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4 years ago

HIJK is a rectangle. Find the value of x and find the length of each diagonals. If hj=19+2x and ik=3x+22

1 answer:

8 0

Hj and ik are opposite sides of the rectangle so they areequal in length.

19 + 2x = 3x + 22
19-22 = 3x-2x
x = -3

We can't find the length of the diagonals as we have no information about the width.

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Read 2 more answers

Suppose x is a normally distributed random variable with µ = 56 and σ = 3. Find a value x0 of the random variable x that satisfi

galina1969 [7]

Answer:

a) 52.15

b) 58.53

c) 62.98

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 56

Standard Deviation, σ = 3

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

Formula:

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

a) We have to find $x_0$ such that

P(X < x) = 0.1

$P( X < x) = P( z < \displaystyle\frac{x_0 - 56}{3})=0.1$

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

$P(z < -1.282) = 0.1$

$\displaystyle\frac{x_0 - 56}{3} = -1.282\\\\x_0 = 52.15$

b) We have to find $x_0$ such that

P(X < x) = 0.8

$P( X < x) = P( z < \displaystyle\frac{x_0 - 56}{3})=0.8$

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

$P(z < 0.842) = 0.8$

$\displaystyle\frac{x_0 - 56}{3} = 0.842\\\\x_0 = 58.53$

c) We have to find $x_0$ such that

P(X > x) = 0.01

$P( X > x) = P( z > \displaystyle\frac{x - 56}{3})=0.01$

$= 1 -P( z \leq \displaystyle\frac{x - 56}{3})=0.01$

$=P( z \leq \displaystyle\frac{x - 56}{3})=0.99$

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

$P(z < 2.326) = 0.99$

$\displaystyle\frac{x_0 - 56}{3} = 2.326\\\\x_0 = 62.98$

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