A jar contains some number of pennies. When pennies are removed 2, 3, 4, 5, 6 or 8 at a
time, one penny is left over. There are no pennies left over when they are removed 7 at a
time. What is the least number of pennies that could be in the jar?

Answers

Answer 1

Answer:

721.

Step-by-step explanation:

The total number must be a multiple of 7

One less than the number is the LCM of 2 3 4 5 6 and 8.

The LCM is worked out as follows

2

3

4 = 2*2

5

6 = 2*3

8 = 2*2*2

LCM = 2*2*2* 3*5 = 120

But 121 is not divisible by 7 so it must be a multiple of 120 + 1 which is divisible by 7.

240 + 1 = 241 - not divisible by 7

480 + 1  = 481 - not divisible by 7

720 + 1 = 721

721/7 = 103

Answer 2

Answer:

Step-by-step explanation:

Let say n the number of pennies in the jar.

n is a multiple of 7 : n=7*k

n-1 is a multiple of 2,3,4,5,6,8 so a multiple of the lcm= 120

n-1=120*t

n-1=120*t

n=7*k

120*t=7k-1

7k=120*t+1

[tex]k=\dfrac{120*t+1}{7}\\k=17*t+\dfrac{t+1}{7}\\t=6+7*a\\k=17*(6+7a)+\frac{6+7*a+1}{7} =102+119*a+1+a=103+120*a\\n=7*k=7*(103+120*a)=721+840a\\\\[/tex]

The least number of pennies is 721 (when a=0)

Proof:

n-1=720

720/2=360

720/3=240

720/4=180

720/5=144

720/8=90

721/7=103


Related Questions

What is each number in scientific notation?



Drag the answer into the box to match each number.

0.0000855 -------
855,000 --------


A.8.55 * 10^-6, B.8.55 * 10^-5, C.8.55 * 10^5, D.8.55 * 10^6

Answers

0.0000855 is B
855,000 is D

After a price increase of 20% the cost of entry to a museum rose to $25.80. Find the original
entry fee

Answers

Answer: 21.5

Explanation:

a x 120/100 = 25.8
a x 6/5 = 25.8
a = 25.8 x 5/6
a = 21.5

Where a is the original price.

Hi

Let call X the origninal price.

if it rose of 20 % , it's mean that it' be multiplicate by 1.20

so :

X*1,2 = 25.8

1.2X=25.8

As math is all about method and training, I let you have a try and resolve the equation. If you do not know how, ask in comments section.

Supplementary angles are two angles that add up to 180 degrees! * Angles A and Care supplementary. Find the measure of angle C.HELPP

Answers

Answer:

106

Step-by-step explanation:

a=74

c=?

180-74=106

Answer:  106 degrees

============================================================

Explanation:

As the hint states at the top, supplementary angles add to 180 degrees

If we glued the angles together, then we'd form a straight line.

angleA+angleC = 180

74+C = 180

C = 180-74

C = 106 degrees

which number line best shows the position of square root of 3
HURRRYYY PLEASE

Answers

Answer:

I think no 4 shows the best position for 3

It’s 4 I think it’s closer

How can I work this problem in adding integers with counters 5 + (-7)

Answers

[tex]\\ \rm\longmapsto 5+(-7)[/tex]

[tex]\\ \rm\longmapsto 5-7[/tex]

[tex]\\ \rm\longmapsto -2[/tex]

Note:-

(-)(-)=(+)(+)(-)=(-)(-)(+)=(-)(+)(+)=(-)

Answer:

is -2

Step-by-step explanation:

because we have (-)+(+) is - so our answer is in minus

10-7+12 dived (2^3-6) May you answer hope this will help

Answers

Answer:

7.5

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

for f(x)=x^2-2, find the rate of change on the interval [-2,4]​

Answers

Answer:

2

Step-by-step explanation:

steps are in picture.Ignore hand writing

Choose each correct statement.

1. Sin A = b/c
2. Cos A = b/c
3. Tan A = b/8
4. M 5. m 6. Sin B= 8/c
7. Cos B = b/c
8. Tan B = b/8
9. Sin A = 8/c
10. Tan A =8/b
11. Sin B = b/c
12. Sin A = Cos A
13. Sin A = Cos B

Answers

Answer:

Step-by-step explanation:

Sin(A) = 8/c    Not correct.Cos(A) = b / c CorrectTan(A) = b / 8 Correct and Makes no sense to meSin(B)= b/c     CorrectCos(B) = 8/c   Not correctTan(B) = b/8   CorrectSee (A)           Not CorrectTan(A)  See 3 Not CorrectSee 6Sin(A)=Cos(A) Not correctSin(A) =Cos(B) Correct

2,3,5,6, 8,11,13          Are correct.

Help me with number 23 plsssssss

Answers

The Answer is:

p=15

5x3=15

So that must mean 15/5=3

Hi! I'm happy to help!

