In a lab, a colony of 100 bacteria is placed on a petri dish. The population triples every hour.

1. How would you estimate the population of bacteria in. Make the minutes into a decimal and tell me what to substitute. Be specific on what you would do

a. 90 minutes?

b. 30 minutes?

2. How would you estimate the number of hours it would take the population to grow to 1,000 bacteria. Be specific on what you would do.

Reply as answers 1a, 1b, 2.

Answer:

75.36

Step-by-step explanation:

3.14(pi) x 24(diameter) = 75.36(circumference)

Answer:

Step-by-step explanation:

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))^3

= {3(cosπ/6 + isinπ/6)}^3

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

The right answer is 27i

Answer:

is there a picture?

Step-by-step explanation:

Answer:

Volume of rectangular prism:

V1 = base x height = 4 x 6 x 12 = 288 ft3

Volume of triangular prism:

V2 = base x height = 4 x (6/2) x 6 =  72 ft3

Volume of composite prism:

V= V1 + V2 = 288 + 72 = 360 ft3

Hope this helps!

:)

Answer:

When you change the inequality as the formula of y>ax+b, it is over the boundary line. While the formula is y<ax+b, it is below the boundary line. So we can get the answer is D.

Step-by-step explanation:

Answer:

dependent and 2/7

Step-by-step explanation:

dependent because you didn't replace it.

1/2 times 4/7 which is 4/14 which equals to 2/7

Answer:

C. 4(x-3)

Step-by-step explanation:

Answer:

y = -0.5x + 100

Step-by-step explanation:

Im not really sure what i was supposed to answer but i hope it helped.

Answer:

A.       y = −0.5x + 100  

Step-by-step explanation:

Answer: $3.6

Step-by-step explanation:

Hi, to answer this question, first we have to calculate watt hours per day:

200 wph x 4 hours = 800 watt hours

Now, we have to convert the watt-hours to kilowatt hours:

800 wh /1000 =0.8 kwh

Since he watches TV 30 days per month:

0.8 kw x 30 days = 24 kwh

Finally we have to multiply that result by the price per kilowatt hour (15 cents)

24 kwh x 15 cents = 360 cents

Converting to dollars:

360/ 100 = $3.6

Lee’s TV cost 3.6 dollars to operate for a month of 30 days

Answer:

9

Step-by-step explanation:

13.5 / 1.5 = 9

Answer:

[tex] \boxed{Speed = 0.15 \: miles \: per \: minute} [/tex]

Given:

Distance travelled = 13.5 miles

Time taken = 1.5 hours = 1.5 × 60 = 90 minutes

Step-by-step explanation:

[tex]Speed = \frac{Distance \: travelled}{Time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13.5}{90} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.15 \: miles \: per \: minute[/tex]

Answer:

The correct answer is A, Point P

Step-by-step explanation:

since the additive inverse of 2 is -2 because -2 + 2 = 0 the correct choice must be choice A, Point P.

Answer:

12π

Step-by-step explanation:

Volume of the cone is πr^2 * h / 3

r = 3

h = 4

9π * 4 / 3 = 12π

Answer: 37.6991118

Step-by-step explanation:

Answer:

Its addition I think so the answer would we 16.7399km for both trials

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer: THE ANSWER IS c

Step-by-step explanation:

Answer:

61 3/5

Step-by-step explanation:

we realize that 8 4/5 can be written as [8 + (4/5)]

hence 7 x 8 4/5

= 7 x [8 + (4/5)]

= 7 [8 + (4/5)]   (use the distributive property, see attached for reference)

= 7(8) + 7(4/5)

= 56 + 28/5  (convert 28/5 into mixed fraction)

= 56 + 5 3/5

= 61 3/5 (answer)

Answer:

Step-by-step explanation:

length² + width² = diagonal²

24² + width² = 40²

576 + width² = 1600

width² = 1600 - 576

width² = 1024

width = √1024 = √32*32

width = 32"

Width of the TV is more than 30"

Answer:

32

Step-by-step explanation:

First off, Bruh, 30" is not prime prime. That's 30 inches.

The base of the TV is 32. This is because A^2+B^2=C^2. 24 is A, 40 is C, and the base is B.

So that means that is we take 24^2 and the base^2, we should get 40^2. 40^2 is 1600. 24 squared is 576. So if we take the base and square it and add 576, we should get 1600. Or we could just take 1600 and subtract 576.

1600-576=1024.

So now, the root of 1024 is the base. Which is 32. Hope that helped.

Answer:

M=25-3D

Step-by-step explanation:

Daniel starts with 25 dollars and spends three dollars per day for a d number of days. So the amount of money in his wallet should be equal to the starting number of dollars minus the amount of money he spends. Therefore we get the equation M=25-3D, where M is the amount of money is his wallet, and D us the number of days he buys a drink and chips.

Answer:

You distribute the 2 to the m=2m

Then you distribute the 2 to the 11 which gives you 22

ANSWER: 2m+22

Answer:

28 min

Step-by-step explanation:

The word combined signals to addition.

if we are adding 12+16, add the ones place first and you will get 8

There are 2 tens in the tens place

1+1=2

Put them together and it is 28 min

Hope this helped :)

Answer:

28

Step-by-step explanation:

because 12 + 16 = 28

Answer:

EK = 1.

