is equal to the following expression:
s = v · t (1)
Where:
v - Speed, in miles per hour.t - Time, in hourNow we proceed to calculate time needed for each speed:
t = s / v
Case 1
t = 100 mi / 5 mi / h
t = 20 h
Case 2
t = 100 mi / 10 mi / h
t = 10 h
Case 3
t = 100 mi / 15 mi / h
t = 6.667 h
Case 4
t = 100 mi / 20 mi / h
t = 5 h
Case 5
t = 100 mi / 25 mi / h
t = 4 h
According to the model for rectilinear uniform motion, the speed is inversely proportional to time.
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convert each of the following base-ten numberals in the indicated bases
456 in base 5
Answers
Answer:
3311
Step-by-step explanation:
The steps are as follows
1. Divide 456 by 5. This gives a quotient of 91 with a remainder of 1. This remainder becomes the least significant digit of the new base number. This would be the right most digit. So the number is _ _ _ 1
2. Take the quotient, 91, divide by 5 again. This gives a quotient of 18 with a remainder of 1. Put this remainder to the immediate left of the previous value. So we have the number as _ _ 1 1
3. Take the previous quotient, 18, divide by 5 again. 18/5 gives quotient of 3 with a remainder of 3. Put this to the immediate left of the previous number giving the number as _ 3 1 1
4. Repeat the division of the new quotient by 5. 3/5 gives a quotient of 0 with remainder of 3 so we stop
Number = 3 3 1 1
Best done by writing a program or using a calculator
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 91 ?
Answers
Answer:
Mark has 18 and Don has 73
Step-by-step explanation:
Let M = Mark and let D = Don
D = 4M + 1
D + M = 91
Substitute and solve for M
4M +1 + M = 91
5M = 90
M = 18
Therefore D = 4(18) + 1 = 73
Construct an angle of measure 45° with the help of a protractor. Bisect it and find the measure of the bisected angles .
Answers
Answer:
See attachment
Step-by-step explanation:
Draw a 45o angle
Bisecting means dividing the angle into 2 halves, which is 22.5o each
The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? (10w +22v) (-2+14w + 22v) (22v + 10 )( 11v +5 )
Help asaP!!!
Answers
Answer:
(22v and 10w)
Step-by-step explanation:
A rectangle is a 4 sided figure. Perimeter is the distance around the rectangle. The total distance would be
(5v -2w) + (5v - 2w) + (6v+7w) + (6v + 7w) Add all the like terms together
5v + 5v + 6v + 6v - 2w - 2w + 7w + 7w
The v's add up to 22 and the w's add up to 10
The dividen is greater that 1,000, The quotient of 52 with a remainder of 18
Answers
The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variable called division.
Let's consider a division problem.
5/2 → 2 + 1
Here 5 is called the dividend,2 is the divisor,2 is the quotient, and 1 is the remainder.
Now,
2 × 2 + 1 = 5
Therefore,divisor × quotient + remainder = dividend
So,
Let's suppose the divisor in the given case is x
Now,
52x + 18 ≥ 1000
52x ≥ 982
x ≥ 18.86
Hence "The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86".
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The given question is incomplete complete question is ;
What is the minimum divisor such that The dividend is greater than 1,000, The quotient of 52 with a remainder of 18
Consider a set of data in which the sample mean is 30.9 and the sample standard deviation is 7.7. Calculate the z-score given that x = 31.1. Round your answer to
two decimal places.
Answers
The value of the z-score is calculated as 0.259.
What is descried as normal distribution?The standard normal distribution is the variable of a normal distribution to mean 0 and variance 1. The normal distribution follows a bell curve. The z-table aids in determining the area beneath the curve.
The normal distribution is also known as the Gaussian distribution, after just a German mathematician.The t-distribution is another distribution that may be described as having a bell shape. It differs as from normal distribution in that the tails are thicker. It is commonly employed in the analysis of small sample size datasets.Now, as per the given question;
The formula for the z-score is;
z = (x - μ)/σ
x = sample size
σ = standard deviation
μ = mean of the sample
For the given values in the question;
x = 31.1
σ = 7.7
μ = 30.9
Substitute the given values in the formula to fine z-score;
z-score = (31.1 - 30.9)/7.7
z-score = 0.259
Therefore, the value of the z-score is computed as 0.259.
