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3 years ago

Solve and graph the following inequality: 3(7x+17) > -19 + 14x

Mathematics

1 answer:

love history [14]3 years ago

5 0

Answer:

Solving the inequality we get: $\mathbf{x>-7}$

Step-by-step explanation:

We need to solve and graph the inequality $3(7x+17) > -19 + 14x$

Solving:

$3(7x+17) > -19 + 14x$

Step 1: Multiply 3 with terms inside the bracket

$21x+51 > -19 + 14x$

Step 2:Subtracting 51 on both sides

$21x+51-51 > -19 + 14x-51\\21x>14x-70\\$

Step 3: Subtract 14x on both sides

$21x-14x>+14x-70-14x\\7x>-70$

Step 4: Divide both sides by 7

$\frac{7x}{7}>\frac{-70}{7}\\x>-10$

Solving the inequality we get: $\mathbf{x>-7}$

The graph is attached in the figure below.

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Answer:

Step-by-step explanation:

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<u>Given:</u>

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Read 2 more answers

A woman is randomly selected from the 18–24 age group. For women of this group, systolic blood pressures (in mm Hg) are normally

Naddik [55]

Answer:

$X \sim N(114.8,13.1)$

Where $\mu=114.8$ and $\sigma=13.1$

We are interested on this probability

$P(X>140)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule:

$P(z>1.924)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(114.8,13.1)$

Where $\mu=114.8$ and $\sigma=13.1$

We are interested on this probability

$P(X>140)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this: $P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140- 1114.8}{2.6})=P(z>1.924)$ And we can find this probability using the complement rule:

$P(z>1.924)=1-P(z$

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3 years ago