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2 years ago

The figures below are similar.

Mathematics

1 answer:

Dafna1 [17]2 years ago

7 0

Answer:

a) 2.5

b) 6.25

Step-by-step explanation:

For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.

<h3>Application</h3>

The ratio of linear dimensions, larger to smaller, is ...

(30 yd)/(12 yd) = 2.5

<h3>a) Perimeter</h3>

Perimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.

The ratio of areas, larger to smaller, is the square of the scale factor for side lengths:

(2.5)² = 6.25

The ratio of the areas of the larger to smaller figure is 6.25.

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Answer:

$P(X>1000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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If we apply this formula to our probability we got this:

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Step-by-step explanation:

Previous concepts

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The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

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Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(950,50)$

Where $\mu=950$ and $\sigma=50$

We are interested on this probability

$P(X>1000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>1000)=P(\frac{X-\mu}{\sigma}>\frac{1000-\mu}{\sigma})=P(Z>\frac{1000-950}{50})=P(z>1)$

And we can find this probability using the complement rule and the normal standard table and we got:

$P(z>1)=1-P(z$

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