Answer:
37 is the smallest positive integer n such that n(n+1)(n+2) is divisible by 247.
Step-by-step explanation:
First we will find the prime factors of 247:
247 = 13 x 19 (which are both prime).
So now we need to find a number (the smallest one) that is of the form (n)(n+1)(n+2) (the product of three consecutive numbers) and that is divisible by both 13 and 19 (and therefore divisible by 247)
Let's take a look at the multiples of 13: 13, 26, 39, 52...
Let's take a look at the multiples of 19: 19, 38, 57...
We can see that the first time we have two multiples close together are the 38 (for 19) and the 39 (for 17).
So, if our number has both 38 and 39 as factors, then it will be divisible by 247.
However, we need not two but three consecutive numbers, and since we want the number to be the smallest positive integer, we will add 37 (since our other choice would be to add 40 and that would make the number bigger) and thus our number is (37)(38)(39) or in other words (37)(37 + 1)(37 + 2) and therefore this is the smallest positive number such that n(n+1)(n+2) is divisible by 247.
The smallest positive integer n such that n(n+1)(n+2) is divisible by 247 is 37.
n(n+1)(n+2) is divisible by 247
Then, n(n+1)(n+2) =247k, where k is an integer
so, [tex]k = \frac{n(n+1)(n+2)}{247}[/tex]
What is an integer?An integer is a number that is not a fraction but a whole number.
Since the prime factors of 247 are 19 and 13.
By hit and trial let us choose the value of n such that n *(n+1) or (n+1) *(n+2) or n *(n+2) become the multiples of 19 *13.
If n = 37
n+1 = 38
n+2 = 39
So, if n=37, ( n+1 )*(n+2) will get divided by 19*13
So, the smallest possible integer 'n' will be 37.
Therefore, the smallest positive integer n such that n(n+1)(n+2) is divisible by 247 is 37.
To get more about the number system visit:
brainly.com/question/17200227
A baker had 1,128 cookies. She put them all in bags, with 24 cookies in each bag. What is the total number of bags that she used?
Please help I will give branlyest
Answer:
3
Step-by-step explanation:
1.3.39
Two minor league baseball players got a total of 312 hits. Washington had 2 more hits than Sanchez. Find the number of hits for each player.
the question.
A flagpole has a height of 25 meters. There are approximately 3.3 feet in 1 meter.
How tall is the flagpole, in feet, rounded to the nearest tenth?
Answer:
Step-by-step explanation:53
The height of the flagpole is 82.5 feet.
What is unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that a flagpole has a height of 25 meters.
We know that there is 3.3 feet in 1 meter.
1 meter=3.3 feet.
Now we have to find the height in feet.
So we have to multiply twenty five with three point three
25×3.3=82.5 feet
25 meters=82.5 feet.
Hence, a flagpole has a height of 82.5 feet.
To learn more on Unit of Measurement click:
https://brainly.com/question/15402847
#SPJ2
HELP PLZ 50 POINTS FOR REWARD
if you could help it'd mean the world to me
Answer: 22
Step-by-step explanation: because if you read it carefully and do math you are sure to get it right!! :)
For 1-3, use the graph of the quadratic function.
A
1- Write the Domain of the functions as an inequality, using set notation and interval notation
Inequality_________
Set notation _______
Interval notation______
2- write the range of the function as an inequality. Using set notation and interval notation
Inequality _______
Set notation _______
Interval notation ________
Describe the end behavior of the function ( as x gets bigger and smaller, what happen to y)
____________
____________
Answer:
Step-by-step explanation:
From the picture attached,
Function given is a parabola, therefore, function is a quadratic function.
Domain of the function : x-values(input values) on the graph
: -∞ ≤ x < ∞
Domain in set notation : {x | x ∈ All real numbers}
Domain in the form interval notation : (-∞, ∞)
End behavior of the function : As both the ends of the function are downwards towards the infinity,
: As x → ∞, y → -∞ [Right end]
: As x → -∞, y → -∞ [Left end]
Find the LCM of 3 and 4
Answer:12
Step-by-step explanation:
May someone help me out?
=============================================
Explanation:
We can set up the following proportion
a/b = c/d
where the numerators 'a' and 'c' represent the scaled down dimensions, and b and d represent the actual real life dimensions.
For this particular problem, we have to keep in mind that 'a' and 'c' are in cm; while b and d are in inches.
So we could have
a = 16.8 cmb = 84 inchesc = 15 cmd = x inches, where x is unknown for nowSince d is in inches, this makes x be in inches as well.
------------------
Let's solve for x
a/b = c/d
16.8/84 = 15/x
16.8x = 84*15 ..... cross multiply
16.8x = 1260
x = 1260/16.8
x = 75
The suspect is 75 inches tall. This converts to 75/12 = 6.25 feet or 6 feet 3 inches (since 0.25 ft = 0.25*12 = 3 ft)
On Monday Elaine ran 5 miles and 3 laps around a trail. On Tuesday she ran 6
miles and 2 laps aorund a trail. She ran the same distance both days. How many
miles long is one lap around the trail?
