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3 years ago

Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities.

Mathematics

1 answer:

lutik1710 [3]3 years ago

5 0

Answer:

Option b (4,1)

Step-by-step explanation:

The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function $f(x, y) = 8x + 8y$

The minimum points are found in the lower vertices of the region.

These vertices are found by equating the equations of the lines::

$3x+2y=14\\-5x +5y=10$

-------------------

$x = 2\\y = 4$

$-8x + 3y = -29\\3x + 2y = 14$

---------------------

$x = 4\\y = 1$

The lower vertices are:

(4, 1) (2, 4)

Now we substitute both points in the objective function to see which of them we get the lowest value of $f(x, y)$

$f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48$

Then the value that minimizes f(x, y) is (4,1).

Option b

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About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil

Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

$P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}$

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

7 0

3 years ago

at a charity casino event, a woman begins playing a slot machine with $10 in quarters in her coin bucket. she plays 15 quarters

irina [24]

Answer:

265 quarters ($66.25)

Step-by-step explanation:

10$ in quarters is 250 quarters.

you subtract the 15 from winning (=235), then add 50 for the jackpot (=285). Subtract another 20 for her final plays (=265).

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2 years ago

Solve this problem using the proper formula. A carpenter is building a bookcase the perimeter of the top is 108 in. What length

lapo4ka [179]

Assuming the length is y and the width is x
Perimeter = y + y + x + x
                = 2y +2x
                = 2 (y + x)
if the is 8 and the perimeter is 108
   108 = 2 (y +8)
    108/2 = y+8
    54    = y +8
    54 - 8 = y
    46 = y

Length = 46 inches

3 0

3 years ago

Read 2 more answers

Box 1 measures 6cm in width, 12cm in length, and 4cm in height. The height is doubled to 8cm to produce a larger box, Box 2 Whic

arlik [135]

Step-by-step explanation:

i don't know but i think this is it

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3 years ago

Janet is designing a frame for a client. She wants to prove to her client that m∠AGE ≅ m∠CHE in her sketch. What is the missing

Amiraneli [1.4K]

Answer:

I believe the answer is transative property. I'm currently taking the test so I'm not 100% sure if I'm right yet.

Step-by-step explanation:

In step one, AGE and HGB are verticle angles since they are opposite of each other. then step two is alternate interior angles because they are interior angles opposite of each other, self-explanatory. the reason I choose the transitive property over the corresponding angles theorem is because the transitive property states: among A B and C, if A=B and B=c then A=C and in this case since AGE=HGB andHGB=CHE then AGE=CHE. I hope this helps and if you know the right answer just put it in the comments, if I'm wrong ofc.

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2 years ago