Please help I know it’s a lot ...?

Answer:

B.

y=2 · 3xy equals 2 times 3 superscript x baseline

Step-by-step explanation:

The bacteria culture starts with 500 bacteria and doubles size every half hour.= 2 hours

32,000

Thus, after three hours, the population of bacteria is 32,000.= 3 hours

A bacteria culture starts with 500 bacteria and doubles in size every half hour.1

(a) How many bacteria are there after 3 hours?

We are told “. . . doubles in size every half hour.” Let’s make a table of the time and population:

t 0 0.5 1.0 1.5 2.0 2.5 3.0

bacteria 500 1000 2000 4000 8000 16000 32000

Thus, after three hours, the population of bacteria is 32,000.

(b) How many bacteria are there after t hours?

In t hours, there are 2t doubling periods. (For example, after 4 hours, the population has doubled 8

times.) The initial value is 500, so the population P at time t is given by

P(t) = 500 · 2

2t

This is an acceptable response, but in calculus and all advanced mathematics and science, we will

almost always want to use the natural exponential base, e. Let’s redo the problem using the natural

exponential growth function

P(t) = P0e

rt

We are given that the initial population is 500 bacteria. So P0 = 500 and we have

P(t) = 500ert

We know that after 1 hour, there are 2000 bacteria. (We could’ve used any other pair from our table

that we wish.) Substituting into our function, we get

P(t) = 500ert

2000 = 500er·1

2000 = 500er

1

500

· 2000 =

1

500

· 500er

4 = er

and now we use the natural logarithm to solve for r

ln (4) = ln (er

)

ln (4) = r · ln (e)

ln (4) = r

1.3863 ≈ r

Thus the function P(t) = 500e1.3863t gives the number of bacteria after t hours.

(c) How many bacteria are there after 40 minutes?

The input t to our function is given in hours, so we must convert 40 minutes into hours. So (40 min)

1 hr

60 min

=

2

3

hr.

P(t) = 500e1.3863t

P

2

3

= 500e1.3863·(2/3)

P

2

3

≈ 1259.9258

Thus, after 40 minutes (2/3 of an hour), there are about 1260 bacteria.

(d) Graph the population function and estimate the time for the population to reach 100,000.

50000

100000

1 2 3 4 5

b

(3.8219, 100,000)

t

P

Using the calc:intersect on the TI-84, we get the point (3.8219, 100000), thus the population will

reach 100,000 in about 3.82 yrs

Answer:

no soultion

Step-by-step explanation:

did on paper

Answer:

exactly one solution

Step-by-step explanation:

got it right on khan lol

Answer:

(1, -1)

Step-by-step explanation:

6 units right changes the x value by +6.

2 units down changes the y value by -2.

-5 + 6 = 1

1 - 2 = -1

Answer:

(1,-1)

Step-by-step explanation:

when x is changed by 6 units to the right, you add 6

-5 + 6 = 1

when y is changed by 2 units down, you subtract 2

1 - 2 = -1

coordinates = (1, -1)

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Given:

In the triangular base of the pyramid,

Base = 4m

Height = 7m

Area of base = 1/2 x Base x Height

=> 1/2 x 4 x 7 = 14 m^2

Now, Volume of Triangular Pyramid = 1/3 x Area of Base x Height

= 1/3 x 14 x 5

= 1/3 x 70

= 23.33 m^2 or 23 1/3 m^2

Answer:

the area of a circle is equal to pi r square that is 3.14×3×3 = 28.26.

Answer:

23x

Step-by-step explanation:

16 - 4(3x-5)

12(3x-5)

36x-60

Answer:

?

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

8 * (10 + 9) =

(8 * 10) + (8 * 9)

Answer:

1/94

Step-by-step explanation:

2/188 = 1/94

Answer:

0.01063829787.

Step-by-step explanation:

Caculator.

Answer: The answer is true im taking that same test

It is TRUE because the piecewise graph shown is the ceiling function.

Answer:

it is B, there is one big outlier, it is 21

Step-by-step explanation:

Answer:

$30000at 8%compound interest

Answer:

$5 is the answer.......

