prove that for every integer exists a multiple of that number that is composed of only ones and zeros in the decimal system

Answers

Answer 1

Let n be a positive integer. Consider the  n+1 integers 1,11, 111,1111,... (where the last integer in this list is the integer with n+1 - 1s in its decimal expansion).

Note that there are n possible remainders when an integer is divided by n. Because there are n+1 integers in this list, by the pigeonhole principle there must be two with the same remainder when divided by n. The larger of these integers the smaller one is a multiple of n, which has a decimal expansion consisting entirely of 0s and 1s.

For example, take n=7

we have, 1,11, 111,1111,...,11111111

The remainder possible when any number is divided by 7 is 0,1,2,3,4,5,6

These are the remainders when the numbers in the first list are divided by 7 gives 1,4,6,5,2,0,1,4.

Now you can see that we have 7 pigeonholes {0,1,2,3,4,5,6} and 8 pigeons {1,11, 111,1111,...,11111111} so there needs to be at least one pigeonhole where 2 pigeons will reside.

In this case, we have 11%7=4 and 11111111%7=4

Their difference, i.e. 11111111-11=11111100 is divisible by 7.

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Related Questions

classify the following differential equation s given in both standard and differential form. Q5 only​

classify the following differential equation s given in both standard and differential form. Q5 only

Answers

The given differential equation is:

y' = 2xy + x

Rewriting it in differential form, we get:

(2xy + x)dx - dy = 0

This is a first-order linear differential equation, which can be written in the form:

y' + P(x)y = Q(x)

where P(x) = -2x and Q(x) = x.

Therefore, the differential equation is a first-order linear differential equation.

A fruit juice company includes 1.858 ounces of pineapple juice in a 6.65-ounce bottle of a mixed fruit
juice. How much of the bottle of mixed fruit juice is NOT pineapple juice?

Answers

4.792 ounces

Remember to put the word ounces to get full credit on the answer

The question is attached below

The question is attached below

Answers

The expected number of pizzas to be stuffed crust is given as follows:

500.

How to calculate a probability?

The parameters that are needed to calculate a probability are listed as follows:

Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The sample size is given as follows:

408 + 224 + 208 + 200 = 1040.

Out of these, 208 are stuffed crust, hence the probability is given as follows:

p = 208/1040.

Out of 2500 pizzas, the expected number is then given as follows:

E(X) = 2500 x 208/1040

E(X) = 500.

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Which set of ordered pairs gives the polygon shown?


(-1, 0.5), (1.25, 0), (0.75, -0.75)

(0.75, -0.75), (-1, 0.5), (0, 1.25)

(-0.75, 0.75), (0.5, -1), (0, 1.25)

(-1, 0.75), (0, 1.5), (0.75, -0.75)

Which set of ordered pairs gives the polygon shown?(-1, 0.5), (1.25, 0), (0.75, -0.75)(0.75, -0.75),

Answers

The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

Option B is the correct answer.

We have,

From the figure,

We have,

The polygon has three points.

The points are in ordered pairs.

We see that,

Each number has four units.

So,

1 unit = 0.25 units

Now,

The coordinates of the polygon are:

(3 units, -3 units) = (0.75, -0.75)

(0, 5 units) = (0, 1.25)

(-4 units, 2 units) = (-1, 0.50)

Thus,

The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

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s = square root of 18d can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes, estimate the speed of the car

Answers

ANSWER:

14.7 miles per hour

STEP-BY-STEP EXPLANATION:

We have that the speed is given by the following function:

\(s=\sqrt[]{18d}\)

where s is calculated in miles per hour and d is given in feet, therefore, we substitute and calculate the value of the speed:

\(\begin{gathered} s=\sqrt{18\cdot12} \\ s=14.7\text{ miles per hour} \end{gathered}\)

The speed of car is 14.7 miles per hour

help pleased now can you help me

help pleased now can you help me

Answers

It drains at a constant rate using the first line find the rate per hour:

-3.5/2 = -1.75 per hour

Now to find the missing totals multiply the hours by the rate:

-1.75 x 9 = -15.75

-1.75 x 23 = -40.25

Now to find the change between the two times subtract:

-40.25 - -15.75 = -24.50

Solve Correctly For Thanks And Brainiest:

Solve Correctly For Thanks And Brainiest:

Answers

Answer:

m=15

Is what I got.

