Given :
A population of protozoa develops with a constant relative growth rate of 0.4142 per member per day.
On day zero the population consists of five members.
Differential equation : [tex]\dfrac{dP}{dt}=0.4142P[/tex]
To Find :
The population size after eight days.
Solution :
Rate of growth , R = 0.4142 .
Now ,
Differential equation is :
[tex]\dfrac{dP}{dt}=0.4142P\\\\P_n=Ce^{0.4142n}[/tex]
For n = 0 .
[tex]5=C(1)\\C=5[/tex]
So ,the relation is [tex]P_n=5e^{0.4142n}[/tex] .
Putting n = 8 .
[tex]P_8=5e^{0.4142\times 8}\\\\P_8=137.42[/tex]
Hence , this is the required solution .
-200 + {37}{3}4.5) -200 + 55.5
Answer:
-294.55
Step-by-step explanation:
-200+ 49.95 -200 +55.5
49.95+55.5-200-200
-294.55
Jose spent $34.50 on a bike rental in Miami, Florida. The rental store charged a base fee of $8.50 for the first hour, and an hourly rate of $3.25 for each additional hour. The following sign is displayed to show the prices for the first 4 hours.
Answer:
8.5+2.25x=34.5
edit***
18.25+3.25h=34.5
Are the two triangles below similar?
PLEASE HELP ME!!!!!!!!!!
Answer:
im going with number 3 sorry if im wrong
Step-by-step explanation:
Answer:
Yes; they have congruent corresponding angles.
Step-by-step explanation:
The two triangles are similar because their angles measure are the same. This is because 70 + 28 + 92 = 180 degrees and all Euclidean triangles angles measures must have a sum of exactly 180 degrees.
To make grape juice by using frozen juice concen-trate, you must mix the frozen juice concentrate with water in a ratio of 1 to 3. How much frozen juice concentrate and how much water should you use to make 11 this problem in two different ways by reasoning about multiplication and division with quanti-ties, explaining your reasoning in each case.
Answer:
To make 11 grape juice, you will need:
11 (1 * 11) frozen juice concentrate and
33 (3 * 11) water.
Step-by-step explanation:
Since you are making 11 grape juice containers and each container requires 1 frozen juice concentrate and 3 quantities of water, to get the maximum quantities of ingredients required, you will multiply each ingredient by 11.
With the sum of ratio as 4 (1:3), we can also say that 44 (4 * 11) units of both frozen juice concentrate and water are required to produce 11 units of the grape juice. Dividing 44 by 4 also gives 11 units. Similarly, dividing the total ingredients of the frozen juice of 11 units by 11 juice concentrate gives 1 unit each and dividing 33 units by 11 quantity of water gives 3 units each in every unit of the juice produced.
convert this statement into a conditional statement: 2 angles that add up to 180 degrees are supplementary
- Complete the following paragraph proof.
Given: 44 -2(3x + 4) = -18
Prove: x = 9
What is the solution set for 8(2−h)>−3h−4?
Answer:
h < 4
Step-by-step explanation:
Simplify both sides
-8h + 16 > -3h - 4
Add 3h to both sides
-5h + 16 > -4
Subtract 16 from both sides
-5h > -20
Divide both sides by -5
-20 divided by -5 = 4
Since you divided by a negative number, you change the inequality sign to < instead of >
Solve for Xon the following Equations.
1. 4 + 7 x X = 22
Step-by-step explanation:
4 + 7 x X = 22
4+7x=22
7x=22-4
7x=18
x=18/7
These tables of values represent continuous functions. For which functions will the y-values be the greatest for very large values of x?
∆....A....∆
1 6
2 18
3 54
4 162
5 486
The function with the greatest y-values for very large values of x is C.
The y-values in function C increase at a much faster rate compared to the other functions as x becomes larger. In function C, the y-values are growing with a constant difference of 200 for each increase in x. This means that for every unit increase in x, the y-value increases by 200. This linear relationship results in significantly larger y-values for larger x-values.
On the other hand, the other functions (A, B, and D) do not exhibit such rapid growth. Function A has a cubic relationship, which does lead to larger values than a linear relationship, but it is still not as rapid as the linear increase in function C. Function B also has a linear relationship, but the constant difference between y-values is much smaller than in function C (only 75).
Function D has a constant difference of 5 between y-values, resulting in a very slow growth as x becomes larger.
In conclusion, function C has the greatest y-values for very large values of x due to its linear relationship with a constant difference of 200 between y-values for each unit increase in x.
To learn more about continuous functions, here
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9. Find the sum of the first 6 terms of the sequence: –3, 1, 5, 9, . . . options: A) 25 B) 48 C) 42
Answer:
C. 42.
Step-by-step explanation:
This is an arithmetic sequence with common difference d = 4 and first term a = -3.
