Question

17 multiple choice 4 points a bag contains 2 red marbles and 3 blue marbles. if one marble is drawn at random, what is the probability that it is red?
18 multiple choice 4 points find the equation of the line which has a slope of \\( \frac { 2 } { 3 } \\) and contains the point \\( ( 0,2 ) \\).
19 multiple choice 4 points what is the product below expressed in scientific notation? \\( ( 2.1 \times 10 ^ { 3 } ) ( 3 \times 10 ^ { 6 } ) \\)

Explanation:

Step1: Calculate total number of marbles

Total marbles = red marbles + blue marbles = \(2 + 3=5\)

Step2: Use probability formula

Probability \(P=\frac{\text{Number of red marbles}}{\text{Total number of marbles}}=\frac{2}{5}\)

Step1: Use slope - intercept form \(y = mx + b\)

Given slope \(m=\frac{2}{3}\) and point \((0,2)\) (where \(x = 0,y=2\)), substituting into \(y=mx + b\) gives \(b = 2\)

Step2: Write the equation

The equation is \(y=\frac{2}{3}x+2\)

Step1: Multiply the coefficients and add the exponents

For \((2.1\times10^{3})(3\times10^{6})\), multiply \(2.1\times3 = 6.3\) and add exponents \(3 + 6=9\)

Step2: Write in scientific notation

The result is \(6.3\times10^{9}\)

Answer:

1. \(\frac{2}{5}\) corresponds to the second option.
2. \(y=\frac{2}{3}x + 2\) corresponds to the fourth option.
3. \(6.3\times10^{9}\) corresponds to the first option.