Answer:

one box cost is $5

Step-by-step explanation:

$25 - $5 = $20 - this is the cos of four cereal boxes

$20 / 4 = $5 each box cost

Answer:

[ 0 ]

Step-by-step explanation:

The order of the matrix [ 3 1 1 ] is 1 by 3 and the order of the other matrix is 3 by 1 so this means that the order of the answer matrix is 1 by 1. So we multiply matrices row by columns.

[ 3 1 1 ] × | 2|

| -6|

| 0|

[ 3 × 2 + 1 × -6 + 1 × 0 ]

[ 6 - 6 + 0 ]

[ 0 ]

Answer:

256, 254

Step-by-step explanation:

Answer:

The answer is A. 63 minutes.

Step-by-step explanation:

I added 27 minutes with each of the answer then multiplied the two added numbers by 30%

27 + 63 = 90 x 30% = 27 minutes (correct answer)

27 + 67 = 94 x 30% = 28.2 minutes (wrong answer)

27 + 70 = 97 x 30% = 29.1 minutes (wrong answer)

27 + 90 = 117 x 30% = 35.1 minutes (wrong answer)

Answer:

3

Step-by-step explanation:

x/3 + 3 = 4

x/3 = 4 - 3

x/3 = 1

x = 3

Answer: x = 3

Step-by-step explanation:

Given

x/3 + 3 = 4

Subtract 3 on both sides

x/3 + 3 - 3 = 4 - 3

x/3 = 1

Multiply 3 on both sides

x/3 × 3 = 1 × 3

[tex]\boxed{x=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

First we need to set this ratio up in the coordinate plane. Because this is tangent, the 3 goes opposite the reference angle and the 4 goes along the x-axis, adjacent to the reference angle. We see that we are missing the third side of the triangle when we do this, namely the hypotenuse. We use Pythagorean's Theorem to find that this side is 5. Now we have to deal with the identities for each sin(2A) and cos(2A).

sin(2A) = 2sin(A)cos(A)

We know from the triangle we drew in the coordinate plane that

[tex]sin(A)=\frac{3}{5}[/tex]  and  [tex]cos(A)=\frac{4}{5}[/tex] so we fill in the formula accordingly and then simplify:

[tex]sin(2A)=2(\frac{3}{5})(\frac{4}{5})=\frac{24}{25}[/tex]

cos(2A) has 3 identities; I just picked the one I thought would be easiest to use and went with that one. Regardless of which one you pick you will get the same answer as long as you do the math correctly.

[tex]cos(2A)=cos^2(A)-sin^2(A)[/tex] and filling in the formula:

[tex]cos(2A)=(\frac{4}{5})^2-(\frac{3}{5})^2\\cos(2A)=\frac{16}{25}-\frac{9}{25}\\cos(2A)=\frac{7}{25}[/tex]

I'm not sure why you have 7/2 there...

Answer:

[tex]distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \sqrt{ {28 - 28)}^{2} + {(6 - - 12)}^{2} } \\ \sqrt{ {0}^{2} + {18}^{2} } \\ = \sqrt{ {18}^{2} } = 18unit \\ thank \: you[/tex]

Answer:

0.548

Step-by-step explanation:

5 x 0.1 = 0.5

4 x 0.01 = 0.04

8 x0.0001 = 0.008

Now add them all together to get 0.548 in standard form.

I hope this helps! :)

Answer:

5 × 0.1 is 0.5

4 × 0.001 is 0.04

8 × 0.0001 is 0.008

so add all number is

0.548

Answer:

3 1/3

Step-by-step explanation:

Answer:

[tex] \frac{r}{2} + ( \frac{7}{8} - s) \\ r = 1 \\ s = \frac{1}{2} \\ then \\ \frac{1}{2} + ( \frac{7}{8} - \frac{1}{2} ) \\ = \frac{1}{2} + \frac{3}{8} \\ = \frac{7}{8} \\ thank \: you[/tex]

Answer:

D

Step-by-step explanation:

Given the input - 1 [tex]\frac{1}{2}[/tex] = - [tex]\frac{3}{2}[/tex] , then

(- [tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] , then subtract 2

[tex]\frac{9}{4}[/tex] - 2 = [tex]\frac{9}{4}[/tex] - [tex]\frac{8}{4}[/tex] = [tex]\frac{1}{4}[/tex]

Then reciprocal which is 1 over the previous value

reciprocal = [tex]\frac{1}{\frac{1}{4} }[/tex] = 4 ← output → D