Answer:
3 laps
Step-by-step explanation:
I think
(d) Given: AB = 4; in and AC = 3
Find: The length of BC or BC
What the answer??
Luke buys 4 tickets for a concert The total cost is 65.80.How much does he pay for each ticket
Answer:
$16.45
Step-by-step explanation:
Divide the total price by the number of tickets.
$65.80/(4 tickets) = $16.45/ticket
Answer: 16.45
Step-by-step explanation:
Total Money = 65.80
Number of tickets Luke buys = 4
Cost of 1 ticket = 65.80/4 = 16.45
Therefore, one ticket costs 16.45
On a number line, the coordinates of X, Y, Z, and W are −7, −2, 2, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and ZW
both drive at a constant speed for 45 minutes, but your speed is 40 miles per hour and your friend’s speed is 35 miles per hour. What is the total distance between your town and your friend’s town?
Answer:
Your distance: 1800 miles Your friend's distance: 1575 miles
Total: 3375 miles
Step-by-step explanation:
Distance= S * T
The s stands for speed and t for time.
Your distance:
D= 45 * 40
D= 1800 miles
Your friend's distance:
D= 35 * 45
D= 1575 Miles
Total distance: 1800 + 1575 = 3375 MILES
HOPE IT HELPED
Point A' is the image of point A under a rotation about the origin, (0,0).
y
1
7
6
A.
5
4
3-
2
1-
-7-6-5-4-3-2
2 3 4 5 6 7
-2
-3
-4
-5
-6
-7-
Answer: it’s 180 degrees
Step-by-step explanation: answered on khan academy
(3.rº – 7x + 2) - (2x² – 4x + 5)
Simplify this^
Answer choices :
A. x2 -11x - 3
B. x2 - 3x + 7
C. x2 -3x -3
D. x2 - 11x + 7
Answer:
choice C: x2 -3x -3
Step-by-step explanation:
(3x^2-7x+2)-(2x^2-4x+5)
becomes
3x^2-7x+2 -2x^2+4x-5
adding
3x^2-2x^2 -7x+4x +2-5
which is
x^2 -3x -3
2,236.8 to the nearest ten
Answer:
Already rounded to the nearest tenth.
2236.8
Step-by-step explanation: k
Answer:
2240
Step-by-step explanation:
find the number in the ten place (3) and look one place to the right for rounding digit 6. Round up if this number is greater than or equal to 5 and round down if it is less than 5.
For every three girls taking classes at a martial arts school, there are 4 boys who are taking classes. If there are 236 boys taking classes, predict the number of girls taking classes at the school
Answer:
177 girls
Step-by-step explanation:
3:4 = girls:boys
3:4 = ?:236
3 = ?
4 = 236
236 divided by 4 equals 59.
Multiply the number of girls by 59 to get your answer.
3*59=177
3:4 = 177:236
girls:boys girls:boys
Four times the number x increased by 15 is 83
Answer:
17
Step-by-step explanation:
83-15=68
68/4=17
Solve the following Equations
A)x-1=5
B)2m-1=9
Answer:
x=6 m=5
Step-by-step explanation:
x-1=5
x=5+1
x=6
2m-1=9
2m=9+1
2m=10
m=10/2
m=5
A total of 500 married working couples were polled about their annual salaries, with the following information resulting: Husband Wife Less than More than $25,000 $25,000 Less than $25,000 212 198 More than $25,000 36 54 For instance, in 36 of the couples, the wife earned more and the husband earned less than $25,000. If one of the couples is randomly chosen, what is (a) the probability that the husband earns less than $25,000
Answer:
36/500
Step-by-step explanation:
The probability that the husband earns less than $25,000 is 0.496.
Given that,
A total of 500 married working couples were polled about their annual salaries, with the following information resulting:
Husband
Wife Less than $25,000 More than $25,000
Less than $25,000 212 198
More than $25,000 36 54
Thus, for instance, in 36 of the couples, the wife earned more and the husband earned less than $25,000. If one of the couples is randomly chosen.
We have to determine,
What is the probability that the husband earns less than $25,000?
According to the question,
The probability that the husband earned less than $25,000 is,
Total number of couples = 500
The count of husbands earning less than $25,000 is 212 and 36.
[tex]\rm Probability = \dfrac{Total \ number \ of \ couples}{Husband \ earn \ less \ than \ 25000}\\\\ Probability= \dfrac{212+36}{212+36+198+54}\\\\Probability = \dfrac{246}{500}\\\\Probability = 0.496[/tex]
Hence, The probability that the husband earns less than $25,000 is 0.496.