To make this equation easier, we can use the inverse operation, multiplication (instead of division).

p÷5=3

3×5=p

Doing this will give you the same answer, it just makes it easier. 3 times 5 is 15, so p=15

We can double check our answer by putting in 15 for p.

p÷5=3

15÷5=3, this is true, so our answer is correct.

I hope this was helpful, keep learning! :D

“Find the measure of angle 1 if angle CUB=78. Name the special pair of angles formed.”

Answers

[tex]\\ \rm\longmapsto <CUB=<CUS+<BUS[/tex]

[tex]\\ \rm\longmapsto <1+48=78[/tex]

[tex]\\ \rm\longmapsto <1=78-48[/tex]

[tex]\\ \rm\longmapsto <1=30[/tex]

Help ASAP I'm in school need help​

Answers

Answer:

B

Step-by-step explanation:

this is the answer to this question

Which of the following describes 977.834? Select all the that apply ​

Answers

[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]

977.834 can be defined as a rational number. Why? Well, 977.834 is not a non-terminating non-recurring/recurring number. Of it was, then it would have been an irrational number. Now, it can be a real number also because real numbers include all sorts of numbers whether it be fractions, decimals, roots, cubes etc. It's not an integer because integers don't include decimals or fractions numbers. So, the answers or options that are correct are

[tex] \sf \hookrightarrow \boxed{\sf\: rational \: number \: \: and \: real \: number}[/tex]

________

Hope it helps.

▅ ▆ ▇ █ RainbowSalt2222 █ ▇ ▆ ▅

please help me!!!!!!!!

Answers

Answer:

$84,320

Step-by-step explanation:

Simple any income above $9001 is taxed at 5.4%

So take 5.4% of $80,000 ($4,320) and add it back in

SO... $84,320

6.
Evaluate the function rule for the given value.

f(x)= 3× for x= -4
A. –12
B. 1/81
C. –64
D. 1/243

Answers

Answer:

B. 1/81

Step-by-step explanation:

f(-4) = 3(-4)

f(-4) = -12

Hope that helps.

-12,1/243,-64 or 1/81

1/81 would be the correct answer to the equation hope this helps

evaluate the function rule for the given value.

f(x)=3^x for x=-4

-----

f(-4) = 3^(-4)

---

 

f(-4) = (1/3)^4

---

f(-4) = 1/81

14) A blizzard produced 9 - inches of snow. The
sun came out for three days and melted 7 - inches
How much snow remains after the three days?

Answers

Answer:

2 3/8 in.

Step-by-step explanation:

[tex]9\frac{1}{2}-7\frac{1}{8}\\\\9\frac{4}{8}-7\frac{1}{8}\\\\2\frac{3}{8}[/tex]

Best Buy has a store brand TV for $700. This is $250 more than 1 of the cost of a deluxe model 4 that they also carry. What is the price of the deluxe model that Best Buy has in their store? Write out the equation.

Answers

Answer:

$950

Step-by-step explanation:

$700 + $250 = $950

If f(n) = 3n+ 5 , find f(-3). soln, 3n+ 5​

Answers

Hope it helps! If it is, Brainliest please!

Answer: f(-3) = -4

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given expression

f(n) = 3n + 5

Substitute values into the expression

f(-3) = 3(-3) + 5

Simplify by multiplication

f(-3) = -9 + 5

Simplify by addition

f(-3) = [tex]\boxed{-4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

please beging help me thanks ​

Answers

Answer:

1)[tex]\frac{7}{12}[/tex] 2)[tex]\frac{1}{4}[/tex]  3)[tex]\frac{2}{12}[/tex] 4)Rs.36 000

Step-by-step explanation:

1)1/3+1/4=4/12+3/12

             =7/12

2)remaining=12/12-7/12

                   =5/12

 other expenses=5/12*3/5

                            =1/4

3)total=7/12+1/4

          =7/12+3/12

          =10/12

          =5/6

remaining=6/6-5/6

                =1/6

fraction of the salary=1/6*2

                                  =2/12

4)1/6=rs.6000

   6/6=rs,36 000

Hey guys answer for points!
Question: 7 = x + 2x - 5 - 5x
Please include your steps and make sure it is accurate! Brainiest for correct answer/good answer!

Answers

Answer:

please mark me brainliest

Step-by-step explanation:

7=3x-5-5x

7=3x-5x-5

7=-2x-5

7+5=-2x

12=-2x

x=12/-2

×=-6

Answer:

-6 = x

Step-by-step explanation:

7 = x + 2x - 5 - 5x

~Combine like terms

7 = -2x - 5

~Add 5 to both sides

12 = -2x

~Divide -2 to both sides

-6 = x

Best of Luck!