Sum of n terms = (n/2)[2a + (n - 1)d]
Sum of six terms = (6/2)[2(-3) + (6 - 1)4]
= 3 * (-6 + 20)
= 42.
Answer:
C) 42
Step-by-step explanation:
Given is an Arithmetic Sequence, where
First term a = - 3
Common Difference d = 1-(-3)= 4
n = 6
[tex]S_6=? \\ \\ \because \: S_n = \frac{n}{2} \{2a + (n - 1)d \} \\ \\ \therefore \: S_6 = \frac{6}{2} \{2 \times ( - 3) + (6 - 1)4 \} \\ \\ \therefore \: S_6 = 3 \{ - 6 + 20\} \\ \\ \therefore \: S_6 = 3 \times 14 \\ \\ \huge \red{ \boxed{ \therefore \: S_6 = 42}}[/tex]
r/4 - 1.4 =1.58 what should be the first step?
Answer:
R/4 - 1.4 =1.58
R/4 = 1.58 + 1.4
R/4 =2.98
r=11.92
Step-by-step explanation:
Warren had d dollars. He bought 5 ice creams which cost x dollars each. How much money does he have left?
Answer:
The answer is: d-5x
Step-by-step explanation:
What I like to do is rewrite the problem with numbers instead of variables.
Example: Warren had 20 dollars. He bought 5 ice creams which cost 2 dollars each. How much money does he have left?
He has 20 dollars, 5x2=10 he spent 10$ on the ice cream so you have to subtract how much he had in the beginning to how much he spent, the answer with numbers would be: 20-5x2
With variables it would be d-5x
can someone help ASAP plzz
Answer:
c. 84 ft²
Step-by-step explanation:
lateral area = 1/2 * base perimeter * height
where
base sides = 6 ft.
height (L) = 7
lateral area = 1/2 x (4*6) * 7
lateral area = 84 ft²
LA = 1/2pl
p = base perimeter
l = length
p = (6 * 4)
p = 24
l = 7
Use the formula and solve.
LA = 1/2(24)(7)
LA = 1/2(168)
LA = 84
Therefore, the answer is C
Best of Luck!
What number is 136% of 12.24?
Answer:
I really don't know but I'm trying to hurry for my quiz lol sorry
Answer:
cxcxcxcxcxgergddgg
Step-by-step explanation:
How would the underline look like
Answer:
the correct answer is C
SOMEONE HELP PLEASE.............
What is the x-coordinate of the solution of the following system of equations?
3x + y = 6
x - y = 6
A. -3
B. 0
C. 3
Answer:
(3,-3) or x = 3
Step-by-step explanation:
I solved this problem with the help of graphing, you would start by sketching each equation. The x-value of the point where both equations intersect would be solution to your equations.
Simplify
(2x– 3) (5x4 – 7x3 + 6x2 – 9)
A. 10x5 – 29x4 + 33x3 - 18x2 18x + 27
B. 10x5 - x4-9x3 – 18x2 -18x - 27
C. 10x5 + 29x4 – 33x3 + 18x2 + 18x - 27
D. 10x5 + x4 + 33x3 + 18x2 + 18x + 27
Answer: (A)=10x5−29x4+33x3−18x2−18x+27
Step-by-step explanation:
How i solved it was by simplifying each answer there was available and (A) was the most compatiable answer!
=(2x+−3)(5x4+−7x3+6x2+−9)
=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)
=10x5−14x4+12x3−18x−15x4+21x3−18x2+27
=10x5−29x4+33x3−18x2−18x+27
Answer:
=(2x+−3)(5x4+−7x3+6x2+−9)
=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)
=10x5−14x4+12x3−18x−15x4+21x3−18x2+27
=10x5−29x4+33x3−18x2−18x+27
Step-by-step explanation:
What is the domain of the function f(x)=
Answer:
The domain of a function is the set of all possible inputs for the function.
Step-by-step explanation:the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
The copper content of 18-carat gold was measured by two methods for six different samples collected from a jewelry production plant. Sample Method 1 Method 2 A 2.2% 2.5% B 1.8% 2.2% C 2.5% 3.0% D 3.0% 3.2% E 2.6% 2.3% F 2.6% 2.7% Which test would you use to determine if the results obtained by the two methods agree within experimental error?
Full question attached
Answer:
Paired t test
Explanation:
The paired sample t test is used to measure or compare the mean of two observations or samples by measuring each subject two times as is seen above with the gold measurement which would result in two sets or pair of samples in a statistical procedure. We observe from the question that we measure each gold with two methods and then compare result of the two methods in terms of their mean error using the paired t test.
Solve the equation . Check your solution
Answer:
x=48/8=6
Step-by-step explanation:
simple form
8x-48=0
fractionized
8(x-6)=0
Solve the following (x+y+z)(x-z)^2
Hey there!
