A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
1- The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
2- The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
3- The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
4- The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
5- The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
A. Cluster Sampling
B. Stratified Sampling
C. Systematic Sampling
D. Convenience Sampling
E. Simple Random Sampling

Answer:

a) 360 mice

b) 364 mice

Step-by-step explanation:

Assume :

A = number of infected mice , B = number of non-infected mice

P( infected mice overcoming infection ) = 70% = 0.7

P ( Infected mice not overcoming infection ) = 1 - 0.7 = 0.3

P( mice becoming infected ) = 40% = 0.4

P ( mice not becoming infected ) = 1 - 0.4 = 0.6

Number of infected mice = 400

Number of non-infected mice = 1000 - 400 = 600

step 1 ; express the probabilities in matrix form

[tex]P = \left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]

[tex]X = \left[\begin{array}{ccc}400\\600\\\end{array}\right][/tex]

step 2 : multiply the matrix above to determine the number of mice that will be infected

a) For next week

PX = [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex]

i.e. 360 mice will get infected next week

next 2 week = P ( PX )

= [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]  * [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]

b) In 3 weeks time

P ( P(PX) = [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]  * [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]  

               = [tex]\left[\begin{array}{ccc}363.6\\636.4\\\end{array}\right][/tex]

i.e.  364 mice will get infected in 3 weeks time

Answer:

1

Step-by-step explanation:

The average rate of change is the gradient _

Gradient = Rise / Run = (y2 - y1) / (x2 - x1)

From the table ;

x2 = 4 ; x1 = - 1 ; y2 = 5 ; y1 = 0

Gradient = (y2 - y1) / (x2 - x1) = (5-0) / (4 - - 1) = 5/5 = 1

Answer:

-4

Step-by-step explanation:

Let say other number is 'x'

Equation:-

4(2 + x) = -8

8 + 4x = -8

4x = - 16

x = - 16/4

x = - 4

Answer:

1/25

Step-by-step explanation:

P of both answers are correct =

P first question is answered correct and P second question is answered correct

in probability,  and = multiplication

P first question is answered correct =1 correct answer/5 possible answers =1/5

P second question is answered correct = 1/5

P of both answers are correct = (1/5) · (1/5) = 1/25

Answer:

7 × 5 :2 it is the answer ,i love you

Answer and Step-by-step explanation:

Simply solve for x (very easy to do).

4x + 9 = 41

Subtract 9 from both sides of the equation.

4x = 32

Divide both sides of the equation by 4.

x = 8

x is equal to 8.

#teamtrees #PAW (Plant And Water)

Answer:

y = 1/2 x + 9

Step-by-step explanation:

y = 1/2 x + b

4 = (1/2)(-10) + b

4 = -5 + b

b = 9

Work Shown:

4(x+2) + 6x

4x+8 + 6x

(4x+6x) + 8

10x+8

3 hour 30 minutes : 36 minutes

1 hour = 60 minutes

3 hour = 3×60 minutes = 180 minutes

3hour 30 minutes = 180 minutes + 30 minutes

                               = 210 minutes

210 minutes : 60 minutes

3 hours 30 minutes : 60 minutes = 6:2

Answer:

c = (ef-ab)/d

Step-by-step explanation:

ab+cd = ef

Subtract ab from each side

ab+cd -ab = ef-ab

cd = ef-ab

Divide by d

cd /d =(ef-ab)/d

c = (ef-ab)/d

Answer:

b+23≥-276

b≥-276-23

b≥-299

Step-by-step explanation:

hope this is helpful

Answer:

10.125

Step-by-step explanation:

Given the data :

28,45,12,34,36,45,19,20

The mean absolute deviation of the data is :

Σ|x - mean| / n

n = number of values = 8

Mean = Σx / n = 239 / 8

Mean = 29.875

Take the sum of the absolute value if the difference between each data value and the mean, then divide by the data size

Using a mean absolute deviation calculator ;

Mean absolute deviation = Σ|x - mean| / n = 10.125

Answer:

