A biologist is developing two new strains of bacteria. Each sample of Type 1 bacteria produces four new viable bacteria, and each sample of Type II bacteria produces three new viable bacteria. Altogether, at least 240 new viable bacteria must be produced. At least 20, but not more than 60, of the original samples must by Type I. Not more than 70 of the original samples can be Type II. A sample of Type I costs $5 and a sample of Type II costs $7. How many samples of each bacteria should the biologist use to minimize the cost? What is the minimum cost?
The cost can be optimized by using a Linear Programming given the linear constraint system
To minimize the cost, the biologist should use 60 samples of Type I bacteria and 0 samples of Type II bacteriaReason:
Let X represent Type 1 bacteria, and let Y, 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
[tex]Y \geq 80 - \dfrac{4}{3} \cdot X[/tex] (Equation for the inequality graphs)The boundary of the feasible region are;
(20, 70)
(20, 53.[tex]\overline 3[/tex])
(60, 0)
(60, 70)
The cost are ;
[tex]\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][/tex]
Therefore, the minimum cost of $300 is obtained by using 60 samples of Type I and 0 samples of Type IILearn more here:
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What is the value of the expression shown?
1/2(7.9−0.08)
Answer:
3 91/100 or 3.91
Step-by-step explanation:
help me please WORTH 20 POINTS
Answer:
1
Step-by-step explanation:
What is the slope of the line represented by the equation y =4/3x-3
Answer:
m, is equal to (4/3)
Step-by-step explanation:
Match the given equation y =(4/3)x-3 to the standard slope-intercept form y = mx + b. By doing so we see that the slope, m, is equal to (4/3).
Simplify 5^4/5^3
5^7
5^-1
1/5
1/5^7
Answer:
5^4-3
5¹
by law
a^m÷a^n= a^m-n
Prove the following relations: 1) (1 - cos²A) (1 + tan²A) = tan²A
Step-by-step explanation:
(1 - cos²A)(1 + tan²A) = tan²A
1 + tan²A - cos²A - cos²A · tan²A = tan²A
1 + tan²A(1 - cos²A) - cos²A = tan²A
1 - cos²A + tan²A(sin²A) = tan²A
sin²A + tan²A(sin²A) = tan²A
sin²A (1 + tan²A) = tan²A
sin²A (sec²A) = tan²A
sin²A (1/cos²A) = tan²A
(sin²A)/(cos²A) = tan²A
tan²A = tan²A → Proved
An angle measures 68° less than the measure of its complementary angle. What is the measure of each angle?
Line A is perpendicular to Line B.
If the slope of Line Ais ,
what is the slope of Line B?
Enter the correct symbol, + or -.
Answer:
-7/3
Step-by-step explanation:
the answer is the negative reciprocal.
If you have 20 dollars how much more will you need to get to 43?
Solve the linear inequality below.
9x−8>4x+7
Enter your answer as the correct inequality. For example, if your answer is x<42, enter it like this: x < 42
Answer:
x > 3
Step-by-step explanation:
How does a sequence of translations , relections , and rotations result in congreunt figures
Answer:
if the size (and shape) of the figure doesn't change then it's congruent
Step-by-step explanation:
Question
Which of the following values are in the range of the function graphed below?
Check all that apply.
A. 2
B. 1
C. O
D. 4
E-4
F. -1
what does this q equal
Answer:
30 degrees
Step-by-step explanation:
Since all triangles' angles add up to 180 degrees, you can add the sum of the angles you already know and subtract it from 180.
126+24=150
180-150=30
so angle Q = 30 degrees
can you help me with these:
1: 2/3x=-8
2: -4.5= - 0.15p
3: 2 1/3c=2 1/10
4: 3m + 5 =14
5: -2k +7 = -3
6: 11 = 1/3a +2
ILL GIVE BRAINLY T WHOEVER DOES ALL THEM AND SHOWS WORK!
Answer:
1. x= -12
2.p= 30
3.c= 9/10 or c= 0.9
4.m= 3
5.k= 5
6.a= 27
Step-by-step explanation:
Please help me out I really can’t afford failing this test
Answer:
I'm not really sure but I think it's 2
Step-by-step explanation:
So here's what I did;
x³+3x-9=x - 1 +2x
x³+3x - x -2x = 9 - 1
x³= 8
x = ³√8
x = 2
I hope this helps
resolver el sistema x-y =6 y este otro 2x+5y= -2 porfaaaa es para mañana
Answer:
x =4
y = -2
Step-by-step explanation:
a) x - y = 6
b) 2x + 5y = - 2
a) x = y + 6
b) 2(y+6) + 5y = -2
2y + 12 + 5y = -2
7y = -2 -12
y = -14/7
y = -2
a) x - (-2) = 6
x +2 = 6
x = 6-2
x = 4
please solve !!!! asap );
Answer:
<7 58
<5 47
<6 75
<4 107
<8 73
<9 49
all triangles add up to 180 and all lines add up to 180
why tHE F is MATH HARD KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
Answer:
well it isn't hard
have a nice day
The cost of a birthday party at a skating rink is proportional to the
number of guests. The skating rink charges $82.50 for 10 guests.
