Dakota mixes two cereals for breakfast. One gram of Cereal A has 6 milligrams of sodium and 7 calories. One gram of Cereal B has 8 milligrams of sodium and 5 calories. She wants the bowl of
cereal to contain no more than 200 milligrams of sodium and 150 calories. Let a equal the number of
grams of Cereal A and b equal the number of grams of Cereal B, where a > 0 and b > 0. Which system
of inequalities represents the possible ways Dakota can mix the cereals?
ба + 7b < 200
Sa + 5b < 150
6a + 3b < 200
7a +55 < 150
6a + 86 < 200
7a + 56 < 150
6a + 76 < 200
8a +56 <150

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis

Need so much on this one how many yards?

Amanufacturing firm has been averaging 16.8 orders per week for several years. however, during a recession, orders appeared to slow. suppose the firm’s production manager randomly samples 31 weeks and finds an average of 15.6 orders with a standard deviation of 2.3 orders. using a 0.025 significance level, test whether the mean number of orders has decreased. type the full 5 step procedure into the answer box, then for multiple choice practice, answer the following: 1. what is the name and symbol of the parameter that you are testing? 2. what is the symbol and value of the point estimate of that parameter? 3. what distribution are you using to test this parameter? 4. what is the critical value? 5. what is the test statistic value? 6. what is the p-value?