For 20a-20b, choose Yes or No to indicate whether the first digit of the quotient is in the hundreds place. 20a.

$$1,523 \div 23$$

20b.

$$2,315 \div 9$$

Analyze the worked example. a. In the worked example, why multiply both sides of the equation by 3? Does the algorithm still work if you multiply by a different number? Explain your reasoning. b. Why do you always divide by one less than the common ratio?

When a nonmetal oxide reacts with water, it forms an oxoacid with the same nonmetal oxidation state. Give the name and formula of the oxide used to prepare each of these oxoacids:

hypochlorous acid;

Suppose $t_0$ is the initial term of a general geometric sequence for which each term of the sequence is multiplied by $r(r \neq 1)$ to get the next term of the sequence.

a. Write the first five terms of this sequence and then find recursive and function formulas for the sequence.

b. Eva explained her function formula as follows. "I started the sequence with $t_0$, then I multiplied by r each time to get the next terms. To get to $t_n$, I multiplied by r, n times. Thus, $t_{n}=t_{0} r^{n}$. Explain how Eva's explanation matches her formula.

c. What are $t_{0}$, r, and n in the situation involving bacterial growth?

d. The constant r is sometimes called the common ratio of terms. Explain why it makes sense to call r the common ratio.

e. Suppose a geometric sequence $t_{0}, t_{1}, t_{2}, \ldots$ begins with $t_{0} = -4$ and has a common ratio of 3. Find function and recursive formulas for this sequence and then find the term $t_{17}$.

Nine of the 30 competitors passed the qualifying round. (a) What fraction of the competitors passed? (b) What was the ratio of competitors who passed to competitors who did not pass?

What Is the percent by mass of sulfur In sulfur dioxide? (1) 32% (2) 33% (3) 50% (4) 67%

Estimate the value of f'(1) by substituting small values for h. Then use algebra to find f'(1) exactly. $f ( x ) = \frac { 1 } { x + 1 }$

Sketch the curve in polar coordinates.

$$r = 4 \theta \quad ( \theta \geq 0 )$$

List all the steps used to search for 7 in the sequence 1, 3, 4, 5, 6, 8, 9, 11 a) a linear search. b) a binary search.

Dansyl chloride, which absorbs maximally at 330 nm and fluoresces maximally at 510 nm, can be used to label amino acids in fluorescence microscopy and FRET studies. Tabulated below is the variation of the fluorescence intensity of an aqueous solution of dansyl chloride with time after excitation by a short laser pulse (with $I_{0}$ the initial fluorescence intensity). The ratio of intensities is equal to the ratio of the rates of photon emission.

$$\begin{matrix} \text{$t / \mathrm{ns}$} & \text{5.0} & \text{10.0} & \text{15.0} & \text{20.0}\\ \text{$I_{r} / I_{\mathrm{o}}$} & \text{0.45} & \text{0.21} & \text{0.11} & \text{0.05}\\ \end{matrix}$$

(a) Calculate the observed fluorescence lifetime of dansyl chloride in water. (b) The fluorescence quantum yield of dansyl chloride in water is 0.70. What is the fluorescence rate constant?

How does the speed of an electron change its fundamental nature?

Rewrite each expression to an equivalent one with no parentheses or negative exponents. a.

$$( - 3 x ) ^ { 2 }$$

, b.

$$( 3 x ) ^ { - 2 }$$

, c.

$$\frac { 2 ( 3 x ) ^ { 2 } } { 3 x ^ { 3 } }$$

, d.

$$\frac { 2 ( 3 x ) ^ { 2 } } { ( 3 x ) ^ { - 2 } }$$

What is true about climate conditions during the Cenozoic? Choose all that apply. a. Global temperature has progressively warmed since the beginning of the Cenozoic. b. Global temperature reached a maximum for the Cenozoic during the Paleocene and Eocene epochs. c. Climate fluctuated between cold and warm episodes in 100000 year cycles during the Miocene. d. Climate has progressively cooled since the Eocene.

Crate three

$$2\times 2$$

matrices, A, B, and C, and show that

$$(A\times B)\times C=A\times (B\times C).$$