Answer:
Step-by-step explanation:
(a³ - b³) = (a - b) (a² + ab + b²)
27x³ - 64 = 3³x³ - 4³
= (3x)³ - 4³ {a = 3x & b= 4)
Substitute in the above formula.
= (3x -4)([3x]² + 3x*4 + 4²)
= (3x - 4)(9x² + 12x + 16)
The expression 27x^3-64 factors to (3x-4) (9x^2+12x+16).
Answer:
If a person selected at random from this group is a man, there is a 31.25% probability that the person favors raising the drinking age.
Step-by-step explanation:
We have these following informations:
There are 1000 people in total.
540 favored raising the age. Of them 390 were female, and 540-390 = 150 were male.
460 were opposed. Of them, 130 were female and 460-130 = 330 were males.
If a person selected at random from this group is a man, what is the probability that the person favors raising the drinking age?
There are 150+330 = 480 males. Of them, 150 favors raising the drinking age.
So

If a person selected at random from this group is a man, there is a 31.25% probability that the person favors raising the drinking age.
First, let's write the given equation in slope-intercept form: y = mx + b
In slope-intercept form, the slope of the line is m, and the y-intercept is b. The slope is a measure of how steep the graph is at any point and is found by doing rise over run. This means the change in y values divided by the change in x values. Next, y-intercept is just where the graph crosses the y axis.
All we need to do to get the equation in slope-intercept form is to divide each term by 3. This will isolate the y.

As you can see, the slope of the line is 2/3, and the y-intercept is -2.
To graph the line, plot a point at (0,-2). This is the point where the graph crosses the y axis. Then from that point, count up two and right 3. Plot a point here as well. Lastly, connect the two points with a straight line.
See attached picture for the graph.
Answer:
1/12
Step-by-step explanation:
1/6 for the number cube
and 1/2 for the coin landing on heads
1/6 times 1/2