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3 years ago

If a system of two inequalities has a solution, then their two half planes intersect , true or false ?

Mathematics

1 answer:

Nana76 [90]3 years ago

7 0

Answer: The answer is true.

Step-by-step explanation: The given statement is

'If a system of two inequalities has a solution, then their two half planes intersect'.

We are to check whether the statement is true or false.

Let a system of two inequalities be

$x+y\geq 3,\\\\2x+5y\leq 10.$

These inequalities has a solution, for example, x = 2, y = 1.

Plotting these inequalities on a graph paper (please see the attached graph), we see that the two half planes intersect, which is represented by the double shaded region in the graph.

Thus, the given statement is TRUE.

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Amanda [17]

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Step-by-step explanation:

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2 years ago

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Find slope of the graph 9x-3y=15

LekaFEV [45]

<h3><u>Explanation</u></h3>

Convert the equation into slope-intercept form.

$y = mx + b$

where m = slope and b = y-intercept.

What we have to do is to make the y-term as the subject of equation.

$9x - 3y = 15 \\ 9x - 15 = 3y \\ \frac{9x - 15}{3} = y$

Simplify

$\frac{9x}{3} - \frac{15}{3} = y \\ 3x - 5 = y \\ y = 3x - 5$

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<h3><u>Answer</u></h3>

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3 years ago

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Aloiza [94]

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2 years ago

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ahrayia [7]

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C. r = 2w; r = 10 D. r = 2w; r = 2.5. T</span>he situation</span> implies that the number of roses is inversely proportional to the number of weeds. In this case, the answer is either a or b. Given 5 weeds,the one that fits is A. <span>A. r= 200 over w; r = 40. </span>

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3 years ago

if in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99%

Dahasolnce [82]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours.

If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?

Given Information:

standard deviation = σ = 30 hours

confidence level = 99%

Margin of error = 6 hours

Required Information:

sample size = n = ?

Answer:

sample size = n ≈ 165

Step-by-step explanation:

We know that margin of error is given by

Margin of error = z*(σ/√n)

Where z is the corresponding confidence level score, σ is the standard deviation and n is the sample size

√n = z*σ/Margin of error

squaring both sides

n = (z*σ/Margin of error)²

For 99% confidence level the z-score is 2.576

n = (2.576*30/6)²

n = 164.73

since number of bulbs cannot be in fraction so rounding off yields

n ≈ 165

Therefore, a sample size of 165 bulbs is needed to ensure a margin of error not greater than 6 hours.

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