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givi [52]
3 years ago
14

Solve for x: |4x + 12| = 16

Mathematics
2 answers:
irina1246 [14]3 years ago
7 0
Solve Absolute value
4x + 12 = 16 or <span>4x + 12 = -1<span>6
</span></span>===============================================
1.) 4x+12=<span>16
Subtract 12 from both sides
</span><span><span>4x+12-1</span>2</span>=<span>16-12
</span>4x = 4
Divide by 4
4x ÷ 4 = 4 ÷ 4
x = 1
=================================================================
2.) 4x+12=-<span>16
</span>Subtract 12 from both sides
<span><span>4x+12-</span>12</span>=-<span>16-12
</span><span>4x</span>=-<span><span>28
</span></span>Divide each side by 4
4x ÷ 4 = -28 ÷ 4
x = -7
================================================================
X = 1 and x = -7 is your answer
JulijaS [17]3 years ago
6 0
4x+12=16
4x=4
x=1

or

-(4x+12)=16
-4x-12=16
-4x=28
x=-7

answer Choice C is correct
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Answer:

b. -36/77

Step-by-step explanation:

As 0 < x < \pi/2 => tan x > 0

As 0< y <  \pi/2 => tan y > 0

We have the formula:

  • \frac{1}{sin^{2}x } =1 + cot^{2}x => \frac{1}{(8/17)^{2} } = 1+cot^{2}x => cot^{2} x=225/64

As tan x = 1/(cotx) => tan^{2}x = \frac{1}{cot^{2}x} =\frac{1}{225/64} = \frac{64}{225}

As tan x > 0 => tan x = 8/15

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Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that \mu = 20, \sigma = 6

Sample of 150:

This means that n = 150, s = \frac{6}{\sqrt{150}}

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}

Z = 2.04

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X = 19.5

Z = \frac{X - \mu}{s}

Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}

Z = -1.02

Z = -1.02 has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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Get x by itself by subtracting 160 to both sides.

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Divide both sides by 50.

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