For more details refer to the link given below.
https://brainly.com/question/17090318
who can answer this
(WITH AN EXPLANATION)
will mark brainlest
Answer:
Factors: (x²y+6)(y²-11)
Step-by-step explanation:
Here's the original equation.
x²y³ - 11x²y + 6y² - 66
Let's separate it into two groups to make it easier.
(x²y³ - 11x²y) + (6y² - 66)
Let's take a look at (x²y³ - 11x²y) first. Do we notice anything that can be removed from the parentheses?
Yes, x²y can be taken from both polynomials to simplify the contents of the parentheses.
Both polynomials have x² and both have at least one y. Combine that to get x²y. That means that within the parentheses y² and - 11 will be left.
So (x²y³ - 11x²y) becomes x²y (y²-11)
This works because if we multiply x²y * (y² - 11) we get (x²y³ - 11x²)
Let's apply this same idea to (6y² - 66).
6 is the only thing in common between the two polynomials.
If we follow the same steps we get 6 (y²-11).
Notice how when we simplified both groups they each had something on the outside and (y² - 11) in the parentheses?
So lets combine the things that were on the outside of both (y² - 11).
What was on the outside of each? x²y was on the outside for the first one, and 6 for the outside of the second one.
This means that if we combine everything and simplify, the factors we have are (x²y+6)(y²-11).
If you want to confirm, work your way backwards using the distributive property. You'll find that when you multiply (x²y+6) * (y² -11) you'll get = x²y³ - 11x²y + 6y² - 66. That was the original equation, so we know that these are the factors.
Hope that helps!
Multiply.
5 x 10 the power of three
Answer:
5000
Step-by-step explanation:
The answer to 5x10^3 is 5000
A research organization studying families in various countries reported the following data for the amount of time that children spent with their fathers each day. What is the mode and the median, respectively? Country Time with Dad (minutes) Belgium 30 Canada 44 China 54 Finland 50 Germany 36 Nigeria 42 Sweden 46 United States 42 A. 42, 42 B. 42, 43 C. 43, 42 D. 43,43
Answer:B. 42, 43
Step-by-step explanation:
STEP 1 Listing out the data set
Country Time with dad
Belgium 30
Canada 44
China 54
Finland 50
Germany 36
Nigeria 42
Sweden 46
United States 42
STEP 2--- finding the mode and median
Mode----The mode of this data set is the number that occurs most frequently in this research date.
Time with dad in ascending order is given as 30, 36, 42, 42, 44,46,50,54
The number that occurred the most is 42 = mode
Median The median is the middle value in a data set
Since these data set is an even number, we take the average of the two middle numbers
Arranging in ascending order, we have
30, 36, 42, 42, 44, 46, 50, 54---------------42 and 44 are the middle numbers
42+ 44/2 =43
Therefore mode and median are 42 and 43 respectively
The population of a town doubles every 4 years.
Complete the sentence,
The population is best represented by an)
function because the population is changing by a constant
Answer:
quizlet probably has your answer
Step-by-step explanation:
36 diveded to 68251500
Answer: do you mean divided
If so the answer is
1895875
Step-by-step explanation:
68251500÷36=1895875
If the radius of circle A is 2 inches, the radius of circle B is 3 1/4 and the radius of circle C is 1 inch, what is the perimeter of ABC?
Answer:
39.26 in
Step-by-step explanation:
This problem, bothers on the mensuration of flat shapes.
we know that the perimeter of a circle is the same as the cirmcumference
we also know that the circumference is given as
C= 2πr
For circle A
C=2*3.124*2
C= 12.56 in
For circle B
C=2*3.124* 3 1/4
C= 2*3.142*13/4
C= 2*3.142*3.25
C= 20.42 in
For circle C
C=2*3.124*1
C= 6.284 in
Now the perimeter of all the circles ABC is
=12.56 +20.42 + 6.284
=39.26 in
Will mark brainlist:)
Answer:
The length of the missing side is 7 yards
Step-by-step explanation:
Simply subtract 9 from 16
16-9=7
The length of the missing side is 7 yards
Hope this helps! Plz award Brainliest : )
The answer is 7yd.
I got this answer by simply looking at the line parallel to it, which would be 16yd. I subtracted 16yd - 9yd = 7yd.
Hope this helped!
Good luck <3
What is the value of X
Answer:
16
Step-by-step explanation:
The angles are vertical angles which means they are equal
8x-8 = 7x+8
Subtract 7x from each side
8x-8-7x = 7x+8-7x
x-8 = 8
Add 8 to each side
x-8+8 = 8+8
x=16
Complete the table to show how many ounces are equivalent to 6 pounds.
A 2-column table with 4 rows. Column 1 is labeled Pounds with entries 6, 8, 10, 12. Column 2 is labeled Ounces with entries question mark, 128, 160, 192.
There are
ounces in 6 pounds.
Answer:
is 96
Step-by-step explanation:
its simple hope you do good
Answer:
It's 96
Step-by-step explanation:
it's 96 because 128-(128/8)=96
PLEASE MARK AS BRAINLEIST
