You are selecting foods to give to a charity. The charity takes certain foods that don’t go bad quickly. You have 5 different cans of vegetables to select from, 7 different canned soups to select from and 6 different pastas to select from. You are giving away 4 items. You want to make sure that at least two vegetables are selected. How many different arrangements of the four foods that you are giving away are possible?

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

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.

Point r divides in the ratio 1 : 3. if the x-coordinate of r is -1 and the x-coordinate of p is -3, what is the x-coordinate of q? a. b. 3 c. 5 d. 6 e. -9