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Karolina [17]
3 years ago
5

How will the solution of the system y > 2x + and y < 2x + change if the inequality sign on both inequalities is reversed t

o y < 2x + and y > 2x + ?

Mathematics
2 answers:
leva [86]3 years ago
7 0

Answer:

The solution will not change.

Step-by-step explanation:

Let y > 2x + p and y < 2x + p,

Where, p is any constant,

∵ If we subtract any number on both sides of an equality, the sign of inequality does not change,

i.e. y - p > 2x   and  y - p < 2x

\implies \frac{y-p}{2} > x\text{ and }\frac{y-p}{2} < x

\implies x\in (-\infty, \frac{y-p}{2})\cap (\frac{y-p}{2}, \infty )-----(1)

Similarly, If the inequality is,

y < 2x + p\text{ and }y > 2x + p

\implies \frac{y-p}{2} < x\text{ and }\frac{y-p}{2} > x

\implies x\in (-\infty, \frac{y-p}{2})\cap (\frac{y-p}{2}, \infty )-----(2)

From equation (1) and (2),

It is clear that, the solution will not change after reversing the sign of inequality.

Gala2k [10]3 years ago
5 0

Answer:

The System of inequality is ,

1. y > 2 x + p

2. y < 2 x + p

Suppose we assign some values to p and q and draw its graph

And, then the inequality sign on both inequalities is reversed

3. y < 2 x + p

4. y > 2 x + p

And , then draw it's graph

it has been found that, the solution set of both the inequality remains same.That is there is no point or set of points , which satisfy both the system of inequality.

The system has no solution.

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SOVA2 [1]

Answer:

<u>Question 1:</u>

<u>(a) </u>P(x<60) = 0.9236

<u>(b) </u>P(x>16) = 0.9564

<u>(c) </u>P(16<x<60) = 0.88

<u>(d) </u>P (x>60) = 0.0764

<u />

<u>Question 2:</u>

<u>(a) </u>P(x<3) = 0.0668

<u>(b) </u>P(x>7) = 0.0062

<u>(c) </u>P(3<x<7) = 0.927

<u />

Step-by-step explanation:

<u>Question 1:</u>

x = no. of mg of porphyrin per deciliter of blood.

μ = 40

σ = 14

(a) We need to compute P(x<60). We need to find the z-score using the normal distribution formula:

z = (x - μ)/σ

P(x<60) = P((x - μ)/σ < (60 - 40)/14)

             = P(z < 20/14)

             = P(z<1.43)

Using the normal distribution probability table we can find the value of p at z=1.43.

P(z<1.43) = 0.9236

so, P(x<60) = 0.9236

(b) P(x>16) = P(z>(16-40)/14)

                 = P(z>-1.71)

                 = 1 - P(z<-1.71)

                 = 1 - 0.0436

    P(x>16) = 0.9564

(c) P(16<x<60) = P((16-40)/14) < x < (60-40)/14)

                        = P(-1.71 < z < 1.43)

This probability can be calculated as: P(z<1.43) - P(z<-1.71)

                                         P(16<x<60) = 0.9236 - 0.0436

                                         P(16<x<60) = 0.88

(d) P(x>60) = 1 - P(x<60)

     we have calculated P(x<60) in part (a) so,

    P(x>60) = 1 - 0.9236

    P (x>60) = 0.0764

<u>Question 2:</u>                              

μ = 4.5 mm

σ = 1.0 mm

In this question, we will again compute the z-scores and then find the probability from the normal distribution table.

(a) P(x<3) = P(z<(3-4.5)/1)

                = P(z<-1.5)

     P(x<3) = 0.0668

(b) P(x>7) = 1 - P(x<7)

               = 1 - P(z<(7-4.5)/1)

               = 1 - P(z<2.5)

               = 1 - 0.9938

    P(x>7) = 0.0062

(c) P(3<x<7) = P(x<7) - P(x<3)

  we have computed both of these probabilities in parts (a) and (b) so,

    P(3<x<7) = 0.9938 - 0.0668

    P(3<x<7) = 0.927

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natulia [17]

Answer:

1648

Step-by-step explanation:

5/9 are girls. The 9 represents the total.

Set up a proportion and you have

5/9 = ?/3708

3708/9=412

412x5= 2060 girls

3708-2060= 1648

8 0
3 years ago
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belka [17]

Answer:

k=13.8

Step-by-step explanation:

Given function:

  • 2.5k+47.4=81.9
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<u><em>Subtract final and middle value:</em></u>

  • 81.9-47.4= 34.5

<em><u>Divide by 2.5:</u></em>

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Therefore, k=13.8..

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Answer:

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Step-by-step explanation:

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Ivan

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(1 & 2/3) ft = 12 inches + 12*(2/3) inches

(1 & 2/3) ft = 12 inches + 8 inches

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If the tree grows 5 inches per year, then it will take 4 years to get to 20 inches since 5*4 = 20. You can also divide to get 20/5 = 4.

So it takes 4 years for the tree to grow 1&2/3 feet tall.

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