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3 years ago

Two consecutive integers add to 51. what are the integers?

Mathematics

2 answers:

Nataly [62]3 years ago

7 0

25 and 26...........

Vedmedyk [2.9K]3 years ago

4 0

Answer: 25 and 26

Step-by-step explanation: This problem states that the sum of two consecutive integers is 51 and it asks us to find the integers. Two consecutive integers can be represented as followed.

X ⇒ <em>first integer</em>

X + 1 ⇒ <em>second integer </em>

Since the sum of our two con consecutive integers is 51, we can set up an equation to represent this.

X + X + 1 = 51

Now, we can simplify on the left side of our equation.

2x + 1 = 51

-1 -1 ← subtract 1 on both sides

2x = 50

÷2 ÷2 ← divide both sides by 2

X = 25

X + 1 = 26

Therefore, our two consecutive integers are 25 and 26.

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Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

EleoNora [17]

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

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3 years ago

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Show that from any subset of 51 numbers taken from {1, 2, 3, ..., 100}, there exists a pair of elements such that one divides an

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Consider the 50 odd numbers 1,3, 5, ..., 99.

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So the first box contains {1,2,4,8, 16,..}

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<h3>What is pigeonhole principle?</h3>

According to the pigeonhole principle, if n items are placed in m containers, with n > m, at least one container must contain more than one item.

For example, if you have three gloves (and none of them are ambidextrous/reversible), you must have at least two right-handed gloves or at least two left-handed gloves, because there are three objects but only two categories of handedness to put them into.

To learn more about pigeonhole principle from the given link

brainly.com/question/13982786

#SPJ4

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