Answer:
[tex]2000 \: and \: 9.[/tex]
[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]
Let's consider a much smaller value and work our way up to the factorial 2009!
Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.
The only solution to a+b = 2 is a = b = 1 as mentioned.
----------
Now move onto a+b = 3. We have two solutions:
a = 1, b = 2
a = 2, b = 1
-----------
Now move onto a+b = 4. We have three solutions
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.
So 'a' counts up to 3, while b counts down from 3.
We cannot reach 4 since 0 is not allowed for a or b.
-------------
The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so
a = 1, b = k-1
a = 2, b = k-2
a = 3, b = k-3
....
a = k-3, b = 3
a = k-2, b = 2
a = k-1, b = 1
Where k > 2
Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.
This confirms there are k-1 solutions listed above.
The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions
Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!
Jane and her friends are going on a hiking trip. Jane wants to make snack packs to take on a trip. She has 24 apples and 36 small bags of trail mix. Each snack pack must have the same number of apples and the same number of bags of trail mix. What is the greatest number of snack packs Jane can make? Explain.
Answer:
The greatest number of snack packs Jane can make is 12 snack packs
Step-by-step explanation:
We solve this question using the greatest common factor method
First step would be to find the factors of 24 and 36
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor amongst the above factors for 24 and 36 is 12.
Therefore, the greatest number of snack packs that she can make is 12 packs.
If a zombie sleep for 96436 year but woke up 329 years ago how long did really sleep?
Answer:
96436-329 = 96107
Step-by-step explanation:
Given that 1 pound equals 16 ounces, how many pounds are in 116 ounce -) A) 6.75 pounds B) 7.25 pounds 7.5 pounds D) 7.75 pounds
Answer:
B)7.25
Step-by-step explanation:
16x7.25=116
write an expression that is equivalent to 25x^2 -20x + 4
12x - 7 = -3x + 8
Uhhh answer plsss
Answer:
x = 1
Step-by-step explanation:
Rearrange
12x + 3x = 8 + 7
Simplify
15x = 15
x = 1
Write an equation of a line in slope-intercept form, which is passing through the point (8, −6) and is parallel to another line, whose slope is −2
Answer:
y=-2x+10
Step-by-step explanation:
slope intercept is written as y=mx+b
the slope or m is -2 and using the slope we can calculate a y-intercept or b of 10.
hope this helps!
Answer:
y=-2x+10
Step-by-step explanation:
Hello there!
First the equation of a line is y=mx+b (m is the slope and b is the y-intercept)
Plugging in the formula, the problem already gives you the slope, which is -2, so y=-2x+b
Next, we have to find the y-intercept! We have a pair, (8,-6), so we can plug that into the current equation we have:
-6 = -2*8 + b
-6 = -16 + b
(add 16 to both sides)
10 = b (or b=10)
Now that we have all of the parts we need, our answer will be y=-2x+10
Hope this helped!
solve to simpilist form 3/4/2 . (3 on top of 4/2) :D
Answer:
5/1
Step-by-step explanation:
Which statement is true for the values of P and Q on this number line? P Q + + + + -2 -1 0 1 -6 -5 -4 لی A) ?>4 (B) PxQ< 5 CP+Q>-4 D P-Q > 0
Answer: B
Step-by-step explanation:
Simplify
-5y - X + 7 - 2y + 3x + 4
Answer:
-7y + 2x + 11
Step-by-step explanation:
-5y - X + 7 - 2y + 3x + 4
-7y + 2x + 11
Answer: 2x-7y+11
Step-by-step explanation:
Add the x's and then add the y's. add the 4 and seven because they do not have a variable.
Estimate this by rounding each number to 1 significant figure
a. 326 X 4.89
HELP. What are the coordinates of -2.5, 2.5 when rotated 180 degrees
Help me someone please I’m lost and confused??
Answer: go to Cymath
Step-by-step explanation: This helped me with like everything in math class! It gives you step by step answers
there are 48 newborn girls in a hospital nursery. For every 3 girls, there are 2 boys. How many newborn babies are in the nursery?
Hi! I believe your answer is 80 newborn babies. To find the number of boys, divide 48 by 3 (since it is for every 3 girls) and you'll get 16. Next, multiply 16 and 2 (for every 2 boys) and you'll get 32. Lastly, add 48 and 32 and you'll get the number of newborn babies in the nursery (80). I hope this helps you! Good luck and have a great day. ❤️✨
Number of total newborn babies = 80
What is ratio?A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.
Given,
Total number of girls = 48
For every 3 girls, there are 2 boys.
