1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
3 years ago
11

James was trying to sleep one night but there was too much noise around him. His clock ticked every

Mathematics
1 answer:
g100num [7]3 years ago
4 0

Answer:

<em>It will occur zero times between midnight and one o'clock.</em>

Step-by-step explanation:

<u>Least Common Multiple (LCM)</u>

Three events keep James from sleeping: his clock ticking every 20 seconds, a tap dripping every 15 seconds, and his dog snoring every 27 seconds.

All three events happened together at midnight. They will happen together again the first time the numbers 20, 15, and 27 have a common multiple. This is the LCM.

List the prime factors of each number:

20: 2,2,5

15: 3,5

27: 3,3,3

Now multiply all the factors the maximum number of times they appear:

LCM=2*2*3*3*3*5=540

(a) All the events will happen together again after 540 minutes.

(b) Since 540 minutes = 9 hours, this event won't happen again until 9 am. Thus, it will occur zero times between midnight and one o'clock.

You might be interested in
Determine the equation of the line that is perpendicular to the lines r(t)=(-2+3t,2t,3t)
Mnenie [13.5K]
<span>Vector Equation
(Line)</span>(x,y) = (x,y) + t(a,b);tERParametric Formx = x + t(a), y = y + t(b); tERr = (-4,-2) + t((-3,5);tERFind the vector equation of the line passing through A(-4,-2) & parallel to m = (-3,5)<span>Point: (2,5)
Create a direction vector: AB = (-1 - 2, 4 - 5) 
= (-3,-1) or (3,1)when -1 (or any scalar multiple) is divided out.
r = (2,5) + t(-3,-1);tER</span>Find the vector equation of the line passing through A(2,5) & B(-1,4)<span>x = 4 - 3t
y = -2 + 5t
;tER</span>Write the parametric equations of the line passing through the line passing through the point A(4,-2) & with a direction vector of m =(-3,5)<span>Create Vector Equation first:
AB = (2,8)
Point: (4,-3)
r = (4,-3) + (2,8); tER
x = 4 + 2t 
y = -3 + 8t
;tER</span>Write the parametric equations of the line through A(4,-3) & B(6,5)<span>Make parametric equations: 
x = 5 + 4t
y = -2 + 3t ; tER
For x sub in -3
-3 = 5 + 4t 
(-8 - 5)/4 = t
-2 = t
For y sub in -8 
-8 = -2 + 3t
(-8 + 2)/3 = t
-2 = t
Parameter 't' is consistent so pt(-3,-8) is on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (-3,-8) on the line?<span>Make parametric equations: 
x = 5 + 4t
y = -2 + 3t ; tER
For x sub in 1
-1 = 5 + 4t 
(-1 - 5)/4 = t
-1 = t
For y sub in -7 
-7 = -2 + 3t
(-7 + 2)/3 = t
-5/3 = t
Parameter 't' is inconsistent so pt(1,-7) is not on the line.</span>Given the equation r = (5,-2) + t(4,3);tER, is (1,-7) on the line?<span>Use parametric equations when generating points: 
x = 5 + 4t
y = -2 + 3t ;tER
X-int:
sub in y = 0
0 = -2 + 3t
solve for t
2/3 = t (this is the parameter that will generate the x-int) 
Sub t = 2/3 into x = 5 + 4t 
x = 5 + 4(2/3)
x = 5 + (8/3)
x = 15/3 + (8/3) 
x = 23/3
The x-int is (23/3, 0)</span>What is the x-int of the line r = (5,-2) + t(4,3); tER?Note: if they define the same line: 1) Are their direction vectors scalar multiples? 2) Check the point of one equation in the other equation (LS = RS if point is subbed in)What are the two requirements for 2 lines to define the same line?
3 0
3 years ago
Tony drove 605 miles in 11 hours At the same rate how many miles would he drive in 7 hours
Vitek1552 [10]

Answer:

He drive for 385 miles

Step-by-step explanation:

11hrs = 605 miles

1hr = 55 miles

7hr = 55 × 7

= 385 miles

7 0
3 years ago
Read 2 more answers
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions
rewona [7]

x-2 is a factor so x = 2 is a root of f(x)

This is because f(x) = (x-2)*g(x) for some polynomial g(x). We don't have to worry about what g(x) is equal to as it doesn't affect the status of the root we're after.

So,

f(x) = 0

(x-2)*g(x) = 0

x-2 = 0 or g(x) = 0

x = 2 or g(x) = 0

This shows how the factor x-2 leads to the root x = 2

Therefore, f(2) = 0

Answer: Choice D

4 0
3 years ago
Read 2 more answers
Please find the m∠DEY
GrogVix [38]

Answer:

41, x=-5

Step-by-step explanation:

m<DEY = m<FEY, by angle bisector theorem

(9x-4) = 41

9x = 45

x = 5

m<DEY = 41

6 0
3 years ago
Pls solve this sum asap
Over [174]
18y + 9 = -12 + 18y
9=-12

I hope that’s right... I haven’t done this in ages
4 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following describes the graph of the equation
    10·1 answer
  • Find the surface area of a square pyramid with base edges<br> of 5 cm and a slant height of 3 cm.
    5·1 answer
  • She put out two more recovery tests smh
    8·1 answer
  • Taylor is buying a new flashlight. He can choose from red, blue, and silver flashlights that come in both a large size and a sma
    8·1 answer
  • What is the answer to this (in the picture above)
    8·2 answers
  • Step by step explanation on how to solve (-3 + 8 x 2 -3)
    14·2 answers
  • Find the value of x
    14·2 answers
  • Help please!!
    15·1 answer
  • Can someone help me with this problem?
    7·1 answer
  • While scuba diving, Rajeev dove to a depth of 12.6 feet below the surface of the water and then descended another 8.7 feet. What
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!