Answer:
28. (H) 24 ft
30. (F) [tex]\frac{5}{52}[/tex]
Step-by-step explanation:
28. A right triangle can be formed, where the length of the cable represents the hypotenuse, and the ground represents the base of the triangle. From the pythagorean theorem,
[tex]a^2 + b^2 = c^2[/tex]
where a and b are legs, and c is the hypotenuse of a right triangle.
So
[tex]18^2 + b^2 = 30^2\\b = \sqrt{30^2 - 18^2}\\b = \sqrt{576}\\b = 24[/tex]
30. The probability of drawing a red 1 is [tex]\frac{2}{52}[/tex] (a red star 1 or a red heart 1), the probability of drawing a black 3 is [tex]\frac{2}{52}[/tex] (a black triangle 3 or a black circle 3), and the probability of drawing a six of hearts is [tex]\frac{1}{52}[/tex] (since there is only one six of hearts in the entire deck). Since each of the cards is mutually exclusive from one another, the probability of drawing any of them is simply all of their probabilities added together. That is,
[tex]\frac{2}{52} + \frac{2}{52} + \frac{1}{52} = \frac{5}{52}[/tex]
