Suppose that during normal respiration, the volume of air inhaled per breath (called "tidal volume") by a mammal of any size is 6.27 mL per kilogram of body mass. (a) Write a function representing the tidal volume \( T(x) \) (in mL ) of a mammal of mass \( x \) (in kg). (b) Write an equation for \( T^{-1}(x) \). (c) Find \( T^{-1}(160) \) and interpret its meaning in context. Round to the nearest whole unit.

7) Simplify the logarithm so that no argument contains a product, quotient or a powe \( \ln \left(e x^{3}\right)= \) a) \( 1-3 \ln x \) b) \( 01+3 \ln x \) c) \( 03-\ln x \) d) \( 3+\ln x \)

Cabinet \( X \) costs \( \$ 30 \), requires 12 sq ft of floor space, and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft ? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( ~ \) .)

Rationalize the denominator: \( \frac{15}{\sqrt{75}} \) \( A=\square \)

Cabinet \( X \) costs \( \$ 30 \), requires \( 12 \mathrm{sq} \mathrm{ft} \mathrm{of} \mathrm{floor} \mathrm{space} \),and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( Y \).)

2) Intensidad de luz: un material traslúcido tiene la propiedad de reducir la intensidad de la luz que pasa a través de él. Un material traslucido de plástico tiene la propiedad de que una hoja de 1 mm de espesor reduce la intensidad de la luz en un \( 10 \% \). ¿Cuantas de tales hojas son necesarias para reducir la intensidad de un rayo de luz a cerca del \( 28 \% \) de su valor original?