Question 8 of 11, Step 1 of 1 Valerie is deciding on her schedule for next semester. She must take each of the following classes: English 102, Music 101, History 102, and Math 120. If there are 16 sections of English 102, 10 sections of Music 101, 11 sections of History 102, and 14 sections of Math 120, how many different possible schedules are there for Valerie choose from? Assume there are no time conflicts between the different classes.

7. The cake tastes very _-_ a) sweet b) sweetness c) sweeter

2. Dada \( f(x)=2 x^{2}-1 \) y \( x_{0}=1 \). (a) Hallar la pendiente de la recta secante a la gráfica de \( f \) que pasa por los puntos \( \left(x_{0}, f\left(x_{0}\right)\right) \) \( y(x, f(x)) \) para los siguientes valores de \( x: 1.5 ; 1.2 ; 0.9 \). (b) Calcular el valor de la pendiente de la recta tangente a la gráfica de \( f \) en el punto \( \left(x_{0}, f\left(x_{0}\right)\right) \). ¿Cómo se relaciona este valor con la definición dada en el ejercicio 1 ? (c) Graficar la función \( f(x) \), las rectas secantes y la recta tangente obtenidas en los incisos anteriores.

Evaluate the variable expression when \( a=-3, b=4, c=-2 \) and \( d=3 \) \[ -\frac{2}{3} d-\frac{1}{3}(b d-a c) \]

EGUNTA 1. (5 ptos) termine el dominio de la función. \[ f(x)=\frac{\sqrt{x-1}}{x^{2}+1} \]

The radioactive isotope Chromium- 51 , used to track red blood cells, has a half-life of 27.7 days. Assume an initial amount of 75 mg . Use the the formula \( A(t)=A_{0} e^{k t} \) to model the situation, where \( A_{0} \) is the initial amount of the material and \( k \) is a constant representing the rate of decay per day. a) Find the exact value of \( k \), the decay constant. Round to 6 decimal places or enter an exact answer. \( k= \) b) Using the \( k \) value from part (a), find a function that gives the amount of the isotope \( A \) that remains after \( t \) days. \( A(t)= \) c) How long will it take for \( 10 \% \) of the material to decay? Round to the nearest tenth of a day. (HINT: If \( 10 \% \) of the material decays, how much is left?)