Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure.

Which of the following is the most appropriate method to use for such an estimate?

I need the answer and the explanation, please.

The most appropriate method to use for the estimate of population of crabs longer   than 35 cm

1 A one sample z interval for the population proportion

Hence option (1) is correct.

Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters.

The biologists will select a random sample of crabs to measure

we have to determine that  of the following is the most appropriate method to use for such an estimate

1. A one sample z interval for the population proportion

2. A one sample z interval for the sample proportion

3. A two sample z interval for the population  proportion

4. A two sample z interval for a difference between population proportion

5. A two sample z interval for a difference between sample proportion

Z interval is a type of confidence interval which tells us about  

a range where we can expect a particular mean or proportion to fall.  

It can be calculated from a known standard deviation.

A confidence interval is a range of plausible values in which the true population parameter  is believed to lie.

Hence option (1) is correct.

For more information please refer to the link below

link

A.one sample z-confidence interval for the population proportion

Step-by-step explanation:

-A confidence interval is a range of values in which the true population mean is believed to lie.

-Given just one sample, the one sample z-confidence interval for the population proportion is appropriate and is defined as:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.