Questions in mathematics

Questions in mathematics

[Done] Three numbers are in the ratio 2:3:4. The sum of their cubes is 33,957. Find the largest number.

[Done] What is the 7th digit of \(\pi\)?

[Done] A student sells small and large greeting cards at a craft fair. The small cards cost $3 per card, and the large cards cost $5 per card. The student collects $95 for selling a total of 25 cards. 1. What are the variables? 2. What is the system of equations? 3. How do you graph it? 4. How many of each type of card did the student sell?

[Done] If an explosive shell can travel 500 yards in 1.5 seconds, and a shell bursts with a 25-yard diameter of damage, while it takes 3 seconds for the fuse in the shell to go off, what is the farthest distance a target could be hit with the shell?

[Done] If the 1600m race is 4 laps, what is the length of each lap?

[Done] Solve this equation for \( x \) in terms of \( y \): \[ 3x + 2y = 4 \]

[Done] Suppose that the function [tex]f(x) = 2x + 12[/tex] represents the cost to rent [tex]x[/tex] movies a month from an internet movie club. Makayla now has $10. How many more dollars does Makayla need to rent 7 movies next month?

[Done] Jeff bought a new car for $10,450. He knows this car's value will decrease by 20% each year. Jeff writes the following function to model the cost of his car after \( t \) years: \[ C(t) = 10,450(0.80)^t \] If Jeff plans to sell the car after five years, what will be the value of the car at that time, to the nearest dollar?

[Done] As the value of x increases, which of the following functions would eventually exceed the others? 1) \( f(x) = 1000x \) 2) \( f(x) = 100x^2 \) 3) \( f(x) = 50x^3 \) 4) \( f(x) = 2^x \)

[Done] Given the lengths of three sides of a triangle, which is a right triangle? 1. 10, 26, 24 2. 20, 12, 18 3. 30, 15, 26 4. 40, 50, 80 Also, explain why it is the answer.