Answer: A) Option B
B) 22.3 minutes.
Step-by-step explanation:
The temperature decreases in an exponential decrease, this means that we can write the equation as:
T(x) = A*r^x + B
Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)
We know that the initial temperature
A = 200° - 72° = 128°
B = 72°
T(x) = 128°r^x + 72°
The only option with those two values is option B.
T(x) = 128(0.989)^x + 72
We should check that when x = 2m, the temperature must be 197°
T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)
So this equation is correct
Now we want to find the time such the temperature is 172°F
then:
172° = 128°(0.989)^x + 72°
100° = 128°(0.989)^x
100/128 = (0.989)^x
x = ln(100/128)/ln(0.989) = 22.3 minutes.
Let's check in our equation:
T(22.3) = 128°(0.989)^22.3 + 72 = 172°
Answer:
You have a 12% chance of pulling out a white marble
Step-by-step explanation:
Their is 25 marbles in the bag and you have 3 out of 25 chance of pulling out a white marble. 3/25=0.12 so you have a 12% chance of pulling out a white marble.
I'll talk you through it so you can see why it's true, and then
you can set up the 2-column proof on your own:
Look at the two pointy triangles, hanging down like moth-wings
on each side of 'OC'.
-- Their long sides are equal, OA = OB, because both of those lines
are radii of the big circle.
-- Their short sides are equal, OC = OC, because they're both the same line.
-- The angle between their long side and short side ... the two angles up at 'O',
are equal, because OC is the bisector of the whole angle there.
-- So now you have what I think you call 'SAS' ... two sides and the included angle of one triangle equal to two sides and the included angle of another triangle.
(When I was in high school geometry, this was not called 'SAS' ... the alphabet
did not extend as far as 'S' yet, and we had to call this congruence theorem
"broken arrow".)
These triangles are not congruent the way they are now, because one is
the mirror image of the other one. But if you folded the paper along 'OC',
or if you cut one triangle out and turn it over, it would exactly lie on top of
the other one, and they would be congruent.
So their angles at 'A' and at 'B' are also equal ... those are the angles that
you need to prove equal.
Answer:
The value of x is -29.
Step-by-step explanation:
We are given an algebraic equation and have one goal: solve for x. We can use simplifying techniques as well as addition and subtraction to solve this equation.
Now that we have solved for x, we can plug in -29 to see if we get a true statement.
Because we ended up with a true statement, we have determined that the value of x is -29.
