Use propositional logic to prove the following argument is valid.
If Alice gets the office position and works hard, then she will get a bonus. If she gets a bonus, then she will go on a trip. She did not go on a trip. Therefore, either she did not get the office position or she did not work hard or she was late too many times.

$97520

step-by-step explanation:

add 6% to the value she got from selling the house.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus