Answer:
Step-by-step explanation:
1st expression: x⁴-y⁴
= (x²)² - (y²)²
= (x² +y²)(x² -y²)
= (x² +y²)(x +y)(x -y)
= (x +y)(x -y)(x² +y²)
2nd expression: x² -y²
= (x +y)(x -y)
3rd expression: x³ -y³
= (x -y)(x² +xy +y²)
Now ,
Lowest Common Multiples (L.C.M.) = common factors * rest factors
= (x+y)(x-y) * (x² +y²)(x² +xy +y²)
= (x² -y²)(x²+y²) * (x² +xy +y²)
= (x⁴ -y⁴)(x² +xy +y²)
Answer:17.3964 males 7.6035 females
Step-by-step explanation:
The first way to calculate the expected uses the marginal percentages. If sex is not related to flavor preference, you would expect the same percentages of males to prefer the same flavors as females. Since overall 20.71% prefer vanilla, you would expect 20.71% of males to prefer vanilla. Now, 20.71% of 84 people is 17.3964, so this is how many males you would expect to prefer vanilla. You would also expect 20.71% of the females to prefer vanilla, which is 17.6035. So you'd expect 17.3964 males and 17.6035 females to prefer vanilla.
Answer:
36.48 cm²
Step-by-step Explanation:
If you take a careful look at the figure given, you'd realise that the area of the shaded portion is actually created by 2 overlapping quarter circle.
The area of the shaded portion = Area of Square - Area of Unshaded part
Area of square = s² = 8² = 64 cm²
Area of the Unshaded portion = 2(Area of Square - Area of Quarter Circle)
= 2(s² - ¼*πr²)
Where, radius (r) = s = 8 cm, take π as 3.14
Area of unshaded part = 2(8² - ¼*3.14*8²)
= 2(64 - ¼*3.14*64)
= 2(64 - 1*3.14*16)
= 2(64 - 50.24)
= 2(13.76)
Area of unshaded part = 27.52 cm²
Area of shaded part = Area of Square - Area of Unshaded part
Area of shaded part = 64 - 27.52 = 36.48 cm²
Short answer:
25 inches is the perimeter of the larger rectangle
Long answer:
Imagine that you have a rectangle where every single side is 1 inch long. The total perimeter of the card is 4 inches, 1+1+1+1. The total perimeter is 4 inches.
Now imagine that you have a larger rectangle which is 1.25 times as wide and long as the smaller rectangle. In other words each side of the larger rectangle is 1.5 inches long. The perimeter of the larger card is 1.25+1.25+1.25+1.25. Because each 1 in the original equation was multiplied by 1.25. The perimeter of your larger rectangle is 5 inches.
Turn that into an equation. 5 inches equals 4 inches times 1.25. In other words, (larger rectangle perimeter) equals (smaller rectangle perimeter) times 1.25
Plug in numbers. You get (Larger rectangle perimeter) equals 20×1.25. Solve that and you get 25. 25 is the answer