Ratio of girls to boy = 3/2
Let there are x boys,
then,
48/x = 3/2
3x = 96
x = 32
Number of boys = 32
Total newborn babies = Number of girls + number of boys
= 48 + 32 = 80
Hence, 80 newborn babies are in nursery.
Learn more about ratio here:
https://brainly.com/question/1504221
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A skateboarder rides by my office every 9 minutes, and a cyclist rides by every 6 minutes. How long will it take for the skateboarder and cyclist to ride by at the same time?
Answer:
6:00
Step-by-step explanation:
The time taken by the skateboarder and cyclist to ride by at the same time is given by A = 18 minutes
What is HCF and LCM?The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the skateboarder rides by the office every 9 minutes
And , a cyclist rides by every 6 minutes
Now , time taken by the skateboarder and cyclist to ride by at the same time be A
where A = LCM of the two numbers
So , the smallest time interval at which both events occur. In other words, we need to find the least common multiple (LCM) of 9 and 6.
Factors of 9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
Factors of 6 : 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
So , common multiple and the LCM is 18
Hence , the time taken is 18 minutes
To learn more about LCM and HCF click :
https://brainly.com/question/20049151
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Help !! Least to greatest -1 1/3 , - 1 8/9 , 1 3/4 , 1 1/2
Answer:
1. [tex]-1[/tex] [tex]\frac{1}{3}[/tex]
2. [tex]-1[/tex] [tex]\frac{1}{2}[/tex]
3. [tex]1[/tex] [tex]\frac{1}{2}[/tex]
4. [tex]1 \frac{3}{4}[/tex]
-1 1/3 is the least of all the numbers. So, this is the first number.
-1 1/2 is the second least number. So, this is the second number.
1 1/2 is the third least number. So, this is the third number.
Finally, 1 3/4 is the greatest number, so it is the fourth number.
Hope this helps you!
how many inches are in a 20 foot rope
Answer:240 inches
Step-by-step explanation:
Answer:
240 in.
Step-by-step explanation:
1 foot is equal to 12 inches. Being that there are 20 feet you would multiply 20 by 12 and get 240.
3 2/3 x 4 1/8 x 2 1/2
Answer:
=2/3^x62
Step-by-step explanation:
32/3^x41/8x21/2
Numbers like 10, 100, 1,000, and so on are
called?
Graph the inequality:
y < − abs(x−3)−2
Answer:
suck dic
Step-by-step explanation:
someone please help me with this problem
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
Why am not being allowed to login?
Answer:
mine is doing the same thing
Step-by-step explanation:
What is the equation of the line that passes through the point (3, -5) and has a
slope of 2/3?
The sand pit has a width of 2.56meters and a length of 8.75meters. Just in case it rains, the principal wants to cover the sand pit with a piece of plastic the night before the event. How many square meters of plastic will the principal need to cover the sand pit
Answer:
The answer is below
Step-by-step explanation:
The piece of plastic needed to cover the sand pit is the same as the area of the sand pit. Since the sand pit has a width of 2.56meters and a length of 8.75meters, it means that the sand pit is rectangular in shape. The area of the sand pit is given by the formula:
Area = length × width
Area = 2.56 meters × 8.75 meters
Area = 22.4 m²
The plastic needed to cover the sand pit needs to have an area of 22.4 m²
what is 87 divided by 15 with remainder
\
Answer:
5.8
Step-by-step explanation:
87/15 = 5.8
Which is a solution of 2(t-1)+3t<2?
t < 0.8
t ∈ ( - oo ; 0.8 )
Step-by-step explanation:Hi there !
2(t - 1) + 3t < 2
2t - 2 + 3t < 2
5t < 2 + 2
5t < 4
t < 4/5
t < 0.8
t ∈ ( - oo ; 0.8 )
Good luck !
What is the expression in factored form?
2x^2+ 19x + 24
Answer:
factor by group the answer will be (2x+3)(x+8)
Step-by-step explanation:
Mark as Brainliest!!!Hope this Helps:)
can u guys help me pls
Answer: The answer to number 1 is 91 adults
Step-by-step explanation: Since 1 on the ratio is 13 people, 13 x 7 is 91.
which three points in the figure are collinear?
Answer:
A, D, and E
Step-by-step explanation:
A, D, and E all fall on the same line, therefore, they are all collinear.
Pls help...
It is chose from A, B or C
Thanks
Answer:
The answer would be 'C'
It follows the criteria accurately.
(-45) + (+3) =
A -42
B -40
C 40
Answer:
Step-by-step explanation:
-42