Answer:
We require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day
Step-by-step explanation:
Let n₁ be the population of A required and n₂ be the population of B required.
Now we require 2 units of the first nutrient for species A and one unit of the first nutrient for species B. The total nutrients required by species A is 2n₁ and that by species B is 1n₂ = n₂. So, the total nutrients required by both species A and B is 2n₁ + n₂. Since this equals the quantity of the first nutrient which is 10,560, then 2n₁ + n₂ = 10,560 (1)
Now we require 5 units of the second nutrient for species A and 6 units of the second nutrient for species B. The total nutrients required by species A is 5n₁ and that by species B is 6n₂. So, the total nutrients required by both species A and B is 5n₁ + 6n₂. Since this equals the quantity of the first nutrient which is 31,510, then 5n₁ + 6n₂ = 31,510 (2).
So, we have two simultaneous equations which we would solve to find the populations of A and B which satisfy both equations.
2n₁ + n₂ = 10,560 (1)
5n₁ + 6n₂ = 31,510 (2)
From (1) n₂ = 10,560 - 2n₁ (3)
Substituting equation (3) into (2), we have
5n₁ + 6(10,560 - 2n₁) = 31,510
expanding the brackets, we have
5n₁ + 63,360 - 12n₁ = 31,510
collecting like terms, we have
5n₁ - 12n₁ = 31,510 - 63,360
simplifying, we have
- 7n₁ = -31,850
dividing both sides by -7, we have
n₁ = -31,850/-7
n₁ = 4,550
Substituting n₁ = 4,550 into (3), we have
n₂ = 10,560 - 2(4,550)
n₂ = 10,560 - 9,100
n₂ = 1,460
So, we require 4,550 of species A and 1,460 of species B that can coexist in the environment so that all the nutrients are consumed each day
Number of Bacteria A and Bacteria B = 4550 and 1460 respectively,
Let the number of bacterias of Specie A and Specie B be = x and y respectively.
Given : 2 Nutrient Requirements of both species of Bacteria A and B , Total Nutrients available
To find : Number of Bacteria 1 and Bacteria 2
Nutrient 1 Constraint Equation : 2x + y = 10560
Nutrient 2 Constraint Equation : 5x + 6y = 31510
Putting the value of y from 1st equation in 2nd equation ;
5x + 6 (10560 - 2x) = 31510
5x + 63360 - 12x = 31510
63360 - 31510 = 7x
7x = 31850
x = 31850 / 7 = 4550 { Bacteria A}
Putting the value of x in 1st equation,
2 (4550) + y = 10560
9100 + y = 10560
y = 10560 - 9100 = 1460 {Bacteria B}
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FFDP, "Under and over it"
. who sings this guys
Answer:
lol
Step-by-step explanation:
Answer:
Five Finger Death Punch
Step-by-step explanation:
Which measure of Center would be most effected if 50 was added to the following data set? 10, 14, 15, 15, 18, 20
Answer:
The mean.
Step-by-step explanation:
The mean because 50 is a lot bigger number than the numbers in the list.
The median (the middle number in an ordered list) would still be 15. Also the mode (15) will also stay the same.
The original mean = sum of the 6 numbers divided by 6
= 92/5 = 15.3.
When 50 is added the mean is (92 + 50) / 7 = 20.3.
Answer:
The mean
Step-by-step explanation:
Because mean is the main measure of center that we solve first before solving the others
Please help me answer number 12
Answer:
It is same.
The PS and RS leg which has the same length allow the use of HL by providing the same degree of angle.
Thank you and please rate me as brainliest as it will help me to level up
Find the measurement
Answer:
AC = 40
Step-by-step explanation:
AC and BD are equal to each other in length. So:
4x-4 = 3x+7
Now you solve for x. Add 4 to each side.
4x= 3x + 11
Then subtract 3x from both sides.
X = 11. There you have X, now you plug 11 in for x in the AC= 3x+7
3(11) + 7 = AC
33 + 7 = AC
40 = AC
please help please
Which relations are functions? Select all that apply.
A. (3, 2), (-1, 7),(-3, 1), (0.9), (2, -4)
В.
х
-4
-2
у
9
12
15
c
x
1
2
3
4
y
2
4
6
13
D
Answer:
A and C
Step-by-step explanation:
For any relation to be considered a function, each domain value (x-value) must have exactly one range value (y-value). If a relation contains an x-value that has two or more y-value related/mapped to it, the relation is not a function.
