Answer:
Manuel received 28 purple pins.
Step-by-step explanation:
This is a simple equation. If he received 40 pounds and 70% of them are purple then the number of purple pins is 40 * 70% = 28.
The simplified version of arccot sqroot 3/3 is
Note : Since unit of currency is not defined, I'll be using units.
Sales tax on a 15000 units car = 540 units
540 = 15000 × tax% / 100
=> 540 = 15000 × tax% / 100
=> 540/15000 = tax% / 100
=> tax% = (540/15000) × 100
=> tax% = 540/140
=> tax% = 3.6
now,
sales tax on a 32000 units car = 32000 × tax%/100
= 32000 × 3.6/100
= 320 × 3.6
= 1152 units
therefore sales tax on a 32000 units car = 1152 units
To do this problem, break the pic up into its individual shapes.
For the top box:
You're given that the length of the bottom shape is 3 2/5, and that the top box is bordered by 1/2 inch of open space on each side. This means the length of the top box is 3 2/5 -(2x1/2), which equals 2 2/5.
The area occupied by the top box is the result of multiplying 2 2/5 (the base) by 1 1/3 ( the height.) therefore, the area of that part is 48/15, or 16/5 in reduced form.
Now for the bottom shape:
Break it up into a rectangle and two triangles, one of which is already drawn in for you. For the other triangle, draw a vertical line connecting the bottom corner of the bottom shape to the edge of the top shape. The line should be parallel to the line that's already drawn in.
Because you're given the 1/2 inch space to either side of the top box, you can conclude that the base of each triangle will be 1/2 inch. You're also given a height. The area of a triangle is b times h divided by two, so the area of each triangle is (1/2)(2)/2, which equals 1/2.
Put together, the area of the two triangular components is 1.
Now, you have one more component to calculate, which is the rectangular component of the bottom shape. Since you already accounted for the bases of the triangular components, subtract those from the base, giving you 3 2/5 -(1/2 x 2), which means the base of the rectangle is 2 2/5. Now just multiply that by the height, which is 2. The area of the rectangle is therefore 24/5.
Final answer: You now have all the component areas, you just need to add them all together to get the total area. 16/5 + 1 + 24/5 = 45/5, which reduces to 9.
Your final answer is B, 9 in^2.
Using the identity a^2 - b^2 = (a - b)(a + b):-
this is 8^2 - (sqrt5)^2 = 64 - 5 = 59 Answer
