Answer:
{x | x < 3}
Step-by-step explanation:
Just easily solve for x.
3x < 9
x < 9 ÷ 3
x < 3
{x | x < 3} means that any number for x is less than 3.
A petri dish is simply a circle; thus, we use the formula of the area of the circle which is <span>πr^2.
Given r = 40 mm
A = </span>π(40)^2 = <span>5026.55 sq. mm
</span>
Population density = bacteria count / area
PD = 2,100 / <span>5026.55
PD = </span><span>0.417782 bacteria / mm sq.
Therefore, the answer is approximately 0.418 </span><span>bacteria per square millimeter.</span>
Answer:
27in
Step-by-step explanation:
1ft=12in
(12*2)+3=27in
Given: <span>9=(1/27)^(a+3)
[Note: Please review rules of PEMDAS.
The question posted as is means
</span><span>9=[(1/27)^a]+3 which is probably not what you mean. It has been interpreted with (a+3) as the exponent, please check.]
</span><span>
Need to find value of a that satisfies above.
We will first isolate a in order to solve for its value.
</span>9=(1/27)^(a+3)
Switch unknown to the left
(1/27)^(a+3) = 9
Since both 27 and 9 are powers of 3, we can take log to base 3.
take log (base 3) on both sides, applying rule of logarithm of exponents.
(a+3)log_3(1/27)=log_3(9)
(a+3)log_3(3^(-3))=log_3(3^2)
Apply definition of logarithm [log_a(a^k)=k]
(a+3)(-3)=2
(a+3)=-2/3
a=-3 2/3=-11/3
Check: (1/27)^(-11/3+3)=(1/27)^(-2/3)=(3^(-3))^(-2/3)=3^(-3(-2/3))=3^2=9 ok
Answer: a=-11/3 or a=-3.667 (approx.)
