We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.
A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles
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</h2><h2 /><h2>when we cross multiply, we get 5p = 240 </h2><h2>we divide both sides by 5 to isolate the variable </h2><h2 /><h3><u>There are 48 purple marbles </u></h3>
Answer:
25 units
Step-by-step explanation:
use the distance formula to get the square root of 24² + 7²
this will give you the square root of 625, which is 25
The tax is 6.5% OF the listed price. "OF" in math means multiply.
First convert the percentage to a decimal
6.5% = .065
Then multiply .065*813.95 = 52.90675. This is the tax.
Simply add the tax onto the cost
813.95 + 52.90675 = $866.86 (rounded)
Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.
In this case, we could say (where 
is the area of the rectangle):
Substituting the values the problem gave us for 
and 
, we can find the formula for 
in terms of 
, which is:
The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.
1) The ball's position is described by:
s(t) = 4.9t² + 450
We want to find the velocity, which is the 1st-order derivative of the displacement function (I assume this is an introductory calculus class)
s'(t) = v(t) = 9.8t
We get this by multiplying 4.9 x 2 and reducing the exponent by 1. Now we simply plug 5 in for t.
v(5) = 9.8* 5
v(5) = 49m/s
2) Our cost function is C(x) = x² - 10,000
To find the average rate of change between these units, we use this formula:
( C(101) - C(100) ) ÷1 .
We find the change in C, and divide by the change in x, which is just one.
C(101) = 101² - 10,000
C(101) = 201
C(100) = 100² - 10,000
C(100= 0
C(101) - C(100) = 201
Average rate of change in cost is 201 dollars/ unit between the two points.