(2x + 35)/3

Step-by-step explanation:

f(2x + 3) = 3x - 8

= 3(2x)/2 - 8

= 3(2x + 3 - 3)/2 - 8

= 3(2x + 3)/2 - 3(3)/2 - 8

= ( 3(2x + 3) - 25)/2

Therefore, f(x) = (3x - 25)/2

Let f(x) = (3x - 25)/2 = y

Therefore,

x = (2y + 35)/3 = f(y)

Hence,

f-¹(x) = f(y) = (2y + 35)/3

Just by merely replacing y,

f-¹(x) = (2x + 35)/3

Answer:

Step-by-step explanation:

[tex]let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\[/tex]

lets assume that f(x) is a line, so f(x)=mx+b

[tex]f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8[/tex]

the follow equation system results:

[tex]2m=3 \\ 3m+b=-8[/tex]

[tex]m=\frac{3}{2}\\\\b=-\frac{25}{2}[/tex]

finally:

[tex]y=f(x)=\frac{3}{2}x-\frac{25}{2}[/tex]

now is time to calculate the inverse function:

[tex]y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}[/tex]

so

[tex]f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}[/tex]

Answer:

(c) 4

Step-by-step explanation:

Given

The piecewise function

Required

The value in f(x) domain

The domain of f(x) is:

[tex]-6 < x \le 0[/tex] and [tex]0 < x \le 4[/tex]

Combine both inequalities:

[tex]-6 < x \le 4[/tex]

List the values of the inequality

[tex]-6 < x \le 4 = \{-5,-4,-3,-2,-1,0,1,2,3,4\}[/tex]

From the list of given options

Only 4 is among the domain

Others are not

Answer:

Step-by-step explanation:

BC=[tex]\sqrt{5^2+5^2}[/tex]

x   =[tex]\sqrt{50}[/tex]

x   = 5[tex]\sqrt{2}[/tex]

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

Step-by-step explanation:

BC=\sqrt{5^2+5^2}52+52

x   =\sqrt{50}50

x   = 5\sqrt{2}2

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

Answer:

55

Step-by-step explanation:

all of the angles in a triangle ALWAYS add up to 180 degrees.

do the math.

Answer:

[tex]A\approx 159.6[/tex]

Step-by-step explanation:

1. Approach

To solve this problem, divide the given figure up into two smaller figures, a rectangle and a semi-circle. Find the area of each figure and add up the values to find the total area. Remember the formula to find the area of a rectangle is as follows ([tex]A=(length)(width)[/tex]). The formula to find the area of a circle is the following, ([tex]A=(\pi)(r^2)[/tex]).

2. Find the area of the rectangle

The radius is the measurement in a circle from the center of a circle to any point on the circle's circumference (outer edge). The diameter is a line going through a circle connecting two opposite edges on a circle and passing through the center of a circle. By its definition, the diameter is always twice the radius of a circle.

As one can see in the rectangle, the side of the rectangle is made of the diameter of the circle. Since the diameter of a circle is twice the radius, one must multiply the radius by (2), then multiply that value by the length of the rectangle to find the area of the rectangle,

[tex]A=(length)(width)\\[/tex]

Substitute,

[tex]A_r=(length)(2(radius))\\A_r=(14)(2(5))[/tex]

Simplify,

[tex]A_r=(14)(2(5))\\A_r=(14)(10)\\A_r=140[/tex]

3. Find the area of the semi-cricle

Now one has to find the area of the semi-circle. Since a semi-circle is half of a circle, one must divide the formula to find the area of a circle by (2) in order to find the area of a semi-circle. Remember parameter (r) represents the radius, and ([tex]\pi[/tex]) represents the numerical value (3.1415...)

