Answer:
The perfect square lockers are the only ones left open.
Step-by-step explanation:
Here is a legit link to an explanation of this old puzzle problem!
https://36university.com/act-math-locker-problem-solution/
Quoting from that page:
Method 2: Who Touches Which Lockers
Identifying which students touch which lockers is a little less of a brute-force approach and would likely have gotten you to the solution a little more quickly.
Here’s what I mean:
Consider locker #1. The only student who touches locker #1 is student #1. Student 1 opens the locker, and since no one else touches it, it will be left open at the end.
Consider locker #2. Student 1 opens the locker, and student 2 closes it. No one else touches the locker, so it will be closed.
Consider locker #10. Students 1 opens the locker. Student 2 closes it. Students 3 and 4 skip right by it. Student 5 opens it. Students 6, 7, 8, and 9 skip right by it. And student 10 closes it. Locker #10 will be closed.
Mental Milestone 1: After looking at several lockers, you should notice that lockers are only changed by student numbers that are factors of the locker number. In other words, locker 12 is changed by students 1, 2, 3, 4, 6, and 12.
Mental Milestone 2: You should also have noticed that factors always come in pairs. This means that for every student who opens a locker, there is another student who closes it. For locker #12, student 1 opens it, but student 12 closes it later. Student 2 opens it, but student 6 closes it later. Student 3 opens it, but student 4 closes it later.
By this logic, every locker would be closed.
But there are exceptions!
Consider locker #25. Student 1 opens it. Student 5 closes it. Student 25 opens it. The locker will be left open, but why? In this case, the factors do not come in pairs. One and 25 are a pair, but five times five is also 25. Five only counts as one factor. This causes the open-close pattern to be thrown off. Locker #25 is left open.
Mental Milestone 3: When factors don’t come in pairs, the locker will be left open. And factors don’t come in pairs when numbers are multiplied by themselves. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…) are the only numbers whose factors don’t come in pairs because one set of factors, the square root, is multiplied by itself. This means that only perfect square lockers will be left open.
Locker #s 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are left open!
- 3/4(12x+16)<9-5x Show your work
Answer:
x > -5.25
Step-by-step explanation:
Question in Image Rearranging Algebra expressions Will give brainliest.
I'M GIVING BRAINLIEST!!!!!!!!!!!
Answer:
i dont know
Step-by-step explanation:
MEEEEEEEEEE please
What is the result of adding these two equations?
5x - y = 6
-2x + y = 8
Answer:
3x = 14
Step-by-step explanation:
Given the two linear equations, 5x - y = 6 and -2x + y = 8:
We can add both equations the same way we add integers. The only difference is that we add the terms with the same variables.
5x - y = 6
+ -2x + y = 8
3x + 0y = 14 or 3x = 14
Therefore, the sum is 3x = 14.
Find the missing side of the right
triangle.
7
4
Х
x= [?]
Enter the number that belongs in the green box,
Step-by-step explanation:
using Pythagoras theorem,
(hypotenuse)² = (perpendicular)² + (base)²
given that, hypotenuse =x, perpendicular =7, base =4
(x)² = 7² + 4²
(x)² = 49 + 16
x = √65
1. Write the following statements in the from of equations.
a. One third of a number plus 7 is 26
Answer: The number is 57
Step-by-step explanation:
Lemme tell you , We dont know the number , so we imagine it as x
so the question says one third of a number , so 1 third is 1 divided by 3 and if we imagene the number as x , we can write x/3 .
So x/3 +7 = 26 , as the equation says one third of a number plus 7 is equal to 26.
So write the lcm of 3 and 7 and then cross multiply , and subtract . you get
x = 57 , and we imagined x as the number so if x is 57 , so the number we have to find is also 57 . Done Easy .
The first term of a geometric sequence is -2 and the common ratio is 3, What is the sixth term of the sequence?
Also, Write the Recursive Rule fo the seqeunce from above ^
Answer:
a₆ = - 486
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = 3 , then
a₆ = - 2 [tex](3)^{5}[/tex] = - 2 × 243 = - 486
The recursive rule allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] with a₁ = - 2
An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his 6 nephews and rented five pairs of ice skates.
He was charged $32. Juanita paid admission fees for her seven grandchildren and rented 5 pairs of ice skates. She was charged $35.25. What is the admission fee?
What is the rental fee for a pair of skates?
Answer:
if we let admission fee per child to be a and the rental fee for the skates to be s.
Then john 6a + 5s =32
Juanita 7a + 5s = 35.25
Solving simultaneously we can eliminate s to solve for a first by subtracting one equation from the other.
6a + 5s = 32
7a + 5s = 35.25
we get -a + 0s = -3.25 therefore a= 3.25
Then we can solve for s by substituting a in either of the two equations
6 (3.25) + 5s =32
19.5 + 5s =32
5s = 12.5
s = 12.5/5
s = 2.5
Therefore, the admission fee: $ 3.25 per person and rental fee: $ 2.5 per pair of skates.
Step-by-step explanation:
1. 24x - 18
-
A. 6(4x-3) B. 6
-
C. 4(6x - 4) D. 12x - 9
It’s a select all that apply question
[tex] \: [/tex]
the right answer is
A. 6(4x-3)Step-by-step explanation:
[tex]24x - 18[/tex]
Factor out 6 from the expression[tex] = 6(4x - 3)[/tex]
so we got the answerhope it helps[tex] \: [/tex]
The quotient of k and 9 is greater than 1/3
Select the correct answer.
