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mars1129 [50]
3 years ago
5

How do you find the largest 6-digit multiple of 11 such that the sum of all its digits equals 40. What is the answer?

Mathematics
1 answer:
alina1380 [7]3 years ago
8 0
There is a certain way to find the answer for your question. First, you must be familiar with the divisibility rule for 11: the difference between the sums of even digits and odd digits should either be 0 or 11 only.  For example, 1430, here the odd digits are 4 and 0 (which are the 3rd and 1st digits); the even digits on the other hand are 1 and 3, placed as the 4th and 2nd digits respectively.

Adding the sums of odd and even digits will give 4 (4+0) and 4 (3+1). Now, the difference of these sums is obviously equal to 0. Therefore, 1430 is divisible by 11. Same case will hold for numbers whose sums of odd and even digits is 11.

Moving on, now let us try to find the biggest 6-digit number divisible by 11. Intuitively, the last digit should be "9" - the hundred thousands digit - for it is the biggest number among numbers from 0-9. Furthermore, since there is no restriction as to whether the same number could or could not repeat, we can still use "9" all throughout the remaining 5 digits (ten thousands down to ones digit), giving the greatest possible 6-digit number, 999,999.

To check if the number we have obtained, 999,999, is divisible by 11, we need to use the divisibility rule for 11. Sum of even digits is 18 (9+9+9); sum of odd digits is 18 (9+9+9) as well. The difference of the sums is 0. Therefore, 999,999 is divisible by 11, hence the greatest 6-digit number multiple of 11.

As for the 6-digit number whose digits' sum is 40 and multiple of 11, we can assume its first 4 digits to be as 999,9** - four 9s is already equal to 36 - we only need to find two numbers whose sum is 4 to make the sum's total be 40. These remaining numbers should also be divisible by 11 since 9999 is already divisible by 11. The remaining numbers should only be 2 and 2 since the sum of its digit is 4, and that if we put them together, 22, a multiple of 11. This is the only combination of numbers that will give a sum of 4 while maintaining its structure a multiple of 11.

At last, the greatest 6-digit number whose digits' sum equal to 40 and is a multiple of 11 is 999,922. True, for 999,922 / 11 is equal to 90,902.

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If 10 candy cost $35. How much candy can I buy with $20
Alika [10]

Answer:

6 candies

Step-by-step explanation:

(find unit rate, cost / quantity)

35/10 = 3.5

20/3.5 = = 5.7142857142857

candies cannot be in decimal so you must round to the nearest whole

8 0
3 years ago
the local Swim Center is making a special offer they regular charge is $7 per day to swim at the pool the special offer would ha
algol [13]
To fill in the first column = 
Every day is 7 dollars, which you have already answered.
The second one would be = 
day 0 = 30 dollars. And then it would be 4$ for days 1 through 10.
Hope this helps!
8 0
3 years ago
If f (x) = x² - 7, evaluate the following: f(12) f(-7)
Julli [10]

Answer: f(12) = 137, f(-7) = 42

Step-by-step explanation: In a function, what you want to do is plug in the value they give you for x. This means you substitute x with the value they are looking for.

In this case, they are looking at 12 and -7. Let's do 12 first.

The equation becomes (12^2) - 7. 12^2 is 144, and 144-7 is 137.

Now we do -7. The equation becomes (-7)^2 - 7. -7^2 is 49, and 49 - 7 is 42.

Hope this helped!

7 0
1 year ago
What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?
Artyom0805 [142]

Answer:

y=\frac{1}{6} (x-4)-\frac{9}{2}

Step-by-step explanation:

∵ The quadratic equation form is :

y = [1/2(b - k)] (x - a)² + (b + k)/2

Where (a , b) is the focus and directrix y = k

∵ The focus is (4 , -3) and directix is y = -6

∵ y=\frac{1}{2(-3-(-6))} (x-4)^{2}+\frac{(-3)+(-6)}{2}

∴ y=\frac{1}{6} (x - 4)^{2}+\frac{-9}{2}

∴ y=\frac{1}{6} (x-4)-\frac{9}{2}

another way:

Assume that (x , y) is the general point on the parabola

∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)

By using the distance rule:

∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)

∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9

∴ 12y - 6y = (x - 4)² + 9 - 36

∴ 6y = (x - 4)² - 27 ⇒ ÷ 6

∴ y = 1/6 (x - 4)² - 9/2

4 0
3 years ago
Curtis threw 15 darts at a dartboard. 40% of his darts hit the bull's-eye. How many darts did not hit the bull's-eye?
uranmaximum [27]
Number of darts that hit the bull's eye = 15 x 40/100 = 6
Number of darts that did not hit the bull's eye = 15 - 6 = 9

3 0
3 years ago
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