Let $x$, $y$, and $z$ be positive real numbers that satisfy\[2 \log_x (2y) = 2 \log_{2x} (4z) = \log_{2x^4} (8yz) \neq 0.\]the value of $xy^5 z$ can be expressed in the form $\frac{1}{2^{p/q}}$, where $p$ and $q$ are relatively prime positive integers. find $p + q$.

No one answered when i posted it so i posted it again i will give 20 points and brainliest the club will base its decision about whether to increase the budget for the indoor rock climbing facility on the analysis of its usage. the decision to increase the budget will depend on whether members are using the indoor facility at least two times a week. use the best measure of center for both data sets to determine whether the club should increase the budget. assume there are four weeks in a month. if you think the data is inconclusive, explain why.

Someone this asap for a group of students attends a basketball game. * the group buys x hot dogs at the concession stand for $2 each. * the group buys y drinks at the concession stand for $3 each. the group buys 29 items at the concession stand for a total of $70. how many hot dogs did the group buy?

A. plot the data for the functions f(x) and g(x) on a grid and connect the points. x -2 -1 0 1 2 f(x) 1/9 1/3 1 3 9 x -2 -1 0 1 2 g(x) -4 -2 0 2 4 b. which function could be described as exponential and which as linear? explain. c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.