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Answer:

$99.19

Step-by-step explanation:

Problem:

On a table there are 1001 pennies lined up in a row. I come along and replace every second coin with a nickel.  Then I replace every third coin with a dime.  Finally, I replace every fourth coin with a quarter.  How much money is on the table now? Why is twelve important?

Solution:

Our first step was to make a line of pennies (as long as possible) in order to see if we could figure out a pattern that would help us determine the total amount of money on the table.  

Then we went through and replace every second coin with a nickel.

Then we went through and replaced every third coin with a dime.

Then we went through and replaced every fourth coin with a quarter.

As a group we then tried to decipher if there was a pattern that would help us determine the total value of coins.  We then noticed that there was a pattern of twelve coins.

= $1.19

= $1.19

= $1.19

We determined the number of times the pattern of twelve coins repeated in the 1001 coins:

1001 ÷ 12 = 83 R5

Since we knew that the pattern repeated itself 83 full times and each time the dollar value is $1.19 we counted to determine the cost of the first 996 coins.

$1.19 X 83 = $98.77

Then we added the remaining 5 coins, which cost $0.42

$98.77 + $0.42 = $99.19

Therefore, there is a total of $99.19 on the table.

Since, the lowest common multiple of 2, 3, and 4 is 12, the pattern will repeat itself every 12th coin.

A sequence or pattern in a series of numbers is a number patterns

The amount of money in coins lined up on the table is $99.19

The reason the above value is correct is as follows:

The given parameters are;

The number of pennies lined up on a table = 1,001

The coin with which every second coin is replaced with = A Nickle = 5 Cents

The coin with which every third coin is replaced with = A Dime = 10 Cents

The coin with which every second coin is replaced with = A Quarter = 25 Cents

[tex]\begin{array}{ccc}Coin \ Position&&Coin \ Value \ (Cents)\\1&&1\\2&&5\\3&&10\\4&&25\\5&&1\\6&&10\\7&&1\\8&&25\\9&&10\\10&&5\\11&&1\\12&&25\\13&&1\\14&&5\\15&&10\\16&&25\\17&&1\\18&&10\\19&&1\\20&&25\\21&&10\\22&&5\\23&&1\\24&&25\end{array}[/tex]

From the above values, we have that the first twelve coins are repetitive, therefore, the number of repeating units is the whole number part of 1,001/12 = 83, which gives;

1 + 5 + 10 + 25 + 1 + 10 + 1 + 25+ 10 + 5 + 1 + 25 = 119

The value sum of the 83 repeating 12 units = 119 × 83 = 9877

The value of the first 12 × 83 = 996 coins = 9,877 Cents

The coin in the;

997th position = 1 Cent

998th position = 5 Cent

999th position = 10 Cent

1,000th position = 25 Cent

1,001th position = 1 Cent

The total value of the coins = (9,877 + 1 + 5 + 10 + 25 + 1) Cents = 9919 Cents

9919 Cents = $99.19

The amount of money that is on the table = $99.19

Learn more about number patterns here:

https://brainly.com/question/14294944

Answer:

History of mathematics

Several civilizations — in China, India, Egypt, Central America and Mesopotamia — contributed to mathematics as we know it today. The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.

Step-by-step explanation:which includes basic operations, multiplication, fractions and square roots. The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in America, the Mayans developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed.

Answer:

la primera

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Cuando se tienen dos exponencial una dentro y otra fuera del paréntesis se suman debido a esto la A es la única que cumple con la ecuación

the answer is D ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

point D

Step-by-step explanation:

go to the left 5 spaces (negatives)

go up 2 spaces

Answer:

a. 12 mm

The Pythagorean Theorem states that a^2 + b^2 = c^2 with a and b being lengths of legs and c being the length of a hypotenuse. So we can use our givens to solve for the remaining leg.  

9^2 + b^2 = 15^2

81 + b^2 = 225

b^2 = 144

b = 12

Step-by-step explanation:

BOOOOOOOOM!!!!!!!!!!!!!!!!!!!!!!

Answer:

x = 1 and x = -3

Step-by-step explanation:

We need to solve the given equation.

[tex]3+x=x^2+3x[/tex]

Taking all terms together,

[tex]x^2+3x-3-x=0\\\\x^2+2x-3=0\\\\x^2+3x-x-3=0\\\\x(x+3)-1(x+3)=0\\\\(x-1)(x+3)=0\\\\x=1\ and\ x=-3[/tex]

So, the solution of the above equation is x = 1 and x = -3.