Let's examine each option given.
Option A: each x-value has exactly one y-value related or assigned to it. Therefore, the relation is A FUNCTION.
Option B: the x-value, 4, has two y-values, 12 and 15 assigned to it. Therefore, the relation is NOT A FUNCTION.
Option C: each x-value has exactly one y-value related or assigned to it. Therefore, the relation is A FUNCTION.
Option D: the x-value, 1, has two y-values, -1 and 1 assigned to it. Also, x-value, 3, has two y-values, 2 and -2 assigned to it. Therefore, the relation is NOT A FUNCTION.
Can someone plz help me
Answer:
16.3 N
Step-by-step explanation:
subtract if the forces are opposite
what is the solution 4x-10=x+3x-2x
Answer:
x=5
Step-by-step explanation:
I need this answer ASAP
Answer:
Step-by-step explanation:
Multiply 13*5 is 65
Answer:
I'm pretty sure the answer is 5
Step-by-step explanation:
Write a quadratic equation in standard form with the given roots. Show your work to find the equation. 2, 7
Answer:
x²-9x+14
Step-by-step explanation:
So the roots are 2,7
So the equation is
(x-2)(x-7)
=x²-2x-7x+14
=x²-9x+14
4 divided by 2/3
pls pls pls pls pls help pls pls
Answer:
4 divided by 2/3 (4 ÷ 2/3) = 6
Step-by-step explanation:
When you divide one number by another , this is the same as multiplying that one number by the reciprocal of that other number. So a/b = a × 1/b = a × b^-1.
Also a reciprocal is the same as taking something to the power of -1.
When you take the reciprocal of a fraction, just flip the numerator, and denominator.
b^-1 = 1/b.
b^-n = 1/b^n.
(a/b)^-1 = b/a
a/b^-1 = ab
Therefore 4 / (2/3) = 4 × 3/2 = 12/2 = 6.
Answer:
6
Step-by-step explanation: 4 ÷ (2 ÷3)=6
Cindy struck out 7, 14, 6, 4, 5, and 6 batters in softball games this season. In discussing her stats with a newspaper reporter, Cindy's coach mentions that the average number of Cindy's strikeouts is 7. Is the coach's statement misleading? Explain why or why not.
Answer:
The coach's statement is not misleading because her average strikeouts is 7.
Where as the coach also tells that it is 7.
Step-by-step explanation:
The average is taken out by adding the observations and dividing by the total number of observations.
X`= ∑x/n where n is the number of observations.
Average = 7 + 14 + 6 + 4 +5 +6 /6
Average = 42/6= 7
The coach's statement is not misleading because her average strikeouts is 7.
Where as the coach also tells that it is 7.
After every eighth visit to a restaurant you receive a free beverage. After every tenth visit you receive a free appetizer. If you visit the restaurant 100 times, on which visits will you receive a free beverage and a free appetizer? At which visit will you first receive a free beverage and a free appetizer? Drag and drop the correct value into each box to complete the statement. You will receive a free beverage and a free appetizer on the and visits, and you will first receive a free beverage and a free appetizer on the visit.
Answer:
40th and 80th visit
the first visit where you receive both is the 40th
Step-by-step explanation:
personally, I believe that the simplest way to solve this is use an excel spreadsheet to see which visits would include both a free beverage and a free appetizer:
both rewards would happen only twice, at the 40th and 80th visit.you can also calculate it mathematically since multiples of 8 and 10 do not repeat themselves very much, only when 8 is multiplied by 5 and 10.
Answer:
Step-by-step explanation:
which expression is equivalent to 8c+6-3c-2
Answer:5c+4
Step-by-step explanation:
Can yall plz help me answer this!!!
Answer:
n= -3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4n+2=6(
1
3
n−
2
3
)
4n+2=(6)(
1
3
n)+(6)(
−2
3
)(Distribute)
4n+2=2n+−4
4n+2=2n−4
Step 2: Subtract 2n from both sides.
4n+2−2n=2n−4−2n
2n+2=−4
Step 3: Subtract 2 from both sides.
2n+2−2=−4−2
2n=−6
Step 4: Divide both sides by 2.
