A survey of 800 students yielded the following information: 519 were seniors, 430 were commuters, and 300 of the seniors were commuters. How many of the 800 surveyed students were seniors or were commuters?

Answers

Answer 1
Answer:

Answer:

The number is  (S \ u \  C  ) = 649

Step-by-step explanation:

From the question we are told that  

      The sample size is  n =  800

       The number of seniors is  S  =  519

         The number of  commuters is  C =  430

         The number of of seniors that are commuters is  (S\  n \ C )=  300

Generally the number of 800 surveyed students who were seniors or were commuters is  mathematically evaluated as

     (S \ u \  C  ) =  S + C  -  ( S \  n  \  C )

=>   (S \ u \  C  ) =  519  + 430   - 300

=>   (S \ u \  C  ) = 649


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Consider the triangle reduction.A larger triangle has side lengths 15.4 centimeters, 15.4 centimeters, and 12.4 centimeters. A smaller triangle has a side length of 3.85 centimeters that corresponds to the sides of the larger triangle with lengths 15.4 centimeters.

The perimeter of the original triangle is 43.2 cm. What is the perimeter of the reduced triangle?

10.8
cm
In the previous problem, you found the perimeter of a reduced triangle. Explain how you found the new perimeter using proportions.

Answers

Answer:

10.8 Cm

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ur welcome ♥️♥️♥️

The value z is directly proportional to c. When z = 20, c = 10. Find an equation relating z and c. *

Answers

Answer:

a) The equation of Z and C is Z =K C

b) K = 2

Step-by-step explanation:

Explanation:-

Given data Z is directly proportional to C

              ⇒   Z ∝ C

               ⇒  Z = K C

The equation of relating Z and C    

               Z = K C

Given Z = 20 and C =10

              20 = K ( 10)

          ⇒ K = 2

Suppose that the weather forecast indicates a 10% chance that cold weather will reduce the citrus grower’s profit from $100,000 to $85,000 and a 10% chance that cold weather will reduce the profit to $75,000. Should the grower spend $5000 to protect the citrus fruit against the possible bad weather?

Answers

Answer:

We can think in this situation as:

There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $15,000

There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $25,000

And in the remaining 80% (or a probability equal to 0.8), the profit does not change.

Then the expected value for the total profit can be written as:

EV = $100,000 + ( 0.1*(-$15,000) + 0.1*(-$25,000) + 0.8*$0)

     =  $96,000

In the case where the citrus grower spends $5000 to protect the fruits against possible bad weather, there is a 100% that is profit will not change, but he must pay $5,000

Then his profit will be:

P = $100,000 - $5,000 = $95,000

So in this case, the profit is $1000 less than the expected profit in the prior case. So the scenario where he does not buy the protection has a larger expected profit, which may mean that is better to not buy it (in a straight mathematical point of view)

One also could think that  the values are really close together, so buying the protection does not mean a big change, and increases the security

Assume that a lost treasure will be in a certain area of the ocean with probability 0.4, and that a search of that area will find the treasure with probability 0.9 if it is there. What is the conditional probability of the treasure being in the area if the area is searched and no treasure is found?

Answers

Answer:

the probability of the treasure being in the area given that no treasure is found is 0.0625 (6.25%)

Step-by-step explanation:

denoting the event N= no treasure is found , then

P(N) = probability that the lost treasure is in the area* probability that the lost treasure is not found in the treasure's area + probability that the lost treasure is not in the area*  probability that the lost treasure is not found in other areas = 0.4*0.1 + 0.6*1 = 0.64

P(N) = 0.64

then we can get the conditional probability using the theorem of Bayes . Denoting the event A= the treasure being in the area

P(A/N) = P(A∩N)/P(N) = 0.4*0.1/0.64 = 0.0625 (6.25%)

where

P(A∩N) = probability of the treasure being in the area and no treasure is found

P(A/N) = probability of the treasure being in the area given that no treasure is found

• Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.
Part
How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?

Answers

Answer:  In 20 minutes, tanks A and B will each have 120 gallons remaining in them.

Step-by-step explanation:

The equation, the amount at which they will be equal, represents the given starting amounts minus the gal/min times the unknown time in minutes, m.

220 - 5m = 180 - 3m Subtract 180 from both sides; add 5m to both sides.

220-180 -5m +5m = 180-180 +5m - 3m  Combine like terms

40 = 2m  Divide both sides by 2

20 = m

Check: Substitute 20 for m in the equation

220 - 5(20) = 180 - 3(20)

220 - 100 = 180 -60

120 = 120   True!

Mist ate 2 slices of cake. Flout ate 1 slice. If Mist ate 2/4 of the cake and all the slices were the same size, what fraction of the cake remained after Mist and Flout had eaten?

Answers

1/4 remained
2/4 - mist + 1/4 -flout = 3/4
4/4 - 3/4 = 1/4
one fourths would be left