Use the following half-reactions to write three spontaneous reactions, and calculate E cell for each reaction:

a. Au⁺ (aq) + e^- ----> Au (s) E= 1.69 V

b. N₂O (g) + 2H⁺ (aq) + 2 e^- ----> N₂ (g) + H2O (l) E= 1.77 V

c. Cr³⁺ (aq) + 3e^- ---> Cr (s) E= -0.74 V

A voltaic cell consists of Cu²⁺/Cu and Cd²⁺/Cd half-cells. Each compartment has a volume of 0.500 L with the following initial concentrations: [Cu²⁺] = 1.250 M; [Cd²⁺] = 0.250 M at 25°C. What is the [Cu²⁺] when the voltage has dropped to 0.719 V? (E⁰ for Cu²⁺/Cu = 0.340 V and E⁰ for Cd²⁺/Cd = -0.400 V.)

a bullet of mass m and speed v is fired at an initially stationary sphere. The bullet goes through the sphere, and exits with a speed of v/3. The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.)

2) a). The resistivity of a wire varies with its

1. length
2. area of cross-section
3. mass
4. material

b) Given the units of a physical quantity. Choose the correct relation (J is for Joule, V is for volt, C is for Coulomb)

A) J = CV

B) J = VA

C) J = C/A

D) V = J C

c) A charge of 3 C moving in a uniform electric field experiences a force 3000 N. The potential difference between two points situated in the field at a distance 1 cm from each other will be

A) 10 V

B) 90 V

C) 1000 V

D) 9000 V

d) Choose the only incorrect relation:

A) ampere = coulomb/second

B) volt = coulomb/joule

C) ohm = volt/ampere

D) coulomb = Joule/volt

e) In an astronomical telescope, the image formed by the objective is I₀   and that formed by eye piece is I_e . Then

A) I₀   and I_e are both real

B) I₀   and I_e are both virtual

C) I₀   is virtual and I_e   is real

D) I₀   is real and I_e   is virtual

How would I write a C++ code that gives me the following out put:

   Enter count of male students: 14

Enter count of female students: 17

Students registered

Total:    31

Male:     14   45.16%

Female:   17   54.84%

   Enter count of male students: 7

Enter count of female students: 2

Students registered

Total:     9

Male:      7   77.78%

Female:    2   22.22%            */

Find the relative frequency for the class with lower class limit 19

Relative Frequency = %

Give your answer as a percent, rounded to two decimal places

A Frequency Distribution Table using data
This list of 16 random numbers has been sorted:

Fill in this table with the frequencies as whole numbers and the relative frequencies as decimals with 4 decimal places for the relative frequencies. Remember: relative frequencies are between 0.0 and 1.0

(This problem does not accept fractions.)

Complete the table.

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

What percent of students take exactly one courses? %

50 part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

a. Complete the table.

b. What percent of students take exactly two courses? %

70 adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:

a. Complete the table (Use 4 decimal places when applicable)

b. What is the cumulative relative frequency for flossing 1 time per week? %

1. Which of the following is/are the most important characteristics of an investment?
   1.      Marketability
   2.     Term
   3.    Return
   4.    Risk
   5.     Liquidity

1. i. and v.
2. i. and ii.
3. iii. and v.
4. iii. and iv.

Let [x]_B be the coordinate vector of a vector x ∈ V with respect to the basis B for V . Show
that x is nonzero if and only if [x]_B is nonzero.