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emmasim [6.3K]
3 years ago
14

How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?

Mathematics
1 answer:
irga5000 [103]3 years ago
6 0
The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5


for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009


The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

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b) -9.25

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Hope this helps!

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2 years ago
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Step-by-step explanation:

a1=2/3

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for numerator a1=2

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so an=(n+1)/(n+2)

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6 0
3 years ago
The table shows the number of markers in different numbers of boxes.
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(2.1 x 104) + (3.5 x 106)
igor_vitrenko [27]

Answer:

the answer is 589.4

Step-by-step explanation:

In doing this equation you do the order of operations:

(2.1 x 104)= 218.4

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2 years ago
If the distance covered by an object in time t is given by s(t)=t^2+5t , where s(t) is in meters and t is in seconds, what is th
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Answer:

E. 44 meters

Step-by-step explanation:

The function that models the distance covered by the object is

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where s(t) is in meters and t is in seconds.

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The distance covered between 1 second and 5 seconds is

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3 years ago
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