Answer:
Option A
Step-by-step explanation:
The complete question is attached here
The rate of increase of bacterial population be K
As we know
![Y = Y_0 * e^{kT}](https://tex.z-dn.net/?f=Y%20%3D%20Y_0%20%2A%20e%5E%7BkT%7D)
where Y is the final population. In this case it is 1000
K is the rate of increase of population i.e 3 times per hour
T is the time in hours
Y0 is the initial population = 5
Substituting the given values, we get -
![1000 = 5 *e^{3*T}\\200 = e^{3*T}](https://tex.z-dn.net/?f=1000%20%3D%205%20%2Ae%5E%7B3%2AT%7D%5C%5C200%20%3D%20e%5E%7B3%2AT%7D)
Taking log on both sides, we get -
ln
= ln ![e^{3T}](https://tex.z-dn.net/?f=e%5E%7B3T%7D)
![2.718 * 2.301 = 3T](https://tex.z-dn.net/?f=2.718%20%2A%202.301%20%3D%203T)
T = 2.084 hours
hence, option A is correct
Answer:
x = 10
Step-by-step explanation:
We would use postulates and theorem to figure out 34 = 3x + 4. Once you set 34 equal to 3x + 4, you would solve for x as can be shown below:
34 = 3x + 4
Subtract 4 from both sides.
30 = 3x
Divide both sides by 3.
10 = x
Answer:
The probability of a customer buying carrots is 0.10.
Step-by-step explanation:
Here, given:
P (Customer buying apples) = 12%
⇒ P(A) = 12 \100 = 0.12
P(Customer Buying apples AND Carrots) = 5%
⇒ P(A ∩ C ) = 5 /100 = 0.05
P(Customer buying apples OR carrots ) = 17%
⇒ P(A∪ C) = 17/100 = 0.17
Now, we know that:
<h3>
P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y ) </h3><h3>
</h3>
Now, here substituting the values, we get:
P(A∪ C) = P(A) + P(C) - P(A ∩ C )
⇒ 0. 17 = 0.12 + P(C) - 0.05
or, 0.17 - 0.07 = P(C)
or, P(C) = 0.10
or, P(Customer Buying Carrots) = 0.10
Hence, the probability of a customer buying carrots is 0.10.
X = [arcsin (square root of 3)/2] = 60 degrees or pi/3 radians
Answer:
![\quad \frac{25x+2}{3}-21](https://tex.z-dn.net/?f=%5Cquad%20%5Cfrac%7B25x%2B2%7D%7B3%7D-21)
Step-by-step explanation:
![3(2x-7)+ 1/ 3 (7x+2)\\\\\mathrm{Expand}\:3\left(2x-7\right):\quad 6x-21\\=6x-21+\frac{1}{3}\left(7x+2\right)\\\\\mathrm{Expand}\:\frac{1}{3}\left(7x+2\right):\quad 7\times\frac{1}{3}x+2\times \frac{1}{3}\\\\=6x-21+7\times\frac{1}{3}x+2\times\frac{1}{3}\\\\\mathrm{Simplify}\:6x-21+7\times\frac{1}{3}x+2\times\frac{1}{3}:\\\\\quad \frac{25x+2}{3}-21](https://tex.z-dn.net/?f=3%282x-7%29%2B%201%2F%203%20%287x%2B2%29%5C%5C%5C%5C%5Cmathrm%7BExpand%7D%5C%3A3%5Cleft%282x-7%5Cright%29%3A%5Cquad%206x-21%5C%5C%3D6x-21%2B%5Cfrac%7B1%7D%7B3%7D%5Cleft%287x%2B2%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BExpand%7D%5C%3A%5Cfrac%7B1%7D%7B3%7D%5Cleft%287x%2B2%5Cright%29%3A%5Cquad%207%5Ctimes%5Cfrac%7B1%7D%7B3%7Dx%2B2%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%3D6x-21%2B7%5Ctimes%5Cfrac%7B1%7D%7B3%7Dx%2B2%5Ctimes%5Cfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%3A6x-21%2B7%5Ctimes%5Cfrac%7B1%7D%7B3%7Dx%2B2%5Ctimes%5Cfrac%7B1%7D%7B3%7D%3A%5C%5C%5C%5C%5Cquad%20%5Cfrac%7B25x%2B2%7D%7B3%7D-21)