A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row. All the lights start out off. The first student walks down the hall and pulls each cord turning them on. The second student pulls the cord on all the even numbered light bulbs turning those ones off. The third student approaches every third light bulb and changes it's state. If it was on, he turns it off, if it was off, he turns it on. The fourth student does the same to every fourth light bulb and so on through the 1,800 students. After all the 1,800 students pass down the hall, how many light bulbs end up in the on position and which ones are they?
Answers
Solution-
A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row.
As all the lights start out off, in the first pass all bulbs will be turned on.
In the second pass all the multiples of 2 will be off and rest will be turned on.
In the third pass all the multiples of 3 will be off, but the common multiple of 2 and 3 will be on along with the rest. i.e all the multiples of 6 will be turned on along with the rest.
In the fourth pass 4th light bulb will be turned on and so does all the multiples of 4.
But, in the sixth pass the 6th light bulb will be turned off as it was on after the third pass.
This pattern can observed that when a number has odd number of factors then only it can stay on till the last pass.
1 = 1
2 = 1, 2
3 = 1, 3
4 = 1, 2, 4
5 = 1, 5
6 = 1, 2, 3, 6
7 = 1, 7
8 = 1, 2, 4, 8
9 = 1, 3, 9
10 = 1, 2, 5, 10
11 = 1, 11
12 = 1, 2, 3, 4, 6, 12
13 = 1, 13
14 = 1, 2, 7, 14
15 = 1, 3, 5, 15
16 = 1, 2, 4, 8, 16
so on.....
The numbers who have odd number of factors are the perfect squares.
So calculating the number of perfect squares upto 1800 will give the number of light bulbs that will stay on.
As, [tex]\sqrt{1800} =42.42[/tex] , so 42 perfect squared numbers are there which are less than 1800.
∴ 42 light bulbs will end up in the on position. And there position is given in the attached table.
Old holiday light strings with bulbs that act as open switches will go out entirely if one bulb fails, while new versions with bulbs that short circuit will keep the remaining bulbs lit. Each bulb in an old 40-bulb series string on 120 V would be 3 V, while in a new 39-bulb series string it would be approximately 3.08 V per bulb. In a series circuit, a 60 W bulb would be brighter than a 100 W bulb.
When holiday lights wired in series have a bulb that burns out, in the old versions with bulbs that act like an open switch, the entire string of lights will go out. This is because the electrical circuit is broken, and current cannot flow through the circuit anymore. If the string operates on 120 V with 40 identical bulbs, the normal operating voltage of each bulb when all are functioning is 120 V / 40 bulbs = 3 V per bulb.
In contrast, newer versions are designed so that when a bulb burns out, it acts like a closed switch. This means the rest of the bulbs will stay lit because the circuit remains closed, allowing current to continue flowing. If one bulb short circuits and there are 39 remaining bulbs, each bulb will have an operating voltage of 120 V / 39 bulbs ≈ 3.08 V per bulb.
Regarding two household lightbulbs rated 60 W and 100 W connected in series, the one with the higher resistance (which is typically the lower-wattage bulb) will be brighter because it drops more voltage across it compared to the higher-wattage bulb with lower resistance.
Related Questions
Find the Distributive Property
8X46=8X(40+
Answers
Hey There!
8x^46=8x(40+
We move all terms to the left:
8x^46-(8x(40+)=0
The Distributive Property of multiplication, a fundamental concept in mathematics, was used to show that 8 x 46 = 8 x (40 + 6), which simplifies to 320 + 48 = 368.
Explanation:
The question is asking you to use the Distributive Property of multiplication, a rule in arithmetic that states that the product of a number and a sum, i.e., a(b + c), is equal to the sum of the products of that number and each term in the sum, i.e., ab + ac.
In this case,
8. x 46 = 8 x (40 + 6)
Using the Distributive Property, you would multiply the 8 by each term in the parentheses:
8 x 40 + 8 x 6.
This equals 320 + 48, which simplifies to 368. Hence 8 x 46 indeed equals 368, demonstrating the Distributive Property.
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What is the reciprocal of 6
Answers
Answer:
Step-by-step explanation:
Reciprocal of 6 is 1/6
What is the difference between the largest prime number less than 50 and the smallest composite number greater than 10?
