1000 is the missing exponent
Answer:
The answers are:
1. The 15-ounce box has a unit rate of 21 cents per ounce
2. The 20-ounce box has a unit rate of 18 cents per ounce
3. The 25.5-ounce box has a unit rate of 16 cents per ounce
Step-by-step explanation:
First, you have to know the relationship between the cent and the dollar ($) and that is:
100 cents = $ 1
Next, let us convert all the prices in dollars to cents, to make calculations easy:
if 100 cents = $1
∴ $3.19 = 3.19 × 100 = 319 cents
$3.59 = 3.59 × 100 = 359 cents
$ 3.99 = 3.99 × 100 = 399 cents.
Next Let us find the unit cost of each box of sereal by dividing the total ounces by their prices:
1. for the 15-ounce box:
15-ounces = 319 cents
∴ 1 ounce (unit cost) = 319 ÷ 15 = 21.26 = 21 cents (to the nearest cent)
2. for the 20-ounce box:
20-ounces = 359 cents
∴ 1 ounce = 359 ÷ 20 = 17.95 = 18 cents (to the nearest cent)
3. for the 25.5 ounce box:
25.5 ounces = 399 cents
∴ 1 ounce = 399 ÷ 25.5 = 15.65 = 16 cents (to the nearest cent)
Answer:
Step-by-step explanation:
For this case we have the following plot on the figure attached.
We know on this case that represent our radius for the square, since we need cross sections perpendicular to the y axis.
We find the intersection points like this:
Since we are assuming squares for the cross sections the area is given by where r = x= -2y+6.
Since our radius is on terms of x we can create a integral with limits on x in order to find the volume, And we can use the following integral in order to find the volume.
On the left part we are using the following property from algebra:
And after do the integral we got this:
There are several ways to do this.
I'll show you two methods.
1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.
slope = m = (y2 - y1)/(x2 - x1)
Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.
Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.
Plug in values into the formula:
m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4
The slope is -1/4
2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.
Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4
As you can see we got the same slope using both methods.