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Hello! My name is Maurizia and I recently graduated with my Bachelor's in Earth Science and minors in Math and Sustainability Science from Kean University. In the fall I will start my Master's in Earth and Environmental Sciences at Montclair State University. I love both math and earth science and try my best to find a way to integrate both fields together. I have tutored algebra for a few semesters at Kean and formed various study groups in my Calculus and Differential Equations classes. Feel free to reach out with any questions!

$ REM $ sleep is the phase of sleep when most active dreaming occurs. In a study, the amount of $ REM $ sleep during the first four hours of sleep was described by a random variable $ T $ with probability density function$$ f(t) = \left\{ \begin{array}{ll} \frac{1}{1600} t & \mbox{if $ 0 \le t \le 40 $}\\ \frac{1}{20} - \frac{1}{1600} t & \mbox{if $ 40 < t \le 80 $ }\\ 0 & \mbox{otherwise} \end{array} \right.$$where $ t $ is measured in minutes.(a) What is the probability that the amount of $ REM $ sleep is between 30 and 60 minutes?(b) Find the mean amount of $ REM $ sleep

Which equation best represents the graph at the right?$$(A.) y=\frac{1}{2} x-2\quad (B.) y=2 x-2\quad (C.) y=2 x$$CANT COPY THE GRAPH

Match the equation with its graph.$$y=\frac{1}{2} x+1$$CANT COPY THE GRAPH

Match the equation with its graph.$$y=\frac{1}{2} x-1$$CANT COPY THE GRAPH

Match the equation with its graph.$$y=x+2$$CANT COPY THE GRAPH

Identify the slope and y-intercept of the graph.CANT COPY THE GRAPH