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
Is VUW similar to
VXY? If yes,explain how you know. If no, explain
why not.
Answer:
Yes, because m<UVW is congruent to m<XVY and m<VUW is congruent to m<VXY
Step-by-step explanation:
Plz help fast will mark brainliest
Answer: -270
Step-by-step explanation:
First, simplify the exponent
[tex]-6*(25+20)[/tex]
Then, distribute
[tex]-150+-120[/tex]
Then, subtract(add a negative)
[tex]-270[/tex]
Hope it helps <3 :)
find the finance charge for a $25,000, three year loan with a 9.25% apr. How much interest is paid
Answer:
$6,937.50
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 25000(.0925)(3)
Arkadaşlar cevapları neler
Answer:
hi
Step-by-step explanation:
i translated your question…
and
[tex]x - 4 = 5 \\ x = 5 + 4 \\ x = 9[/tex]
[tex]3 - x = - 4 \\ x = - 4 - 3 \\ x = - 7[/tex]
[tex]5 - x = 7 \\ x = 7 - 5 \\ x = 2[/tex]
hope it helps
Have a nice day bye
help me iv been trying from this morning
Answer:
i did the first
Step-by-step explanation:
1st way
Standard form: a(X-h)²+k = ( -2/3X² -16/3X -32/3) +32/3 -17/3 = -2/3(X +4)² +5
y = -2/3*X^2-16/3*X-17/3
X = -4 ±√( 15/2) = -6.7386, or -1.2614
Axis of symmetry: X= -4; Vertex (maximum)=(h,k)=( -4, 5); y-intercept is (0,-5.66666666667)
two real roots: X=-1.2613872124776866 and -6.738612787477313
Answer:
b) y = -2/3(x + 4)² + 5c) y = 1/2(x + 8)² - 5d) y = 3/8(x + 7)² - 2Step-by-step explanation:
Vertex form is:
y = a(x - h)² + kVertex of the function is point (h, k)
b) Congruent to y = 2/3x² and opens down means:
a = -2/3Maximum value at (-4, 5) means:
h = -4, k = 5The function is:
y = -2/3(x + 4)² + 5c) Congruent to y = 1/2x² and has minimum value y = -5 at x = -8:
a = 1/2, h = -8, k = -5The function is:
y = 1/2(x + 8)² - 5d) Vertex (-7, -2) and passes through the point (-3, 4)
y = a(x + 7)² - 2Substitute coordinates and find a:
4 = a(-3 + 7)² -26 = 16aa = 3/8The function is:
y = 3/8(x + 7)² - 2wich one doesn't belong
Answer:
The answer is 3 because its a constant value and the rest are variables
ay you should help me with this tyty
Answer:
C. [tex]m=20[/tex], [tex]n=10[/tex]
Step-by-step explanation:
Since the triangle is a special 30°-60°-90° triangle, the hypotenuse is twice the size of the shortest leg. The long leg is [tex]\sqrt{3}[/tex] of the short leg.
Write the equation of a line parallel to the y-axis and passing through the point
(-3,-4).
Answer:
x = -3 is the answer. Writing this cause brainly requires a 20 character answer.
help me with maths :)
For the triangle it is given that AE2 + EB2 = 9 and BE2 + EC2 = 16
Find AC =
Answer:
Step-by-step explanation:Given : right triangle ABC , AE^2 + EB^2 =9 and BE^2 + EC^2 = 16
To find : AC
Solution:
BE ⊥ AC
∠AEB = 90°
=> ΔAEB is right angled
=> AB² = AE² + EB²
=> AB² = 9
∠BEC = 90°
=> ΔBEC is right angled
=> BC² = BE² + EC²
=> BC² = 16
∠ABC = 90°
=> AC² = AB² + BC²
=> AC² = 9 + 16
=> AC² = 25
=> AC = 5
AC = 5
The length of AC is 5 units.
What is a Triangle?Any three-sided polygon having three edges and three vertices is referred to as a triangle in geometry. The most important attribute of a triangle is that its internal angles sum to 180 degrees. The triangle's angle sum attribute is what is known as.
As per the given data:
We are given the diagram of ΔABC which is right-angled.
BE is perpendicular to AC.
