\( = \frac { n ( \sum x y ) - ( \sum x ) ( \Sigma y ) } { \sqrt { [ n \Sigma x ^ { 2 } - ( \sum x ) ^ { 2 } ] [ n \Sigma y ^ { 2 } - ( \Sigma y ) ^ { 2 } ] } } \)

Joey is standing on a diving board that is 5.6 feet above sea level. Joey dives into the water to a depth of -8.6 feet below sea level. Which equation can be used to determine Joey's change in altitude during the dive? (1) \( 5.6-(-8.6)=14.2 \) (i) \( 5.6+3.0=8.6 \) (i) \( -5.6+14.2=-8.6 \) (i) \( 5.6-8.6=-14.2 \)

2. Para alimentar a mi mascota compré una bolsa de 30 kgrs de alimento, al día siguiente gasté \( 2 / 5 \) de ella y tres días después gasté \( 1 / 3 \) de lo que me quedaba. ¿cuántos kilogramos me quedaron? ¿qué fracción del total me quedó?

Write an equivalent logarithmic equation for the following exponential equations and solve for \( x \). Leave your answers in logarithmic form. a. \( 2^{x+1}=5 \) \( x=\square \) b. \( 4^{x-1}=4 \) \( x=\square \) c. \( 5^{x+6}=7 \) \( x=\square \)

d. What is the \( z \)-score for a music artist that uses 6,400 unique words in their songs?

Factor the binomial completely. \( x^{7}-x^{3} \)