(4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

PARTICIPATION 3.3.3: Ratios. АCTIVITY 1) A daycare center expects 20 babies on a given day. How many staff should the center have work that day to maintain a 1/4 ratio? Check Show answer 2) An adult soccer league requires a ratio of at least 2 women per 7 men on the roster. If 14 men are on the roster, how many women are needed to maintain that ratio? Check Show answer 3) A lemonade recipe requires 1 cup sugar per 8 cups water, for a 1/8 ratio. Andy's daughter is helping and accidentally puts 2 cups of sugar into the pitcher. "No problem," says Andy, "we'll just add more water." How many total cups of water should be put in the pitcher to maintain the 1/8 ratio? Check Show answer

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A freshly brewed shot of espresso has three distinct components: the heart, body, and crema. The separation of these three components typically lasts only 10 to 20 seconds. To use the espresso shot in making a latte, a cappuccino, or another drink, the shot must be poured into the beverage during the separation of the heart, body, and crema. If the shot is used after the separation occurs, the drink becomes excessively bitter and acidic, ruining the final drink. Thus, a longer separation time allows the drink-maker more time to pour the shot and ensure that the beverage will meet expectations. An employee at a coffee shop hypothesized that the harder the espresso grounds were tamped down into the portafilter before brewing, the longer the separation time would be. An experiment using 24 observations was conducted to test this relationship. The independent variable Tamp measures the distance, in inches, between the espresso grounds and the top of the portafilter (i.e., the harder the…