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
In the month of February I spent 37.45 on coffee and a mug.... How many refills did I get?
8.95 +1.50r= Total
Someone help ASAP!
a
y = 2x + 5
C.
Find an equation of the line perpendicular to the graph of 10x - 5y = 8 that passes through the point at (-4, 7)
Answer:
c .....the answer is c.....
Step-by-step explanation:
I hope this helps
Need help te slim is designing a cover for a book he wants to have a rectangler grid
Answer:
The answer is A
Step-by-step explanation:
If you do (x-3)(x-7) you get x^2 - 10x + 21
What is the measure of the missing angle? *
H
60°
82%
Answer:
38 degrees
Step-by-step explanation:
180 - (60 + 82) =
180 - 142 =
38 degrees
Hope that helps!
whats the error in this question
Answer:
line 1
Step-by-step explanation:
This is because when using the distribitive property they did not multiply the 1 in parenthese which would be x-5x+5=3x+2
Answer:
PROBABLY LINE ONE
Step-by-step explanation:
BECAUSE THE FOLLOWING LIKE THE ANSWER IS WRONG
Kaylee surveyed 920 of the students in her school about their favorite color. 95% said
their favorite color was blue. How many students' favorite color was blue?
Answer:
x = 874
Step-by-step explanation
Set up your equation like this: Part/whole = percent/100
Assign the variable x to the unknown part of the equation and add in the known numbers:
So in this situation it would be: x/920 = 95/100
Solve for x:
100 times X = 920 times 95. (cross multiply)
That leaves you with 100x = 87,400
Divide both sides by 100:
x = 874
How do I Determine whether Rollie's theorem can be applied to F on the closed interval (AB) F of X = -x squared
Answer:
See Explanation
Step-by-step explanation:
Your question is incomplete. I will take the complete question as:
[tex]f(x) = -x^2[/tex]
[tex]Interval: [-1,1][/tex]
Required
Determine whether Rollie's theorem can be applied or not
First, find the coordinates of the endpoints on the closed interval [-1, 1]
[tex]f(x) = -x^2[/tex]
[tex]f(-1) = -(-1)^2 = -1[/tex] ------ [tex](-1,-1)[/tex]
[tex]f(1) = -(1)^2 =-1[/tex] ---- [tex](1,-1)[/tex]
Find the derivative of f(x)
[tex]f(x) = -x^2[/tex]
[tex]f'(x) = -2x[/tex]
Calculate the slope (m) of the secant line i.e. [tex](-1,-1)[/tex] and [tex](1,-1)[/tex]
[tex]m = \frac{-1 - (-1)}{1 - (-1)}[/tex]
[tex]m = \frac{-1 +1}{1 +1}[/tex]
[tex]m = \frac{0}{2}[/tex]
[tex]m=0[/tex]
Set the derivative to the calculated slope:
[tex]f'(x) = m[/tex]
[tex]-2x = 0[/tex]
[tex]x=0[/tex]
Plug in 0 for x in f'(0)
[tex]f'(x) = -2x[/tex]
[tex]f'(0) = -2 * 0[/tex]
[tex]f'(0) = 0[/tex]
Since f'(0) is differentiable at x = 0. We can conclude that Rollie's theorem can be applied
How many 3-inch thick bags of mulch should Noemi buy to cover 100 square feet at a depth of 4 inches? The length is 3.2ft and the width is 2.5ft.
Answer:
Approximately 17 bags.
Step-by-step explanation:
The length of the bag of mulch = 3.2 ft
The width of the bag of mulch = 2.5 ft
The thickness of the bag of mulch = 3 inch = 0.25 ft
Volume of a bag of mulch = length x width x thickness
= 3.2 x 2.5 x 0.25
= 2 cubic feet
So that, the volume of a bag of mulch is 2 cubic feet.
The area to be covered = 100 square feet
The depth of the area = 4 inches = [tex]\frac{1}{3}[/tex] feet
volume of the portion to be covered = area x depth
= 100 x [tex]\frac{1}{3}[/tex]
= 33 [tex]\frac{1}{3}[/tex] cubic feet
The volume of the portion to be covered is 33 [tex]\frac{1}{3}[/tex] cubic feet.
The number of bags of mulch needed = [tex]\frac{33\frac{1}{3} }{2}[/tex]
= 16[tex]\frac{2}{3}[/tex]
= 16.6667
The number of bags of mulch needed is 17.
Please help me on this I need help
Answer:
49.92
Step-by-step explanation:
Square = 30
5 x 6 = 30
Half Circle = 9.42
6 x 3.14 = 18.84 divided 2 since it’s a half circle equals 9.42
Triangle = 7.5
3 x 5 = 15 divided by 2 = 7.5
So, 30+ 9.42 + 7.5 = 49.42
please help this is so important and i need it now
Angle B will be 23 degrees
bs ng to the top left of the most popular c.hatrooms trooms aren't for the best in the United Arab Republic of Ireland in the United Arab Republic in the same time the error occurred to him in a few years later
Step-by-step explanation:
Against the law is a healthy lifestyle of the world of difference between the two of the most important thing is that the only thing we will not...❤️❤️
Pls tell me so quotes of not giving up
Answer:
Step-by-step explanation:
Knowledge is knowing a tomato is a fruit, wisdom is not putting it in a fruit salad
Your time is too valuable to waste on those who don't deserve it
Never give up great things take time
Failure is not an acception
As a wise fish once said "Just Keep Swimming" the more u swim the closer you get to your goal.
