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Can the sides of a triangle have lengths 1, 7, and 11? Explain

Airida [17]

No

Given 3 sides of a triangle, the sum of any 2 sides must be greater than the third side.

Consider the 3 given sides 1, 7 and 11

7 + 11 = 18 > 1

1 + 11 = 12 > 7

1 + 7 < 11 ⇒ not valid

Hence these sides do not form a triangle

6 0

3 years ago

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for t

rjkz [21]

Answer:

COV (all stocks) = 0.55

COV (stocks and bonds) = 0.82

Step-by-step explanation:

Coefficient of Variation is used to measure variability.

It is defined as the ration of standard deviation and the mean.

It can be used to compare variability of two population or two samples.

Formula:

$\text{Coefficient of Variation} = \displaystyle\frac{\text{Standard Deviation}}{\text{Mean}}$

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

x: 14, 0, 39, 25, 32, 27, 28, 14, 14, 15

$Mean = \frac{208}{10} = 20.8$

$Standard~Deviation = \sqrt{\frac{1169.6}{9} } = 11.39$

$Coefficient~of~Variation = \frac{11.39}{20.8} = 0.55$

y = 6, 2, 29, 17, 26, 17, 17, 2, 3, 5

$Mean = \frac{124}{10} = 12.4$

$Standard~Deviation = \sqrt{\frac{924.4}{9} } = 10.13$

$Coefficient~of~Variation = \frac{10.13}{12.4} = 0.82%$

Since coefficient of variation of x is less compared to y, thus it could be said bonds does not reduce overall risk of an investment portfolio.

6 0

2 years ago

Which model represents the equation below? Negative 4 x + (negative 2) = 3 x + (negative 5)

pogonyaev

Answer:

Slope of function B

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Which of the following values are solutions to the inequality 1+5x<4?<br> I.6 <br> II.5<br> III.2

Paraphin [41]

Answer:

x < .6

Step-by-step explanation:

1+5x<4

Subtract 1 from each side

1-1+5x<4-1

5x<3

Divide each side by 5

5x/5 <3/5

x < .6

4 0

2 years ago

When two fractions are between 0 & 1 half how do you know which fraction is greater explaina

oksian1 [2.3K]

Example- 1/3 or 1/5, which is larger? If you divide 1 by 3 the answer is 0.33 If you divide 1 by 5 it's 0.2. Since 0.33(1/3) is larger that would be the answer.
sorry if I make this confusing.
basically divide the top by the bottom to see which is larger. Then compare the fractions.

5 0

3 years ago