Which graph shows a function and its inverse?
Answer:
B
Step-by-step explanation:
If we consider a point on the line (x, y ) then the corresponding point on the inverse, the other line will be (y, x )
A function and its inverse are reflections in the line y = x
Consider the point (1, 5 ) on the red line, the corresponding point on the blue line will be (5, 1 )
This is the case in graph B
The graph showing a function and its inverse is the graph D.
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The graph of a function and its inverse are symmetric with respect with the line y = x.
On each graph you are given, plot the line y = x. If the two functions are symmetric with respect to the line y = x, then the graph does show a function and its inverse.
You will see this is true only for choice D.
Hence, the correct graph is D
Learn more about graphs, click;
https://brainly.com/question/17267403
#SPJ7
To make five dinners 1/3 cup of flour is used how many cups of flour are needed to make 3 dozen dinner rolls
Answer:
2.4 cups of flour or 2 2/5 cups of flour
Step-by-step explanation:
(1/3) divided by 5 = 0.06666666666
3 dozen = 36
0.06666666666 x 36 = 2.4
also, did you mean to make 5 dinner rolls?
what is the slope of the equation above?
The casino will pay you $20 for every dollar you bet if your number comes up. How much profit is the casino making on the bet
Answer:
The casino is making 47 cents profit on your $1 bet
Step-by-step explanation:
19(1/38) + (-1)(37/38) = -0.4736
An online store charges $5 to ship one box and $10 to ship two boxes. Write an explicit formula for an arithmetic sequence to represent the amount the online store pays to ship n boxes. Use the explicit formula to determine how much the online store charges when shipping 11 items.
Write an explicit formula for an arithmetic sequence to represent the amount the online store pays to ship n boxes.
From what we know so far,
y = 5n
Use the explicit formula to determine how much the online store charges when shipping 11 items.
y = 5(11)
y = 55 dollars
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
$55
Step-by-step explanation:
Since we are not given much information in this problem, we know this must be a pretty simple sequence. If we make a sequence of Natural Numbers and match it up to the prices we've been given, we get
1,2,3,4...
5,10,15...
The price is increasing by five dollars for every "n", so our sequence is just 5n. Extrapolating this out gives us $55 for n=11
8 less than 4 times a number is 76. Find the number.
Answer:
the answer is twenty one
Which of the following properties of equalities can’t be used when solving 3x+6=10-x
Answer:
Step-by-step explanation:
C
Answer:
c) multiplication
Step-by-step explanation:
Which point is in the graphed solution set of this system of inequalities?
4x-3y<12
6x+3y>5
A. (2,2) B. (0,-6) C. (2,-1) D. (-2,0)
Answer:
01110100 01101000 01100101 00100000 01101101 01100001 01110100 01110010 01101001 01111000
Step-by-step explanation:
8m - 8 - 8 = 16
equation
Answer:
8m-16 =16
8m=16+16
8m =32
m=32/8
m=4
Step-by-step explanation:
HOPE THAT THIS IS HELPFUL.
HAVE AN AWESOME DAY
solve for f
M-5N= f/t
Answer:
3.2
Step-by-step explanation:
Answer:
With the context you gave the awnser would be m≠5n
Step-by-step explanation:
What are the terms in the expression 4 + 9V +6w?
Answer:
4, 9v, and 6w
Step-by-step explanation:
I'm pretty sure it's right
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7
Answer:
The answer is B final answer becuase its all positive.
Can somebody help me with this question, im stuck on it.
Answer:
180 degrees
Step-by-step explanation:
Transformations don't change the size or angles of a triangle.
We know the angle of T & S. We need to find R.
To do this we will do...
180 - (60+40) =
= 180-100
=80
R is 80 degrees.
Now to find Triangle ABC we will add up 60+40+80 to get 180 degrees.
Also, remember that triangles will ALWAYS add up to 180 degrees.
Hope this helps! Please give this a rating and press the heart button! Thanks!
Four times a number, increased by 10, is -2
what is the number?
Answer:
-3
Step-by-step explanation:
-3 × 4 = -12
-12 + 10 = -2
Find the missing side K
K
53
45
Answer:
k=28
Step-by-step explanation:
ryan lives 3 1/4 miles from school. kayla lives 2 3/4 miles from school. how much farther from school does ryan live than kayla?
What is more important: to formulate a believable, testable hypothesis or to develop a good strategy to test the hypothesis accurately
Answer:
It's a matter of opinion. In my opinion you can hypothesize all you want, when you get to do it in practice it's almost 100% garantee of failure or incomplete hypothesis. So testing is way more important IMO.
Step-by-step explanation:
List the congruent sides.
Answer:
PQ≅ST; QR ≅TW; PR ≅SW
Step-by-step explanation:
Sam and Diane each open a savings account at the same time. Sam invests $4,500 in an account yielding
3.2% simple interest, and Diane invests $5,000 in an account yielding 6.2% simple interest. After twelve
years, who has the greater total of money, and how much greater is it?
Answer:
Step-by-step explanation:
help me with this one guys......
Answer:
[tex]7^-^1[/tex]
Step-by-step explanation:
So, when multiplying numbers with exponents that have the same base, all you have to do is combine the exponents.