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The pH of a solution is defined by the equation pH = –log H^+

where the concentration of hydronium ions, H+ , in a solution is measured in moles per litre.


Determine algebraically the pH of a solution that is 50 times less acidic than vinegar, which has a pH of 2.5


D. Consider the following sets:


U= {1, 2, 3, 4, 5, 6, 7, 8, }, A= {1, 2, 3, 4, 5, 7}, B= {1, 5, 6, 7}, C= {1, 2, 3, 6}



16-20. Illustrate the Venn Diagram for the sets A, B, and C.




Demonstrate the stages of early number learning


Water is poured into a vessel of the form of a straight circular cone. If the vessel is installed with the <<sharp>> end down then the distance from the water level to the base of the cone is 1 m. When the vessel was turned over, it turned out that the distance from the water level to the <<sharp>> end of the vessel is root(3, 13) * m . Find the height of the vessel; give your answer in meters, rounded to two decimals if needed. The volume of a cone can be found by the V = 1/3 * S * h formula , where S is the area of its base and h is its height.


Discuss the standard unit's goals of measurement.


Consider the following matrix equation.

( "\\begin{matrix}\n 2 & -1 & 0 \\\\\n 1 & 2 & -1 \\\\\n 0& 1&3\n\\end{matrix}" ) ( "\\begin{matrix}\n x1 \\\\\n x2 \\\\\nx3\n\\end{matrix}" ) = ( "\\begin{matrix}\n 2 \\\\\n 1 \\\\\n3\n\\end{matrix}" )

Solve the equation by using Thomas algorithm.


Option 1: Company ABC’s selling stock is ₱ 1,500.00 per share that will have a dividend of ₱ 200.00 per year. The stock can be sold after two years at ₱2,000.00 and the market requires a rate of return of 15%. The stock can be sold after two years at ₱2,000.00 and the market requires a rate of return of 7%. Determine the stock yield ratio? *

ROUND OFF, NUMBERS ONLY, DO NOT PUT COMMA, PERIOD, ZERO OR PERCENTAGE SIGN.


1.      Eight girls went to a pizza parlor. Each of them ate 1 ¾ slices of pizza. How many slices of pizza did they eat in all                                                                                

Operation/s:                                                                                                            

Answer:                                                                                                                       

Unit (Label)?

2.     Kyle used 1/8 cup of flour to make two hotcakes. How many cups of flour will he need to make a dozen of hotcakes?                                                          Operation/s:                                                                                                           Answer:                                                                                                                   Unit (Label)?3.     A student works for 3 3/5 hours a day in a printing shop. If he is scheduled to work on Monday – Friday, how many hours does he work in a week?Operation/s:                                                                                                          Answer:                                                                                                                   Unit (Label)?4.     Bill earned Php 450 in selling donuts. He spent 1/5 of the money on flowers for his mother’s birthday. How much of Bill’s money was left after buying the flowers?                                                                                                                  Operation/s:                                                                                                           Answer:                                                                                                                              Unit (Label)?5.     Mark climbed a palo sebo. The pole is 15 meters high. He already climbed 7/10 of the pole. How many meters did he need to climb to reach the top of the pole?            Operation/s:                                                                                                            Answer:                                                                                                                              Unit (Label)?  

vector has y component ay= 13.0m

Activity 5.b. Choose a quantity to be represented by a variable, the write a mathematical expression for each.

1. Lota’s age in 5 years

2. a three-digit number whose hundred digits is half the tens digit and the tens digit is 2 more than the units digit.

3. The total interest earned after one year when P100, 000 is invested, part at 6% annual interest rate and the remaining part at 7.5% annual interest rate.

4. The distance traveled by a man driving at the rate of 60 kph

5. The total distance traveled by a boat 1 hour upstream and 30 minutes downstream in which the rate of current is 3kph.





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