These exercises involve the formula for the area of a circular sector. The area of a sector of a circle with a central angle of

$$140 ^ { \circ }$$

is

$$70 \mathrm { m } ^ { 2 }$$

. Find the radius of the circle.

List all of the pairs of congruent angles and sides of the figures. Rhombus $W X Y Z \cong$ rhombus DEFG _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____ _____ $\cong$ _____

$$\left. \begin{array} { l } { \text { Suppose that in the definition of a group } G , \text { the condition that for } } \\ { \text { each element a in G there exists an element b in } G \text { with the prop- } } \\ { \text { erty } a b = b a = e \text { is replaced by the condition } a b = e . \text { Show that } } \\ { b a = e . \text { Thus, a one-sided inverse is a two-sided inverse. } ) } \end{array} \right.$$

Multiply, and then simplify each product. Assume that all variables represent positive real numbers. $\sqrt{3}(\sqrt{12}+2)$

A roller coaster travels at variable angular speed $\omega(t)$ and radius r(t) but constant speed $c=\omega(t) r(t)$. For the centripetal force $F(t)=m \omega^{2}(t) r(t)$, show that $F^{\prime}(t)=m \omega(t) r(t) \omega^{\prime}(t)$. Conclude that entering a tight curve with r'(t)<0 but maintaining constant speed, the centripetal force increases.

With reference to HIV/AIDS, explain how drug resistance arises in a pathogen population:

In which organelle does cellular respiration take place? a nucleus, b. chloroplast, c. chlorophyll, d. mitochondrion

Find the missing numbers: S + 727 = 915

How far does a plane fly in 15 s while its velocity is changing from 145 m/s to 75 m/s at a uniform rate of acceleration?

What is $\frac { 1.6 \times 10 ^ { 7 } } { 6.4 \times 10 ^ { 2 } }$ in scientific notation? A $2.5 \times 10 ^ { 4 }$, B $0.25 \times 10 ^ { 5 }$, C $2.5 \times 10 ^ { 6 }$, D $4 \times 10 ^ { 5 }$

Use integration by substitution to find the area under the curve

$$y=\frac{1}{\sqrt{x}+x}$$

between x=1 and x=4.

A company is performing a failure analysis for two of its products. It found that for the first product 76 out of 243 failures were due to operator misuse, while for the second product 122 out of 320 failures were due to operator misuse. Construct a 99$\%$ two-sided confidence interval for the difference between the two products of the probabilities that a failure is due to operator misuse. Based on this confidence interval, is there evidence that these probabilities are different for the two products?

During the next two months, General Cars must meet (on time) the following demands for trucks and cars: month 1—400 trucks, 800 cars; month 2—300 trucks, 300 cars. During each month, at most 1,000 vehicles can be produced. Each truck uses 2 tons of steel, and each car uses 1 ton of steel. During month 1, steel costs $400 per ton; during month 2, steel costs$600 per ton. At most, 1,500 tons of steel may be purchased each month (steel may only be used during the month in which it is purchased). At the beginning of month 1, 100 trucks and 200 cars are in inventory. At the end of each month, a holding cost of $150 per vehicle is assessed. Each car gets 20 mpg, and each truck gets 10 mpg. During each month, the vehicles produced by the company must average at least 16 mpg. Formulate an LP to meet the demand and mileage requirements at minimum cost (include steel costs and holding costs).

Evaluate. log 0.01