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1. The price of one kg grapes is 60p, find the total price of 30 kg grapes in pounds.
2. The price of one kg carrots is 35p, find the total price of 40-kg carrots in pounds.
3. The price of one kg grapes is 60p and the price of one kg bananas is 40p per kg, find the total price of 30 kg grapes and 40kg bananas in pounds.
4. The price of one kg oranges is 90p and the price of bananas is 30p per kg, find the total price of 30 kg oranges and 40kg bananas in pounds
Answers
Maths:
Round 1
1) Grapes cost £1.50 per kg and carrots cost £1.00 per kg. How much would it costs for 3kg of
grapes and half a kilogram of carrots? £5
2) Jenny decides to share her sweets between herself and her 3 friends. She has 212 green
sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jenny and her friends
get each? 256
3) Large chocolate bars come with 32 pieces. Medium chocolate bars come with 24 pieces.
Barry buys 8 large bars of chocolate and 6 medium bars. How many pieces of chocolate will he
have altogether? 400
4) A flower shop sells roses for £1.79, carnations for £1.25 and buttercups for £1.30. Holly
decides to buy 3 roses and a buttercup. How much does she spend? £6.67
5) Pencils come in packs of 12 and each pack costs £1.19. Mr Green needs to buy a pencil for
each of the 50 children in his class. How much will he spend on pencils? £5.95
Round 2
1) Mrs Orange decides to share her savings between her six grandchildren. She has £350 in
her savings tin and £1450 in her savings account. How much will each of her grandchildren get?
£300
2) Green lollipops come in packs of 5, yellow lollipops come in packs of 6 and blue lollipops
come in packs of 4. A school buys 32 packs of blue lollipops and 18 packs of green lollipops.
How many lollipops will they buy altogether? 218
3) The baker’s oven can bake 28 loaves of bread at a time. In a day, it can go through 30 full
bakes. How many loaves of bread would be baked after 1 week? 5880
4) Ms Purple sells cars for a living. In one day, she sells 2 blue cars (at £4500 each), 7 yellow
cars (at £6000 each) and 12 black cars (at £8000 each). How much money does she take in car
sales in that one day? £147,000
5) Coaches carry 58 people. A school decides to take its 300 pupils and 38 staff on a visit to the
beach. A single coach costs £128. How much will the total cost of the coaches come to? £768
Topic:
Fruit Veg
Quince
raspberry
Lettuce
garlic
tomato
strawberry
grape
pumpkin
blackberries
nashi
kiwi
chilli
pear
passion fruit
cantaloupe
fig
eggplant/aubergine
cucumber
lemon
peach
lime
watermelon
pineapple
Zucchini/courgette
grapefruit
persimmons
mango
plum
cauliflower
Broccoli
Leeks
Fennel
Carrots
Coriander
Silverbeet
Snow peas
Beans
Celery
Beetroot
Peas
Artichoke
Sweet potato
Please help solve number 24
Answers
Check out the attached photo
At the movie theatre, child admission is $5.90 and adult admission is $9.00. On Saturday, 137 tickets were sold for a total sales of $1003.60. How many adult tickets were sold that day?
Answers
The number of adult tickets, that were sold that day at the movie theatre was 62
What are simultaneous equations?
