There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π) Area of a circle = πr2 0.02 bacteria per square millimeter 0.42 bacteria per square millimeter 2.39 bacteria per square millimeter 52.5 bacteria per square millimeter

Answers

Answer 1

Answer:

The population density is 0.418 bacteria per mm².

What is Area of Circle?

A circle's area is the area that it takes up in a two-dimensional plane.

The formula for area of circle is, A = πr², where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.

Given:

Radius= 40 mm

So, Area of petri dish = πr²

= 3.14x(40 mm)²

= 3.14 x 1600 mm²

= 5024 mm²

and, Population Density

= 2100 / 5024

= 0.418 bacteria per mm²

Hence, the population density is 0.418 bacteria per mm².

Learn more about area of circle here:

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Answer 2

Answer: Population Density = # bacteria/area

Area = πr^2
= 3.14•(40 mm)^2
= 3.14•1600 mm^2
= 5024 mm^2

Pop Density = 2100 / 5024
= 0.418 bacteria per mm^2

The answer is 0.42 bacteria per square mm

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A solid metal sphere of radius 32cm is melted down and recast to make 64 identical small spheres.what will be the radius of each small sphere?

Answers

$V_1=(4)/(3)\pi R^3\n\nR=32cm\n\nV_1=(4)/(3)\pi\cdot32^3=(131072)/(3)\pi\ (cm^3)\n\nV_2=V_1:64\n\nV_2=(131072)/(64)\pi:64=(131072)/(3)\pi\cdot(1)/(64)=(2048)/(3)\pi\ (cm^3)\n\nr=?\n\nV_2=(4)/(3)\pi r^3$

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Which logarithmic function has x = 5 as its vertical asymptote and (6, 0) as the x-intercept? (x is the variable.). The logarithmic function is f(x) = log ?

Answers

Answer: f ( x ) = log ( x - 5 )

Explanation:

1) Take g(x) = log (x) as the parent function

2) The horizontal asymptote of g(x) is x = 0, and the y-intercept is (1,0).

3) Then, translating the asymptote to x = 5, and the y-intercept to (6,0), means that the graph of the parent function is being shifted 5 units to the right.

4) The rule is that the translation of the function g(x) a constant value to the right, say it is k, results in the function f(x) = g(x - k).

5) Therefore, the logarithmic function searched is f(x) = g(x - 5) = log (x - 5), and that is the answer.

6) You can prove that log (x - 5) meets the two conditions:

i) $\lim_(x \to \n5+) log(x-5) = - \infty$ , which means x = 5 is a vertical asymptote

ii) f(6) = log (6 - 5) = log (1) = 0 ⇒ point (6,0) is the x-intercept

The parent function:
f ( x ) = log x
Domain of a new function: x ∈ ( 5, +∞ )
Answer: f ( x ) = log ( x - 5 )

Solve and get brainliest!!
please be sure of your answer!!!!

Answers

Answer:

hope this helps youuuuu

4x2 + 25y2
factor the following

Answers

Answer:

see explanation

Step-by-step explanation:

This polynomial is irreducible, that is cannot be factored.

4x² + 25y² ← is a prime polynomial

Answer:

1, the polynomial itself

Step-by-step explanation:

This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)

Jen wants to tile the floor of her kitchen . The floor is recrangular and measures 12 feet by 8 feet. If it costs $2.50 per square foot for the materials, what is the total cost of the materials, what is the total cost of the materials for tiling the kitchen floor?

Answers

Given:
rectangular floor
length = 12 feet
width = 8 feet

Area = 12 ft * 8 ft = 96 ft²

Cost of $2.50 per square foot

96 ft² * $2.50 = $240

The total cost of the materials for tiling the kitchen floor is $240.

we know that

The area of the floor of the kitchen is equal to the area of a rectangle

Step 1

Find the area of the kitchen

we have

$A=12*8\n A=96 ft^(2)$

Step 2

Find the cost

we know that

the cost is $ $2.50$ per square foot

by proportion

$(2.50)/(1) =(x)/(96) \n\n x= 2.50*96\n x=240$

therefore

the answer is

the total cost of the materials for tiling the kitchen floor is $ $240$

There were 45 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 3/5 of the remaining runners dropped out. How many runners finished the race?

Answers

45/3=15 45-15=30 30/5=6 3x6=18 30-18=12 the answer is 12

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