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ANEK [815]
3 years ago
10

Does (-1, 5) make the inequality y < 3x + 8 true?

Mathematics
2 answers:
Kobotan [32]3 years ago
7 0

Answer:

<u>(–1, 5) does NOT make </u><u><em>y</em></u><u> < 3</u><u><em>x</em></u><u> + 8 true.</u>

Step-by-step explanation:

First, let's substitute the values into the inequality. It's the one way to see if the point (–1, 5) is in the range of <em>y</em> < 3<em>x</em> + 8

5 ≟ 3(–1) + 8

5 ≟ 8 – 3

5 = 5 ✘

This means (–1, 5) does NOT make the inequality <em>y</em> < 3<em>x</em> + 8 true.

ioda3 years ago
3 0

Answer:

No

Step-by-step explanation:

as X=-1. and y=5

according to this y<3x+8

which means 5< 3*-1 +8

5<-3+8

5<5

which is not true.. as 5=5

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The function g(x) is created by applying an <em>horizontal</em> translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

<h3>How to determine the characteristics of rigid transformations by comparing two functions</h3>

In this problem we have two functions related to each other because of the existence of <em>rigid</em> transformations. <em>Rigid</em> transformations are transformations applied to <em>geometric</em> loci such that <em>Euclidean</em> distance is conserved at every point of the <em>geometric</em> locus.

Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of <em>horizontal</em> translation 4 units in the + x direction:

f'(x) = - 2 · cos (x - 1 + 4) + 3

f'(x) = - 2 · cos (x + 3) + 3     (1)

Now we apply a reflection over the x-axis:

g(x) = - [- 2 · cos (x + 3) + 3]

g(x) = 2 · cos (x + 3) - 3

Therefore, the function g(x) is created by applying an <em>horizontal</em> translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

To learn more on rigid transformations: brainly.com/question/1761538

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4 0
1 year ago
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a rand
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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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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