Antonio's toy boat is bobbing in the water next to a dock. antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. the vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. the first time it reaches its highest point is after 1.31.31, point, 3 seconds. its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. find the formula of the trigonometric function that models the vertical height hhh between the dock and the boat's mast ttt seconds after antonio starts his stopwatch. define the function using radians.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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