The choices show the number of guests and the total cost for four
different parties that were hosted at different locations. Select each
party that was hosted with the same constant of proportionality, or
unit rate, as the skating rink's unit rate.
Answer:
Step-by-step explanation:-
-
-
-
-
-
-
-
-
The required magnitude of the constant of the proportionality is 8.25.
Given that,
The cost of a birthday party at a skating rink is proportional to the number of guests. The skating rink charges $82.50 for 10 guests.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
Here,
Let the number of the guest be x and the total charge for the party be y,
y = kx
Where K is the constant of proportionality,
Substitute the values in the equation for the number of guests and corresponding charges,
82.50= K(10)
K = 8.25
Thus, the required magnitude of the constant of the proportionality is 8.25.
Learn more about proportionality here: https://brainly.com/question/22620356
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76 people left before the movie ended 124 people remained how many people were in the theater when it was full 
Answer:
Step-by-step explanation:
124 + 76 = 200 ☺
help ill give brainliest
Answer:
venti, it has more liquid per ounce
two companies listed a revenue for the year in their respective websites. Company a has revenue in the amount of 1.6×10^6 and company b has revenue in the amount of 7.2x10^8. how many Times greater is the revenue for company b?
A line has slope −5/3. Through which two points could this line pass?
A: (11, 13) & (8, 18)
B: (12, 13) & (17, 10)
C: (16, 15) & (13, 10)
D: (0, 7) & (3, 10)
Answer:
A:
Step-by-step explanation:
[tex]m=\frac{18-13}{8-11} =\frac{5}{-3} =-\frac{5}{3}[/tex]
I hope this help you
Jon painted 4/5 of his house on Saturday on Sunday he paints 2/3 of what was left how much still needs to be painted
Answer: Jon has 1/5 left to paint
Identify the initial condition and the rate of change
y=−5x+32
for the given graph :
y = -5x + 32rate of change = -5
Initial condition = 32
Determine if (0,-5) is a
solution to the equation
y = -5x
Plug (0,-5) into the equation -
-5 = -5(0)
-5 times 0 is 0
-5 = 0
(0,-5) is NOT a solution to the equation.
Good luck!
Answer:
No, it is not the solution to the equation.
Step-by-step explanation:
(0, -5)
y = -5x
So we have to plug in the values for x and y. 0 is our x value and -5 is our y value.
-5 = -5(0)
-5 = 0
Therefore, (0, -5) is not a solution to the equation
will give brainlist 2 best answer
Reflect (7, 3) in (a) the x-axis and (b) the y-axis.
a. x-axis reflection: ( , )
b. y-axis reflection: ( , )
Answer:
(a) (7, -3)
(b) (-7, 3)
Step-by-step explanation:
What is the range of the function f(x) = 3x + 2
when the domain is {-2,-1,2}?
Answer:
Im going to give them as ordered pairs, you can pick out the range (Y values): (-2,-4), (-1,-1), (2,8)
Step-by-step explanation:
All that needs to be done for this problem is one thing: substitute the given domain values for the "x" in the equation. Domain is just a fancy way of saying x coordinate. All f(x) is is "function of x." This can still be your Y coordinate, or your range. I hope this process helps!
Does x=5 satisfy the equation 3x + 2 +5x= 95 explain
Answer:
No
Step-by-step explanation:
3x + 2 +5x
if x=5
3(5)+2+5(5)
=15+2+25
=42 which is not equal to 95
No, it doesn't satisfy the equation
Step-by-step explanation:
3x + 2 +5x = 95
Now putting the value of x
3×5 + 2 + 5×5 = 95
15 + 2 + 25 = 95
42 ≠ 95
Hence, x = 5 doesn't satisfy the equation 3x + 2 +5x= 95
Pls help Evaluate (7-3) = 2
Answer:
2
Step-by-step explanation:
subtract the. divide it once
Answer: 4 = 2
Step-by-step explanation:
1. (7-3) = 4
2. 4=2