Answers
Answer: 35
Step-by-step explanation: The largest prime number less than 50 is 47, and the smallest composite number greater than 10 is 12 (do the math yourself if you're not sure about this).
To get your answer, subtract 12 from 47, like so:
47 - 12
Once you calculate that, you will receive an answer of 35
Answer:
The largest prime number less than 50 is 47, and the smallest composite number greater than 10 is 12 (do the math yourself if you're not sure about this).
To get your answer, subtract 12 from 47, like so:
47 - 12
Once you calculate that, you will receive an answer of 35
Step-by-step explanation:
(-3x + 7) - 4(2x - 6) - 12 > 7
Answers
Step 1. Simplify brackets
-3x + 7 -4(2x - 6) -12 > 7
Step 2. Cancel 7 on both sides
-3x -4(2x - 6) -12 > 0
Step 3. Expand
-3x - 8x + 24 - 12 > 0
Step 4. Simplify -3x - 8x + 24 - 12 to -11x + 12
-11x + 12 > 0
Step 5. Subtract 12 from both sides
-11x > -12
Step 6. Divide both sides by -11
x < -12/-11
Step 7. Two negatives make a positive
x < 12/11
The answer is x < 12/11.
If f(x)= 6x+7, determine the value of f(-5)
Answers
f(-5)= 6(-5) +7.
f(-5)= -30+7
f(-5)= -23
As a result, the value of f(-5) is -23
Write the number in standard notation. 5 x 10^5
Answers
10^5 is 10 multiplied by itself 5 times. So in other words 10 x 10 x 10 x 10 x 10
So the solution is as follows:
5 x 10^5
= 5 x 10 x 10 x 10 x 10 x 10
= 500000.
what is the patern in the values as the exponents increase?
powers of 3. value
3^-1. 1/3
3^0. 1
3^1. 3
3^2. 9
A. add 3 to the previous value
B. subtract 3 from the previous value
C. divide the previous value by 3
D. multiply the previous value by 3
Answers
Answer:
D. multiply the previous value by 3
Step-by-step explanation:
The pattern of values as the exponents increase is
1/3, 1, 3, 9
Comparing 1/3 to 1, we either add 2/3 or multiply by 3.
Comparing 1 to 3, we either add 2 or multiply by 3.
Comparing 3 to 9, we either add 6 or multiply by 3.
The constant in this pattern is multiplication by 3.
Jannelle can drive an average of 295 miles on one tank of gas. How many miles can she drive on 16 tanks of gas?
Answers
Jannelle could go 4,720 miles hope this helps
4720 miles can be driven with 16 tanks of gas.
What is Proportion?Two or more ratios setting to be equal to each other is termed as proportion.
If two quantities are directly proportional, if one increases. other also increases and if one decreases, other also decreases.
If two quantities are inversely proportional, if one increases other decreases and if one decreases, other increases.
Solve this problem using proportional concept.
Jannelle can drive an average of 295 miles on one tank of gas. We have to find the miles she can drive on 16 tanks of gas.
Miles Jannelle can drive on one tank of gas = 295 miles
Miles Jannelle can drive on 16 tanks of gas = 16 × 295
= 4720 miles
Hence Jannelle can drive 4720 miles on 16 tanks of gas.
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Solve the following equation for y: 2x-3y=6
Answers
2x-3y=6
-y=6
y=-6
Check your Work
-6(2) - 3(-6)=
-12-(-18)=
-12+18=6
Solve for x.
3/4+x=12
Answers
Sorry for the crossing out. The answer and working out is below. Hope this helps!
Answer,
45/4 or 11.25 in decimal form
Explanation,
Step 1: Simplify both sides of the equation.
x + 3/4 = 12
Step 2: Subtract 3/4 from both sides.
x + 3/4 - 3/4 = 12 - 3/4 = 45/4
Hope this helps :-)
Find the equation of the line that is parallel to y=1/2x-4 and contains the point (4,5).
Answers
then fill it in with k being your coefficient. you will not be able to get a yet. it should look like this.
5=(1/2)(4)+a
5=2+a
now solve
5-2=a
a=3
now to finish this off you need to make the equation which will be in the same format but without the x and y filled in.
y=(1/2)x+3
Answer:y=(1/2)x+3
Step-by-step explanation:
microeconomics chapter 7
Answers
That's a good chapter!
