−4(w−1)≤32 and 4+w<12 Step 3 of 4 : Using your answers from the previous steps, solve the overall inequality problem and express your answer in interval notation. Use decimal form for numerical values.

interval notation for −4(w−1)≤32: [−7,∞)
interval notation for 4+w<12: (-∞,8)

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8