C

9000150502

Level: 
C
Two hotels and a lake are in a satellite photo. The distance between the hotels is \(400\, \mathrm{m}\) which is \(4\, \mathrm{cm}\) in the photo. The area of the lake in the photo is \(30\, \mathrm{cm}^{2}\). Find the real area of the lake.
\(3\cdot 10^{5}\, \mathrm{m}^{2}\)
\(3\cdot 10^{1}\, \mathrm{m}^{2}\)
\(3\cdot 10^{3}\, \mathrm{m}^{2}\)
There is not enough information to solve this problem.

9000150504

Level: 
C
The object \(y\) is projected using a lens with foci at \(F\) and \(F'\). The focal length of the lens (the distance from the focus to the lens) \(f = 20\, \mathrm{cm}\). The distance from the object \(y\) to the lens \(a = 60\, \mathrm{cm}\). Find the distance from the lens to the image \(y'\).
\(30\, \mathrm{cm}\)
\(600\, \mathrm{cm}\)
\(\frac{20} {3} \, \mathrm{cm}\)
\(25\, \mathrm{cm}\)

9000153302

Level: 
C
A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Which of these characteristics is dimensionless?
coefficient of variation
variance
standard deviation
mean

9000153303

Level: 
C
A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Unit of which of these characteristics is meter?
the mean and the standard deviation
only the variance
only the standard deviation
only the mean
the standard deviation and the variance
the standard deviation, the variance and the coefficient of variation

9000150104

Level: 
C
Evaluate the following integral on \(\mathbb{R}\). \[ \int \cos x\cdot \left (-3 +\sin x\right )^{5}\, \mathrm{d}x \]
\(\frac{\left (-3+\sin x\right )^{6}} {6} + c\text{, }c\in \mathbb{R}\)
\(6\left (-3 +\sin x\right )^{6} + c,\ c\in \mathbb{R}\)
\(\frac{\left (-3+\cos x\right )^{6}} {6} + c,\ c\in \mathbb{R}\)
\(6\left (-3 +\cos x\right )^{6} + c,\ c\in \mathbb{R}\)

9000146710

Level: 
C
Divide the following two polynomials using long division. \[ \left (x^{3} + 3x^{2} - x + 4\right ) : \left (x^{2} - x + 1\right ) \]
\(x + 4 + \frac{2x} {x^{2}-x+1}\)
\(x + 4 + \frac{2x+8} {x^{2}-x+1}\)
\(x + 2 + \frac{6-2x} {x^{2}-x+1}\)
\(x + 2 + \frac{2x+2} {x^{2}-x+1}\)