Microeconomics explores the actions of individual agents within the economy, focusing on consumer behavior, production costs, and market structures. It discusses the reasons behind individuals' and firms' decision-making processes, emphasizing the importance of markets and the role of government intervention.
Explanation:Understanding Microeconomics
Microeconomics is a branch of economics focused on the actions of individual agents within the economy, such as households, workers, and business firms. It dives into the fundamentals of consumer behavior, production and costs, and various market structures, including some aspects of game theory. The theory of the consumer and the theory of the firm are central to microeconomics, explaining how individuals and firms make decisions about what goods to buy or produce, and at what prices.
In microeconomics, key themes include individuals responding to incentives, the importance of markets in facilitating interactions among firms and households, and the role of government intervention. Chapters 5 through 10 cover the theories of consumer behavior, production and costs, and different market structures. Subsequent chapters delve into applied microeconomic policy issues like public goods, externalities, competition and antitrust policies, environmental challenges, poverty, and income inequality, among others. This comprehensive approach helps students understand not only the theoretical underpinnings but also the application of economic theory in addressing real-world issues.
Identify the range of the function.
Answers
The range of the function is -4 < x ≤ 4.
The range of a function is all of the values of y that the graph could contain. In this case, x varies between -4 and 4. We should have a < symbol at -4 because it doesn't include -4 due to the open circle. We should have a ≤ with 4 since it has a closed dot.
If my company pays 60%of my health insurance and I pay 72 dollars What is the total cost of my insurance
Answers
Total Cost * .60 = My payment
Total Cost = My Payment / .60 = 120
Kathy organised a wedding , guests had to choose their meal from pasta , chicken or beef 1/3 chose pasta 5/12 chose chicken and 24 guests chose beef how many guests were at the wedding ?
Answers
so together the amount of people who chose beef should be 4/12 since you must find the greatest commen factor. Then you should add 4/12 and 24 im thinking and you would get 24.3333 but if your looking for a mix number it would be 24 3333/1000
hope this helps!
The question is a math problem involving the sum of fractions reflecting food choices at a wedding. By considering fractions and its equivalent counts, we find that the total number of guests at the wedding was 96.
Explanation:The subject of this question is mathematics, specifically a problem dealing with fractions. To determine the total number of guests at the wedding, we need to consider all the meal choices and their counts. 1/3 of the guests chose pasta and 5/12 of them chose chicken. The rest, as given, were 24 guests who chose beef. To find the total, we need to convert fractions to a common denominator. In this case, 12 is a convenient choice:
Pasta: 1/3 = 4/12
Chicken: 5/12
So, 4/12 + 5/12 = 9/12 of the guests chose either pasta or chicken. Since the remaining guests chose beef, that means 24 guests represent the remaining 3/12 of the total guests. Therefore, if 3/12 of the guests is 24, one 'part' (1/12) is equal to 24/3, which is 8. That means the total number of guests (12 parts) is 12 * 8, which equals 96. Therefore, there were 96 guests at the wedding.
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If A =bc+us,which equation is solved for s?
Answers
You first subtract both sides by bc to get the us term alone, then divide everything by u to get s term alone.
after the first hour of the monsoon 23 mm precipitation has fallen after the second hour a total of 61 mm of precipitation at Fallen how many millimeters of precipitation fell during the second hour
Answers
61mm-23mm is 38mm
What’s the slope of a line with the equation y=5x+2/5
Answers
answer: the slope of the line would be 5
explanation:
slope-intercept formula ==> y = mx + b
m would be the slope, and b would be the y-intercept. therefore the answer would be 5
hope this helps! ❤ from peachimin
Which system of equations is satisfied by the solution shown in the graph?
A. x + 2y = 6 and x − y = 10
B. x + y = 6 and x − 2y = 10
C. x + 2y = 10 and x − y = 6
D. x + y = 6 and x − y = -10
Answers
In order to find correct system for the given graph, we need to find the slopes and y-intercepts of the lines in shown graph.
For red line we have y-intercept = 10 because it is cutting y-axis at 10.
And slope of the red line is rise/run = 1/1 that is 1.
Using slope-intercept form y=mx+b
The equation of red line is y=1x +10 or x-y =-10.
For black line we have y-intercept = 6 and slope is rise/run = -1/1 = -1.
The equation of black line is y = -1x + 6 or x+y=6.
