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3 years ago

PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.

Mathematics

2 answers:

aliina [53]3 years ago

7 0

Answer:

$x \geq -91/2$

Step-by-step explanation:

$6(x+8) \geq -43 + 4x$

Resolving Parenthesis

$6x+48 \geq -43 + 4x$

Collecting like terms

$6x - 4 x \geq -43-48$

$2x \geq -91$

Dividing both sides by 2

$x \geq -91/2$

amid [387]3 years ago

5 0

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : $6(x+8) = 6x + 6 8 = 6x + 48$

$6x + 48 \geq - 43+4x$ - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

$48 \geq - 43-2x$ - now add 43 to either side,

$91\geq -2x$ - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

$- 91 / 2 \leq x$ , or in other words $x \geq - 91 / 2$ . This is our solution.

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2 years ago

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

$\= x = 13.4$ . $E = 2.3$

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

3 years ago

One winter day, the outside temperature, y, was never below −1°. The inside of a car was always warmer than the temperature outs

sammy [17]

Answer:

The correct option is;

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Step-by-step explanation:

The inequality representing the first line is y ≥ -1

The inequality representing the second line is y > x + 4

Therefore, the first line is a solid horizontal line with the shaded region above the line

The second line is a line with a broken line with positive slope slope with the shaded region being above the line and to the left

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3 years ago

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