there are 200 vegetable plants in a garden. a...
there are 200 vegetable plants in a garden. a) 24 b) 16 c) 32 d) 28 7. two marbles are randomly drawn from a bag containing 3 purple, 1 blue, and 1 yellow marble. the first marble is blue and is not replaced. find the probability of drawing a second marble that is purple. a) 3/4 b) 2/5 c) 3/5 d) 3/20 8. a crate is shaped like a rectangular prism. the crate is 1.2 feet wide, 3 feet long, and 4.5 feet tall. what is the volume of the crate in cubic feet? a) 81 ft³ b) 5.4 ft³ c) 16.2 ft³ d) 12 ft³
Answer
### Explanation:
#### Step1: Calculate probability for marble - drawing problem
The bag initially has \(3 + 1+1=5\) marbles. After drawing a blue marble (1 blue marble in the bag) and not - replacing it, there are \(5 - 1 = 4\) marbles left, out of which 3 are purple. The probability of drawing a purple marble as the second marble given the first is blue and not replaced is \(\frac{3}{4}\).
#### Step2: Calculate volume of rectangular - prism crate
The volume \(V\) of a rectangular prism is given by the formula \(V = l\times w\times h\), where \(l = 3\) feet (length), \(w = 1.2\) feet (width), and \(h = 4.5\) feet (height). So \(V=3\times1.2\times4.5=16.2\) cubic feet.
### Answer:
7. a) \(3/4\)
8. c) \(16.2\ ft^{3}\)