2n
2
=
−6
2
n=−3
Answer:
n = -3
Step-by-step explanation:
The first step you want to do is try to get rid of those parenthesis and to do that you want to distribute the 6 into 1/3n and 2/3 and you get
4n + 2 = [tex]\frac{6}{3}[/tex]n - [tex]\frac{12}{3}[/tex]
that can be simplified to
4n + 2 = 2n - 4
subtract 2n from both sides and you get
2n + 2 = -4
subtract 2 from both sides
2n = -6
divide both sides by 2 you get
n = -3
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation
(x – 8)2 = 144, x represents the side measure of the original lawn.
Answer:
The answer is 20 feet by 20 feet. Let's solve the equation: (x – 8)^2 = 144. (x - 8)^2 = 12^2. Since a^2 = b^2 is the same as a = b, then (x - 8)^2 = 12^2 can be simplified to: x - 8 = 12. Now, solve for x. x = 8 + 12. x = 20. Therefore, the dimensions of the original lawn were 20 feet by 20 feet.
A circle of radius 8 is inscribed in an isosceles trapezoid. The length of the larger base of the trapezoid is 20. Find the length of the shorter base.
PLEASE ANSWER FAST
Answer:
ayy
Step-by-step explanation:
sup
Answer:
12 4/5
Step-by-step explanation:
you can use just mark x as half of the leg of the trapezoid and then use pythagorean theorem to get x^2+8^2+10^2+8^2=(10+x)^2 and then solve
what the slope of(12,7) (5,9)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]slope = \frac{9 - 7}{5 - 12} \\ [/tex]
[tex]slope = \frac{2}{ - 7} \\ [/tex]
[tex]slope = - \frac{2}{7} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
[tex]\boxed {\boxed {\sf m= -\frac{2}{7}}}[/tex]
Step-by-step explanation:
The slope of a line can be found using the following formula:
[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]
Where (x₁,y₁) and (x₂,y₂) are the points on the line.
We are given the points (12,7) and (5,9). Therefore:
[tex]x_1=12\\y_1=7\\\\x_2=5 \\y_2=9[/tex]
Substitute the values into the formula.
[tex]m=\frac{9-7}{5-12}[/tex]
Solve the numerator.
Subtract 7 from 9 9-7=2[tex]m=\frac{2}{5-12}[/tex]
Solve the denominator.
Subtract 12 from 5 5-12= -7[tex]m=\frac{2}{-7}[/tex]
This fraction cannot be reduced further, so it is the answer.
The slope of the line is -2/7
Helpp plzzz!! Identify the corresponding side to side MN.
Answer:
st i think
Step-by-step explanation:
Answer:
I seem to have learned this, but I just don't remember how to do it? Even if I remember, I don't know how to count it?
What steps would you follow in order to solve the equation?
w/8 - 4 = 20
add 4 on each side and divide by 8
subtract 4 on each side and multiply by 8
add 4 on each side and multiply by 8
subtract 4 on each side and divide by 8
Answer:
Step-by-step explanation:
w/8-4=20
add 4 to each side
w/8=24
multiply by 8 to clear out the w on one side
w=192
Solve the problem. A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $16.25. Another customer buys 5 hot dogs and 4 bags of potato chips for $19.50. Find the cost of each item.
A. $2.75 for a hot dog; $2.00 for a bag of potato chips
B.$2.50 for a hot dog; $1.75 for a bag of potato chips
C.$2.50 for a hot dog: $2.00 fora bag of potato chips
D. $1.75 for a hot dog; $2.50 for a bag of potato chips
Answer
ok the answer is C
Step-by-step explanation:
1.75*4=7
.75*2=1.5
7+1.5=8.50
Please tell me the answer
Answer:
(-∞,∞) Bottom answerI hope this helps you with your algebra
Answer:
Infinity
Step-by-step explanation:
Give brainiest to the other guy/girl they deserve it!!
(Hope dis helps!!!)
If you leave your house at 1:00 and get to your friends house at 5:00, what was your average speed
Denise guessed that the elephant at the zoo weighed 10,000 pounds. It actually weighed 12,400 pounds. Yesia guessed that the hippopotamus weighed 2,500 pounds and it actually weighed 3,600 pounds.Whose guess had the smaller percent error?
Answer: weight of elephant has smaller percent error.
