The cost can be optimized by using a Linear Programming given the linear constraint system
- To minimize the cost, the biologist should use <u>60 samples of Type I</u> bacteria and <u>0 samples of Type II</u> bacteria
Reason:
Let <em>X</em> represent Type 1 bacteria, and let <em>Y</em>, represent Type II bacteria, we have;
The constraints are;
4·X + 3·Y ≥ 240
20 ≤ X ≤ 60
Y ≤ 70
P = 5·X + 7·Y
Solving the inequality gives;
4·X + 3·Y ≥ 240
(Equation for the inequality graphs)
The boundary of the feasible region are;
(20, 70)
(20, 53.
)
(60, 0)
(60, 70)
The cost are ;
![\begin{array}{|c|c|c|}X&Y&P= 5\times X + 7 \times Y\\20&70&590\\20&53.\overline 3&473.\overline 3\\60&0&300\\60&70&790\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7C%7DX%26Y%26P%3D%205%5Ctimes%20X%20%2B%207%20%5Ctimes%20Y%5C%5C20%2670%26590%5C%5C20%2653.%5Coverline%203%26473.%5Coverline%203%5C%5C60%260%26300%5C%5C60%2670%26790%5Cend%7Barray%7D%5Cright%5D)
- Therefore, the minimum cost of $300 is obtained by using <u>60 samples of Type I</u> and <u>0 samples of Type II</u>
Learn more here:
brainly.com/question/17646656
Since the triangles are similar, they have the same ratio to all corresponding sides. Let's find the ratio of ΔDEF to ΔPQR.
DF/RQ = 25/24
Similarly,
DE/PQ = 25/24
Thus,
PQ = 24/25 DE
PQ = 0.96DE
This means that the length of PQ is 96% of the length of DE.
I hope I was able to help you. Have a good day.
(2,5) (9,2)
Before finding slope intercept form (y=mx+b) we must find point slope form. Point slope for is y-y1 = m(x-x2) where m is slope and (x1,y1) is a coordinate pair on the line. To find slope we use the formula (y2-y1)/(x2-x1). Since we have two points given, we simply plug them in to this equation.
(5 - 2)/(2 - 9) = 3/- 7 so m = -3/7.
Now we can fill in the point slope equation using either coordinate pair provided. Will be using the one with smaller numbers (2,5). Plug your values in!
y - 5 = -3/7(x-2)
Now to get to slope intercept form you simply multiply or distribute and move over the 5.
y - 5 = -3/7x + 6/7 ---- Now add 5 or 35/7 to both sides
y = -3/7x + 6/7 + 35/7 ----- Simplify to get a final answer if y = -3/7 + 41/7 which is the second choice on the screen.
The formula for the area of a circle is A = πr^2
Since we know the length of the square is 7cm and the circle fills the full length, 7cm is the diameter.
To get the radius you divide the diameter by 2.
7/2 = 3.5
So, your radius is 3.5.
Now your formula looks like this: A = π(3.5)^2
Next you would square 3.5 because (3.5)^2 means to multiply 3.5 by 3.5
3.5^2 = 12.25
Now, you just multiply 12.25 by the approximate version of pi, which is 3.14.
12.25*3.14 = 38.465
Now, that you have the area of the circle, you subtract it from the area of the square.
If you already haven't figured out the area of the square it is 49 cm.
This is because the formula for the area of a square is A = bh or A = lw
Since the length (l) or base (b) is 7, we know that the other sides are 7 because squares have equal sides.
So now we subtract 38.465 from 49 and we get 10.535 which rounds to 10.54
So, your final answer is D. 10.54 cm^2
Hope this helps!
A has both 6 and -6 as a answer
