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Answer:

There is a 95% chance that values will be within ±2 standard deviations of the mean.

Step-by-step explanation:

Normal Probability Distribution:

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

The Empirical Rule 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 question:

According to the empirical rule, 95% of the measures are within 2 standard deviations of the mean. So the correct statement is:

There is a 95% chance that values will be within ±2 standard deviations of the mean.

Answer:

2/8 are seniors

Step-by-step explanation:

one half = 4/8

4/8 + 1/8 + 1/8 = 6/8.

What's left is 2/8

Answer:

She earned 221.25 in commission

Step-by-step explanation:

2.5% of 8850 is 221.25

Answer:

3 liquid gallons

Step-by-step explanation:

3 + 4 + 5 = 12

12 ÷ 4 = 3 liquid gallons

Answer:

6

Step-by-step explanation:

because its the middle number

Answer:

Yes, this is a right triangle

Step-by-step explanation:

a² + b² = c²

65² + 72² = 97²

4225 + 5184 = 9409

9409 = 9409

Since the hypotenuse equals the 2 legs, it's a right triangle

Answer:

Is this called

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Answer:

A tropism (from Greek τρόπος, tropos, "a turning") is a biological phenomenon, indicating growth or turning movement of a biological organism, usually a plant, in response to an environmental sti

Answer:

[tex]2k - 9[/tex]

Step-by-step explanation:

jsjsjsjsjjsjsksksksksksksksksksjskkwjwjwjwkw

Answer:

y = 0.14t + 481

Population in 17 years: 483.38

Step-by-step explanation:

y = (m) (x) + b

y = (slope) (x) + starting value

Answer:

No, the sample is too small compared to the size of the shipment.

Step-by-step explanation:

Answer:

85/100*x=51

Step-by-step explanation:

85x=5100

Answer:

Your answer is A <3

Step-by-step explanation:

Answer:

400 thousand people > 300 thousand people, so there are more people living in Miami.

Answer:

414π

Step-by-step explanation:

Volume of a cylinder = area of circle/ cross-section x height

Area of cross-section = πr² = 6²π = 36π

36π x 11.5 = 414π

Answer:

1300.61936 cm

Step-by-step explanation:

:))

Step-by-step explanation:

480 is the answer // provide picture for better answer

Answer:

The bushes will be located 6 meters apart from each other.

Step-by-step explanation:

Given that at a walking path 78 mile long Colleen planted 14 bushes the same distance apart along the path, to determine how far away are the 1st 2 bushes along the path, the following calculation must be performed:

78/13 = X

6 = X

Thus, since the first bush is at meter 0, the remaining 13 bushes will be located 6 meters apart.

Answer:

6(4X-1) = 24X -6 , (2 . 12X ) - (2 . 3) .

24X+6 = (6 . 4X) + (6 . 1) , 6( 4X + 1 ) .

(4 . 6X) - (4 . 2) = 24X + 8 , 4(6X + 2) .

Step-by-step explanation:

Hope it was helpful dear , good luck ^^

Answer:

7144

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

there should be a cross multiplication

3(8x)=2

expanding bracket

24x=2

multiple both sides by 24

x=1/12

Answer:

7: 7.75   8: 6.98

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Well four weels in every car so it’s 4 times cars (a)

4 times A=W

Step-by-step explanation: im smart also if u do multiply it by a by 4 it equals  W

Answer:

Mixed number: [tex]2\frac{83}{100}[/tex]

Improper Fraction: [tex]\frac{283}{100}[/tex]

Answer:

[tex]\frac{238}{100}\\\\2\frac{38}{100}[/tex]

Step-by-step explanation:

2.83/1

To make this a normal fraction, the top has to be a whole number, so we can multiply the top and bottom by 100 to slide the decimal point twice.

238/100

This can be shown as a mixed number by removing the 200 which is divisible by 100

[tex]2 \frac{38}{100}[/tex]

Note: The reason the question says not to simplify is because 283 is a prime and cannot be simplified

9514 1404 393

Answer:

  20.78 square units

Step-by-step explanation:

The area of a regular polygon of radius r and number of sides n is given by ...

  A = (n/2)r²sin(360°/n)

For this regular 3-gon of radius 4, the area is ...

  A = (3/2)(4²)sin(360°/3) = 24(√3/2) = 12√3 . . . square units

The area is about 20.78 square units.

The exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].

The exact values of trigonometric functions are values of trigonometric functions of certain angles that can be expressed exactly using expressions containing real numbers and roots of real numbers. These values are also called analytic values of trigonometric functions or trigonometric values of special angles.

The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.

According to the given question.

We have a trigonometric function

[tex]cos(\frac{11\pi }{8} )[/tex]

We have to find the exact value of the above trigonometric function.

since,

[tex]\frac{11\pi }{8}[/tex] can be written as [tex](\pi +\frac{3}{8\pi } )[/tex]

[tex]\implies cos(\frac{11\pi }{8} ) = cos(\pi +\frac{3}{8}\pi )[/tex]

And we know that,

Cos(π + θ) = -cosθ

Because, π + θ lies in third quadrant and in third quadrat cos gives negative values.

Also,

[tex]cos\frac{\alpha }{2} = \pm\sqrt{\frac{1+cos\alpha }{2} }[/tex]        ....(i)

Therefore,

[tex]cos(\pi +\frac{3}{8} \pi )[/tex]

[tex]= -cos(\frac{3}{8} \pi )[/tex]

[tex]= -cos(\frac{3}{2(4)} \pi )[/tex]

[tex]= -\sqrt{\frac{1+cos\frac{\pi }{4} }{2} }[/tex]

[tex]= -\sqrt{\frac{1+\frac{1}{\sqrt{2} } }{2} }[/tex]

[tex]= -\sqrt{\frac{1+\frac{\sqrt{2} }{2} }{2} }[/tex]

[tex]= -\sqrt{\frac{2+\sqrt{2} }{4} }[/tex]

Hence, the exact value of [tex]cos(\frac{11\pi }{8} )[/tex] is [tex]-\sqrt{\frac{2+\sqrt{2} }{4} }[/tex].

Thus, option A is correct.

Find out more information about exact value of trigonometric function here:

https://brainly.com/question/19552534

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