Step-by-step explanation:

Here we have KP = PE (tangents from outside the circle)

Therefore, 2KP = PE + 1 = KP + 1

Hence, 2KP - KP = 1 or KP = 1 = PE

Since KE is the base of triangle KPE, where  ∡ KPE = 60, and KP = PE, we have an isosceles triangle such that ∡PKE = ∡PEK

Hence, in ΔKPE, ∡KPE + ∡PKE + ∡PEK  = 180

Therefore, 60° + ∡PKE + ∡PEK  = 180

Hence, ∡PKE + ∡PEK  = 180° - 60° = 120°

Because ∡PKE = ∡PEK, (base angles of isosceles triangle), we have;

∡PKE + ∡PEK = 2·∡PEK = 120° which gives

∡PEK = 60° = ∡PKE

Therefore, ∡KPE = ∡PEK = ∡PKE = 60°

Hence, ΔKPE is an equilateral triangle and KP = PE = EK = 1

EK = 1.

Answer:

Step-by-step explanation:

We have that the focus is at (p,0) and that the directrix is x=-p. Take the point (-p,0) of the directrix. We know that the vertex of the parabola is at the middle point ot the line segment that joins the points (p,0) and (-p,0). To get the middle piont, we take the average coordinate by coordinate. That is, the middle point is [tex](\frac{-p+p}{2}, \frac{0+0}{2}) = (0,0)[/tex]. The general formula of a parabola of vertex (h,k) that opens to the right or to the left is given by

[tex](y-k)^2 = 4p(x-h)[/tex]

Where |p| is the distance from the focus to the vertex. If the parabola opens to the right, then p>0 and p<0 otherwise. In our case, h =0=k, so we get that

[tex]y^2 = 4px[/tex]

Answer:

y^2 = 4px

Step-by-step explanation:

edg 2021

Answer:

Yes

Step-by-step explanation:

(1, -2)

y > -6x – 3

-2 > -6(1) - 3

-2 > -6 - 3

-2 > -9 Yes

Answer:

8 outcomes

Step-by-step explanation:

A coin has two possible outcomes: heads or tails.

The spinner has four possible outcomes: 1, 2, 3 or 4.

If we combine then, the number of outcomes will be the product of their number of outcomes:

2 * 4 = 8

So we will have a total of 8 outcomes:

heads, 1 / heads, 2 / heads, 3 / heads, 4 /

tails, 1 / tails, 2 / tails, 3 / tails, 4

Answer:

x=8

Step-by-step explanation:

5x+8

5x8=40

x=40

Answer:

x = 25.6

Step-by-step explanation:

1. Both angles towards the bottom equal 48 degrees, so the angle on the left (already shown) and across on the right equal 48. Add/multiply both of them

        48 * 2 = 96

Now, like triangles, figures with 4 sides add up to a certain number of degree. Four sided figures or quadrilaterals (the ”fancy” math word for it) add up to 360 degrees.

2. Adding up to 360 degrees means that all four angles have to be evenly split, you already know that the corners are 48 degrees, the bottom corners, you don’t know yet, therefore, we subtract 360 by 96 and divide the difference.

360 - 96 = 264

264/2 = 132

3. From the explanation above, you now know that the bottom corners will equal 132 degrees, therefore you will set the equation to be equal to 132 degrees.

5x + 8 = 132

5x = 128

x = 25.6

The answer is x = 25.6, I hope this explained everything, there are some theorems which make remembering these steps a lot easier, and alternative approaches you could have taken, but this is my approach.

Answer:

see below

Step-by-step explanation:

8(n + 2)(n + 4) = 1,144

FOIL

8(n^2 +2n+4n+8) = 1144

Divide each side by 8

8/8(n^2 +2n+4n+8) = 1144/8

(n^2 +2n+4n+8) = 143

Combine like terms

n^2 +6n+8 = 143

Subtract 143 from each side

n^2 +6n+8 -143= 0

Combine like terms

n^2 +6n -135 =0

Factor

What two terms multiply to -135 and add to 6

-9*15 =-135

-9+15 = 6

(n-9) (n+15) =0

Using the zero product property

n-9 =0    n+15=0

n = 9   n=-15

The length cannot be negative so n = -15 cannot be  a solution

n =9

Answer:

n = 9

Step-by-step explanation:

8(n + 2)(n + 4) = 1,144

(n + 2)(n + 4) = 143

n² + 2n + 4n + 8 = 143

n² + 6n - 135 = 0

n² + 15n - 9n - 135 = 0

n(n + 15) - 9(n + 15) = 0

(n - 9)(n + 15) = 0

n = 9, -15

since n is a length, it can not be negative

Therefore the only solution is n = 9

Answer:

whats the question i dont see the link

Step-by-step explanation:

Answer:

Height of tree =  28.2 ft (Approx)

Step-by-step explanation:

Given:

Angle from ground to top of the tree = 62°

Distance from a point to base of tree = 15 ft

Height of tree = [tex]X[/tex]

Find:

Height of tree = [tex]X[/tex]

Computation:

Using trigonometric application:

[tex]Tan\ 62 = \frac{Height\ of\ tree}{Distance\ from\ a\ point\ to\ base\ of\ tree} \\\\Using\ calculator\ , Tan62 = 1.88\\\\1.88=\frac{Height\ of\ tree}{15} \\\\Height\ of\ tree=28.2ft[/tex]

Height of tree =  28.2 ft (Approx)

Answer:

[tex]AC=13.5[/tex]

Step-by-step explanation:

Use the Law of Sines as follows:

[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

Insert the values (use the steps from the last problem):

[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]

Isolate b. Multiply both sides by b:

[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]

Multiply both sides by 14:

[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]

Isolate b. Divide both sides by sin 25:

[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]

Insert the equation into a calculator and round to the nearest tenth:

[tex]b=13.5[/tex]

The length of AC is 13.5 units.

:Done

Answer:

SAS

Step-by-step explanation: