Marni writes this system to determine how much of each ingredient Alyssa plans to buy. She uses x to represent cups of frozen fruit puree and y to represent cups of yogurt.

x + y = 6,
2x + 3y = 14

To solve this system using the linear combination method, Marni multiplies the first equation by −2 to eliminate the x variable.

−2x − 2y = −12
2x + 3y = 14

Finish solving the system to determine how many cups of fruit puree and yogurt Alyssa will buy.

Marni determined that Alyssa plans to purchase
cups of fruit puree and

cups of yogurt.

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.

Jenny made a scale drawing of a city. the scale she used was 5 inches = 1 yard. what is the scale factor of the drawing?

Let us imagine that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands (b1), alcoholic beverage sales in $10,000 (b2), and decrease in the price of gasoline in cents (b3). furthermore, imagine that the regression formula has been calculated as: y = a + b1x1 + b2x2 + b3x3 where y = the number of automobile accidents, a = 7.5, b1 = 3.5, b2 = 4.5, and b3 = 2.5 calculate the expected number of automobile accidents for a football weekend if the region has 25,000 registered vehicles, $75,000 worth of beer is sold, and a gas war causes a 10 cent drop in a gallon of gas.