Simultaneous equations are two or more equations that must be solved concurrently in order to derive the values of the unknown, the total sales, as well as the total number of tickets sold, can be modeled into equations as below:
let x be the number of adult tickets
let y be the number of children's tickets
9x+5.90y=1000.60....... equation 1
x+y=137.................. equation 2
solve for y in equation 2
y=137-x
substitute for y in equation 1
9x+5.90(137-x)=1000.60
9x+808.30-5.90x=1000.60
9x-5.90x=1000.60-808.30
3.10x=192.30
x=192.30/3.10
x=adult tickets=62
children tickets=137-62
children tickets=75
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below
(3 - i)(3 + 1) =
Answers
Answer:
12-4i
Step-by-step explanation:
i means √-1
(3 - i)(3 + 1) =
3*3=9
3*1=3
-i*3= -3i
-i*1 = -i
9+3-3i-i=
12-4i <--- answer
(3 - i)(3 + i) =
3*3=9
3*i=3i
-i*3= -3i
-i*i = -(√-1)*(√-1) = -(-1) = 1
9+3i-3i+1 =
10 <--- answer
Vicente is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 10 years. Determine what Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years.
Answers
The amount Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years is $15,384.62
What is simple interest?
The simple interest on the savings is determined as the deposit multiplied by the annual interest rate and the number of years that deposit would last in the account
I=PRT
I=simple interest
P=principal=deposit=unknown
R=annual simple interest=3%
T=number of years=10
A(amount in 10 years)=P+PRT
A=P(1+RT)
$20,000=P(1+3%*10)
$20,000=P*1.30
P=$20,000/1.30
P=$15,384.62
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In Florida, as of Nov 19, 1,020,000 had people tested positive for corona virus. This was a
0.18% increase from the previous day. If that percent increase continued, how many people
would be infected on Dec 19th?
Answers
The number of people that would be infected on Dec 19th, based on the daily growth rate of 0.18% is 1,076,542
What is interval in days between Nov. 19th and Dec.19th?
The interval between November 19th and December 19th is a period of 30 days, since there are 11 more days in November and 19days in December, in essence, using the future value formula, we can compute the number of people tested positive for corona virus on 19th December as shown below:
FV=PV*(1+g)^N
FV=number of people tested positive for corona virus on 19th Dec.=unknown
PV=number of people tested positive for corona virus on Nov. 19th=1,020,000
g=growth rate=0.18%
N=number of days between 19th Nov. and Dec.
FV=1,020,000*(1+0.18%)^30
FV= 1,076,542
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Answer for this please see image attached m
Answers
3x+18
-18. -18
3x=162
x=54
54+11=65=a
54+7=61=c
b=54
If it is asking you for the whole triangle then 180, all triangles equal 180 degrees
Answer:
angle A=125 angle B= 114 angle C= 121
Step-by-step explanation:
first you have to find x so that you can find each angle
the interior angles of a triangle is equal to 360
add the angles together x+x+7+x+11=360
combine like terms 3x+18=360
subtract 18 on both sides 3x=342
divide by 3 on both sides x=114
to find angles:
plug in X to each side
(114)+7 = angle C
(114)+11= angle A
114= angle B
If angle YXZ measures 90 degrees, which statement is true?
(answers are below)
segment XZ is perpendicular to segment WY
WX =XY
segment XZ is a perpendicular bisector of segment WY
X is the midpoint of segment WY
Answers
The true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
What are Perpendicular Segments?Perpendicular segments are line segments that intersect at a point to form right angles which is equal to 90 degrees. The point where perpendicular segments meet have an angle measure of 90 degrees.
In the given diagram, we are told that angle YXZ is equal to 90 degrees. This means that at the point where segment XZ and segment WY meet have an angle measure of 90 degrees.
This means they are perpendicular segments.
Therefore, the true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
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NO LINKS!! Please help me with these problems. Part 4a
Answers
Answer:
(a) --> f(x) = -(x - 4)²
(b) --> f(x) = x² + 3
(c) --> f(x) = (x - 2)²
(d) --> 6. f(x) = 3 - x²
Parent function of all the graphs is y = x²
(a)
The graph makes a sad face meaning the coefficient will be negative.
Comparing to the parent function y = x², the graph has been translated 4 units to the right.
Equation: f(x) = -(x - 4)²
(b)
The graph makes a happy face meaning the coefficient will be positive.
Comparing to the parent function y = x², the graph has been translated 3 units up.
Equation: f(x) = x² + 3
(c)
The graph makes a happy face with translation 2 units to the right.
Equation: f(x) = (x - 2)²
(d)
The graph makes a sad face with translation 3 units up across y axis.