Answer:

[tex]4=(x+1)^{2}[/tex]

x= -1 ±2

Khan Academy

Answer:

i not sure sorry ..........

Step-by-step explanation:

1. 48 decide by 16 = 3 per min

2. Decide by 7 you will get 5:2

3. 24 per hour so 3 hours is 3 times 24 which is 72

4. 5cm per hour

5. 175:326.

6.1080 decide by 9 you get 120

120 times 13 is 15607.

7. 2520 decide by 9 is 280

Sara got 560 while Hina got 19608.

8. Ali is the fastest. He can fold 8 in a minute

9. I dont understand your question

10. A is 3

Answer:

He needs to sell at least 12 boxes.

Answer:

Step-by-step explanation:

Corresponding sides have same ratio in similar figures:

Correct option is A

Answer:

Line Segment

Step-by-step explanation:

A line segment has dots on both ends of the line. A line has nothing at either end of it. A ray has an arrow at one end of the line. Line BC is a line segment.

Hope it helps!

Explanation:

This is because we have two fixed endpoints, B and C, where the line does not go on forever beyond those endpoints. This means BC is some fixed length. The terms "line segment" and "segment" are the same thing.

A ray on the other hand would have the line go on forever in one direction, while it only has one fixed endpoint. As the name suggests, think of the ray of sunlight as an example. So we can rule out "ray". We can also rule out "line" because it doesn't extend forever in both directions.

Answer: C. 0 ≤ x ≤ 230

When the  A golfer hit a golf ball from a tee box that is 6 yards above the ground so the domain of the function is [0,260].

Here the domain is the values of 'x' in the function f(x).

the position at which the golfer is hit the ball is (0,6) and the position where the ball hits the ground is (230,0)

So, the domain of the function for this situation is [0,260].

Learn more about domain here: https://brainly.com/question/18573273

Answer:

15/4

Step-by-step explanation:

Answer:

[tex]\frac{23}{4}[/tex]  

Step-by-step explanation:

5 [tex]\frac{3}{4}[/tex] = [tex]\frac{5 x 4 + 3 }{4}[/tex]  = [tex]\frac{23}{4}[/tex]

Hope is right!!!

Answer:

We'd need to see the full circle to answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

angles 2 and 6 are corresponding angles and are congruent if the transversal crosses through two parallel lines

Answer:

gvhgfcbvhgfc

Step-by-step explanation:

yee

Answer:

The correct answer is D. 8

Step-by-step explanation:All you have to do is count the data points on the graph.

Have a good day and stay safe!

There were 8 data points in the table.

Option D is the correct answer.

We have,

From the graph of the scatterplots,

We can consider the points as the coordinates:

(10, 15)

(20, 20)

(20, 30)

(20, 40)

(25, 30)

(30, 35)

(35, 45)

(45, 49)

Now,

There are 8 coordinates from the graph.

This means,

There are 8 data points plotted on the graph of the scatterplot.

Thus,

There were 8 data points in the table.

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ2

Answer:

It is not a function

Step-by-step explanation:

This is not a function because it does NOT pass the vertical line test. The vertical line test is just as it sounds: if you were to draw a vertical line from 3 to -3, it would pass through two outputs for every one input. Therefore, it's not a function.

Answer:

13 cm

Step-by-step explanation:

A^2+12^2=15^2

A^2+144=225

A^2=81

A=9

9x2=18

31-18=13 cm

Find the perimeter of a rectangle whose width is 3 cm and whose diagonal is 3 √5 cm long.

A^2+3^2=3√5^2

A^2+9=45

A^2=36

A=6

3+3+6+6=18 cm

Answer:

x+y=900

x-y=300

2x=1200

x=600

Answer:

answer is provided below

Step-by-step explanation:

5 ----> constant

+ ------> operator

2 ------> coefficient

2x ------> variable term

x --------> variable

Hope the above solution helps

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

Explanation:

We replace every copy of x with 5. Then we apply the order of operations PEMDAS to simplify.

f(x) = -2x+1

f(5) = -2(5)+1 ..... x replaced with 5

f(5) = -10+1

f(5) = -9

Answer:5

Just use a caculator

92124w1322

Answer:

f(3) = 512

Step-by-step explanation:

f(3) = 8^3

f(3) = 512

= 512