Other Math Answers

A football stadium has R00,000 seats (where R is last digit of registation no; use 1 if last digit is zero) . In a game with full capacity people with the following ticket and associated cost attended the game:

Determine the number of people that attended the game in each cost category if the total revenue was $4,897,000, there were 11,000 more alumni than faculty, the number of public plus alumni together was 10 times the number of veterans, the number of faculty plus alumni together was the same as the number of students, and the number of faculty plus students together was four times larger than the number of guests and veterans together.

(solve by using numerical method)

Identifying Impacts of Hazards

Instruction:

Give an analysis on the impacts of certain hazards according to specific locations.

Figure 1. Map of locations and suggested scenarios.

A: Family in concrete house near the highway far from river and mountain.

B: Mountain climbers going up the slope.

C: Exchange learners in a local family home in the barrio near the river.

D: Friends in a beach resort.

E: Fishermen out on the sea.

F: Passengers in a jeep along a road with moderate traffic.

Post-Activity

a. Are the impacts of each hazard the same?

b. What kinds of hazards affected everyone? What kind of hazards did not?

c. What would you do if you were caught in one of these hazards?

Often the units for raw test scores are not informative. You might know that

you scored 76 out of 100 on a test but it doesn’t give you much information of what

your score means. Scores are more meaningful if percentile rank is given. What do

you mean by a percentile? If your teacher told you that your score in test is in the

90th percentile. What does it mean?

1. 4 boys and 3 girls are to be seated in a row of 7 chairs. How many ways can it be done under the following conditions:

a. boys stay together?

b. girls stay together?

c. boys and girls are seated alternately?

2. Permute the letters of the word SAINT. How many permutations

a. begin with vowels?

b. end with consonants?

c. begin with a vowel and end with a consonant?

d. begin with a consonant and end with a vowel?

3. In how many ways can 4 people sit a round table if

a. two people insist in sitting beside each other?

b. two refuse to sit beside each other?

c. one has a reserved seat?

The second stage reaction is,

HCO₃^- Û CO₃^2- + H⁺                                                                                                      (5)

and we can express the equilibrium concentrations of these chemicals as,

                                                                             (6)

You can see that both reactions (3) and (5) result in the generation of H⁺ ions.  The pH of a solution is a log transform of the concentration of H⁺, [H⁺]:

pH = -log₁₀[H⁺]                                                                                                                 (7)

Square brackets, [], indicate the concentration of a particular chemical and each bracketed term can be considered as a term like x in more familiar equations.

This concentration will increase as CO₂ builds up in the atmosphere.  The carbonic acid dissociates (comes apart) in water over two stages.  The first stage reaction is,

H₂CO₃ Û HCO₃^- + H⁺                                                                                                    (3)

and we can express the equilibrium concentrations of these chemicals as,

5.  Carbon dioxide (CO₂) is a naturally occurring atmospheric gas, the concentration of which is being increased by the burning of fossil fuels by energy intensive economies.  CO₂ dissolves in water (H₂O) to form carbonic acid (H₂CO₃), in simplistic terms,

CO₂ + H₂O Û H₂CO₃                                                                                                     (1)

The Û symbol indicates that a balance, or equilibrium, exists between all these chemicals.  If we increase the atmospheric partial pressure (i.e. the concentration) of the gas CO₂ then we can expect an increase in the concentration of H₂CO₃ dissolved in water exposed to the atmosphere.  Where natural waters are at equilibrium with the present-day partial pressure of CO₂ in the atmosphere, then the carbonic acid concentration is given by

[H₂CO₃] = 1.2×10^-5 mol ^-1                                                                                             (2)

1. Reduce the following expression to rectangular form:

a. 3i^24 - 4i^13 + i^8 + 5i - 8

b. 23∠42°

c. 5 cis 45°

d. 2e^0.234i

2. Convert the following complex numbers in exponential form and use principal value of argument.

a. 0.2 + 2.1i

b. 3.7∠45°

c. 4 cis 54°

3. Express the following complex numbers in polar form and use principal value of argument.

a.9 - 2i

b.4e^3i

c. 3 cis π/3

Express the given integral as an equivalent integral with the order of this integral reversed "\\int _{1 }^{e }\\:\\int _{ 0}^{ln x }\\:f(x,y)dydx"

Use the Lagrange multipliers to find the maximum and minimum values of "f(x,y,z)" subject to the given constraint. Also find the points at which these extreme values occur.