nodel of carry-on luggage has a length that is 7 inches greater than its depth. Airline reg quire that the sum of the length, width, and depth cannot exceed 25 inches. These condit e assumption that this sum is 25 inches, can be modeled by the function \( V(x) \) that gives e luggage's volume, in cubic inches, in terms of its depth, \( x \), in inches. If its volume is 240 bic inches, determine two possibilities for its depth. \( \begin{array}{l}\text { Volume }=\text { depth }- \text { length } \cdot \text { width: } 25-(\text { depth }+ \text { length }) \\ V(x)=x \cdot(x+7) \cdot \\ V(x)=x(x+7)(18-25)\end{array} \) wo possibilities for its depth are \( \square \) inches. Use a comma to separate answers as needed. Round to the nearest tenth of an inch as n

Simplify the following \( 1 \frac{2^{a+1}-2^{a-1}}{2^{a}} \) \( 2 \frac{x^{2}-x+1}{x^{3}+1} \div \frac{2 x}{2 x+2} \)

Question 8 ( 1 point) Read the description of a proportional relationship. Pablo is making his special punch for the Starry Night homecoming dance. There is a proportional relationship between the number of cans of peach juice concentrate in a bowl, \( x \), and the corresponding number of bottles of lemon-lime soda, \( y \). The equation that models this relationship is \( y=4 x \). How many cans of peach juice concentrate would Pablo put in a bowl of punch that has 16 bottles of soda? Enter your answer as a whole number or decimal. cans

e \( \quad \frac{3}{10} \quad \frac{1}{4} \)

Strontium- 90 is a radioactive material that decays according to the function \( A(t)=A_{0} e^{-0.0244 t} \), where \( A_{0} \) is the initial amount present and \( A \) is the amount present at time \( t \) (in years). Assume that a scientist has a sample of 800 grams of strontium- 90 . (a) What is the decay rate of strontium- 90 ? (b) How much strontium-90 is left after 10 years? (c) When will only 200 grams of strontium- 90 be left? (d) What is the half-life of strontium- 90 ?

1. A right pyramid consist of a square base of side 13 cm and 4 isoseeles triangle whor equal side are each, 27 cm . Cafculate its; (a) Surface area (TSA) (b) The volume of the pyramid (a) How many liters of water it can contain.