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3 years ago

There is a bag filled with 5 blue, 2 red and 3 green marbles,

Mathematics

1 answer:

nikdorinn [45]3 years ago

5 0

Answer:

0.62

Step-by-step explanation:

There are a total of 10 marbles in the bag.

P(blue and not blue) = 5/10 × 5/10 = 25/100

P(red and not red) = 2/10 × 8/10 = 16/100

P(green and not green) = 3/10 × 7/10 = 21/100

P = 25/100 + 16/100 + 21/100

P = 62/100

P = 0.62

Alternatively, you can calculate it this way:

P(both blue) = (5/10)² = 25/100

P(both red) = (2/10)² = 4/100

P(both green) = (3/10)² = 9/100

P = 1 − (25/100 + 4/10 + 9/100)

P = 1 − 38/100

P = 62/100

P = 0.62

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Answer:

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Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

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Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

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This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

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$y(-2) = 0$

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$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

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