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For any ring R, let GLn(R) denote the group of units of Mn(R). Show that for any ideal I ⊆ rad R, the natural map GLn(R) → GLn(R/I) is surjective.
Show that R is a radical ring iff it has no simple left (resp. right) modules.
Show that if ab is left quasi-regular, then so is ba.
In R, define a ◦ b = a + b − ab. Show that this binary operation is associative, and that (R, ◦) is a monoid with zero as the identity element.
Zachary invested $50 and was able to triple his money in two years. Kayla also began with $50 investments, and was able to cube her money in two years. Who had more money after two years?
the king ask archimedes if his crown is made from pure gold. he knows that the crown is either pure gold or it may have some silver in it. archimedes figures out that the volume of the crown is 125 cm3 and that its mass is 1.8 kilograms. he also knows that 1kilogram of gold has a volume of about 50 cm3 and 1kilogram of silver has a volume of about 100 cm3. is the crown pure gold? explain how you know
3. Which of the following mobile networks has a better offer? Justify you answer.
World Celcom: Php 500 monthly charge
Free calls and texts to World Celcom subscribers
Php 6.50 per minute of call to other networks.

Smartlink: Php 650 monthly charge
Free calls and texts to Smartlink subscribers
Php 5 per minute of call to other networks.
1. Which of the following is more economical when renting a vehicle? Justify your answer.
LG’s Rent a Car: Php1,500 per day plus Php 35 per kilometer travelled
Rent and Drive: Php 2, 000 per day plus Php 25 per kilometer travelled
an order for 1lb 4% zinc oxide paste is prepared using the pharmacy stock 10% paste and 1% paste. how much of each stock paste must be mixed to obtain the desired concentration:

A. 115g of 10%, 330g of 1%
B. 151g of 10%, 303g of 1%
C. 330g of 10%, 115g of 1%


need to know how to show my work I am really lose but I do think its a allegation problem
kindly tell me how to solve (1+0.075)^10
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