University:
Purdue University
Course:
MA 15300 | College Algebra
Academic year:

2024
Views:

120

Pages:

3
Author:

Delphinixxc3

Question 1 What is the value of 5 1 4 × 4 9 5 4 1 × 9 4 ? Answer 1 Convert 5 1 4 5 4 1 to an improper fraction: 5 1 4 = 21 4 5 4 1 = 4 21 Now, multiply 21 4 × 4 9 4 21 × 9 4 : 21 4 × 4 9 = 21 × 4 4 × 9 = 84 36 4 21 × 9 4 = 4×9 21×4 = 36 84 Simplify by dividing both the numerator and the denominator by 12: 84 36 = 7 3 36 84 = 3 7 So, the answer is 7 3 3 7 or 2 1 3 2 3 1 . Question 2 How do you write 2 7 8 2 8 7 as an improper fraction? Answer 1 To convert 2 7 8 2 8 7 to an improper fraction: Multiply the whole number (2) by the denominator (8): 2 × 8 = 16 2×8=16 Add the numerator (7): 16 + 7 = 23 16+7=23 So, 2 7 8 2 8 7 as an improper fraction is 23 8 8 23 . Question 3 How do you write 0.24 in percent form? Answer 1 To convert a decimal to a percentage, multiply by 100: 0.24 × 100 = 24 % 0.24×100=24% So, 0.24 in percent form is 24%. Question 4 Consider a sector with angle 𝜋 3 3 π radians, and radius 3.5 m. What is the arc length and area? Answer 1 Arc Length: The formula for the arc length 𝐿 L when the angle is in radians is: 𝐿 = 𝑟 𝜃 L=rθ Substituting 𝑟 = 3.5 r=3.5 and 𝜃 = 𝜋 3 θ= 3 π : 𝐿 = 3.5 × 𝜋 3 = 3.5 𝜋 3 ≈ 3.665 m L=3.5× 3 π = 3 3.5π ≈3.665 m Area of the Sector: The formula for the area 𝐴 A of a sector is: 𝐴 = 1 2 𝑟 2 𝜃 A= 2 1 r 2 θ Substituting 𝑟 = 3.5 r=3.5 and 𝜃 = 𝜋 3 θ= 3 π : 𝐴 = 1 2 × ( 3.5 ) 2 × 𝜋 3 = 49 𝜋 24 ≈ 6.414 m 2 A= 2 1 ×(3.5) 2 × 3 π = 24 49π ≈6.414 m 2 So, the arc length is approximately 3.665 m, and the area is approximately 6.414 m². Question 5 18 is 9% of what number? Answer 1 To find the number 𝑥 x for which 18 is 9%: Set up the equation: 0.09 × 𝑥 = 18 0.09×x=18 Solve for 𝑥 x by dividing both sides by 0.09: 𝑥 = 18 0.09 = 200 x= 0.09 18 =200 So, 18 is 9% of 200.