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2 years ago

Which graph represents the given equation?

Mathematics

1 answer:

Alchen [17]2 years ago

7 0

9514 1404 393

Answer:

Step-by-step explanation:

The axis of symmetry of quadratic ax²+bx+c is x=-b/(2a). For the given equation, the axis of symmetry is ...

x = -4/(2(3/2)) = -4/3

The only graph with its vertex at x=-4/3 is graph A.

_____

<em>Additional comment</em>

You can also make the correct choice by evaluating the equation at a couple of different values of x. Convenient ones are x= -1, or 0, or +1. The value at x=0 is the y-intercept, (0, -2), which seems to be a point on all of the graphs. The value at x=1 is 3/2+4-2 = 3.5, which looks like it is only seen on graph A.

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$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$ In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$ And the variance is given by:

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Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

For this case we have the following distribution given:

X 3 4 5 6

P(X) 0.07 0.4 0.25 0.28

We can calculate the mean with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$

In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$

And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

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