Answer:
139,999
Step-by-step explanation:
If the digit sum of n is divisible by 5, the digit sum of n+1 can't physically be divisble by 5, unless we utilise 9's at the end, this way whenever we take a number in the tens (i.e. 19), the n+1 will be 1 off being divisble, so if we take a number in the hundreds, (109, remember it must have as many 9's at the end as possible) the n+1 will be 2 off being divisble, so continuing this into the thousands being three, tenthousands being 4, the hundred thousands will be 5 off (or also divisble by 5). So if we stick a 1 in the beginning (for the lowest value), and fill the last digits with 9's, we by process of elimination realise that the tenthousands digit must be 3 such that the digit sum is divisible by 5, therefore we get 139,999
Notice that a number is only divisible by 5 if it ends in 5 or 0.
Only using this, we will find that the number is 49,999
Suppose we wanted the sum of the digits to end in 5, then we could have something like:
23
2 + 3 = 5
if we add 1, we get:
23 + 1 = 24
2 + 4 = 6
This will happen always.
instead, if we use a 0 as the last digit of the sum, we get:
For example, the simplest one:
19
we have:
1 + 9 = 10
10 is divisible by 5.
if we add 1, we get:
19 + 1 = 20
2 + 0 = 2
2 is not divisible by 5.
We have a problem again, but this time you can see that the whole structure of the number does change. So we should keep trying with ones and nines.
Now we need to modify our number to the point we get n + 1 to be divisible by 5.
if we add a 9 to the right side of our number, we get:
199
1 + 9 + 9 = 19
clearly, not divisible by 5.
Here we need to add a 1 at the left side to make it divisible by one, so we get:
1199
1 + 9 + 1 + 9 = 20
this is divisible by 5.
now let's add 1:
1,199 + 1 = 1,200
1 + 2 = 3
3 is not divisible by 5.
Now, if you look at the two numbers we used, we can see that:
for 19, the sum of the digits + 1 gave us a 2.
for 1,199, the sum of the digits +1 gave us a 3.
then just let's add two ones and two nines.
We will get:
11,119,999
adding the digits:
1 + 1 + 1 + 1 + 9 +9 +9 +9 = 40
is divisible by 5.
Adding one to our number, we can get:
11,119,999 + 1= 11,120,000
Adding the digits:
1 + 1 + 1 + 2 + 0 + 0+ 0+ 0 = 5
divisible by 5.
Now, we can group the ones together, so instead of the number 11,119,999
we can have 49,999, which is way smaller.
Adding the digits, we get:
4 + 9 + 9 + 9 + 9 = 40
And adding one to our number, we get:
49,999 + 1 = 50,000
Adding the digits:
5 + 0 + 0 +0 + 0 = 5
So we found the smallest number n such that the sum of the digits of n is divisible by 5, and the sum of the digits of n + 1 is also divisible by 5.
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Add. Write your answer as a fraction in simplest form. 6+(−4 3/4)+(−2 1/8)=
Kareem is putting 8 books in a row on his bookshelf. He will put one of the books, Pride and Prejudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf
Answer:
720
Step-by-step explanation:
He has 8 books. He knows the placement of 2... so
8 - 2 = 6
To find the total... 6!
6*5*4*3*2*1 = 720
The required number of the ways the book is arranged on the shelf is 720 ways.
Given that,
Kareem is putting 8 books in a row on his bookshelf. He will put one of the books, Pride, and Prejudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf is to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
here,
There are 8 books to be arranged, 1st and last place is fixed,
now remaining books = 8 - 2 = 6
now, a number of combinations can be formed with the number 6,
= 6!
= 6×5×4×3×2×1
= 720
Thus, the required number of the ways the book is arranged on the shelf is 720 ways.
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pls help!! it will mean a lot thank you:)
one angle of linear pair is 4 time the other find the angles
need answer asap
Answer: The angles are 36 and 144.
Step-by-step explanation:
Let the linear pairs be 4x and x
so
4x + x = 180 (being linear pair)
or, 5x = 180
or, x = 180/5
so, x = 36
so, 4x = 4*36 = 144
A recipe for cookies uses sugar and baking powder. The recipe uses uses 3/4 cups of sugar and 1/2 teaspoon of baking powder
Answer:
5/4 or 1 . 1/4
Step-by-step explanation:
3/4 + 1/2 = 5/4 or 1 . 1/4
The perimeter of a triangle is 16x−6. If two sides measure 3x+2 and 4x−9, then how long is the third side?
Perimeter of a triangle is the sum of measures of its all three sides, let the other be y,
we know,
[tex] \hookrightarrow \: y + 3x + 2 + 4x - 9 = 16x - 6[/tex]
[tex] \hookrightarrow \: y + 7x - 7 = 16x - 6[/tex]
[tex] \hookrightarrow \: y = 16x - 6 - 7x + 7[/tex]
[tex] \hookrightarrow \: y = 6x + 1[/tex]
hence, measure of the third side is 6x + 1
15=a/3-2
please help !!
