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3 years ago

|x| + 4 > 7 plz help and hurry

Mathematics

1 answer:

Talja [164]3 years ago

4 0

Answer:

The solution is $(-\infty,-3)\cup(3,\infty)$ .

Step-by-step explanation:

Given:

The inequality given is:

$|x|+4>7$

In order to simplify for 'x', we first isolate 'x' on one side.

Adding -4 on both sides, we get:

$|x|+4-4>7-4\\\\|x|>3$

Now, $|x|$ is an absolute value function which is defined as:

$|x|=\left \{ {{-x}\ \ x$

Therefore, the given inequality can be rewritten as:

$-x > 3\\x$ and $x > 3$

Therefore, the solution is $(-\infty,-3)\cup(3,\infty)$ .

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Suppose that the average and standard deviation of the fine for speeding on a particular highway are 111.12 and 13.04, respectiv

antoniya [11.8K]

Answer:

3) (98.08, 124.16)

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 111.12

Standard deviation = 13.04

Calculate an interval that is symmetric around the mean such that it contains approximately 68% of fines.

68% of the fines are within 1 standard deviation of the mean speed. So

From 111.12 - 13.04 = 98.08 to 111.12 + 13.04 = 124.16

The interval notation in the smallest value before the highest value.

So the correct answer is:

3) (98.08, 124.16)

8 0

3 years ago

Pleas help me find the answer and show the work to this question

lions [1.4K]

Answer:

$Leg\ 1 = 8$

$Leg\ 2 = 15$

Step-by-step explanation:

Given: See Attachment

Required

Determine the length of the legs

To do this, we apply Pythagoras theorem.

$Hyp^2 = Adj^2 + Opp^2$

In this case:

$17^2 = x^2 + (2x- 1)^2$

Open Bracket

$17^2 = x^2 + 4x^2- 2x-2x + 1$

$17^2 = 5x^2 - 4x + 1$

$289= 5x^2 - 4x + 1$

Collect Like Terms

$5x^2 - 4x + 1 - 289 = 0$

$5x^2 - 4x - 288 = 0$

Solving using quadratic formula:

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So:

$x = 8$ or $x = -7.2$

Since, x can't be negative, then:

$x = 8$

One of the leg is:

$Leg\ 1 = x$

$Leg\ 1 = 8$

$Leg\ 2 = 2x - 1$

$Leg\ 2 = 2*8 - 1$

$Leg\ 2 = 16 - 1$

$Leg\ 2 = 15$

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3 years ago

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