Answer:
[tex]P(t) = (2t + 50)^2[/tex]
Step-by-step explanation:
A certain population increases at a rate proportional to the square root of the population.
This means that the population can be described by the following differential equation:
[tex]\frac{dP}{dt} = r\sqrt{P}[/tex]
In which r is the growth rate.
Solving by separation of variables, we have that:
[tex]\frac{dP}{\sqrt{P}} = r dt[/tex]
Integrating both sides:
[tex]2\sqrt{P} = rt + K[/tex]
In which K is a random constant
[tex]\sqrt{P} = 0.5rt + K[/tex]
Finding the squares of both sides:
[tex]P(t) = (0.5rt + K)^2[/tex]
Finding the value of K
The initial population is of 2500. That is, when [tex]t = 0, P = 2500[/tex]. So
[tex]P(t) = (0.5rt + K)^2[/tex]
[tex]2500 = (0.5r(0) + K)^2[/tex]
[tex]K^2 = 2500[/tex]
[tex]K = \sqrt{2500}[/tex]
[tex]K = 50[/tex]
So
[tex]P(t) = (0.5rt + 50)^2[/tex]
Finding the value of r
Population of 3600 in 5 years(when t = 5). So
[tex]P(t) = (0.5rt + 50)^2[/tex]
[tex]3600 = (0.5r(5) + 50)^2[/tex]
[tex](2.5r + 50)^2 = 3600[/tex]
Taking the square root of both sides
[tex]\sqrt{(2.5r + 50)^2} = \sqrt{3600}[/tex]
[tex]2.5r + 50 = 60[/tex]
[tex]2.5r = 10[/tex]
[tex]r = 4[/tex]
So, the equation for the population at the end of t years is given by:
[tex]P(t) = (0.5rt + 50)^2[/tex]
[tex]P(t) = (0.5(4)t + 50)^2[/tex]
[tex]P(t) = (2t + 50)^2[/tex]
What is the implicit premise in the following argument? Because it is hard to find four-leaf clovers, I will be lucky to find one.
Answer: Either it is not hard to find four leaf clovers, or i would be lucky to find one.
Step-by-step explanation:
An assumption is any assertion or concept that is taken to be true and on which an argument or argument may be based.
From the argument is centered on the probability of finding a four leaf clover.
It is an already established fact that four leaf clovers are rear to come by so it would require a lot of luck to actually find one.
2-2(x-25) what is the answer?
Answer:
F= 2
F=-2
F=x-25
Step-by-step explanation:
Determine if the statement is true or false. Any linear system with more variables than equations cannot have a unique solution.
Answer:
True
Step-by-step explanation:
Suppose a system contains a large number of variables than equations, then there is a need to make assumptions of some values for the extra variables in order to solve the system. So, the assigning of these values can be done in several ways. Thus, the system cannot contain a unique solution.
Also, for a system of the linear equation:
[tex]AX = B[/tex] can have a unique solution if:
Augmented matrix(rank) = coefficient matrix(rank) = no. of variables.
Provided that there exist fewer equations and more variables,
Then;
coefficient matrix(rank) < no. of variables
Thus, the system cannot contain a unique solution.
This list shows the number of years that 99 U.S. Supreme Court Justices served.
0
4
6
8
13
15
18
22
26
31
1
4
6
9
13
15
19
23
26
32
1
4
6
9
14
16
19
23
27
33
2
5
7
9
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
34
3
5
7
10
15
17
20
24
29
34
3
5
8
11
15
17
20
24
30
34
3
5
8
13
15
18
21
26
30
36
4
5
8
13
15
18
21
26
31
Miguel is making a frequency table of this data. He decides to group the years in intervals of 5 beginning with 0 to 4, 5 to 9, 10 to 14 and so on. How many intervals will he need all together?
a.
5
c.
7
b.
6
d.
8
Answer:
8
Step-by-step explanation:
0
4
6
8
13
15
18
22
26
31
1
4
6
9
13
15
19
23
26
32
1
4
6
9
14
16
19
23
27
33
2
5
7
9
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
33
2
5
7
10
14
16
20
23
28
34
3
5
7
10
15
17
20
24
29
34
3
5
8
11
15
17
20
24
30
34
3
5
8
13
15
18
21
26
30
36
4
5
8
13
15
18
21
26
31
a.
5
c.
7
b.
6
d.
8
Answer:
The correct answer is:
Step-by-step explanation:
D.)8
Which of the following is not a function?
The answer is the first choice
Step-by-step explanation:
because the two goes into 4 and 5, in order for it to be a function the x value has to be used once
1 foot = 12 inches therefore 5 feet = what
Answer:
60 inches
Step-by-step explanation:
1 foot = 12 inches
5 feet = ?