AE² + EB² = 9 ...(i)
BE² + EC² = 16 ..(ii)
By using the Pythagoras theorem in ΔABE:
AE² + EB² = AB²
From comparing with eq (i)
AB² = 9
AB = √9 = 3 units
By using the Pythagoras theorem in ΔCBE:
BE² + EC² = BC²
From comparing with eq (ii)
BC² = 16
BC = √16 = 4 units
By using the Pythagoras theorem in ΔABC:
AB² + BC² = AC²
AC² = 3² + 4²
AC² = 9 + 16 = 25
AC = 5 units.
The length of AC is 5 units.
Hence, The length of AC is 5 units.
To learn more on Triangle, click:
brainly.com/question/19976619
#SPJ2
write Down a rational number that lies between -9 and -8
Franco said that when the speed and distance are known,you only have to multiply them to get the time. Is Franco's statement correct? Explain why or why not.
Answer:
No, you have to divide
Step-by-step explanation:
Speed = distance/time
distance/speed = time
Find the value of x.
Answer: x = 20
Step-by-step explanation:
The angle is 90 degrees so we can make an equation
with it.
3x + 10 + x = 90
Combine like terms
4x + 10 = 90
subtract 10 from both sides to cancel it out
4x = 80
Now divide by 4 to leave x by itself
x = 20
Now you can check if it's correct by plugging in x to the equation given
3(20) + 10
60 + 10
70
20 + 70 = 90 degrees
Answer:
D: 20 degrees
Step-by-step explanation:
First, we add 3x+10 and x together because they are within a right angle, which is 90 degrees. This gives the equation 4x+10=90. We solve from here.
We subtract 10 from both sides to isolate the x-variable. 90 minus 10 equals 80. This gives us the equation 4x=80. To further isolate the x-variable, we divide both sides by 4. 80 divided by 4 equals 20.
This leaves us with x=20.
Hope this helped!
select all the numbers between 80 and 100 that have exactly 4 factors, one of which is 5.
80
85
90
95
100
Answer:
90.
Step-by-step explanation:
Here 5 is one of the 4 prime factors, so dividing the lower (80) and upper limit (100) by 5 we have new lower limit 16 and new upper limit 20.
So the product of other 3 factors should be greater than 16 and less than 20. And we can have it from 18 only. Hence the number is 90.
The numbers between 80 and 100 having factor 5 are
80, 85, 90, 95, 100
16 = [tex]2^{4}[/tex]
17 = 17
18 = 2× 3 × 3
19 = 19
20 = [tex]2^{2}[/tex] × 5
90 = 2 × [tex]3^{2}[/tex] × 5
Que es una Progresión Aritméticas
A hotel manager is adding a tile border around the hotel's rectangular pool. Let represent the width of the pool, in feet. The length is 5 more than 3 times the width, as shown. Write two expressions that represent the perimeter of the pool which exspressions are right
2(4p+5)
8p+5
8p+10
4p+5
4(p+3p+5)
2p+3p+5
im almost out of points plss help
Answer:
A and CStep-by-step explanation:
Width = pLength = 3p + 5Perimeter:
2(w + l) = 2(p + 3p + 5) =2(4p + 5) =8p + 10Correct options are A and C
Answer:
2(4p+5)8p+10Step-by-step explanation:
to understand thisyou need to know about:algebracreating algebraic expressionPEMDAStips and formulas:parameter of rectangle:2(l+w)let's solve:let width be p
according to the first condition
The length is 5 more than 3 times the widththerefore
the length is
3×p+5
3p+5
Parameter of a rectangle
=2(l+w)
=2(3p+5+p)
=2(4p+5) {combine like terms}
=8p+10{distribute 2}
Find the next two terms of each geometric sequence (show work)
1. -15, -30, -6, __, __
2. 90, 30, 10, __, __
3. 1/4, 3/8, 9/16, __, __
Answer:
[tex]\huge\boxed{1.\ -120,\ -240}\\\boxed{2.\ \dfrac{10}{3},\ \dfrac{10}{9}}\\\boxed{3.\ \dfrac{27}{32},\ \dfrac{81}{64}}[/tex]
Step-by-step explanation:
[tex]\text{if}\\a_1,\ a_2,\ a_3,\ ...\text{is a geometric sequence}\\\text{then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=const.=r\\\\a_n=a_{n-1}r[/tex]
[tex]1.\\-15,\ -30,\ -6\\\\\dfrac{-30}{-15}=-2;\ \dfrac{-6}{-30}=\dfrac{1}{5}[/tex]
it,s not a geometric sequence...