Here is your answer. Hope this helps you.
Answer:
51
Step-by-step explanation:
15= a/3 -2
17= a/3
51=a
Lee started the week with the balance of -$120 in his checking account . He then deposited some money into the account . The ending balance is -$110 how much did lee deposit
Which function is the same as the linear function represented by the table ?
Answer:
A) y = 3x – 2
Step-by-step explanation:
Just check the results: when you put the numbers of the x-colum from the table, the result will be the corresponding numbers of the y-colum. and that means this is the right equation
simplify each expression
Answer:
3
Step-by-step explanation:
Given
[tex]\sqrt[3]{\sqrt{729} }[/tex]
Evaluate from the ' inside- out ' , that is
[tex]\sqrt{729}[/tex] = 27 , then
[tex]\sqrt[3]{27}[/tex]
= 3
Answer:
3
Step-by-step explanation:
[tex] \sqrt[3]{ \sqrt{729} } [/tex]
[tex] = \sqrt[3]{ \sqrt{ {27}^{2} } } [/tex]
[tex] = \sqrt[3]{27} [/tex]
[tex] = \sqrt[3]{ {3}^{3} } [/tex]
[tex] = 3[/tex] ✅
admission to local art museum is $8 for each adult. How much does it cost for $4 adults to attend the museum
what is the answer to 90π + 2π(7.5)2
Answer:
635.75
Step-by-step explanation:
90π + 2π(7.5)²
~Simplify
90π + 2π(56.25)
~Multiply
282.5 + 2(176.625)
~Simplify
282.5 + 353.25
635.75
All this was simplified using PEMDAS.
Best of Luck!
Each letter stands for a different digit. What
number does ABC represent?
АА
ВВ
+СС
____
АВС
Answer:
A = 1, B = 9, C = 8Step-by-step explanation:
Given:
AA + BB + CC = ABCRewrite it as:
11A + 11B + 11C = 100A + 10B + C89A = B + 10CSince all A, B, C are integers from 0 to 9, A can be 1 only, then we have:
B + 10C = 89or
CB = 89It gives us:
C = 8, B = 9The equation is:
11 + 99 + 88 = 198Answer:
ABC=198
Step-by-step explanation:
If you do 11+99+88 then you get 198 which is true to the problem that you have.
Neeeeeeed helpppppppppppppp
Answer:
[tex]2^{1} + 3^{1}[/tex], [tex]2^{3} - 2^{1}[/tex], [tex]3^{2}[/tex]
Step-by-step explanation:
[tex]3^{2}[/tex] = 9
[tex]2^{3} - 2^{1}[/tex] = 6
[tex]2^{1} + 3^{1}[/tex] = 5
Step-by-step explanation:
Simplify the expressions
[tex]2 {}^{3} - 2 {}^{1} = 2 {}^{3} - 2 = 8 - 2 = 6[/tex]
[tex]2 + 3 = 5[/tex]
[tex] {3}^{2} = 9[/tex]
So the expressions from least to greatest is
[tex]2 {}^{1} + 3 {}^{1} < 2 {}^{3} - 2 {}^{1} < 3 {}^{2} [/tex]
Question 7
Which graph best represents the solution to the following inequality?
+ 5 > 11
A
16
17
19 20 21 22
23 24 25
O
15
16
17
18 19 20 21 22
23
24 25
c.
10 11
3 4 5
12
15
13 14
D.
8
10
11
12
13
14
15
Answer:
D
Step-by-step explanation:
x + 5 > 11
is the same as
x > 6
and because it is ">" and not ">=", the solution point is not included.
therefore the right graph is D and not C. an empty little circle means "excluded", while a filled, black circle means "included".
B. Find the equation of the line parallel to 6x+2y = 10
and passing through (-3,5).
Answer:
[tex]The\,\,derived\,\,equation\,\,is\\6x+2y=-8[/tex]
Step-by-step explanation:
Given, equation of line
[tex]6x+2y = 10......(i)\\\\Parallel\,\,line\,\,of\,\,the\,\,equation\,\,(i),\\6x+2y=k.....(ii)\,\,;[here,\,\,k\,\,is\,\,a\,\,constant]\\\\The\,\,line\,\,(ii)\,\,passes\,\,through\,\,the\,\,point\,\,(-3,5),\\6*(-3)+2*(5)=k\\So,\,\,k=-8\\\\Therefore,\,\,the\,\,derived\,\,equation\,\,is\\6x+2y=-8[/tex]
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Is 8 1/4 an irrational number?
Mike weights 200 pounds and plans to lose 1.5 pounds a week. Jeff weights 180 pounds and plans to lose 0.5 pounds a week. When mike and Jeff weigh the same?
Answer:
20 weeks
Step-by-step explanation:
200-1.5w=180-0.5w
You can double-check by substituting 20 for w (weeks), if it is equal, then the equation is correct.
Is the set of real numbers closed under addition? Explain why or why not. If it is not closed, give an example
Answer: Yes, the set of real numbers is closed under addition.