5*12 = 60
[tex]1\cdot \text{foot} = 12\cdot \text{inches} \implies 5 \cdot\text{foot} =5\cdot 12 \cdot\text{inches} \implies 5 \cdot\text{foot} =60 \cdot\text{inches}[/tex]
Please help me I’m so close to passing
Answer:
314 meters
Step-by-step explanation:
The circumference of any circle is pi (3.14). To find your answer, Multiply 3.14 with 100 (as in meters) to get 314. Your answer is 314 meters.
-12 plus what equals -0.75?
PLZZ HELP THIS IS DUE IN 10 MINS
Answer:
-12 + 0.35
Step-by-step explanation:
i tried XD
Answer:
11.25
Step-by-step explanation:
-12+x= -0.75
+12 +12
x=11.25
-12+11.25= -0.75
Determine which, if any, of the given values is a solution.
8p − 16 = 40
p = 5; p = 7; p = 9
p = ?
Answer:
p – 7 = -12
The answer
P = 7
8p - 16 = 40
40 + 16 = 56
8p = 56
56 ÷ 8 = 7
According to a survey of workers,2/20 of them walk to work, 1/20 bike, 4/20 carpool,13/20 and alone. What percent of workers walk or bike to work?
HELP PLS! whoever gets it right gets brainliest!!
Answer:
(7, -4)
Step-by-step explanation:
it's the only one remotely close to the line.
Pleaseeeeeeee helppp
Failure to turn in the assignment on time will result in a loss of 5 points.
a
If you do not turn it in by Monday, January 17, 2021, at 8:00 a.m., you will receive 0 points for the assignment.
4 A store is having a 10% -off sale on all merchandise.
If Mai buys one item and saves $18, what was the original price of her purchase?
Answer:
Step-by-step explanation:
If may buys an item that, after 10% sale, costs 18 dollars
let x be original price
discount is 10%x=0.10 x
x- 0.10x=18
0.90x=18
x=18/0.90=20
x=20
What kind of transformation is it when it gets bigger? Like a small star to a bigger star.
Bananas cost $3 a bunch and apples cost $0.50 each. If b represents the number of bunches of bananas and a represents the number of apples, which of the following expressions represents the total cost?
Answer:
it's 3a+.50b
Step-by-step explanation:
17/15 - 4/5 please answer
Answer:
1/3
Step-by-step explanation:
17/15-4/5
17/15-4*3/5*3
17/15-12/15
17-12/15
5/15
1/3
The equivalent value of the fraction is A = 1/3
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first fraction be p
Let the second fraction be q
Now , A = p - q
when the value of p = 17/15
And , when the value of q = 4/5
On simplifying the equation , we get
A = 17/15 - 4/5
So , the left hand side of the equation is equated to the right hand side by the value of ( 17/15 - 4/5 )
A = ( 17/15 - 4/5 )
Taking the LCM of the denominators of the fraction , we get
A = ( 17 - 12 ) / 15
On simplifying , we get
A = 5/15
A = 1/3
Therefore , the value of A = 1/3
Hence , the fraction is A = 1/3
To learn more about fractions click :
https://brainly.com/question/29766013
#SPJ6
2) You traveled 210 miles in 3.5 hours.
How many miles will you travel per hour?
Answer:
= 56.7 miles per hour
Step-by-step explanation:
Step-by-step explanation:
To find the average speed for the entire journey, we need to find the entire distance and the total time
Entire distance = 210 miles + 130 miles = 340 miles
Total time = 3.5 hours and 2.5 hours = 6 hours
Average speed = distance/ time = 340 miles/ 6 hours
= 56.66666666666 miles per hour
Rounding to the nearest tenth
= 56.7 miles per hour
Answer:
60 miles
Step-by-step explanation:
Step 1:210=3.5
x =1
Step 2: cross multiply3.5×x= 210×1
3.5x=210
Step 3: divide both sides by the coefficient of x which is 3.53.5x/3.5=210/3.5
x=60
Answer= 60 miles
m= 12 and the y-intercept is (0, 11)
Answer:
y=12x+11
Step-by-step explanation:
using y=mx+b
m is the slope and b is the y intercept, using that you just plug in the numbers.
Can anyone give me any answers for the first 2 in each coloured section please
A yard is 3.1 meters long and 1.4 meters wide. What is the area of the yard? Group of answer choices
Answer:
The area of the yard is 4.34.
Step-by-step explanation:
a = l x w
a = 3.1 x 1.4
a = 4.34
Help I’ll mark brainliest
Answer:
ACD
Step-by-step explanation:
What is the value of the expression 9 x to the power of 2 minus 12 x plus 4 when x equal 3 ?
A.22
B.49
C.85
D.697
Answer:
22
Step-by-step explanation:
because it just is
Alex has a video game membership that costs $36 per month. Which table shows the sum of the amounts that Alex will pay for his video game membership over the next 4 months?
