Laws have been instituted in Florida to help save the manatee. To establish the number of manatees in Florida, manatees were tagged. A new sample was taken later, and among the manatees in the sample, were tagged. Approximate the number of manatees in Florida. brainly

Answers

Answer 1

Answer:

It think this should be the complete question: Laws have been instituted in Florida to help save the manatee.To establish the number of manatees in Florida, 150 manatees were tagged. A new sample was taken later, and among the 40 manatees in the sample, 3 were tagged. Approximate the number of manatees in Florida.

The approximate number of manatees in Florida is 2,000

Step-by-step explanation:

To solve this problem, we will use the formula

N= (C*R)/M

Where N is the toal estimated population

C is the total first capture

R is the total recapture after the first

M is the total tagged from recapture

Thus, we have:

N = (150*40)/3

N = 6000/3

N= 2,000

Answer 2

Answer:

So, the approximate manatee is $2000$ .

Ratio and Proportion:

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of $a:b$ , then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science. the proportion is represented by,

$(a)/(b)=(c)/(d)$ .

Let us assume $x$ represents the unknown observed manatee, which is actually total manatees so the proportion is, $(40)/(3)=(x)/(150)$ .

Now, cross multiplying the given proportion as,

$3x=40* 150\nx=(40* 150)/(3) \nx=2000$

Learn more about the topic Proportion: brainly.com/question/24320792

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Jay simplify the expression 3x( 3+12÷3)-4 over his first step he added 3+12 to get 15 what was jays error? Find the correct answer

Answers

Hello there!

To simplify this expression, you must follow PEMDAS.

3x(3+12÷3) parentheses first
3x(3+4) do the division
3x(7) addition inside of parentheses
21x multiplication

This means that Jay is incorrect in doing addition first.

I really hope this helps!
Best wishes :)

distribute 3x through all the numbers in () then solve for x and you get 21x-4

Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.B: Compare your answer in part A to a real soda can, which has a volume of 256cm^3, a radius of 2.8 cm, and a height of 10.7 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface area of the top and bottom are now twice their values in part A.

B: New radius=?

New height=?

Answers

Answer:

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

Step-by-step explanation:

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

$V=\pi r^2h=256$

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

$S=2\pi rh+2\pi r^2$

To solve this, we can express h in function of r:

$V=\pi r^2h=256\n\nh=(256)/(\pi r^2)$

And replace it in the surface equation

$S=2\pi rh+2\pi r^2=2\pi r((256)/(\pi r^2))+2\pi r^2=(512)/(r) +2\pi r^2$

To optimize the function, we derive and equal to zero

$(dS)/(dr)=512*(-1)*r^(-2)+4\pi r=0\n\n(-512)/(r^2)+4\pi r=0\n\nr^3=(512)/(4\pi) \n\nr=\sqrt[3]{(512)/(4\pi) } =\sqrt[3]{40.74 }=3.44$

The radius that minimizes the surface is r=3.44 cm.

The height is then

$h=(256)/(\pi r^2)=(256)/(\pi (3.44)^2)=6.88$

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

$S=2\pi rh+2*(2\pi r^2)=2\pi rh+4\pi r^2$

We derive and equal to zero

$(dS)/(dr)=512*(-1)*r^(-2)+8\pi r=0\n\n(-512)/(r^2)+8\pi r=0\n\nr^3=(512)/(8\pi) \n\nr=\sqrt[3]{(512)/(8\pi)}=\sqrt[3]{20.37}=2.73$

The radius that minimizes the real surface is r=2.73 cm.

The height is then

$h=(256)/(\pi r^2)=(256)/(\pi (2.73)^2)=10.92$

The height that minimizes the real surface is h=10.92 cm.

Final answer:

The minimal surface area for a cylindrical can of 256cm^3 is achieved with radius 3.03 cm and height 8.9 cm under uniform thickness, and radius 3.383 cm and height 7.14 cm with double thickness at top and bottom. Real cans deviate slightly from these dimensions possibly due to practicality.

Explanation:

For a cylinder with given volume, the surface area A, radius r, and height h are related by the formula A = 2πrh + 2πr^2 (if the thickness is uniform) or A = 3πrh + 2πr^2 (if the top and bottom are double thickness). By taking the derivative of A w.r.t r and setting it to zero, we can find the optimal values that minimize A.

For a volume of 256 cm^3, this gives us r = 3.03 cm and h = 8.9 cm with uniform thickness, and r = 3.383 cm and h = 7.14 cm with double thickness at the top and bottom. Comparing these optimal dimensions to a real soda can (r = 2.8 cm, h = 10.7 cm), we see that the real can has similar but not exactly optimal dimensions. This may be due to practical considerations like stability and ease of holding the can.

Learn more about Optimal Dimensions here:

brainly.com/question/32818645

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7/9 and 5/7 does this ratio form a proprtion? yes or no?

Answers

Proportion says that two ratios (or fractions) are equal.

7/9 and 5/7 is not a proportion

A proportion is when the ratios are the same.

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A disease has hit a city. The percentage of the population infected t days after the disease arrives is approximated by p(t)equals7 t e Superscript negative t divided by 13 for 0less than or equalstless than or equals39. After how many days is the percentage of infected people a maximum? What is the maximum percent of the population infected?

Answers

Answer:

t = 13 days

p(13) = 33.47%

Step-by-step explanation:

p(t) is the percentage of the population infected:

p(t) = 7*t*e∧(-t / 13)

where 0 ≤ t ≤ 39 days

we can apply p'(t) = 0 to get number of days where the percentage of infected people is maximum:

p'(t) = (7*t*e∧(-t / 13))' = 7*(t*e∧(-t / 13))' = 7*((t)'*e∧(-t / 13)+t*(e∧(-t / 13)') = 0

⇒ 7*(1*e∧(-t / 13)+t*e∧(-t / 13)*(-1 / 13)) = 7*e∧(-t / 13)*(1 - (t / 13)) = 0

∴ 1 - (t / 13) = 0 ⇒ t = 13 days

then we get the maximum percent of the population infected as follows

p(13) = 7*13*e∧(-13 / 13)

⇒ p(13) = 33.47%

Sarah practices her violin 45 minutes each practice session. She sets a goal to practice 6,075 minutes.How many practice sessions will it take for Sarah to reach her goal?

Answers

Answer:

135 times

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

Solve for n+4 + n/6=16

Answers

Answer:

n = 10.286 aprox.

Step-by-step explanation:

n+4 + n/6 = 16

n/6 = 16 - 4 - n

n = 6(12-n)

n = 6*12 + 6*-n

n = 72 - 6n

n + 6n = 72

7n = 72

n = 72/7

n = 10.286 aprox.

verify:

10.286 + 4 + (10.286/6) = 16

14.286 + 1.714 = 16

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