5 because I think so

a company was offering a special on cell phones for $3 each but only if you spent 5 dollars a month for 2 months how much would it end up costing you total if u bought 1 phone ?

Answers

Answer:

10 dollars

Step-by-step explanation:

5 + 5

17.
Peter transports metal bars in his van.
The van has a safety notice: "Maximum Load 1200 kg".
Each metal bar has a label: "Weight 60 kg".
For safety reasons, Peter assumes that:
1200 is rounded correct to 2 significant figures, and
60 is rounded correct to 1 significant figure.
Calculate the greatest number of bars that Peter can safely put into the van if his assumptions are
correct.

Answers

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

Range of values

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

Safe loading

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

How many solutions does -3x+15=3(5-x) have

Answers

Answer:

Infinite solutions

Step-by-step explanation:

So if simplified it would be

-3x+15=15-3x

Which is basically the same thing if arranged

15-3x=15-3x

-3x+15 can also be 15-3x still the same thing as adding 15 to -3x

So since these are equal anything could be used

like try 0

Both get 15

Try 1

Both get 12

Try legit any number

youll get the same results (I would choose 3 positive easy ones, 0,1,2 and 3 negative ones -1,-2,-3)

100 POINTS!! ASAP - Pls Show all WORK

100 POINTS!! ASAP - Pls Show all WORK

Answers

Answer:

x ≈ 28.7 ft

Step-by-step explanation:

Step 1: Define variables

Height (vertical leg of triangle) = 2 ft

∅ = 4°

We are trying to find the length of the hypotenuse x

Step 2: Use trig

sin∅ = opposite over hypotenuse

sin4° = 2/x

Step 3: Solve for x

xsin4° = 2

x = 2/sin4°

x = 28.6712

x ≈ 28.7 ft

Answer:

the Length of ramp is 28.7 feet.

Step-by-step explanation:

see attached image for clarity

give:

height (h) of clinic = 2 feet

angle of ramp = 4°

find:

Length (L) of ramp

using the formula : sin(Ф) =                height (h)                    

                                              Length of ramp (hypothenuse)

plugin values into the formula:

sin (4) =    2    

               L

L   =    2    

      sin(4)

L = 28.7 feet

therefore,

the Length of ramp is 28.7 feet.

100 POINTS!! ASAP - Pls Show all WORK


Based on the 2010 US census, the population of Milwaukee, Wisconsin, was about 96% of the population of Baltimore, Maryland. In 2010, if Milwaukee's population was about 595,000, which of the following is the best
approximation of Baltimore's population?
A 620,000
B 570,000
C 300,000
D 95,000

Answers

Answer: A

Step-by-step explanation:

Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A

(
2
x
4
+
5
x
3
+
8
x
+
24
)
÷
(
x
+
2
)

Answers

Answer:

47 + 8x

 x + 2

_________________________

Excluded values answer:

x = -2

Step-by-step explanation:

What is the equation of the directrix?

What is the equation of the directrix?

Answers

The equation of the directrix is y = -5

How to determine the directrix equation?

The equation is given as:

(x -1)^2 = 12(y + 2)

Express 12 as a product of 4 and 3

(x -1)^2 = 4 * 3(y + 2)

The parabola is represented as:

(x -h)^2 = 4p(y - k)

Where the directrix is

y = k - p

By comparison, we have:

k = -2 and p = 3

So, we have:

y = -2 - 3

Evaluate

y = -5

Hence, the equation of the directrix is y = -5

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what is 5 6/7 + 8 1/14=​

Answers

\(5\frac{6}{7}+8\frac{1}{14} =13+\frac{13}{14}=13\frac{13}{14}\)

Hope I helped you!Success!

Answer:

\(13 \frac{13}{14} \)

Step-by-step explanation:

\(5 \frac{6}{7} + 8 \frac{1}{14} \)

\((5 + 8) + ( \frac{6}{7} + \frac{1}{14} )\)

\(13 + ( \frac{6}{7} + \frac{1}{14} )\)

\(13 + \frac{13}{14} \)

\( = 13 \frac{13}{14} \)

How many real solutions does the equation have? y=x² + 4x - 6​

Answers

There are 2 real solutions for the quadratic equation y=x²+4x-6​.

