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2 years ago

Triangle angle sum theorem What is the value of p?

Mathematics

1 answer:

monitta2 years ago

8 0

The angle sum property of triangle states that the sum of all angles of a triangle should be equal to 180°...

According to this theorem,

$\sf54 + p-20 + p-48 = 180$

$\sf \: -14 + 2p = 180$

$\sf \: 2p = 180 +14$

$\sf \: 2p = 194$

$\sf \: p=97$

<em>The value of p is 97... </em>

Now, Let's find the value of all angles with the help of value of p

Angle 1 = 54°
Angle 2 = p-48 = 97-48 = 49°
Angle 3 = p-20 = 97-20 = 77°

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The scores for a certain test of intelligence are normally distributed with mean 85 and standard deviation 11. Find the 90th per

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Answer:

99.1 is the 90th percentile of these scores.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 85

Standard Deviation, σ = 11

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

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

We have to find the value of x such that the probability is 0.90

$P( X < x) = P( z < \displaystyle\frac{x - 85}{11})=0.90$

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

$P(z \leq 1.282) = 0.90$

Putting values, we get,

$\displaystyle\frac{x - 85}{11} = 1.282\\\\x = 99.1$

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