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3 years ago

Solve the system of inequalities 1-12y<:3y+1; 2-6y>4+4y

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

8 0

For 1 - 12y < 3y+1; y > 15

For 2 - 6y > 4 + 4y; y < -0.2

The given inequalities are:

1 - 12y < 3y + 1

2 - 6y > 4 + 4y

For 1 - 12y < 3y + 1:

1 - 12y < 3y + 1

Collect like terms

-12y - 3y < 1 - 1

-15y < 0

Multiply both sides by -1

-1(-15y) > 0(-y)

15y > 0

Divide both sides by 15

y > 0/15

y > 15

For 2 - 6y > 4 + 4y

Collect like terms

-6y - 4y > 4 - 2

-10y > 2

Multiply both sides by -1

-1(-10y) < 2(-1)

10y < -2

y < -2/10

y < -0.2

Learn more here: brainly.com/question/11316045

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the variable Z is invery proportional to X. when X is 3, Z has the value 6. what is the value of Z when X = 12

MrMuchimi

"inversely proportional," please.

z = k/x

When x is 3, z = 6; find k: 6 = k/3, or k = 18.

Then z = 18/x. When x = 12, z = 18/12 = 2/3 (answer)

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3 years ago

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Lostsunrise [7]

Answer:

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step by step explanation

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2 years ago

Calculate the sample standard deviation of data from Question 1<br> 76,45,64,80,92

mash [69]

Answer:

$S.D = 15.98$

Step-by-step explanation:

Given: 76,45,64,80,92

Required: Determine the standard deviation

We start by calculating the mean

$Mean = \frac {\sum x}{n}$

Where x-> 76,45,64,80,92 and n = 5

$Mean = \frac {76+45+64+80+92}{5}$

$Mean = \frac{357}{5}$

$Mean = 71.4$

Subtract Mean (71.4) from each of the given data

$76 - 71.4 = 4.6\\45 - 71.4 = -26.5\\64 - 71.4 = -7.4\\80 - 71.4 = 8.6\\92 - 71.4 = 20.6$

Determine the absolute value of the above result

$|4.6| = 4.6\\|-26.5| = 26.5\\|-7.4| = 7.4\\|8.6| = 8.6\\|20.6| = 20.6$

Square Individual Result

$4.6^2 = 21.16 \\26.5^2 = 702.25\\7.4^2 = 54.76\\8.6^2 = 73.96\\20.6^2 = 424.36$

Calculate the mean of the above result to give the variance

$Mean = \frac {\sum x}{n}$

$Mean = \frac{21.16 + 702.25 + 54.76 + 73.96 + 424.36}{5}\\Mean = \frac{1276.49}{5}\\Mean = 255.298$

Hence, Variance = 255.298

Standard Deviation is calculated by $\sqrt{Var}$

$SD = \sqrt{255.298}$

$S.D = 15.9780474402$

$S.D = 15.98 (Approximated)$

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3 years ago

When Brooklyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard dev

KonstantinChe [14]

Using the Empirical Rule, it is found that her finishing time will be between 70 and 82 seconds in 95% of her races.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

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

In this problem, the mean is of 76 seconds and the standard deviation is of 3 seconds, then:

76 - 2 x 3 = 70.

76 + 2 x 3 = 82.

Which means that values between 70 and 82 seconds are within 2 standard deviations of the mean, hence the percentage is of 95%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

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Step-by-step explanation:

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