According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267 . Suppose you sit on bench in a mall and observe people's habits as they sneeze. Complete parts (a) through (c). (a) What is the probability that among 16 randomly observed individuals, exactly 7 do not cover their mouth when sneezing? Using the binomial distribution, the probability is (Round to four decimal places as needed.)

a \( \frac{3}{4} \) of \( \$ 16 \quad \) b \( \frac{5}{4} \) of \( \$ 12 \quad \) c \( \frac{5}{2} \) of 4 metres

What is the sum of the next two numbers in the pattern below? \( 2,12,26,36,50 \)

\( f ^ { 2 } ( x ) - 2 f ( x ) = e ^ { 2 x } + 1 \)

Let \( l \) be the length of a diagonal of a rectangle whose sides have lengths \( x \) and \( y \), and assume that \( x \) and \( y \) vary with time. If \( x \) increases at a constant rate of \( \frac{1}{4} \mathrm{ft} / \mathrm{s} \) and \( y \) decreases at a constant rate of \( \frac{1}{8} \) \( \mathrm{ft} / \mathrm{s} \), how fast is the size of the diagonal changing when \( x=1 \mathrm{ft} \). and \( y=4 \mathrm{ft} \) ? Answer:

Máximo comun divisol (10) Halla di maximo comun divisor de cada prupo de numeros, utilizando la descomposicion en lacto res primos. \( \begin{array}{ll}\text { a. med }(4,6) & \text { e. med }(10,15,25) \\ \text { b. med }(8,12) & \text { i. med }(35,42,70) \\ \text { d. med }(36,24) & \text { 8. med }(27,90,45) \\ \text { d. med }(38,16,28) & \text { h. med }(10,45,27)\end{array} \)