A weather forecaster made the following statement during a live broadcast on Sunday evening. "In our city where the temperature has been 5 degrees throughout this week, the weather will suddenly warm up starting tomorrow and winter will give way to spring-like weather. On Monday afternoon, the air temperature throughout the city will have increased by 6 to 10 degrees compared to the previous day." Based on this information, which of the following inequalities expresses the range of values that the temperature in the city could take on Monday afternoon? A) $|x - 13| \leq 2$ B) $|x - 10| \leq 6$ C) $|x - 6| \leq 5$ D) $|x - 1| \leq 6$ E) $|x - 11| \leq 2$
are shown. Accordingly, $$\mathrm{K} = \{\mathrm{AÇELYA}, \mathrm{AHMET}, \mathrm{AYSUN}, \mathrm{BEREN}, \mathrm{KENAN}, \mathrm{NERMIN}\}$$ how many elements of the set are elements of the set represented by the shaded regions in the figure? A) 1 B) 2 C) 3 D) 4 E) 5
In the rectangular coordinate plane, the graphs of functions $f$, $g$, and $h$ are given in the figure. Accordingly, for a real number $a$ satisfying the condition $0 < a < 2$ I. When $f(a) < g(a)$, then $g(a) < h(a)$ holds. II. When $g(a) < h(a)$, then $h(a) < f(a)$ holds. III. When $h(a) < f(a)$, then $f(a) < g(a)$ holds. Which of the following statements are true? A) Only I B) Only II C) Only III D) I and II E) I and III
Let $P(x)$ be a polynomial. A number $a$ satisfying the equation $P(a) = 0$ is called a root of this polynomial. For polynomials $P(x)$ and $R(x)$ $$\begin{aligned}
&\mathrm{P}(\mathrm{x}) = \mathrm{x}^{2} - 1 \\
&\mathrm{R}(\mathrm{x}) = \mathrm{P}(\mathrm{P}(\mathrm{x}))
\end{aligned}$$ the following equations are given. Accordingly, I. $-1$ II. $0$ III. $1$ which of these numbers are roots of the polynomial $\mathbf{R}(\mathbf{x})$? A) Only I B) Only II C) Only III D) I and III E) II and III
In a data group, when the numbers are arranged from smallest to largest, if the number of data is odd, the number in the middle is called the median of the data group, if the number of data is even, the arithmetic mean of the two middle numbers is called the median, and the number that appears most frequently in the data group is called the mode (peak value). Consisting of integers and arranged from smallest to largest $$6, x, 10, y, 14, z, 23$$ in the data group, only two values are equal to each other. Given that the mode, median, and arithmetic mean values of this data group are equal to each other, what is the value of $\mathbf{z}$? A) 22 B) 21 C) 18 D) 16 E) 15
Filiz creates cup towers by placing identical cardboard cups inside each other. The distance between the bases of every two consecutive cups is equal in all the cup towers she creates. Then, she places these towers on a table and measures their heights. Filiz observes that the sum of the heights of two towers with 6 and 9 cups equals the height of the tower with 18 cups. Accordingly, to what height of a cup tower is the sum of the heights of two towers with 8 and 12 cups equal? A) 23 B) 24 C) 26 D) 27 E) 29