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3 years ago

The sum of the interior angles of a polygon is 14 × 180 . Work out the number of sides of the polygon.

Mathematics

1 answer:

labwork [276]3 years ago

5 0

Answer:

Number of sides of the polygon = 16

Step-by-step explanation:

Sum of the interior angle of a polygon = (n - 2) × 180°

Here, n = Number of sides of the polygon

If sum of the interior angles = 14 × 180°

Therefore, (n - 2) × 180° = 14 × 180°

(n - 2) = 14

n = 14 + 2

n = 16

Number of sides of the polygon = 16

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at a store, the probability that a customer buys socks is 0.15. the probability that a customer buys socks given that the custom

leva [86]

Answer: Option B

Step-by-step explanation:

First we assign a name to the events:

Event S: a customer buys socks

Event H: a customer buys shoes.

We know that :

$P (S) = 0.15$

We also know that the probability of S given that H occurs is:

$P(S|H) =\frac{P(S\ and\ H)}{P(H)}=0.20$

If two events S and H are independent then:

$P (S) * P (H) = P (S\ and\ H)$

This mean that if two events S and H are independent then:

$P(S|H) =\frac{P(S)*P(H))}{P(H)}$

$P(S|H) =P(S)$

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This means that S and H events are dependent.

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3 years ago

Q6. (15 points) IQ examination scores of 500 members of a club are normally distributed with mean of 165 and SD of 15.

melamori03 [73]

Answer:

a) 0.8413

b) 421

c) $P_{95} = 189.675$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 165

Standard Deviation, σ = 15

We are given that the distribution of IQ examination scores is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(IQ scores at most 180)

P(x < 180)

$P( x < 180) = P( z < \displaystyle\frac{180 - 165}{15}) = P(z < 1)$

Calculation the value from standard normal z table, we have,

$P(x < 180) = 0.8413 = 84.13\%$

b) Number of the members of the club have IQ scores at most 180

n = 500

$\text{Members} = n\times \text{P(IQ scores at most 180)}\\= 500\times 0.8413\\=420.65 \approc 421$

c) P(X< x) = 0.95

We have to find the value of x such that the probability is 0.95

$P( X < x) = P( z < \displaystyle\frac{x - 165}{15})=0.95$

Calculation the value from standard normal z table, we have,

$P(z < 1.645) = 0.95$

$\displaystyle\frac{x - 165}{15} = 1.645\\\\x = 189.675$

$P_{95} = 189.675$

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