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3 years ago

In parallelogram HIJK, the measure of angle H is 45 degrees. 1.Find the measure of J and explain how you know

Mathematics

1 answer:

s2008m [1.1K]3 years ago

8 0

Answer:

45°

Step-by-step explanation:

A parallelogram is a polygon with 4 sides and 4 angles (that is a quadrilateral).

For a parallelogram ABCD, Opposite sides and opposite angles are equal (i.e. BC = AD and ∠A = ∠C).

Consecutive angles are supplementary that is ∠A + ∠B = 180°.

The diagonals of a parallelogram bisect each other also separating the parallelogram into two congruent triangles.

In parallelogram HIJK, ∠H and ∠J are opposite angles. hence:

∠H = ∠J (opposite angles of a parallelogram are equal)

∠J = 45°

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2 years ago

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4 years ago

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Sindrei [870]

Answer:

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And replacing we got:

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And replacing we got:

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Step-by-step explanation:

We have the following distribution

x 0 1 2 3 4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

$P(X=3) = 0.1$

Part b

We want this probability:

$P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

Part c

For this case we want this probability:

$P(X=4) = 0.3$

Part d

$P(X=0) = 0.2$

Part e

We can find the mean with this formula:

$E(X)= \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

Part f

We can find the second moment with this formula

$E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

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