C

9000007809

Level: 
C
The price of a goods in a shop is \(\$15\) per item. The Internet price in an e-shop is cheaper by \(\$2\) per item. The shipping cost of the e-shop is \(\$125\). What is the minimal number of items, which makes the total cost for a transaction smaller in the e-shop?
\(63\)
\(9\)
\(62\)
\(125\)
\(126\)

9000007810

Level: 
C
A fuel tank in a car has the capacity \(40\) litres. The current volume of the fuel in the fuel tank is \(6\) litres. The speed of fuelling is \(1\) litre of gasoline each \(3\) seconds. Find the function which describes the volume of the gasoline in the fuel tank (in litres) as a function of time (in seconds).
\(V = \frac{1} {3}t + 6,\ t\in [ 0;102] \)
\(V = 3t + 6,\ t\in [ 0;102] \)
\(V = 3t + 6,\ t\in [ 0;40] \)
\(V = 3t + 6,\ t\in \mathbb{R}_{0}^{+}\)
\(V = \frac{1} {3}t + 6,\ t\in [ 0;40] \)

9000009301

Level: 
C
An automatic machine produces \(12\) components per minute and stores them in a box with capacity \(1\: 500\) components. The machine starts with an initial amount of \(240\) components in the box. In what time will be the box full?
\(1\, \mathrm{h}\) \(45\, \mathrm{min}\)
\(1\, \mathrm{h}\) \(55\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(5\, \mathrm{min}\)
\(2\, \mathrm{h}\) \(15\, \mathrm{min}\)

9000007201

Level: 
C
Consider the function \[ f(x) = [x + 2] \] defined on the domain \(\mathop{\mathrm{Dom}}(f) = (1;2)\). Find the parameters \(a\) and \(b\) in the linear function \[ g(x) = ax + b \] which ensure that the functions \(f\) and \(g\) are identical on the domain of \(f\). \[ \] Hint: The function \(y = [x]\) is a floor function: the largest integer less than or equal to \(x\). For positive \(x\) it is also called the integer part of \(x\).
\(a = 0\), \(b = 3\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 3\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 0\), \(b = 4\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = -3\), \(b = 0\); \(\mathop{\mathrm{Dom}}(g) = (1;2)\)