Therefore, correct option is D. x + y = 6 and x − y = -10.The solution shown in the graph satisfies the system of equations x + y = 6 and x - y = -10. The correct option is D.
The correct system of equations satisfied by the solution shown in the graph is x + y = 6 and x - y = -10.
To verify this, we can substitute the x and y values from any point on the graph into these equations.
If the values satisfy both equations, then the system is correct.
For example, let's take the point (2, 4) on the graph. If we substitute x = 2 and y = 4 into the equations, we get:
x + y = 6: 2 + 4 = 6, which is true
x - y = -10: 2 - 4 = -10, which is also true
Since both equations are satisfied by the point (2, 4), the correct system of equations is x + y = 6 and x - y = -10.
Therefor the correct option is D.
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Can 15 over 240 be simplified
Answers
divide both by 15 to get the answer
Simplify. 4^3 · 4^4/4^9 A) 41^6 B) 4^2 C) 1/4^2 D) 1/4
Answers
cause the and to that is 1/16
Answer:
c
Step-by-step explanation:
c 1/4>2
cause the and to that is 1/16
The solution to the problem -4(x - 3) ≤ 16 is that x is greater than or equal to ______.
answer choices
-1
1
Answers
X is greater than or equal to -1.
what is the lcm of 6 and 7
Answers
The lcm of 6 and 7 is 42.
The least common multiple of 6 and 7 is 42.
The least common multiple of 2 or more numbers, is the lowest multiple that all the numbers have in common. Here are the multiples of 6 and 7 up to 42, to show that 42 is the LCM.
6: 6, 12, 18, 24, 30, 36, 42.7: 7, 14, 21, 28, 35, 42.Thus making 42 the Least Common Multiple.
I hope this helps!
-25=-4x show your work
Answers
-25 = -4x
divide by -4
25/4 =x
6*4 =24 25-24 = 1
6 1/4 = x
Divide each side by -4
three more than a number is 12
Answers
hello there
i belive you are asking a number which whn added three equals 12 so your answer is 9
The statement 'three more than a number is 12' represents an algebraic equation. It can be expressed as 'x + 3 = 12'. Solving this equation, we find that the unknown number is 9.
Explanation:The question 'three more than a number is 12' is a basic algebraic equation. The unknown number is represented by a variable, let's call it x. So, the equation would read 'x + 3 = 12'. We solve for x by subtracting 3 from both sides of the equation. This gives us 'x = 12 - 3', which simplifies to 'x = 9'. Therefore, the number that, when increased by three, yields 12 is 9.
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If two figures are similar, the corresponding sides are?
Answers
The corresponding sides of similar figures can be equal, but if they are different in any way, they will always be proportional.
Corresponding angles, however, will always be equal.
If two figures are similar , the corresponding sides are proportional.
What are similar figures?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar.
They will have thesame shape , if possible thesame corresponding angles. But different sides. The ratio of the corresponding sides are equal or we can say that the corresponding sides are proportional.
This ratio of the sides is called scale factor.
Scale factor is expressed as;
scale factor = New dimension /old dimension.
Therefore, the corresponding sides of similar figures are proportional.
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WILL GIVE BRAINLIEST. is my answer correct
Answers
Yes, I believe so, because the equation is already as simplified as it can be with the given information and the graph is correct for the equation given.
If I’m remembering correctly then yes
Work out the probability it is a humbug.
Please help!!
Answers
The probability of an eclair is 1/15, which means for every 1 eclair there is a total of 15 sweets.
Since the table says there is 3 eclairs, there is 3 x 15 = 45 total sweets.
Now add the 3 different sweets together to equal 45:
3 + 2x+6 + x = 45
Combine like terms:
3x +9 = 45
Subtract 9 from each side:
3x = 36
Divide each side by 3:
X = 36 /3
x = 12
Now you have x, calculate the number of humbugs:
2x +6 = 2(12) +6 = 24 + 6 = 30 total humbugs.
The probability of picking one would be 30/45, which reduces to 2/3.
3x+8+2ax≥3ax−4a what is x?
Answers
[tex] - \frac {4 (2 + a)}{3 - a} [/tex]
solve the inequality by finding the roots and creating test intervals.
on her first quiz in social studies, Meg answered 92% of the questions Correctly. On her or 2nd quiz, she answered 27 out of 30 questions correctly. On which quiz did Meg have a have the better score
Answers
I THINK