Step-by-step explanation:
Percent error = [tex]\dfrac{|\text{estimated value -actual value}|}{\text{actual value}}]\times100[/tex]
Estimated weight of elephant = 10,000 pounds
Actual weight of elephant = 12,400 pounds
Percent error of weight = [tex]\dfrac{|12400-10000|}{12400}\times100\%\approx19.35\%[/tex]
Estimated weight of hippopotamus = 2,500 pounds
Actual weight of hippopotamus = 3,600 pounds
Percent error of weight = [tex]\dfrac{|2500-3600|}{3600}\times100\%\approx30.55\%[/tex]
Since 19.35 < 30.55
hence, weight of elephant has smaller percent error.
Assume Katelyn's loan was for $5,000 and that she will make 48 monthly payments of $117.42 to repay the loan. How much total interest will she pay over the life of the loan?
Answer:
Step-by-step explanation:
48*117.42=5636.16
Principle of the loan is $5000. Payback is $5636.16. She pays $636.16 in interest or 12.7232%. I got that by dividing the 636.16 of interest by 5000.
Gary wants to buy a video game with a selling price of $48, on sale for 50% off. The sales tax in his state is 4.5%. How much does will Gary have to pay in all? If he has $25, can he afford to purchase the game?
Answer:
i. $26.16ii. He cannot afford the video gameStep-by-step explanation:
Step one:
given
selling price = $48
discount is 50%
tax= 4.5%
Step two:
let us first compute the amount in discount
=50/100*48
=0.5*48
=$24
also, let us compute the tax added
=4.5/100*48
=0.045*48
=$2.16
The total amount Garry has to pay is
=48-24+2.16
=$26.16
Step three:
If he has $25, he cannot afford the video game, he will have a deficit of $1.16
Answer: Gary will have to pay $25.08 in all, and if he has exactly $25, he can't afford to purchase the game because he only has $25, and he has to pay $25.08. $25.08 is more than $25, so he can't afford the game.
Step-by-step explanation:
First, subtract the $48 and 50% to find how much the video game costs.
So, $48-50%=24
Then, add the price of the video game, $24, to the 4.5% tax.
24+4.5%=25.08
Thus, Gary will need to pay $25.08 in all.
Given f(x) = 17x - 18, find x when f(x) = 33.
Answer:
f(x) = 17x - 18
y=17x-18
y=17(33)-18
y=561-18
y=543
f(x)=543
Step-by-step explanation:
Answer:
x = -3
Step-by-step explanation:
Plug in 33 for f(x) into the first equation:
33 = 17x - 18
17x = -51
x = -3
4 pairs of shoes cost $80. What is the cost of 7 pairs of shoes?
Answer:
560 $
Step-by-step explanation:
4 shoes is 80
so, we have to multiply
$140
Or
£140
You are American so its the first one
Albert wants to buy two pomegranates and some peaches • The price of one pomegranate is $1.59. • The price of peaches is $1.19 per pound. Albert wants to no more than $10.00. Which graph represents the number of whole pounds of peaches Albert can buy?
Answer:
He can buy 5 pounds of peaches.
Step-by-step explanation:
2 pomegranates cost $3.18 so, subtract that from $10.00 and you get $6.82. Multiply the different number of pounds with the cost per pound until you go over $6.82. Then go back a pound and multiply. 5 pounds times $1.19 equals $5.95.
(a2 - b2)/(2 + d3)
a=6
b=4
d= 1 over 2
one of the answers is
A. 28.17
B. 13.18
C. 28.47
D. 10.125
E. 1.975
F. 9.4118
Answer:
28.47
Step-by-step explanation:
Answer:
F
Step-by-step explanation:
Given
[tex]\frac{a^2-b^2}{2+d^3}[/tex] ← substitute given values into the expression
= [tex]\frac{6^2-4^2}{2+(\frac{1}{2}) ^{3} }[/tex]
= [tex]\frac{36-16}{2+\frac{1}{8} }[/tex]
= [tex]\frac{20}{\frac{17}{8} }[/tex]
= [tex]\frac{20}{2.125}[/tex]
≈ 9.4118 ( to 4 dec. places ) → F
Write a cubic function whose graph passes through the points (-4,0)(4,0)(0,6) and (2,0)
Answer: 3/16(x+4)(x-4)(x-2)
Step-by-step explanation: