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?
Answers
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:
https://brainly.com/question/17646656
Related Questions
Q1 (pic 1)
Triangle ABC is similar to triangle WYZ.
Select all angles whose cosine equals 35.
Question 1 options:
Angle W
Angle Y
Angle C
Angle B
Angle Z
Angle A
Q2 (pic 2)
Triangle ABC is similar to triangle WYZ.
Determine whether the following statement is true or false.
sin(B)>sin(Y)
Question 2 options:
True
False
Answers
Answer:
Question 2 = True
I don't know the first question, the test wouldn't tell me:/
Angle C, Angle Z, Angle A, and Angle W are all angles whose cosine equals 35 and the statement that Sin B is greater than Sin Y is false.
What is a similar triangle?The two triangles are said to be similar that have the same proportion of sides and angles.
Corresponding sides are in the same ratio.
a/p = b/q = c/r
In triangle ABC
AB = 5, AC = 3, BC = 4
Cos A = base/ hypotenuse
= 3/5
Cos B = base/ hypotenuse
= 4/5
Cos C = base/ hypotenuse
= 3/5
In triangle WYZ
Cos W = base/ hypotenuse
= 3/5
Cos Z = base/ hypotenuse
= 4/5
Hence, Angle C, Angle Z, Angle A, and Angle W are all angles whose cosine equals 35.
In triangle WYZ
WY = 13
In triangle ABC
CB = 24, AC = 10
Sin B = Perpendicular/ hypotenuse
= 10/26
Sin Y = Perpendicular/ hypotenuse
= 5/13
Since both angles are equal also they are similar to each other.
Therefore, the statement that Sin B is greater than Sin Y is false.
Learn more about similar triangles;
https://brainly.com/question/25813512
can anyone help me with this
Answers
Answer:
1. 7
2. 3
3. 105
49/7 = 7 which means 7 shot equals 1 minute
The path of a rope bridge can be modeled by a quadratic equation h(l), where h is the height at a point on the bridge relative to the two ends of the bridge and l is the distance from one end of the bridge. One such bridge connects two ends that are 24 meters apart. The lowest point of the bridge is 3 meters lower than the two ends of the bridge Assuming the two ends of the bridge are at an equal height of h = 0 meters, which of the following graphs could be the graph of h (l)?
Answers
for brainiest:):):):):):):)
Answers
Answer:
1: 55
2: 128
3: 175
Step-by-step explanation:
I believe that this is correct.
At a concert 3 out of 10 people who entered the Alamodome Nike shoes based on this information if there are 1200 people add the music concert how many people could be expected to be wearing Nike shoes?
Answers
Complete Question
At a concert 3 out of 10 people who entered the Alamodome wore Nike shoes based on this information if there are 1200 people at the music concert how many people could be expected to be wearing Nike shoes?
Answer:
360 people
Step-by-step explanation:
The fraction of people wearing Nike shoes = 3/10
The total number of the people at the concert = 1200 people
Therefore, the number of people cthat ould be expected to be wearing Nike shoes is calculated as:
3/10 × 1200 people
= 360 people
The answer is 360 people
help pls D; I’ll mark brainliest :D
Answers
Answer:
6, -6 is the answer
36 is in the second quadrant that’s why.
Step-by-step explanation:
URGENT!!!!!
Select expression that represents the following statement multiply six by the sum of three and eight
Answers
Hi
6 * (3+8) = 6 * 11 = 66
Answer:
66
Step-by-step explanation:
6 (3+8) aka 6×(3+8)
6 (11)
= 66
Identify the volume of the figure in cubic units.
Answers
Answer:
8 cubic units
Step-by-step explanation:
Count it. It's all visible for this question.
1. ris 4 more than the product of 7 and 8
Answers
Answer:
i dont know if this is the answer u want
4+(7*8)=x
x= 60
Step-by-step explanation:
Help plz due now will mark brainliest if correct
Answers
Answer:
2^3
Step-by-step explanation:
you subtract the exponents if they have the same coefficient when dividing them.
9-6=3
I need help! Answer this please! I will give brainliest!! ASAP
Answers
Answer:
it's 9 or 21
Step-by-step explanation:
is 628/1300 the same as 628 divided by 1300?
Answers
Answer:
Step-by-step explanation:
Yes
Answer:
yes
Step-by-step explanation:
here 628/1300 means
[tex] \frac{628}{1300} [/tex]
where
[tex] \frac{628}{1300} means 628 \div 1300[/tex]
where the sign ÷ shows divide
so we can say 628/1300=628 divided by 1300
hope it helps you
A cylindrical gasoline storage tank has a diameter of 3.8 ft and a height of 10.9 ft.
What is the total surface area of the tank.
HELP PLZ !!! Extra points will be given !!!
Answers
BRAINLIEST FOR CORRECT ANSWER!
What is the transformation rule for a translation 3 units right?
Answers
Answer:Translation happens when we move the image without changing anything in it. ...
Rotation is when we rotate the image by a certain degree. ...
Reflection is when we flip the image along a line (the mirror line). ...
Dilation is when the size of an image is increased or decreased without changing its shape.
A marble is selected at random from a jar containing 30 red marbles, 10 yellow marbles, and 60 green marbles. Find the theoretical probability that it is either red or green.
Answers
there is a 90% chance its a red or green or a 90/100 chance
Step-by-step explanation:
first you need to count your whole which would be the sum of adding all the marbles which is 100 then add the red and green that's 90 lastly you make a fraction 90/100 (simple the fraction if asked )
OMG OMG THE MISS IS ASKING ME THIS AUESTION BEFORE MY OTHER CLASSMATE PLS HELP FAST IM CRYING AND SHAKING I CANT TYPE TOO PLEASEEE
Answers
They are the same
Step-by-step explanation:
Explanation: 3/4 and 6/8 are equal
Pls help asap thx its about Operations with Exponents
7.
8.
9.
10.
Answers
Answer:
7. 2s^7
8. 2s^4/5s^2
9. 108s^9
10. h^7
Step-by-step explanation:
7) (2s^3)^4
= 2s^(3+4)
= 2s^7.
8) (2s^2/5s)^2
= (2s^4/5s^2)
= 2s^4/5s^2.
9) 3s^5 × 4s^-2 × 9s^6
= 12s^{5+(-2)} × 9s^6
= 12s^3 × 9s^6
= 108s^9.
10) h^5/h^-2
= h^{5-(-2)}
= h^7.
if it helps don't forget to like and mark me
simplify. i need help with this
Answers
Answer:
4^4
144x^9
3^24 x^20
Step-by-step explanation:
4^7/ 4^3 keep the base number and subtract the exponent
(12x^4) (2x^5) Multiply the numbers then add your exponents
(3^6 x^5)^4 multiply the exponents inside by exponent 4
Nicole runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?
Answers
Answer:
30 minutes
Step-by-step explanation:
6=45
4=x
6x2/3=4
45x2/3=30
x=30
Answer:
66 minutes
Step-by-step explanation:
Solve the inequality. Graph the solution.
Answers
Answer:
Don't see it. Sorry.
Step-by-step explanation:
Bella surveyed the first 15 students in the lunch line.
Is this sample of the students in the school likely to be representative?
yes
no
Answers
Answer:
No
Step-by-step explanation:
Only people in the lunch line got surveyed, that on it's own is biased.
Only 15 people out of the entire school.
Only the first people got surveyed.
Given DE || BC, find the length of BD.
Answers
Answer:
BD = 12.5
Step-by-step explanation:
Full answer in the attachment!!
Solve the equation for the indicated variable
Answers
Answer:
-1
Step-by-step explanation:
5(3x+7)=20-2(x+1)
15x+35=20-2x-2
17x=-17
x=-1
check answer:
5(3(-1)+7)=20-2(-1+1)
5(4)=20-0
20=20
Can anyone help with these ?
Answers
1. b
2. d
3. d
4. b
5. (4,2); (5,-2); (8,4)
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
15
16
What is the equivalent decimal?
Answers
Answer:
15= 0.15 15% 16=0.16 1 6/100
Step-by-step explanation:
HURRYY!!!
Beginning with Rodney’s first month of high school, his father deposits $5 into Rodney’s savings account. Each month after the first month, his father deposits $2 more than the previous month. The total amount deposited in Rodney’s account after four years can be represented using the expression . How much total money has been deposited?
$2,496
$2,544
$2,640
$2,688
Answers
Answer:
A
Step-by-step explanation:
Edge 2021
The sum of the 48 terms will be $2,496. Then the correct option is A.
What is the arithmetic sum of sequence?Let a₁ be the first term, n the number of the terms, and l be the last term of the sequence.
Then the sum of all the terms will be given as,
S = [n (a₁ + l )] / 2
Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as
[tex]\rm a_n = a_1 + (n - 1)d[/tex]
Beginning with Rodney’s first month of high school, his father deposits $5 into Rodney’s savings account.
Each month after the first month, his father deposits $2 more than the previous month.
Then the first term is $5 and the common difference is $2.
The total amount deposited in Rodney’s account after four years can be represented using the expression.
Then the total number of the terms will be
n = 4 x 12
n = 48 months
Then the 48th term of the sequence will be
a₄₈ = 5 + (48 – 1) · 2
a₄₈ = 5 + 47 · 2
a₄₈ = 5 + 94
a₄₈ = 99
Then the sum of the 48 terms will be
S = 48 (5 + 99) / 2
S = 24 × 104
S = $2,496
Then the correct option is A.
More about the arithmetic sum of sequence link is given below.
https://brainly.com/question/14021449
#SPJ5
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Select three options. The inequality should be written as 25 s less-than 300. The inequality should be written as 25 s greater-than 300. The circle is open. The circle is closed. The arrow points left.
Answers
Answer:
A, C, E
Step-by-step explanation:
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Please help ASAP!!!
Rewrite the following expression 36+18 using the GCF and the distributive property.
Answers
Answer:
18 ( 2 + 1 )
Step-by-step explanation:
Factors of 36.
1 x 362 x 183 x 124 x 96 x 6Factors of 18
1 x 182 x 9 3 x 6The Greatest common factor they have is 18.
Complete the equation of this circle:
(x - [ ? ])2+(y - [ ])2= []
Answers
The complete equation of the circle graphed is (x - 2)² + (y + 2)² = 9
Determining the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (2, -2)
Radius, r = 3 units
The equation of the circle graphed is represented as
(x - a)² + (y - b)² = r²
So, we have
(x - 2)² + (y + 2)² = 3²
Evaluate
(x - 2)² + (y + 2)² = 9
Hence, the equation is (x - 2)² + (y + 2)² = 9
Read more about circles at
brainly.com/question/24810873
#SPJ1
if you borrow $840.00 and you pay back 1/5 how much do you still owe?
Answers
Hello, I Am BrotherEye
Answer: 672 Dollars
Step-by-step explanation:
It Is Simple 1/5 Of 840 Is = 168
168 - 840=672
Thus The Money Owed is
672 Dollars
Best Of Luck
~
BrotherEye