Trehalose is a disaccharide that can be obtained from yeasts, fungi, sea urchins, algae, and insects. Deduce the structure of trehalose from the following information: 1. Acid hydrolysis of trehalose yields only D-glucose. 2. Trehalose is hydrolyzed by $\alpha$ -glucosidase but not by $\beta$ -glucosidase enzymes. 3. Trehalose is a nonreducing sugar; it does not mutarotate, form a phenylosazone, or react with bromine water. 4. Methylation of trehalose followed by hydrolysis yields two molar equivalents of 2,3,4,6 -tetra-O-methyl-D-glucose.

A random sample of 20 student records was used to determine the average number of absences per student during the school year. The number of absences on each record is listed below.

$$\begin{array}{lllllllll} 3 & 2 & 1 & 4 & 3 & 1 & 2 & 1 & 0 & 2 \\ 2 & 3 & 5 & 1 & 4 & 8 & 9 & 0 & 4 & 1 \end{array}$$

Construct a frequency table for these data.

For the following exercises, use function composition to verify that f(x) and g(x) are inverse functions. $f(x)=-3 x+5 \text { and } g(x)=\frac{x-5}{-3}$

Solve each multi-step equation. $-m+3(m+1)=11$

State the sign (positive or negative) of the sine, cosine and tangent in the quadrant. Quadrant IV

We have encountered Kepler's first and third laws. Using a library or the Internet, respond to the following. Read about Kepler's life, and write in your own words how he came to discover his three laws of planetary motion.

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by $h(t)=-4.9 t^{2}+24 t+8.$ How long does it take to reach maximum height?

For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $h(x)=2 x^{2}+8 x-10$

For the following exercises, find the slope of the line that passes through the two given points. (−1, 4) and (5, 2)

Graph. each point on coordinate plane. $C(0,-4)$

Identity the information that is given on a typical box from the periodic table.

For the following exercises, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation. $m(x)=\frac{1}{2} x^{3}$

Analyze the excerpt and answer the questions that follow. "Whereas Member States have pledged themselves to achieve ... the promotion of universal respect for and observance of human rights ..." Why does the preamble refer to what the Member States have pledged?

Simplify $0.45 \div 10^{2}$