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Katarina [22]
3 years ago
13

What is the exact value of the expression the square root of 486. − the square root of 24. + the square root of 6.? Simplify if

possible.
Mathematics
1 answer:
kenny6666 [7]3 years ago
8 0
Sqrt(486) - sqrt(24) + sqrt(6)

find the factors of 486 that we can remove from under the square root sign
 2 * 243
 2 * 3 * 81
 2 * 3 * 9 * 9 (we have 2 nines, we can move a 9 outside the sqrt sign)
sqrt(486) = 9 sqrt(6)

Repeating for sqrt(24)
2 * 12
2 * 2 * 6
2 * 2 * 2 * 3 (we can move a 2 outside the sqrt
sqrt(24) = 2 sqrt(6)

Finally, add all 3 terms together

9 sqrt(6) - 2 sqrt(6) + sqrt(6)
8 sqrt(6)

8 times square root of 6 is the final answer
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What does gemdas and pemdas stands for?
DanielleElmas [232]

Answer:

For pemdas

P Parentheses

E Exponents

M Multiplication

D Division

A Addition

S Subtraction

And for gemdas

G Grouping

E Exponents

M Multiplication

D Division

A Addition

S Subtraction

8 0
3 years ago
Read 2 more answers
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th
aliya0001 [1]

Answer:

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

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 17.42 ppm and a standard deviation of 3.25 ppm.

This means that \mu = 17.42, \sigma = 3.25

Sample of 12:

This means that n = 12, s = \frac{3.25}{\sqrt{12}}

Find the probability that the mean printing speed of the sample is greater than 18.12 ppm.

This is 1 subtracted by the p-value of Z when X = 18.12.

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

By the Central Limit Theorem

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

Z = \frac{18.12 - 17.42}{\frac{3.25}{\sqrt{12}}}

Z = 0.75

Z = 0.75 has a pvalue of 0.773.

1 - 0.773 = 0.227

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

4 0
3 years ago
A fish tank is in the shape of an open glass cuboid 30 cm deep with a base 16 cm by 17 cm, these measurements being external. If
omeli [17]

Answer:

3.24 kg

Step-by-step explanation:

internal Vol = (30-0.5)(16-1)(17-1) = 7080 cm^3 = 7.08ltrs

external Vol= 30* 16* 17 = 8160cm^3 = 8.16ltrs

Vol of thickness = 8160 - 7080 = 1080cm^3

Mass of the tank= density * volume = 3*1080 = 3,240g = 3.24 kg

8 0
2 years ago
The diagonal of a square is x units. What is the area of the square in terms of X?
lesantik [10]

Answer:

\frac{1}{2}x^2 square units

Step-by-step explanation:

The simple formula we need here is:

d=s\sqrt{2}

Where

d is length of diagonal

s is length of side of square

Let's find side length of square from information given:

d=s\sqrt{2} \\x=s\sqrt{2} \\s=\frac{x}{\sqrt{2}}

Now,

we know area of square is  s^2

We know s, and now we find area

Area = s^2\\(\frac{x}{\sqrt{2}})^2\\\frac{x^2}{2}\\\frac{1}{2}x^2

The first answer choice is right, 1/2x^2 sq. units.

5 0
3 years ago
Which of the expressions below are equivalent to 0.5( 4x + 12)
kogti [31]
The correct answer is B.
0.5(4x + 12)
2x + 6
5 0
2 years ago
Read 2 more answers
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