Question

1. the length of a rectangle measures 4.7×10² cm and the width measures 3.6×10¹ cm. calculate the area of the square.

a) 16,920 cm c) 16.92 cm
b) 1012 cm d) 16.6 cm

1. the length of an equilateral triangle is 5.1×10¹ inches. find the perimeter of the triangle.

a) 2601 in c) 26.01 in
b) 15.3 in d) 153 in

1. the lowest salary for a teacher in colorado is 4.3×10⁴ dollars and the highest salary for a teacher in colorado is 1.19×10⁵ dollars. find the range in teachers salaries in colorado.

a) $41.81 c) $155,000
b) $76,000 d) $44.19

1. the thickness of a cats hair is 1×10⁻⁴ mm and the thickness of a dogs hair is 1×10⁻³ mm. which animal has thicker hair?

a) cat b) dog

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$, where $l = 4.7\times10^{2}$ cm and $w=3.6\times 10^{1}$ cm.
$A=(4.7\times10^{2})\times(3.6\times10^{1})=(4.7\times3.6)\times(10^{2 + 1}) = 16.92\times10^{3}=16920$ cm².

Step2: Calculate perimeter of equilateral triangle

The perimeter formula for an equilateral triangle is $P = 3s$, where $s = 5.1\times10^{1}$ inches.
$P=3\times(5.1\times10^{1})=(3\times5.1)\times10^{1}=15.3\times10^{1} = 153$ inches.

Step3: Calculate salary range

The range formula is $R=H - L$, where $H = 1.19\times10^{5}$ dollars and $L = 4.3\times10^{4}$ dollars. First, rewrite $4.3\times10^{4}=0.43\times10^{5}$. Then $R=(1.19\times10^{5})-(0.43\times10^{5})=(1.19 - 0.43)\times10^{5}=0.76\times10^{5}=76000$ dollars.

Step4: Compare hair - thickness

The thickness of cat's hair is $t_{cat}=1\times10^{-4}$ mm and dog's hair is $t_{dog}=1\times10^{-3}$ mm. Since $1\times10^{-3}>1\times10^{-4}$, the dog has thicker hair.

Answer:

1. A. $16920$ cm²
2. D. $153$ in
3. B. $\$76000$
4. B. Dog