Step-by-step explanation:
You should study the exponential laws. Remember that (a/b) to the exponent of m is the same as a to the exponent of m over b to the exponent of m.
Therefore, 2 to the exponent of 5×4 over 3 to the exponent of 2×4 equals to 1048576/6561.
Answer:
45.8
Step-by-step explanation:
Say the number Malachy was thinking of is <em>x</em>.
Doubling it gives 2x, which we see also equals 91.6. Set these equal to each other:
2x = 91.6
To solve, we divide both sides by 2 and get x = 45.8, which is our answer.
Answer:
21cm; 28cm; 14cm
Step-by-step explanation:
There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.
Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.
Let O is AK and BM cross point.
Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)
=> triangle ABM is isosceles => AB=AM (1)
1. Let AC=21 So AM=21/2=10.5 cm
So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm
Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)
2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.
3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm
We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB
=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.
Let check if this triangle exists ( if the triangle's inequality fulfills).
BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.
This variant is the only possible solution of the given problem.
Answer:
Negative
Step-by-step explanation:
It's negative because my math teacher said so a few years ago. Sorry for the not so great explanation... I didn't pay attention that day.
<u>During the first hour</u> . . .
5% of the 1,000 bacteria die. At the end of the hour, 95% of them are left.
95% of 1,000 = 950
Then 100 are added : 950 + 100 = 1,050
<em>1,050</em> bacteria swimming around in the soup as the second hour begins.
<u>During the second hour</u> . . .
5% of the 1,050 bacteria die. At the end of the hour, 95% of them are left.
95% of 1,050 = 997.5
Then 100 are added : 997.5 + 100 = 1,097.5 . . . . . <em>1,098</em> rounded
===================================
<u>Playing with this some more</u>:
If the same process continues, and the result at the end of each hour
is rounded to the nearest whole number, then the number of bacteria
steadily increases, but only for 88 hours. At the end of the 88th hour,
there are 1991 of the little critters, and after that, the population stays
constant at 1991. That's because the 5% loss during each hour after
that is (5% of 1,991) = 99.55 , which rounds to 100, and those are
replaced by the 100 new ones.