Which two lines are parallel?
Which line is the transversal? How do you know

please help,its a grade

Answers

Answer: The 2 red lines are parallel and the blue line is transversal

Step-by-step explanation:

The 2 red lines are parallel (align with each other)

The blue line goes thru the other 2 lines meaning its transversal.

How do you solve
ca=dr, for a

Answers

Answer:

a = dr/c

Step-by-step explanation:

ca = dr

Divide both sides by c. This gets a by itself on the left side.

a = dr/c

What is the opposite of 8.5?

Answers

Answer:

-8.5

Step-by-step explanation:

If I'm not mistaken this is true because the opposite of a whole number (That isn't 0) is always the negative

You have to evaluate
3³+11-10÷2×4=w

Answers

Answer:

18

Brainliest, please!

Step-by-step explanation:

3^3 + 11 - 10 / 2 x 4 = w

27 + 11 - 10 / 2 x 4 = w

27 + 11 - 5 x 4 = w

27 + 11 - 20 = w

38 - 20 = w

w = 18

One cookie recipe calls for 23cups of sugar. Another recipe calls for 114cups of sugar. How many cups of sugar are needed in both recipes?

Answers

Answer:

does the sugar levels matter just bake the da*n cookies man

the ground line is 12 cm and width is 10 cm find out the area of the ground and parameter of the ground​

Answers

Answer:

2(x+6) + 2(x) =40

2x +12+2x=40

4x+12=40

4x=28

x=7

Now to find area it is LxW

7x13=91

So the area of the rectangle is 91 meters squared

Step-by-step explanation:

Answer:

Area=120[tex]cm^{2}[/tex]

Perimeter =44[tex]cm^{2}[/tex]

Step-by-step explanation:

area=length(l)*width(w)    

      =12*10                        

     =120[tex]cm^{2}[/tex]

perimeter=2(length+width)

                =2(12+10)

                =2*22

               =44[tex]cm^{2}[/tex]

Which best describes a compass tool?
a. a plastic straightedge with equidistant units in inches or centimeters
b. a long wooden tool with a ruler on one side and a sliding holder on the other
c. a metal instrument with two legs-one with a point and one for a pencil
d. a curved plastic tool in the shape of the letter D with markings on the face

Answers

Answer:

I believe its c

Step-by-step explanation:

just for reference I can't guarantee

The best described compass tool is a metal instrument with two legs-one with a point and one for a pencil option (c) a metal instrument with two legs-one with a point and one for a pencil.

What is a magnetic field?

The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.

It is given that:

A tool is a compass tool which is an indicating the north direction.

As we know,

The magnetic field is defined as the field the magnetic materials generate.

A metal object with two legs, one for a pencil and one with a tip.

Thus, the best describes compass tool is a metal instrument with two legs-one with a point and one for a pencil option (c) a metal instrument with two legs-one with a point and one for a pencil.

Learn more about the magnetic field here:

brainly.com/question/14848188

#SPJ2

PLEASE HELP ME, I WILL CROWN BRIANLIEST FOR THE FIRST PERSON TO REPLY

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5

Mean: 16.52

Median: 16.95

Standard Deviation: 3.11

IQR:5.5

How does adding 5 to each of the values in the data set impact the measures of variability?

Answers

Answer:

see below:

Step-by-step explanation:

the median will become a larger, different number. The mean will also become a larger number, since it will still be dividing by the same amount of numbers in the equation, only the quantity will become larger. Same with standard deviation. The IQR will change, because the amount of the two numbers you'll be subtracting will end up greater than before.

(this is just what mine said, i hope this helped at least a little bit!! Sorry if our websites are different, have a nice day!) :)

Bài 12: Cho đa thức M(x) = 4x + 2x -x2 - x + 2x2–x+1−3x
a) Sắp xếp đa thức trên theo lý thừa giảm dần của biến
b) Tính M(-1) và M(1) .
c) Chứng tỏ đa thức trên không có nghiệm
A(x) = -4x -x + 4x" +5x+7+4x – 6x?

Answers

Answer:

what?

Step-by-step explanation:

Please anyone help please I’m stuck with this question please help please ASAP show work Too

Answers

This is the flip side of the previous one I answered. The range is the set of all y-values or outputs. Since you can only spend increments of $1.25, you cannot have all the numbers from 12 to 0 in your range.

The range is 12 dollars minus all possible increments of 1.25, until you can’t buy any more candy.

12
12-1.25 = 10.75
10.75-1.25 = 9.50
And so on.

The answer is D.

please help me will mark braniliest

Answers

Answer:

The correct answer is option A. Line DB

Step-by-step explanation:

When you write that M is a line, the sign for this would be a line with arrows on both of its end like this :  <------------>

Now, due to the fact that lines look like this  <------------>, we can cross out option C and D as they both aren't lines but points. Points go like this: ---->

Option B says, "line EB", this can't be true because E corresponds with the letter F, it can't become a line with B hence why the only option true here is choice A.

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