Omg- I need mega help- Ok- WHATS 1+1?! fr- this is such a hard question
Answer:
hkññaaqedx jurx jkñlnbgl dpsnish mija
A fossilized leaf contains 8% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.
Answer:
Step-by-step explanation:
0.5^(t/5600) = 0.08
2^(-t/5600) = 0.08
-t/5600 = log₂0.08
t = -5600 log₂0.08 ≈ 20406 years
Can someone help me how to do these two please
Answer:
1.B
2.B
hope this helps
Answer:
B. 62mph
B. 55weeks
Step-by-step explanation:
496 ÷ 8 = 62
15weeks/3houses = x weeks/11houses
15 × 11 ÷ 3 =55weeks
good luck, i hope this helps :)
Factorise the following
Answer:
D
Step-by-step explanation:
First take out a factor of 2:
2(1 - 25x^2)
Then factor the difference of squares:
2(1 -5x)(1+5x)
How do you write 6.14 × 105 in standard form?
Answer:
644.7
Step-by-step explanation:
PLSSSS HELPPPPP ASAPPPP
Answer:
b
Step-by-step explanation:
Draw graph of straight lines to find approximate solution to these simultaneous equations . y = 3x + 7 and 2y + x = 2
Answer:
(-1.714, 1.857)
Step-by-step explanation:
Here, we want to find the approximate solution to the system of linear equations
We start by plotting the graph of the lines
We have the plot as shown below;
the red line represents the first equation while the blue line represents the second equation
We have the solution as the point at which the two lines meet
The solution to this is;
(-1.714, 1.857)
You took a test that had 45 questions. You got 42 correct. What percent of the questions did you get correct
Write down a different ratio equivalent to 42 : 12
Step-by-step explanation:
simplify it maybe
try it with 2 and 3
Answer:
Another ratio that is equivalent to this is 7:2.
Step-by-step explanation:
If we divide both sides by 6, we get 7 and we get 2. Since 42 comes first, we put the 7 in place of the 42. Then we replace 12 with 6. After this, we get the ratio 7:2.
:
Two boats are traveling toward a lighthouse that is 200 feet (ft) above sea level at its top. When the two boats and the lighthouse are collinear, the boats are exactly 250 feet apart and the boat closest to the lighthouse has an angle of elevation to the top of the lighthouse of 15°, as shown.
What is the value of x, rounded to the nearest hundredth?
Answer:
Which Number Is x, You Didnt Specify
The number of bacteria in a Petri dish increases by 18% every hour. If there were initially 200 bacteria placed in the Petri dish, which function can be used to determine the number of bacteria in the Petri dish in exactly x hours?
Answer:
Step-by-step explanation:
an exponential equation has the form y=ar^x where y=final amount, a=initial amount, r=rate, and x=time, in this case
y=200(1.18)^x
HEEEEELLLLPPPP
write a short explanation of why the distance formula works and include a discussion of why either point can be point 1 or point 2
Answer:
Finding the distance between two distinct points on a plane is the same as finding the hypotenuse of a right triangle. From this perspective, the distance formula states that the distance of two distinct points on a plane is equal to the square root of the sum of the square of the rise and run.
I can not Put Out The Points So Im sorry.
A human’s DNA code, found in nearly all body cells, can be condensed into chromosomes.
Answer:
I'm a alien, sorry.
Step-by-step explanation:
Answer:
True
Strands of DNA are or can be condensed to chromosomes.
~Hope this helps~
Please help! I need the steps too!
Answer:
The answer is -3 2/7
Step-by-step explanation:
5- 1x1 - -4x4 + 3/2-1-4-4
5 - 1 +16+3/2-1-4-4
4+16+3/-7
23/-7
or - 3 2/7
Hello I'm Chloe Can you help me, Thank you :)
800.5 x (2x 10^6)
A. 1.7 x 10 ^7
B. 1.601 x 10^7
C. 1.7 x 10^9
Answer:
b is correct
Step-by-step explanation:
A shipping container will be used to transport several 80-kilogram crates across the
country by rail. The greatest weight that can be loaded into the container is 26500
kilograms. Other shipments weighing 6300 kilograms have already been loaded into
the container. Write and solve an inequality which can be used to determine x, the
number of 80-kilogram crates that can be loaded into the shipping container.
Answers:
The inequality to solve is [tex]80x+6300 \le 26500[/tex]The solution to the inequality is [tex]x \le 252.5[/tex]Interpretation: The most crates we can load is 252 since we can only load a positive whole number of crates, and because 253 is too many.==============================================================
Explanation:
x = number of 80-kilogram crates
x is some positive whole number
1 crate weighs 80 kilograms, so x of them will weigh 80x kilograms.
