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KATRIN_1 [288]
1 year ago
9

Fing the LCM of 54 and 81

Mathematics
2 answers:
mina [271]1 year ago
5 0
The lcm of 54 and 81 is the smallest positive integer that divides the numbers 54 and 81 without a remainder. Spelled out, it is the least common multiple of 54 and 81
Lilit [14]1 year ago
5 0

Step-by-step explanation:

Factor of 54

= 2 \times 3 \times 3 \times 3

Factor of 81

= 3 \times 3 \times 3 \times 3

Now ...

Common factor = 3 × 3 × 3

= 27

LCM = common factor × remaining factors..

= 27 × 2 × 3

= 162

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Answer:

The formula for the area of the triangle is:

\displaystyle A=24x^2

When <em>x</em> = 3, the area is 216 square centimeters.

When <em>x </em>= 2.4, the area is 138.24 square centimeters.

And when <em>x</em> = 5, the hypotenuse of the triangle is 50 centimeters.

Step-by-step explanation:

We are given a right triangle with a height of 8<em>x</em> and a base of 6<em>x</em>.

The area of a triangle is given by the formula:

\displaystyle A=\frac{1}{2}bh

So, by substitution:

\displaystyle A=\frac{1}{2}(8x)(6x)=24x^2

When <em>x </em>= 3, the area will be:

\displaystyle A(3)=24(3)^2=216\text{ cm}^2

And when <em>x</em> = 2.4, the area will be:

A(2.4)=24(2.4)^2=138.24\text{ cm}^2

When <em>x </em>= 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.

By the Pythagorean Theorem:

a^2+b^2=c^2

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And f(t) is the amount of money in Gavin's investment account after t years

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The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sampl
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Answer:

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Step-by-step explanation:

Things to understand before solving:

  • - <u>Normal Probability Distribution</u>
  1. The z-score formula can be used to solve normal distribution problems. In a set with mean ц and standard deviation б, the z-score of a measure X is given by: Z=\frac{X-u}{a}

The Z-score reflects how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value associated with this z-score. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. Subtracting 1 from the p-value yields the likelihood that the measure's value is larger than X.

  • - <u>Central Limit Theorem</u>
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As long as n is more than 30, the Central Limit Theorem may be applied to a skewed variable. A specific kind of steel cable has an average breaking strength of 2000 pounds, with a standard variation of 100 pounds.

This means, ц  = 2000 and б = 100.

A random sample of 20 cables is chosen and tested.

This means that n = 20, s=\frac{100}{\sqrt{120} } =22.361

Determine the sample mean that will exclude the top 95 percent of all size 20 samples drawn from the population.

This is the 100-95th percentile, or X when Z has a p-value of 0.05, or X when Z = -1.645. So Z=\frac{X-u}{a}

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Z=\frac{X-u}{a} \\-1.645=\frac{X-2000}{22.361} \\X-2000=-1.645*22.361

X =1963.2

<h3>Answer:</h3>

The sample mean that will cut off the top 95% of all size 20 samples obtained from the population is 1963.2 pounds.

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