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Serhud [2]
4 years ago
5

Find the length of the side of an equilateral triangle whose area is 9√3 cm2

Mathematics
1 answer:
Hunter-Best [27]4 years ago
8 0

Answer:

s = 6 cm

Step-by-step explanation:

The area (A) of an equilateral triangle is calculated as

A = \frac{s^2\sqrt{3} }{4} ( s is the length of side )

Here A = 9\sqrt{3} , thus

\frac{s^2\sqrt{3} }{4} = 9\sqrt{3} ( multiply both sides by 4 to clear the fraction )

s²\sqrt{3} = 36\sqrt{3} ( divide both sides by \sqrt{3} )

s² = 36 ( take the square root of both sides )

s = \sqrt{36} = 6

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Quadrilateral ABCD has coordinates A (3,1) B (4,4) C (7,5) D (6,2). Quadrilateral ABCD is a ?
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3 years ago
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Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule
Yuri [45]

Answer:

(a) 68% of people has an IQ score between 87 and 113​.

(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139​.

Step-by-step explanation:

Given information:Scores of an IQ test have a​ bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between \overline{x}-\sigma and \overline{x}+\sigma.

95% data lies between \overline{x}-2\sigma and \overline{x}+2\sigma.

99.7% data lies between \overline{x}-3\sigma and \overline{x}+3\sigma.

(a)

\overline{x}-\sigma=100-13=87

\overline{x}+\sigma=100+13=113

[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113​.

(b)

\overline{x}-2\sigma=100-2(13)=74

\overline{x}+2\sigma=100+2(13)=126

[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126​.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126​.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

\overline{x}-3\sigma=100-3(13)=61

\overline{x}+3\sigma=100+3(13)=139

[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139​.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139​.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139​ is

P=\frac{1}{2}(0.3\%)=0.15\%

Therefore 0.15% of people has an IQ score greater than 139​.

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Answer:

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