Mathematics, 06.07.2019 21:00 blessed4628

Use the chinese remainder theorem to solve the systems of congruences: a. find x mod 77 if x ≡ 2 (mod 7) and x ≡ 4 (mod 11). b. x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 1 (mod 5).

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Answer from: cjjjjjjjjjjjjj

(a) Suppose we let

x=2+4=6

Modulo 7, we're left with $x\equiv2+4\pmod7=6\mod7$ , but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now

$x=2+4\cdot7=30$

and $x\equiv2\pmod7$ , but modulo 11, we have $x=\equiv2+28\equiv2+4\equiv6\pmod{11}$ . But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write

$x=2\cdot11+4\cdot7=50$

but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have $2\cdot6=12$ , and $12\equiv1\pmod{11}$ , so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now

$x=2\cdot11\cdot2+4\cdot7\cdot2\cdot4=268$

We have

$x=268=3\cdot77+37\implies x\equiv37\pmod{77}$

(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with

x=2+3+3=8

Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.

$x=2\cdot2+3+3\cdot4=19$

Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of $3\times2\equiv12\equiv2\pmod5$ . We have $3\cdot2\equiv6\equiv1\pmod5$ , so we multiply by 3.

$x=2\cdot2\cdot5+3\cdot5+3\cdot4\cdot3=71$

Now

$x=71=1\cdot(3\cdot4\cdot5)+11=1\cdot60+11$

which means the smallest positive solution for the system would be x=11

Answer from: Quest

answer: the dogs need to shift their focus to human scent.

its because the dogs being trained are for search and rescue thus they need to be able to track humans and their specific scent

Answer from: Quest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

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Use the chinese remainder theorem to solve the systems of congruences: a. find x mod 77 if x ≡ 2 (m...

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