Equation: f(x) = -x² + 3
Translation rules:f(x + a) : translation a units left in the x axis.
f(x - a) : translation a units right in the x axis.
f(x) + b : translation b units up in the y axis.
f(x) - b : translation b units down in the y axis.
The city of Raleigh has 10,300 registered voters. There are two candidates for City Council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 300 randomly selected registered voters was conducted. 9595 said they'd vote for Brown, 182 said they'd vote for Feliz, and 23 were undecided.
Answers
Answer:
What do I solve for?
Step-by-step explanation:
Find the difference. 5 1/9 - 3 4/9
A.
B.
C.
D.
Answers
Answer: 1 6/9, or 1 2/3
Step-by-step explanation:
Regroup the 5 and 1/9 to get 4 10/9. Subtract the 3 4/9 from the 4 10/9, getting 1 6/9. Simplified, this is 1 2/3. Hope this helps!
Which describes the collection of all points in the same plane that are 81/2 inches from point T
Answers
The figure will be a sphere with center T and radius 8 1/2 inches, that is, option D.
A circle is a closed curve constituting of the set of all points in a plane that are equidistant from a given point. This point is the center of the circle and the distance is the radius of the circle.
A circle is a 2-dimensional figure, and the two dimensional does not contain the set of all points in the 3-dimensional plane.
A sphere is a round geometrical object and is the set of all points that are equidistant from a given point, in the three-dimensional space.
Here, we are given that there is a point T and we need to describe the collection of all points in the same plane that are 8.5 inches from point T.
Going by the definitions given above, we can infer that it is a sphere with center T and radius 8.5 inches. If we take it to be a circle then it will not include the points in the 3D plane, hence, sphere.
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Your question was incomplete, check for the full content below-
Which describes the collection of all points in the same plane that are 8 1/2 inches from point T?
A.) Circle T with radius 8 1/2 inches
B.) circle T with diameter 8 1/2 inches
C.) circle T with radius 17 inches
D.) a sphere with center T and radius 8 1/2 inches
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York.
Three adults and four children must pay $116
Two adults and three children must pay $82
Find the price of the adult's ticket and the price of a child's ticket.
Answers
The price of the adult's ticket is $20 and the price of a child's ticket is $14.
How to calculate the valuesLet adults = a
Let children = c
The appropriate equation will be:
3a + 4c = 116
2a + 3c = 82
Multiply equation I by 2
Multiply equation ii by 3
6a + 8c = 232
6a + 9c = 246
Subtract
c = 14
Price for children = 14
Since 2a + 3c = 82
2a + 3(14) = 82
2a + 42 = 82
2a = 82 - 42
2a = 40.
a = 40/2
a = 20
Therefore, the price of the adult's ticket is $20 and the price of a child's ticket is $14.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
3,18/5, 108/25...
Find the 10th term
Answers
Answer:
15.479
Step-by-step explanation:
This is a geometric series with common ratio of 6/5
Any term is 6/5 times the previous term
The general formula for the nth term of a geometric series given the common ration r and the first term a₁ is
[tex]a_n = a_1\cdot r^{n-1}[/tex]
Here r = 6/5 and n = 10
So the 10th term is
[tex]a_{10} = 3\cdot(\dfrac{6}{5})^9[/tex]
= 3 x (6⁹/5⁹) = 3 x (10077696/1953125) = 30233088/1953125 = 15.479
how many days will it take to finish a 20 pound bag of rice when you use 0.4 pounds each day
Answers
Answer:
50
Step-by-step explanation:
divide 20 by 0.4
= 20/0.4 = 20 * (1/0.4)
= 20*2.5
= 50
Step by step explanation:
20/0.4 = 50
How do you solve this??
Answers
Answer: 0.100
Step-by-step explanation: In the table, it shows that the number of people who have a Bachelor's Degree AND are aged 50 or over is 1958. The total amount of residents in the town are 19623. 1958/19623 gives us the probability. In decimal, the answer is 0.09978086938, which rounds to 0.100