According to a survey conducted at the local DMV, \( 55 \% \) of drivers who drive to work stated that they regularly exceed the posted speed limit on their way to work. Suppose that this result is true for the population of drivers who drive to work. A random sample of \( 14 \) drivers who drive to work is selected. Use the binomial probabilities table (Table I of Appendix B) or technology to find to \( 3 \) decimal places the probability that the number of drivers in this sample of \( 14 \) who regularly exceed the posted speed limit on their way to work is ?

0.571

A Ferris wheel ride can be represented by a sinusoidal function. A Ferris wheel at Armencity Theme Park has a diameter of \( 30 m \) and travels at a rate of \( 6 \) revolutions per minute in a clockwise rotation. You get on the ride from a platform \( 1 m \) above the ground at \( t = 0 \)

a) Determine the equation of the graph in the form \( H ( t ) = a \cos [ k ( t - d ) ] + c \) by finding the exact values of a. \( k \) , \( d \) , and \( c \) values.

b) If the Ferris wheel does not stop, determine the height above the ground after \( 28 s \)

A rocket was launched and its height, \( h \) , in metres, above the ground after time, \( t \) , in seconds, is represented by \( h = 11 + 10 t - 2 t ^ { 2 } \) . For how many seconds was the rocket in the air?

a.about \( 5.93 s \) c. about \( 6.64 s\)

b. about \(6.27 s\) d. about \( 7.35 s\)

Which of the following best describes the graph of \( w ( x ) = - ( x + 4 ) ^ { 2 } \) ? The image of \( f ( x ) = \)

(a)\(\square \) \( x ^ { 2 } \)\(\square \) \( x \) \(\square \) \(\sqrt { x} \)\(\square \) \(| x | \)\(\square \) \(x ^ { 3 } \)

after a (select all that apply)

(b)

\(\square \) reflection across the \(x\) -axis

\(\square \) translation \( 4 \) units up

\(\square \) vertical compression by a factor of \( \frac { 1 } { 4 } \) units

\(\square \) vertical stretch by a factor of \(4\) units

\(\square \) translation \(4\) units to the right

\(\square \) translation \(4\) units to the left

\( \square \) translation \( 4 \) units down

\(\square \) reflection across the \(y\) -axis

Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real numbers, state this.

\( \frac { y - 2 } { y ^ { 2 } - 4 } \)

A. \( \square \)(Use a comma to separate answers as needed.)

B. The rational expression is defined for all real numbers.

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Passing through \( ( 8 , - 6 ) \) and perpendicular to the line whose equation is \( y = \frac { 1 } { 2 } x + 3 \)

Write an equation for the line in point-slope form.

\( \square \)(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Write an equation for the line in slope-intercept form.

\( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)