Which of the following graphs represents the solution set for the inequali -35-2x +1 <11

Mathematics

1 answer:

OLga [1]2 years ago

3 0

Answer:

You did not give the options, so i just will graph it.

The inequality is:

-35 - 2*x + 1 < 11.

Now we would want to isolate the x in one side, so we can start by adding 35 in both sides.

(-35 -2*x + 1) + 35 < 11 + 35

-2x + 1 < 46

now we can subtract 1 in both sides:

-2x + 1 - 1 < 46 - 1

-2x < 45

Now we can divide by -2, remember that if we multiply or divide by a negative number, then the "direction" of the sign changes.

(-2x)/-2 > 45/-2

x > -22.5

Then the graph of the set is an open dot at the point x = -22.5 (this means that the set does not include this point) and a line that extends to the right. (Extends to the right because x is larger than -22.5)

Below is an example of how to draw the graph that represents the set of solutions.

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a) 0.033

b) 0.468

c) 100

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 105.3

Standard Deviation, σ = 8

The amount x of miraculin produced (measured in micro-grams per gram of fresh weight) had a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(x > 120)

$P( x > 120) = P( z > \displaystyle\frac{120 - 105.3}{8}) = P(z > 1.8375)$

$= 1 - P(z \leq 1.8375)$

Calculation the value from standard normal z table, we have,

$P(x > 120) = 1 - 0.967 = 0.033 = 3.3\%$

b) P(x between 100 and 110)

$P(100 \leq x \leq 110) = P(\displaystyle\frac{100 - 105.3}{8} \leq z \leq \displaystyle\frac{110-105.3}{8}) = P(-0.6625 \leq z \leq 0.5875)\\\\= P(z \leq 0.5875) - P(z \leq -0.6625)\\= 0.722 - 0.254 = 0.468 = 46.8\%$