Answer:
$144 at the end of 4 months
Step-by-step explanation:
$36 x 4 =144
Answer:
It will be $144
Step-by-step explanation:
because you do 36 times 4 and u get $144
A 16 ft tall adult giraffe standing next to a
baby giraffe casts a 8 ft shadow. If the
baby giraffe is 6 ft tall, then how long is
its shadow?
Answer:
The shadow is 3 ft tall
Step-by-step explanation:
The older giraffe is 16 ft tall and 8 is half of 16 and 8ft is the length of the shadow so that means that half of the small girafe would be 3ft because half of 6 is 3.
Sorry if its not correct
Simplify (-32) ÷ (-4)
[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{Guide\downarrow}[/tex]
[tex]\bold{Negative}[/tex] & [tex]\bold{Negative}[/tex] =[tex]\bold{Positive}[/tex]
[tex]\bold{Positive}[/tex] & [tex]\bold{Negative}[/tex] = [tex]\bold{Negative}[/tex]
[tex]\bold{Positive}[/tex] & [tex]\bold{Positive}[/tex] = [tex]\bold{Positive}[/tex]
[tex]\bold{Negative}[/tex] & [tex]\bold{Positive}[/tex] = [tex]\bold{Negative}[/tex]
[tex]\bold{(-32)\div(-4)}[/tex]
[tex]\bold{=32\div4}[/tex]
[tex]\bold{=8}[/tex]
[tex]\boxed{\boxed{\bold{Answer: 8}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
4
Step-by-step explanation:
Since both of these numbers are negative, it means that the answer will be negative, since 2 negatives make a positive, since now you know that, you can easily do 32/8 which is 4.
-32/ -8 = 4
Check....
-8 * 4 = -32
-32 / 4 = -8
When there is a negative number and a positive number being multiplied or divided by, it will always result in a negative number.
Hope this helped!
Have a supercalifragilisticexpialidocious day!
HELP! whoever gets it right gets brainliest!!
The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorter leg. Find the side lengths of the triangle.
a. Find the length of the shorter side
b. Find the length of the longer side
c. Find the length of the hypotenuse
d. Find the side lengths of the triangle.
Answer: Shorter side = 10 feet
Longer side = 24 feet
Hypotenuse = 26 feet
The side lengths of the triangle are 10ft, 24ft and 26ft.
Step-by-step explanation:
Let the length of the shorter leg be x.
The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. This will be: = 2x + 4
The length of the hypotenuse is 6ft more than twice the length of the shorter leg. This will be: = 2x + 6
Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:
x² + (2x + 4)² = (2x + 6)²
x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)
x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36
x² + 4x² + 16x + 16 = 4x² + 24x + 36
5x² + 16x + 16 = 4x² + 24x + 36
Collect like terms
5x² - 4x² + 16x - 24x + 16 - 36 = 0
x² - 8x - 20 = 0
x² - 10x + 2x - 20 = 0
x(x - 10) + 2(x - 10) = 0
Therefore, x - 10 = 0
x = 10
a. length of the shorter side = 10ft
b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft
c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft
d. The side lengths of the triangle are 10ft, 24ft and 26ft.
Answer:
egg
Step-by-step explanation:
yes
5 A contractor is laying out the sides of a
rectangular porch. She knows that the porch will
form a rectangle if it can be broken up into two
right triangles, as shown below.
The lengths of the two longer sides of the porch
are 24 feet and the lengths of the two shorter
sides are 17 feet. Enter the length of the diagonal
of the porch in feet, rounded to the nearest tenth.
please hurry!!!
For the class picnic, 25 liters of punch were purchased. 6 liters were left over. How many gallons of punch were used at the picnic? (1 liter is approximately 0.26 gallons)
Answer:
Gallons of punch used = 4.94 gallons
Step-by-step explanation:
Given that:
Liters of punch purchased = 25 liters
Liters of punch left over = 6 liters
Liters of punch used = 25 - 6 = 19 liters
According to the given statement;
1 liter = 0.26 gallons
19 liters = 0.26*19 gallons
19 liters = 4.94 gallons
Hence,
Gallons of punch used = 4.94 gallons
Does anyone know how to do this, I’m failing math and I need this to boost my grade. Someone help please
Answer:
Step-by-step explanation:
Hey, I'm not sure if I am right, but I hope it can create a spark or something.
8. Find x
10x - 1 = 14x - 37 Combine like terms
+37 +37
10x + 36 = 14x Combine like terms
-10x -10x
36 = 4x Divide to isolate x
36 = 4x
4 4
9 = x
You can also do this method with the others.
PS: I am still not sure if this is the right method, lol. I just really want to help.