Question

rick went on a hike with his family in big bend national park. during the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes. select all of the statements that describe the data. rick saw fewer jackrabbits than foxes. deer and lizards are both modes of the data. more than a quarter of the animals rick saw were scorpions or snakes. less than half of the animals rick saw were lizards.

Explanation:

Step1: Analyze the number of jackrabbits and foxes

Rick saw 3 jackrabbits and 2 foxes. Since \(3>2\), the statement "Rick saw fewer jackrabbits than foxes" is false.

Step2: Determine the mode

The mode is the number that appears most frequently. The number of lizards is 6 and the number of deer is 6. So deer and lizards are both modes of the data.

Step3: Calculate the proportion of scorpions and snakes

The total number of animals is \(6 + 1+2 + 3+6 + 2=20\). The number of scorpions and snakes is \(1 + 2=3\). A quarter of 20 is \(20\times\frac{1}{4}=5\). Since \(3<5\), the statement "More than a quarter of the animals Rick saw were scorpions or snakes" is false.

Step4: Calculate the proportion of lizards

Half of 20 is \(20\times\frac{1}{2} = 10\). Since \(6<10\), the statement "Less than half of the animals Rick saw were lizards" is true.

Answer:

• Deer and lizards are both modes of the data.
• Less than half of the animals Rick saw were lizards.