Larry wants to make a mixed nut blend of 20% almonds. he has 18 kilograms of mixed nuts that are 15% almonds. he also has a large bag of mixed nuts that are 25% almonds. how many kilograms of the 25% almond mix does larry need to add to the 15% almond mix to make a mix of 20% almonds?

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?