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Doss [256]
3 years ago
6

I am a number less than 3000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder 44. What numb

er am I?
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
3 0
Let Q1 and Q2 be the quotients from dividing 32 and 58 respectively.Then 32 Q1 + 30 = 58 Q2 + 4432 Q1 = 58 Q2 + 1416 Q1 = 29 Q2 + 716 Q1 = (16 + 13)Q2 + 716 Q1 = 16 Q2 + 13 Q2 + 716(Q1 - Q2) = 13 Q2 + 7Because Q1 and Q2 are integers, we have to find Q2 whereby 13Q2 + 7 is divisible by 16.After some try-and-error, we get Q2 = 13.  That is 13*13 + 7 = 176Therefore, Q1 - Q2 = 11  -->  Q1 - 13 = 11  -->  Q1 = 2432*24 + 30 = 58*13 + 44 = 798.I am 798
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Let's call the event of the red die to show a six as event A, and the event of the green die to show a six as event B.

The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. On both dices, we have 6 possible outcomes(the numbers from 1 to 6), with one favourable outcome(the number 6), therefore, the probabilities of those events are:

P(A)=P(B)=\frac{1}{6}

Each roll is independent from each other, then, the probability of both events happening simultaneously is given by their product:

P(A\:and\:B)=P(A)P(B)

Using the additive rule of probability, we have the following equation for our problem:

\begin{gathered} P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B) \\ =P(A)+P(B)-P(A)P(B) \\ =\frac{1}{6}+\frac{1}{6}-\frac{1}{6^2} \\ =\frac{2}{6}-\frac{1}{36} \\ =\frac{12}{36}-\frac{1}{36} \\ =\frac{12-1}{36} \\ =\frac{11}{36} \end{gathered}

the probability that the red die shows a six or the green die shows a six is 11/36.

7 0
1 year ago
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dexar [7]
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3 years ago
ANSWER ASAP I WILL MAKE BRAINLYIST
aniked [119]

X+2y=4

+-x-4y=-14

——————

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8 0
3 years ago
Read 2 more answers
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