Explanation:
Let x and y be two real numbers. Their sum x+y is some other real number. This is what it means when we say the set of real numbers is closed under addition. Taking any two numbers and adding them will get us some other real number.
There is no way to have x+y be nonreal while x,y are both real.
Expand [tex](x-\frac{1}{x})^{1\\2}[/tex] , simplifying the coefficients
the right answer is [tex]x^{5}-5x^{3}+10x-\frac{10}{x} +\frac{5}{x^{3} }-\frac{1}{x^{5} }[/tex]
but i can't work it out
PLEASE HELP!
Answer:
Step-by-step explanation:
In reality it is : [tex](x-\frac{1}{x} )^5\\[/tex]
[tex]Pascal'sTriangle\\\\\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\\\end{array}\\\\\\(x-\frac{1}{x} )^5\\\\=x^5+5*x^4*\frac{1}{x} *(-1)+10*x^3*\frac{1}{x^3}*(-1)+5*x*\frac{1}{x^4} +\frac{1}{x^5} *(-1)\\\\\\\boxed{(x-\frac{1}{x} )^5=x^5-5x^3+10x-\frac{10}{x} +\frac{5}{x^3} -\frac{1}{x^5} }[/tex]
Write an equation in point-slope form of the line that passes through the given point and
has the given slope: (3,4), m=1/3
Answer:
y - 4 = 1/3 (x - 3)
Step-by-step explanation:
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 10 times t squared plus 50 times t end quantity over the quantity t squared plus 4 times t plus 3 end quantity comma where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points) Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is [tex]t \ge 0[/tex] The greatest concentration of the medication is 5mg/LGiven that:
[tex]C(t) = \frac{-10t^2 + 50t}{t^2 + 4t + 3 }[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is:
[tex]t \ge 0[/tex]
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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A function assigns the values. The greatest concentration of the medication that a patient will have in their body is when the time is t=1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) Given the function of the concentration of medication in the body as to[tex]C(t)=\ \frac{\left(-10t^{2}+50t\right)}{t^{2}+4t+3}[/tex] where t is the time. Since the time can not be negative, therefore, the domain of the function is t≥0.
B.) The graph of the function can be plotted as shown below. Now, the greatest concentration of the medication that a patient will have in their body is when the time is t=1.
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PLEASE HELP!!!! Im being timed
Please help me I’ll give a brainly! It’s due soon!
Hi! I'm happy to help!
First, we need to get our two equations, so we need to look at what facts we have throughout the equation. It tells us that x is 3 times as much as y. We can use this to write our first equation:
3y=x
All of the interior angles inside of a triangle add up to 180°, and because we already have 3 angles, we can use this information to make our second equation:
x+y+45=180
Now, we have to use these equations together to get our answer.
Since we can replace 3y for x (first equation) we can replace it in our second equation:
3y+y+45=180
We edit both sides of the equation in the same way to get the same outcome, but to simplify. Since we are solving for y, let's isolate it by subtracting 45 from both sides:
3y+y+45=180
-45 -45
3y+y=135
Let's combine the 3y and y to make things simpler:
4y=135
From here, we divide both sides by 4, to isolate y:
y=33.75
Now that we have our y value, we can use our first equation to solve for x:
3y=x
3(33.75)=x
101.25=x
We used our equations to get both our x and y values: 33.75, and 101.25.
I hope this was helpful, keep learning! :D
the difference between 2 numbers is 12. the larger number is 3 times the smaller. what are the numbers
Step-by-step explanation:
hope it helps you check it if there is a mistake sorry!! for that
Please help it is geometry will mark branliest
the one on the left is (2,2) the one on the right is (8,2)
Find the value of the expression 4a4 − 2b2 + 40 when a = 2 and b = 7.
Answer:
44
Step-by-step explanation:
4×(2)×4-2×(7)×2+40=?
8×4-14×2+40=?
32-28+40=
=44
Find an
expression which represents the sum of (-X – 7) and (-9x + 6) in
simplest terms.
Answer:
sum is -(10x + 1)
Step-by-step explanation:
[tex]( - x - 7) + ( - 9x + 6) \\ = ( - x - 9x) + (6 - 7) \\ = - 10x - 1 \\ = - (10x + 1)[/tex]
Answer:
[tex]( - x - 7) + ( - 9x + 6) \\ = - x - 7 - 9x + 6 \\ = - 10x - 1 \\ thank \: you[/tex]
How many dollars does 3 bottles of water cost ?
Answer:
$7.5
Step-by-step explanation:
if we set up the proportion [tex]\frac{10}{4} =\frac{x}{3}[/tex] with cost on top and water bottles on bottom, we can divide 10/4 too get 2.5, which we can then multiply by 3 to get our x value, 7.5.
whhat is the degree of x2 y3 + a3 b4 -7
Given Polynomial
[tex]\\ \sf\longmapsto x^2y^3+a^3b^4-7[/tex]
Calculate degrees of all variables
x=2y=3a=3b=47=1B has highest degree
Hence degree of polynomial is 4
It is a tetranomial