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3 years ago

Please explain, 2 (4m-5) - (6m-11) =33

Mathematics

1 answer:

zlopas [31]3 years ago

7 0

Answer:

m = 16

Step-by-step explanation:

2(4m - 5) - (6m - 11) = 33 (Given)

8m - 10 - 6m + 11 = 33 (Distribute)

2m + 1 = 33 (Combine like terms)

2m = 32 (Subtract 1 on both sides)

m = 16 (Divide 2 on both sides)

You can check by substituting your answer into the equation:

2(4(16) - 5) - (6(16) - 11) = 33

2(64 - 5) - (96 - 11) = 33

2(59) - (85) = 33

118 - 85 = 33

33 = 33

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3 years ago

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

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4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

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3 0

3 years ago

Whilst shopping, the probability that Caroline buys fruit is 0.4. The probability that Caroline independently buys a CD is 0.2.

AleksandrR [38]

Answer:

probability that Caroline buy both CD and fruit = 0.52

Step-by-step explanation:

We have given that the probability of Caroline buys a fruit P = 0.4

So probability of Caroline does not buy the fruit = 1 - 0.4 = 0.6

Probability Caroline buys a CD P = 0.2

So probability of Caroline does not buy the CD = 1 - 0.2 = 0.8

So probability that Caroline does not buy either buy CD or fruit = 0.8×0.6=0.48

So probability that Caroline buy both CD and fruit =1-0.48 = 0.52

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3 years ago