The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.
Answer:46
Step-by-step explanation:Regular polygons are shapes made of straight lines with certain relationships among their lengths. For instance, a square has 4 sides, all the same length. A regular pentagon has 5 sides, all the same length. For these shapes, there are formulas for finding the area. But for irregular polygons, which are made of straight lines of any length, there are no formulas, and you need to be a little creative to find the area. Fortunately, any polygon may be divided into triangles, and there is a simple formula for the area of triangles.
Label the vertices (points) of the polygon starting with 1 at an arbitrary vertex and continuing clockwise around the polygon. There should be as many vertices as there are sides. E.g. for a pentagon (five sides) there will be five vertices.
Draw a line from vertex 1 to vertex 3. This will make one triangle, with vertices 1, 2, and 3. If there are only 4 sides, it will also make a triangle with vertices 1, 3 and 4.If the polygon has more than 4 sides, draw a line from vertex 3 to vertex 5. Continue in this way until you run out of vertices.
Compute the area of each triangle. The formula for the area of a triangle is 1/2 * b * h, where b is the base and h is the height.
Add up the areas, and this is the area of the polygon.
Answer:
I think its 1.56
Step-by-step explanation:
if its right can I please get the brainlest
<u>Answer:</u>
If the spool has 10 cm of circumference or perimeter, this means that 10 cm of thread fits the whole circumference of the spool, which also means that
<h2>
1 unwind is equivalent to 10 cm of thread.
</h2>
Then, we have to make the following question:
If 10 cm of thread is equivalent to 1 unwind, to how many unwinds is equivalent 80 cm of thread?
If we want to know how many time does Alex need to unwind the spool, we can use the following relation also called the <u>Rule of Three:
</u>
<u>
</u>
The answer is:
Alex must unwind the spool 8 times in order to get 
cm of thread
A composite figure is a figure made up of simple shapes. To find the total surface area of a composite figure, you break up the composite figure into simple shapes whose surface areas you can find using existing formulas. Then you add all the areas of the simple shapes to find the total surface area of the composite figure.
The figure in this problem is a cylinder with a cone on top. The visible areas are: 1) The lower base of the cylinder; 2) The lateral area of the cylinder (the vertical wall all around the cylinder); 3) The lateral area of the cone.
The base of the cone and top base of the cylinder are not visible because they are interior to the composite figure. We only have the three surfaces described above to calculate and add together.
1) The lower base of the cylinder is a circle. We use the formula for the area of a circle using a radius of 4 cm.
2) The lateral area of the cylinder is the area of a rectangle whose length is the circumference of the base and whose width is the height of the cylinder.
3) The lateral area of the cone is given by the formula:
To find the total surface area, we add the three surface areas we found above.
The exact area is:
The approximate area in terms of pi is:
