Question

1. convert 1.02 to a simplified mixed number and a percentage.
2. evaluate: $2^4 + 2^3 - 2^2 + 2^1 - 2^0$
3. find the perimeter and area of this triangle. dimensions are in yards.

(image of a right triangle with hypotenuse 17, height 15, base 8)

Explanation:

Question 16

Step1: Convert to mixed number

1.02 can be written as \(1 + 0.02\). Since \(0.02=\frac{2}{100}=\frac{1}{50}\), the mixed number is \(1\frac{1}{50}\).

Step2: Convert to percentage

To convert a decimal to a percentage, multiply by 100. So \(1.02\times100 = 102\%\).

Step1: Calculate each power

• \(2^4 = 16\)
• \(2^3 = 8\)
• \(2^2 = 4\)
• \(2^1 = 2\)
• \(2^0 = 1\)

Step2: Substitute and simplify

Substitute these values into the expression: \(16 + 8 - 4 + 2 - 1\).
First, \(16+8 = 24\).
Then, \(24 - 4 = 20\).
Next, \(20 + 2 = 22\).
Finally, \(22 - 1 = 21\).

Step1: Find the perimeter

The perimeter of a triangle is the sum of its sides. The sides are 8, 15, and 17. So perimeter \(P=8 + 15 + 17\).
\(8+15 = 23\), then \(23 + 17 = 40\) yards.

Step2: Find the area

This is a right - triangle (since \(8^2+15^2 = 64 + 225=289 = 17^2\) by Pythagorean theorem). The area of a right - triangle is \(\frac{1}{2}\times base\times height\). Here, base = 8 and height = 15. So area \(A=\frac{1}{2}\times8\times15\).
\(\frac{1}{2}\times8 = 4\), then \(4\times15 = 60\) square yards.

Answer:

Mixed number: \(1\frac{1}{50}\), Percentage: \(102\%\)

Question 18