What is meant by quadratic function?

A second-order polynomial equation in one variable, x, using the formula ax2+bx+c=0, is known as a quadratic equation. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic. The terms "quadratic polynomial" and "quadratic function" were practically interchangeable until the 20th century since it was difficult to tell a polynomial from its corresponding polynomial function.  A quadratic function with only one variable, for instance, has the following form:

The quadratic equation presented is y=x²+4x-6

We must ascertain how many possible solutions exist for this function.

x²+4x-6.

x²+4x-6=0

= (-4±√16-4(1)(-6))/2

=(-4±√-40)/2

= -2±10

Therefore, there are 2 real solutions for the quadratic equation

y=x²+4x - 6​.

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A golf course rents golf clubs for $10 plus $4 for each hour the golf clubs are rented. An expression for the total cost of renting the golf clubs for h hours is 10 + 4h.
Complete the table by finding the total cost of renting the golf clubs for h hours.

Answers

To complete the table, we can use the expression 10 + 4h to calculate the total cost of renting the golf clubs for different values of h.

Table below:

h Total cost

1 14

2 18

3 22

4 26

5 30

For example, if the golf clubs are rented for 1 hour, the total cost is $14 (10 + 4(1) = 14). If they are rented for 2 hours, the total cost is $18 (10 + 4(2) = 18), and so on.

What is the expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented?

The expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented is 10 + 4h.

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Which of the following graphs is described by the function given below?
y = 2x2 + 6x + 3
5
101
10
10
-20
20
- 10
10
-10
20-
101
A.
B.
C.
D.
A. Graph A
B. Graph B
O C. Graph C
D. Graph D

Answers

Answer:

Which of the following graphs is described by the function given below?

y = 2x2 + 6x + 3

-A. Graph A

The function y = 2x^2 + 6x + 3 is a quadratic function that has a vertex of (-1.5,-1.5)

How to determine the graph of the function?

The equation of the function is given as:

y = 2x^2 + 6x + 3

Differentiate

y' = 4x + 6

Set to 0

4x + 6 = 0

This gives

4x = -6

Divide by 4

x = -1.5

Substitute x = -1.5 in y = 2x^2 + 6x + 3

y = 2(-1.5)^2 + 6(-1.5) + 3

Evaluate

y = -1.5

This means that the function y = 2x^2 + 6x + 3 has a vertex of (-1.5,-1.5)

See attachment for the graph of y = 2x^2 + 6x + 3

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Which of the following graphs is described by the function given below?y = 2x2 + 6x + 351011010-2020-

6) Given the points A(-4, 5) and B(6, 0), find
bolthe coordinates of the point P on the line
segment AB that partitions AB into the
ratio 2:3. Plot P along with segment AB.

Answers

Answer: (0, 3)

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A salesperson increases the amount of sales, in dollars,each quarter by 15%. If the salesperson has $45,000 in sales in the 1st quarter, what is the
amount of total sales by the end of the 4th quarter, to the nearest cent?

Answers

Using an exponential function, it is found that the amount of total sales by the end of the 4th quarter is of $224,671.875.

What is an exponential function?

An increasing exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

A(0) is the initial value.r is the growth rate, as a decimal.

In this problem, the parameters are r = 0.15 and A(0) = 45000.

Then:

For the first quarter, A(0) = 45000.For the second, A(1) = 45000(1.15) = 51720.For the third quarter, A(2) = 45000(1.15)² = 59512.5.For the fourth quarter, A(3) = 45000(1.15)³ = 68439.375

Then, the total amount is:

T = A(0) + A(1) + A(2) + A(3) = 45000 + 51720 + 59512.5 + 68439.375 = $224,671.875.

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Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Answers

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

                                 \(f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}\).

This definition of the absolute function can be explained geometrically to be similar to the straight line   \(\textbf{\textit{y}} \ = \ \textbf{\textit{x}}\)  , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line  \(\textbf{\textit{y}} \ = \ \textbf{\textit{x}}\)  where \(\textbf{\textit{x}} \ < \ 0\) (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

                                             \(3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3\).

