There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 7/9.
There are 45 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

There must be 35 red marbles.

Step-by-step explanation:

This question can be solved using a rule of three.

A probability is the number of desired outcomes divided by the number of total outcomes.

The probability of randomly choosing a red marble is 7/9.

This means that for each set of 9 marbles, 7 must be red.

There are 45 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

How many red marbles out of 45?

7 red - 9 marbles

x red - 45 marbles

Simplifying by 9

There must be 35 red marbles.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

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