3 years ago

Phoebe took a survey of her classmates' favorite sport. The results are in the table below:

Mathematics

1 answer:

Kitty [74]3 years ago

6 0

The relative frequency for football is the number of people who like football divided by total people:

4/28 = 0.14

Answer: 0.14

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The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).

Alex17521 [72]

Answer:

Step-by-step explanation:

<em>[using calculus] </em>When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have $h'(t) = -32t + 48$ , which equals zero when $t = 3/2 = 1.5$ . The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

<em>[without calculus] </em>This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.