ANSWER: [tex]x^2y-2xyz+yz^2+x^3-x^2z-xz^2+z^3[/tex]EXPLANATION:[tex](x+y+z)(x-z)^2[/tex]
Simplify.
[tex]x^2y-2xyz+yz^2+x^3-x^2z-xz^2+z^3(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
Step-by-step explanation:
x³+yx²+zx²-2x²z-2xzy-2xz²+x²z-z²y+z³
in Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies.
Answer: There are 15 more goldfish than guppies.
Step-by-step explanation:
Since there are 6 times as many goldfish as guppies, then. Now 3 + 18 = 21 the total fish in the tank. Hence there are 3 guppies and 18 goldfish. and 18 - 3 = 15, thus there are 15 more goldfish than guppies.
A car is traveling down a highway at a constant speed, described by the equation d=65t, where d represents the distance, in miles, that the car travels at this speed in t hours. How many miles does the car travel in 1.5 hours?
Answer:
A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels - 1138… ... How many miles does it take the car to travel 26 miles at this speed? c. ... the distance, in miles, that the car travels at this speed in t hours.
Step-by-step explanation:
Hope this helps
1.For this problem, 200 meters of fencing will all be used to place fence on all four sides of the rectangle. Your task is to write the area that can be enclosed as a function of the width, w, of the rectangle.
Area equation:
What is the domain for this function (what values do you expect the width to fall between)?
Answer:
Step-by-step explanation:
Given that:
the perimeter of the fencing (rectangle) = 200
Let recall that the area equation of a rectangle = L × w
The perimeter now = 2(L + w)
The perimeter = 2L + 2w
∴
200 = 2L +2w
Dividing both sides by 2
100 = L + w
Making Length L the subject; we have:
- L = -100 + w
L = 100 - w
Thus;
A(w) = (100 - w) w
and the domain of the function is (0,100)
On Monday a team of street sweepers cleaned 4 city blocks. Tuesday, the team cleaned 2 1/6 times as many blocks as on Monday. How many city blocks did the street sweepers clean on Tuesday?
1/5 is the answer :0000
There will be twelve and a half city blocks of the street sweepers clean on Tuesday.
What is a fraction?The numerator, which is found at the top of the fraction number, and the denominator, which is located at the bottom, are its two component components.
It is given that, four city blocks were cleaned by a crew of street sweepers on Monday. The crew cleaned 2 1/6 as many blocks on Tuesday as they did on Monday.
Suppose the number of city blocks the street sweepers cleaned on Tuesday will be x,
x = 4 + 2 1/6 × 4
x=4+13/6×4
x=12.6≈ 12 1/2
Thus, the street sweepers will clean twelve and a half city blocks on Tuesday.
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The sum of two numbers is 91.one is 37 more than the other.Find the numbers
Step-by-step explanation:
Hey there!!
Here, According to the question;
Let one number be x then another number will be x+37. (as one number is 37 more than other number. )
Now,
Their sum is 91.
It would be like;
[tex]x + (x + 37) = 37[/tex]
[tex]2x + 37 = 91[/tex]
[tex]2x = 91 - 37[/tex]
[tex]x = \frac{54}{2} [/tex]
Therefore the value of x is 27.
So, one number is 27 and another number is 64.
Hope it helps....
4|m-n| if m= -7 and n=2
Find the area of a square with a side of length 2 Square root of 3+6 square root of 7 inches
Answer:
(264+24√21) in²Step-by-step explanation:
Area of a square = Length * Length
A = L²
Given the length of a square as [tex]2\sqrt{3}+6\sqrt{7}[/tex] inches' The area of the square will be calculated as shown;
[tex]A = (2\sqrt{3}+6\sqrt{7})^2\\\\A = (2\sqrt{3}+6\sqrt{7})(2\sqrt{3}+6\sqrt{7})\\\\A =(2\sqrt{3})(2\sqrt{3})+(2\sqrt{3})(6\sqrt{7})+(6\sqrt{7})(2\sqrt{3})+(6\sqrt{7})(6\sqrt{7})\\\\A = 4\sqrt{9}+12\sqrt{21}+12\sqrt{21}+36\sqrt{49}\\\\A = 4(3)+24\sqrt{21}+36(7)\\ \\A = 12+24\sqrt{21}+252\\\\A = 264+24\sqrt{21}[/tex]
Hence the area of the square is (264+24√21) in²
ILL MARK BRAINLIST !! SHOW WORK
Answer: Here is your answer dude
-7x+4y+9-4x=-7-5-5(-x-3y)
Answer:
for x = −11y/16+ 21/16
for y = 16x/11 +21/11
Step-by-step explanation: