Son ciertas o falsas las siguientes oraciones? Corrige las falsas. Cipriano ve la televisión con frecuencia.

The _______ grew from the work of many scientists who studied cells, beginning in the $1600s$.

The convex surface of a plano-convex lens has an absolute value of radius of curvature of 40 mm. The index of refraction for the glass of which the lens is made is 1.5. (a) What is the focal length of the lens? (b) You take some measurements and determine that the 40-mm radius of curvature is correct but the focal length is 100 mm instead of the value calculated in part a. What must the index of refraction for the glass be?

Write the series in summation notation. Use the index $i$ and let $i$ begin at $1$ in each summation.

$$2+4+6+8+10+12$$

Consider a two-dimensional harmonic oscillator Hamiltonian:

$$\begin{align*} \hat{H}=\frac{1}{2 m}\left(\hat{P}_x^2+\hat{P}_y^2\right)+\frac{1}{2} m \omega^2\left(\hat{X}^2+\hat{Y}^2\right)(1+\lambda \hat{X} \hat{Y}), \end{align*}$$

where $\lambda \ll 1$.
(a) Give the wave functions for the three lowest energy levels when $\lambda=0$.
(b) Using perturbation theory, evaluate the first-order corrections of these energy levels when $\lambda \neq 0$.

In the past, it was common for people with phenylketonuria (PKU) who were placed on a low-phenylalanine diet after birth to be allowed to return to a normal diet during their teenage years. Although the levels of phenylalanine in their blood were high, their brains were thought to be beyond the stage of being harmed. If a woman with PKU becomes pregnant, however, a problem arises. Typically the fetus is heterozygous but is unable at early stages of development to metabolize the high levels of phenylalanine that arrive from the mother's blood. Why is the fetus heterozygous? What do you think would happen to the fetus during this "maternal PKU" situation? What would be your advice to a woman with PKU who wants to have a child?

Use the second derivative test to identify the local extrema of y = 2x³ + 3x² - 12x - 3

Suppose the economy is experiencing a high rate of inflation. As chair of the Federal Reserve Board, what actions would you take to put the economy back on track?

Complete the following sentences with the correct indirect object pronoun. A Uds. ____ gusta el programa nuevo en la television.

Write the expression as a single logarithm.

$$3 \log _5 u+4 \log _5 v$$

A contractor purchases a bulldozer for $36,500. The bulldozer requires an average expenditure of$9.25 per hour for fuel and maintenance, and the operator is paid $18.50 per hour.

Use the result of part (c) to find the break-even point (the number of hours the bulldozer must be used to gain a profit of 0 dollars).

Imagine rolling a fair, six-sided die, like the kind used in many board games. What is the probability of getting a 4? Justify your answer.

The product is shown without the decimal point. Use number sense to place the decimal point appropriately.

$$6.22 \times 3=1866$$

Consider the following price data from $2002$ to $2010.$

$$\begin{array}{|l|c|c|c|c|c|c|c|c|c|} \hline \text { Year } & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ \hline \text { Price } & 3.20 & 3.46 & 3.51 & 4.02 & 4.18 & 4.30 & 4.59 & 4.50 & 4.70 \\ \hline \end{array}$$

a. Compute the simple price index using $2002$ as the base year.

b. Update the index numbers with a base year revised from $2002 to 2005 .$

c. Plot the index numbers with a base year of 42002$and a base year of$2005$. Compare the two plots.