[tex]A=\frac{(\pi)(r^2)}{2}[/tex]

Substitute,

[tex]A_s=\frac{(\pi)(5^2)}{2}[/tex]

Simplify,

[tex]A_s=\frac{(\pi)(5^2)}{2}\\A_s=\frac{(\pi)(25)}{2}\\A_s=12.5\frac{(\pi)}{2}\\A_s\approx19.635[/tex]

4. Find the total area

To find the total area of the figure, one must add up the two components, add the area of the rectangle to the area of the semi-circle,

[tex]A=A_r+A_s\\[/tex]

Substitute,

[tex]A=140+19.635[/tex]

Simplify,

[tex]A=159.635[/tex]

[tex]A\approx 159.6[/tex]

Answer:

[tex](5x - 4) \degree = (2x + 14)\degree \\ 3x = 18\\ x = 6[/tex]

Answer:

I believe that the answer is 80X (or C)

Step-by-step explanation:

it looks like it is just under a right angle so i believe that it would be 80X

Answer:

y=6x

Step-by-step explanation:

Answer:

1 and 1/6 cups more

Step-by-step explanation:

1/3 cup sugar

*1 2/4 cups flour = 6/4 cups flour

*assuming it’s 1 and 2/4 and not 12/4 =3

6/4 - 1/3 = (18-4)/ 12 = 14/ 12 = 1 and 1/6

Answer:

D

Step-by-step explanation:

The figures are the same just flipped. We can tell AD=NM ON=AB, BC=OP. Thus DC =MP

DC has the length of 6 and because MP is congruent to DC it also has 6.

Answer:

ASA

Step-by-step explanation:

they share the side in the middle (reflexive property) and have two congruent angles

Answer:

Point a

negative means on a number line to the left side

Step-by-step explanation:

Answer:

dang good luck

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Find the common ratio by dividing one of the numbers in the sequence by the previous one:

480/768

= 0.625

Convert this to a fraction:

0.625

= 5/8

So, the common ratio is 5/8

9514 1404 393

Answer:

  5x +2y = 20

Step-by-step explanation:

Suppose 'a' is the x-intercept of the line.

Then the slope is given by the slope formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (0 -5)/(a -2)

And the y-intercept is ...

  b = y -mx = 5 -(-5/(a-2))(2) = 5 +10/(a -2)

The area of the triangle is half the product of 'a' and 'b', so is ...

  A = 1/2ab

  A = 1/2(a)(5 +10/(a -2)) = 2.5a +5a/(a-2)

The area is minimized when the derivative of this is zero.

  A' = 2.5 -10/(a -2)^2 = 0

Solving for 'a' gives ...

  (a -2)^2 = 10/2.5 = 4

  a = 2 + 2 = 4 . . . . . . . . . . . x-intercept

  b = 5 +10/(4 -2) = 10 . . . . . y-intercept

  m = -5/(4 -2) = -5/2 . . . . . . slope

An equation of the line is ...

  y = -5/2x +10 . . . . . slope-intercept form

  5x +2y = 20 . . . . . standard form

__

You may have noticed that the x-and y-intercepts are double the x- and y-values of the given point. That is, the given point is the midpoint of the hypotenuse of the triangle with minimum area. That is the general solution of this sort of problem.

Answer:

4 units

Step-by-step explanation:

P of a square is P =4s

A of a square is A = s^2

4s = s^2

Divide each side by s

4s/s = s^2/s

4 =s

Answer:

C

Step-by-step explanation:

8×26×6=1200 cubic centimeters

hence, C is the closest

Answer:

900,900 outcomes are possible.

Step-by-step explanation:

Arrangements with repetition:

The number of possible arrangements of n elements, considered that they are divided in classes of [tex]n_1,n_2,...,n_n[/tex] elements, is given by:

[tex]A = \frac{n!}{n_1!n_2!...n_n!}[/tex]

A dancing competition has 13 competitors

This means that [tex]n = 13[/tex]

Four are American, two are Mexicans, four are Russians and three are Italians.

This means that [tex]n_1 = 4, n_2 = 2, n_3 = 4, n_4 = 3[/tex]

How many outcomes are possible?

[tex]A = \frac{13!}{4!2!4!3!} = 900900[/tex]

900,900 outcomes are possible.