A petri dish is a small, shallow dish of thin glass or plastic, used especially for cultures in bacteriology. A 2-inch-radius petri dish, containing nutrients upon which bacteria can multiply, is smeared with a uniform suspension of bacteria. Subsequently, spots indicating colonies of bacteria appear. The distance of the center of the first spot to appear from the center of the petri dish is a variable with density curve y= x/2 for 0 < x <2 and y=0 otherwise.

a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number x between 0 and 2 equals x2/4.
c. What percentage of the time is the distance of the center of the first spot to appear from the center of the petri dish

1. at most 1 inch?
2. between 0.25 inch and 1.5 inches?
3. more than 0.75 inch?

Answer:

a) attached below

b) Area = 1/2 ( base ) (height )

        = 1/2 ( x ) ( x/2)

        = x^2 / 4

C) i)25%     ii) 54.69%      iii) 85.94%

Step-by-step explanation:

Given density curve y = x/2  for 0 < x < 2  and y = 0

a) Graph the density curve of this variable

attached below

b) show that the area under the density curve to the left of any number x between 0 and 2 equals x^2/4

base of triangle = x

height = x/2

Hence to show the area under the density curve is equal to x^2/4 we will calculate the area to the left

Area = 1/2 ( base ) (height )

        = 1/2 ( x ) ( x/2)

        = x^2 / 4

c) Determine the percentage of the time of the distance of the center of the first spot to appear from the center of the petri dish

i) At most 1 inch

(area to the left of 1 ) = 1^2 / 4

= 1/4 = 0.25 ≈  25%

ii)   between 0.25 inch and 1.5 inches?

( area between 0.25 and 1.5 ) = ( area to the left of 1.5 ) - ( Area to the left of 0.25 )

= (1.5^2 / 4 )- ( 0.25^2 / 4 )

= 0.5469 = 54.69%

iii) more than 0.75 inch

( Area to the right of 0.75 ) = 1 - (0.75^ / 4)

                                            = 0.8594 = 85.94 %

What is the correct order of operations? *
PEMDAS
O MDPASE
ASPEMD
PASEMD

HELPPPPPPP

what is the order from least to greatest(38%,3/8,0.4,1/3,41%,0.33)

Pls help it’s about angles

helppppppppppppppppppppp

A relation R on a set A is defined to be irreflexive if, and only if, for every x ∈ A, x R x; asymmetric if, and only if, for every x, y ∈ A if x R y then y R x; intransitive if, and only if, for every x, y, z ∈ A, if x R y and y R z then x R z. Let A = {0, 1, 2, 3}, and define a relation R2 on A as follows. R2 = (0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) Is R2 irreflexive, asymmetric, intransitive, or none of these? (Select all that apply.) R2 is irreflexive. R2 is asymmetric. R2 is intransitive. R2 is neither irreflexive, asymmetric, nor intransitive.

Please Help i give brainies

.
* 6 cupcakes for $14
* 12 cupcakes for $30
* 24 cupcakes for $54
The unit price for the 6 cupcakes is
The unit price for the 12 cupcakes is
The unit price for the 24 cupcakes is
The lowest unit price is for

Given APQR and ASTU, what is mZQ PLEASE HELP

Jackie says that 200 ÷ 18 = 25. Is Jackie correct? Explain.

Which mode of transportation did you choose? Why?

Given: binom(119, 0.57)
What is the Expected Value?

Are Brainy tutors still a thing if not I’m gonna fail algebra

Graham wrote the system of equations. 67 – 8y = -16 y = x+8 What is true about the system of equations that Graham wrote? It has no solution. B It has 1 solution It has 2 solutions It has infinitely many solutions​

What is the value of x in the figure below?

if the price of a sweater is marked down from $80 to $68, what is the percent markdown?

HELLPP DUE BY 1pm PACIFIC HELLPP ASAP

Which expression is equivalent to -6(3x-3)?
O 2x+4
2
-3X-6
O 3 6
-18.X+ 12
- 15x+4

3^x=2 solve for x without using calculating utility?

Which of the following sets represents continuous data?
A. {1, 2, 3, ...)
B. (4,7)
C. {5, 13, 16, 20, 30)
D. {..., -9, -6, -3}

After a birthday only 1/4 cake ramains what fraction is equivalent 1/4

Can someone help me!!!!
Also dont put the answers: 201.06 or 131.1 bc I've tried those. :)

In a recent survey in a Statistics class, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 88% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays? (Hint: the above problem is based on conditional probability concept and the Bayes theorem)

Find the ratio a : b , if it is given that ...
5a +3b =6b

PLEASE HELP ME!!

Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ.

n = 290, p = 1/4

Anyone can help with this

A number is added to 12, and the result divided by 2. the answer is the same as you get by subtracting the number from 4. what is the number?​

Please help me I always sleep late doing homework and I do not want to today begging ya. You don’t have to do 1,2,3

HELLPPPPPPPPPPPPPPppppppppppp

work out 4/5 - 1/5
work out 9/11 +5/11
work out 3/4 + 1/8

Surface area and volume