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Umnica [9.8K]
3 years ago
10

A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will brin

g in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will bring in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.
Mathematics
1 answer:
pentagon [3]3 years ago
8 0

Answer:

$6,200

Step-by-step explanation:

The question is to find the expected value.

We know the expected value of a scenario is the sum of the products of each probability of event and its profit or loss.

There are 3 probabilities in the scenario:

Rainy: 20% = 20/100 = 0.2

Sunny: 50% = 50/100 = 0.5

Cloudy: Rest, which is 100 - (50+20) = 100 - 70 = 30% = 30/100 = 0.3

Now, the gain and loss is:

Rainy: Lose 5000 means -5000

Cloudy: Gain 4000 means +4000

Sunny: Gain 12,000 means +12,000

Now, the expected value is:

Expected Value = (0.2)(-5000) + (0.5)(12000) + (0.3)(4000) =  $6,200

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The number according to the given statement is x<-0.55.

Given the statement is five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​.

A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Five and three-tenths of a number means 5.3x.

And two and seven-tenths means 2.7.

So, five and three-tenths times a number plus two and seven-tenths means 5.3x+2.7.                ......(1)

It is also given that three and three-tenths times a number means is 3.3x.      

And one and six-tenths means 1.6.

So, three and three-tenths times a number plus one and six-tenths​ means 3.3x+1.6         .......(2)

Now, we will substitute equation (1) less than equation (2) according to the given statement is

5.3x+2.7<3.3x+1.6

Further, we will subtract 2.7 from both sides, we get

5.3x+2.7-2.7<3.3x+1.6-2.7

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Now, we will divide both sides by 2, we get

2x/2<-1.1/2

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Hence, the number for the given statement "five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​" is -0.55.

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Percent to decimal:

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