I think it should be:
[tex]-15,\ -30,\ -60,\ ...\\\\\dfrac{-30}{-15}=2;\ \dfrac{-60}{-30}=2\\\\next\\\\-60\cdot2=-120\\-120\cdot2=-240[/tex]
[tex]2.\\90,\ 30,\ 10,\ ...\\\\\dfrac{30}{90}=\dfrac{1}{3};\ \dfrac{10}{30}=\dfrac{1}{3}\\\\next\\\\10\cdot\dfrac{1}{3}=\dfrac{10}{3}\\\\\dfrac{10}{3}\cdot\dfrac{1}{3}=\dfrac{10}{9}[/tex]
[tex]3.\\\dfrac{1}{4},\ \dfrac{3}{8},\ \dfrac{9}{16},\ ...\\\\\dfrac{\frac{3}{8}}{\frac{1}{4}}=\dfrac{3}{8}\cdot\dfrac{4}{1}=\dfrac{3}{2};\ \dfrac{\frac{9}{16}}{\frac{3}{8}}=\dfrac{9}{16}\cdot\dfrac{8}{3}=\dfrac{3}{2}\\\\next\\\\\dfrac{9}{16}\cdot\dfrac{3}{2}=\dfrac{27}{32}\\\\\dfrac{27}{32}\cdot\dfrac{3}{2}=\dfrac{81}{64}[/tex]
485 [tex]485 divided by 9[/tex]by 9
Answer:
54.3
Step-by-step explanation:
485 / 9 = 54.3333(ect)
You just round and it would be 54.3
HELP ASAP I WILL MARK BRAINLIEST
Answer:
It's the first one...!!!
Write an Equation given the point (1, -1) and a rate of 2.
Answer:
y+1=2(x-1)
Step-by-step explanation:
use point slope form
Help with math work please I am bad at math the question is on the image!!
In my knowledge
2 × 8 + 5 = 21
Hope it helps ;)
The yield in bushels from a grove of orange trees is given by
Y = x(600 − x),
where x is the number of orange trees per acre. How many trees will maximize the yield?
_________ trees
Answer:
Y=x(600-x)
Step-by-step explanation:
How many trees?
500
inequalities!! please help!!
Answer:
x=24
Step-by-step explanation:
$;$"+";$;";";'+$-$$+$+$+_+
What is an equation of the line that passes through the points (-6, -2) and
(6,8)?
Answer:
y=5/6x+b
Step-by-step explanation:
use formula (y2-y1)/(x2-x1) to look for the slope:
(8-(-2))/(6-(-6))
=10/12
=5/6 (simplified)
then, use the formula y=mx+b to get the equation by substituting m and x, y to either (-6, -2) or (6, 8):
8=5/6(6)+b
8=5+b
3=b (subtract 5 on both sides)
equation:
y=5/6x+3
BIG IDEAS MATH
d 1: BTS > Chapter 5: Percents > Section Exercises 5.5 > Exercise 12
Write 34% as a fraction or mixed number in simplest form.
The simplest form is
Basic
Answer:
17/50.
Step-by-step explanation:
In order to write 34% as a fraction or mixed number in simplest form, the following calculation has to be done:
34% = 0.34 = 34/100
34/100 = 17/50
Thus, given that 17 is a prime number that cannot be divided by other number than 1 or 17, the simplest form to write 34% as a fraction is 17/50.
I BET NO ONE KNOWS THIS How many moles of helium are in 3.5 x 10^22 atoms of helium? _______ mol He
Answer:
Step-by-step explanation:
0.226 gram.
can somebody help me
Answer:
m=1/2
Step-by-step explanation:
your answer is right
Complete these statements.
1. An algebraic expression with one or more terms is called a
The difference in means is about ____ times the mean absolute deviations
Answer:
A little more than 3 times
Step-by-step explanation:
help. i’ll mark brainliest or whatever
Answer:
angle 1 is 140 degrees and angle 2 is 70 degrees
Step-by-step explanation:
it is two parallel lines with an intersecting line. This means that the two angles will be the same. Your welcome btw ur mom is hot
Answer:
Angle 1 is 140 degrees and Angle 2 is 70 degrees.