This is added on top of the 6300 kg from the other cargo already on board.
We have a total weight of 80x+6300. Let's call this T.
So T = 80x+6300
We want T to be 26500 or smaller. Otherwise, we've gone over capacity.
This must mean we want [tex]T \le 26500[/tex] which is the same as saying [tex]80x+6300 \le 26500[/tex] after replacing T with 80x+6300.
---------------------------
Let's follow PEMDAS in reverse to isolate x
[tex]80x+6300 \le 26500\\\\80x+6300-6300 \le 26500-6300 \ \text{ ... subtract 6300 from both sides}\\\\80x \le 20200\\\\\frac{80x}{80} \le \frac{20200}{80} \ \text{ ... divide both sides by 80}\\\\x \le 252.5\\\\[/tex]
The inequality sign stays the same the entire time. It would only flip if we divided both sides by a negative number.
In the last step, we get a decimal value. However, as stated earlier, x is a positive whole number.
We cannot round to 253 because that's too high. We can check x = 253 is too high by noticing that...
80x+6300 = 80*253+6300 = 26,540
which is over the 26,500 mark by 40 kg
So we must round down to the nearest whole number and find that x = 252 is the largest x value possible. Let's check to see if we're under the weight limit
80x+6300 = 80*252+6300 = 26,460
We're under the 26,500 weight limit (with 40 kg to spare)
In short, the most crates that we can load is 252 crates in addition to the other cargo that collectively weighs 6300 kg (which may or may not consist of those 80-kilogram crates).
Solve the system.
3x + 2y + 4z = 11
2x – y + 3z = 4
5x – 3y + 5z = -1
Enter your answer as an ordered triple.
Someone help please!!
Answer: (x, y, z) = (-3, 2, 4)
In other words, x = -3, y = 2 and z = 4.
You'll enter the number only into each box.
===============================================================
Explanation:
There are a few routes we can take to solve this. I'll use substitution.
First let's isolate y in the second equation.
2x - y + 3z = 4
2x + 3z = 4+y
4+y = 2x+3z
y = 2x+3z-4
This is then plugged into the first equation
3x+2y+4z = 11
3x+2( y )+4z = 11
3x+2( 2x+3z-4)+4z = 11 .... replace y with 2x+3z-4; since y = 2x+3z-4
3x+4x+6z-8+4z =11
7x+10z-8 = 11
7x+10z = 11+8
7x+10z = 19 .... we'll call this equation (4) and come back to this later
--------------------------------------
Move onto the third equation (of the original equations given)
Plug in y = 2x+3z-4
5x - 3y + 5z = -1
5x - 3( y ) + 5z = -1
5x - 3( 2x+3z-4 ) + 5z = -1
5x - 6x - 9z + 12 + 5z = -1
-x - 4z + 12 = -1
-x - 4z = -1-12
-x - 4z = -13 ..... let's call this equation (5)
--------------------------------------
To recap, we found equation (4) and equation (5) to be
7x+10z = 19-x - 4z = -13We can then solve for x in equation (5) like so
-x - 4z = -13
-x = -13 + 4z
-x = 4z - 13
x = -(4z - 13)
x = -4z + 13
This is then plugged into equation (4)
7x+10z = 19
7(-4z+13)+10z = 19 .... note how we now have one variable
-28z+91+10z = 19
-18z+91 = 19
-18z = 19-91
-18z = -72
z = -72/(-18)
z = 4
We can use this value of z to find x
x = -4z+13
x = -4(4)+13
x = -16+13
x = -3
Use the values of x and z to find y. We'll revisit the first equation in which we isolated y
y = 2x+3z-4
y = 2(-3)+3(4)-4
y = -6+12-4
y = 6-4
y = 2
So overall, the solution to this system is (x, y, z) = (-3, 2, 4)
-------------------------------
Checking the answer:
We'll replace x,y,z with the values we found.
In the first equation, 3x+2y+4z = 11 becomes 3(-3)+2(2)+4(4) = 11 and that simplifies to 11 = 11. In other words, the expression 3(-3)+2(2)+4(4) turns into 11. This confirms the first equation.Repeat the same idea for the second equation. We have 2x-y+3z=4 turn into 2(-3)-2+3(4) = 4 and that simplifies to 4 = 4. The answer is verified here. The third equation 5x-3y+5z = -1 becomes 5(-3)-3(2)+5(4) = -1 which simplifies to -1 = -1. We get a true equation here as well.Since all three equations are true when (x, y, z) = (-3, 2, 4), this verifies the answer completely. This is the only solution to the system. The system is independent and consistent.
The circle shown has a radius of 4 cm.
Not drawn
to scale
What is the length of the diameter of the circle?
cm
Answer:
8 cm
Step-by-step explanation: diamater is half the radius
solve for x,y and z in the following diagrams