We, now, can simply visualise the straight line,  \(y \ = \ x \ + \ 1\) , as a line having its y-intercept at the point  \((0, \ 1)\) and its x-intercept at the point \((-1, \ 0)\). Then, imagine that the segment of the line where \(x \ < \ 0\) to be reflected along the x-axis, and you get the graph of the absolute function \(y \ = \ \left|x \ + \ 1 \right|\).

Consider the inequality

                                                    \(\left|x \ + \ 1 \right| \ < \ 3\),

this statement can actually be conceptualise as the question

            \(``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"\).

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when \(x \ \geq \ 0\))

                                                \(x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2\)

Case 2 (when \(x \ < \ 0\))

                                            \(-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4\)

           *remember to flip the inequality sign when multiplying or dividing by

            negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

                                                     \(-4 \ < \ x \ < \ 2\).

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| &lt; 9
Which of the following graphs shows the solution set for the inequality below? 3|x + 1| &lt; 9

if 3(2x+5)=90, what is the value of x

Answers

Answer:

x = 12.5

Step-by-step explanation:

3(2x + 5) = 90 ( divide both sides by 3 )

2x + 5 = 30 ( subtract 5 from both sides )

2x = 25 ( divide both sides by 2 )

x = 12.5

6xAnswer:

6x + 15 =90

6x = 90 - 15

6x= 75

x=12.5

Find the slope (0.-4) and (-2,-2) help me

Answers

The answer is -1.

You do -2- -4 and get 2.
Then do -2-0 and get -2.
The last step is to do 2 divide -2 and you get -1.

\(30 \frac{1}{6}\)≈

Answers

Hello,

The answer is: 181/6 or 30.16667

Three blocks are shown: Block A has mass 3 kilograms, length 8 centimeters, height 2 centimeters, and width 1 centimeters. Block B has mass 4 kilograms, length 1 centimeters, height 8 centimeters, and width 2 centimeters. Block C has mass 4 kilograms, length 8 centimeters, height 1 centimeters, and width 2 centimeters. Which statement is correct? (1 point) a Block A has the greatest density. b Block B has the least density. c The density of Block A is equal to the density of Block B. d The density of Block B is equal to the density of Block C.

Answers

Answer:

b & c

Step-by-step explanation:

a florist makes 24 bouquets from 18 roses and 30 tulips. all of the bouquets will include both roses tulips. what do you notice about the number of bouquets and the numbers of roses in each bouquet?

Answers

Answer: There isn't enough roses to include even just one rose in every bouquet. In addition, the number of tulips in each bouquet would be more than the amount of roses.

Step-by-step explanation:

You would have two flowers per bouquet,

18 + 30= 48

48 / 2= 24 bouquets.

A loan of $50,000 is to be repaid in 8 equal end-of-year payments at 10% a. After 3 years, how much of the loan would be paid? b. How much would it cost to buy down the interest to 9%?​

Answers

Answer:

a)  = 13550 paid  by end yr 3                                                                                 b) 36450 * 0. 01 = $364.5 buy down interest by 1%

Step-by-step explanation:

50000 * 0.10 = 5000 paid yr 1 = 5000 /8 = 625 per payment   45000 * 0.10 = 4500 paid yr2  40500 *0. 10 = 4050 paid 40500-4050= 36450 left to pay 50000-36450 = 13550 paid    b) 36450 * 0. 01 = $364.5 buy down interest by 1%

Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?

Answers

Answer:

The answer is 216

Step-by-step explanation:

if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.

What are the values of x and y that simultaneously satisfy the two linear equations graphed below? HELP PLEASE

What are the values of x and y that simultaneously satisfy the two linear equations graphed below? HELP

Answers

Answer:

D

Step-by-step explanation:

x=9 and y=4 is given in the graph, this makes the answer between B and D

Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5

So the answer is D

A 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. How many containers of sugar will the 9 pound bag create? (sorry i forgot the 2/3 last time!)

Answers

Answer:

You would create 13 and a half containers of sugar from the 9 pound bag.

Step-by-step explanation:

You divide 9 by 2/3 and it would give you 13.5 which is 13 and a half containers of sugar.

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