A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells.

Required:
a. Find the relative growth rate.
b. Find an expression for the number of cells after t hours.
c. Find the rate of growth after 6 hours. (Round your answer to the nearest integer.)
d. Find the number of cells after 6 hours.

Answer:

1

step by step explanation

hope this helps :)

Answer:

12 miles

Step-by-step explanation:

Let the amount of hours it takes Leroy to catch up to Kevin equal x. Since speed multiplied by time is distance, Leroy would have run a total of 6x miles(6*x). Kevin already had a head start of 24 minutes, which is the same as 2/5 of an hour. In 2/5 an hour, Kevin ran 2 miles as 2 is 2/5 *5. For the next x hours his distance would be a total of 5x(5*x). This means, after x hours, Kevins distance is 5x + 2. In this case, catching up to someone is the same as having the same distance value. This means we can set the two expressions equal to each other, and solve:

6x = 5x + 2

x = 2

The time it took Leroy to catch up is 2 hours, but we are looking for the distance, which is represented by 6x. We substitute in 2 to get:

6(2) = 12

This means Leroy had to run 12 miles.

I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).

The sheriff wants 390 mL of the mixed dressing, so that

x + y = 390

x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means

0.05x + 0.15y = 35.1

Solve for x and y :

y = 390 - x

0.05x + 0.15 (390 - x) = 35.1

0.05x + 58.5 - 0.15x = 35.1

23.4 = 0.10x

x = 234

y = 156

Answer:

Step-by-step explanation:

The combinations are:

Total number of combinations:

Correct choice is B

there are 8different combinations are modeled by the diagram.

Answer:

Solution given:

orange:2

grape:2

apple:2

grapefruit:2

no of term:4

now

total no. of combination ia 4*2=8

Answer:i think it is b not really sure      

Step-by-step explanation:

Answer:

12 x^5y^12

Step-by-step explanation:

3x^2y^5 * 4x^3y^7

Multiply the constants

3*4 = 12

Multiply the x terms

x^2 * x^3

We know a^b* a^c = a^(b+c)

x^(2+3) = x^5

Multiply the y terms

y^6 * y^7 = y&(5+7) = y^12

Put them back together

12 x^5y^12

Answer:

x = 20°

Step-by-step explanation:

x + 2x + (x+10) =90° {being a right angle triangle}

3x + x + 10 = 90°

or, 4x = 90° - 10°

or, 4x = 80°

or, x = 80°/4

so, x = 20°

Answer:

[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]

Step-by-step explanation:

Given

See attachment for question

Required

The piece-wise function

From the attachment, we have:

(1) $4/hr for first 2 hours

This is represented as:

[tex]C(x) = 4x[/tex]

The domain is: [tex]0 \le x \le 2[/tex]

(2) $2/hr for next 4 hours

Here, we have:

[tex]Rate = 2[/tex]

The total cost in the first 2 hours is:

[tex]C(x) = 4x[/tex]

[tex]C(2) = 4*2 = 8[/tex]

So, this function is represented as:

[tex]C(x) = C(2) + Rate * (Time - 2)[/tex] ----- 2 represents the first 2 hours

So, we have:

[tex]C(x) = C(2) + Rate * (Time - 2)[/tex]

[tex]C(x) =8 + 2(x - 2)[/tex]

Open brackets

[tex]C(x) =8 + 2x - 4[/tex]

Collect like terms

[tex]C(x) =8 - 4+ 2x[/tex]

[tex]C(x) =4+ 2x[/tex]

The domain is:

[tex]2 < x \le 2 + 4[/tex]

[tex]2 <x \le 6[/tex]

(3) 0 charges for the last 2 hours

The maximum charge from (2) is:

[tex]C(x) =4+ 2x[/tex]

[tex]C(6) = 4 + 2*6[/tex]

[tex]C(6) = 4 + 12[/tex]

[tex]C(6) = 16[/tex]

Since there will be no additional charges, then:

[tex]C(x) = 16[/tex]

And the domain is:

[tex]6 < x \le 8[/tex] --- 8 represents the limit

So, we have:

[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]

Answer:

11.34464...

Step-by-step explanation:

it is not a 3-dimensional cone, it is a 2-dimensional segment of a circle. and you need to find its area.

which is also why you are asked to find the area, because for a 3-dimensional object you would have been asked about the volume of the surface.

now, about a circle and its segments.

you know how to get the area of a circle ?

it is pi×r²

that is for the full circle.

you know how many degrees it is to go "full circle" ?

360 degrees.

so, here we have only a segment of 52 degrees out of the full 360 degrees.

in other words we are dealing with 52/360 = 13/90 of the full circle.

all we have to do is therefore multiply the area of the full circle with that fraction, and we have our result.

pi×r²×13/90 = pi×5²×13/90 = pi×5×13/18 = 11.34464...

Answer:

Option C

We need to make the negative exponent positive.

The rule is: [tex]A^{-B} =\frac{1}{A^{B} }[/tex]

Here, A=x, B= 12

[tex]so,[/tex] [tex]x^{-12}[/tex]

[tex]=\frac{1}{x^{12} }[/tex]

OAmalOHopeO

9514 1404 393

Answer:

  A.

Step-by-step explanation:

If you can find the given points (pounds, dollars) = (2, 3.50), (3, 5.25), and (4, 7.00) on the graph, then it is an appropriate graph. If the graph label matches the value it shows for 1 pound, then that graph and label are the one you want.

Graph A meets these requirements. It shows the cost of 1 lb to be $1.75, as the label says.

Answer:

chocolate chips are $2.00 per pound.

nd walnuts must be $3.50 per pound.

Step-by-step explanation:

Let x be the price of walnuts and y the price of chocolate chips.

2x + 5y = 17 (i)

8x + 3y = 34 (ii)

Multiply (i) by 4 to get

8x + 20y = 68

Subtract (ii) to get

 17y = 34

Dividing by 17, we see that chocolate chips are $2.00 per pound.

Substituting y=2 in (i) or (ii), walnuts must be $3.50 per pound.

Answer:

The answer is that the runner can run 10 miles in 70 minutes.

Step-by-step explanation:

To solve for the number of miles that the runner can run in 70 minutes, start by setting up the information given from the problem in the form of a proportion.

A proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In a proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportion for this problem will look like [tex]\frac{2 miles}{14 minutes}=\frac{x}{70 minutes}[/tex]. (x) will be used as the variable for the number of miles that the runner can run in 70 minutes.  

To solve the proportion, start by cross multiplying to form an equation, and the equation will look like [tex](14)(x)=(2)(70)[/tex]. Next, simplify the equation, which will look like [tex](14)(x)=140[/tex]. Then, solve the equation by dividing both sides of the equation by 14, and it will look like [tex]x=10[/tex]. The final answer is that the runner can run 10 miles in 70 minutes.

Answer:

the ans is 45⁰ BC it is a right angle

Step-by-step explanation:

Is this a trigonometry ratio

Answer:

Factorise out x and y terms:

[tex]{ \tt{ = \frac{ {x}^{2} {y}^{4} (5x - 3y)}{45} }} \\ [/tex]

Step-by-step explanation:

-x+4y= -15

-2x-3y=-8

the intersection point isn't (3,-5)

it's approximately (-1.1818 ,3.45455 )

Answer:

see below

Step-by-step explanation:

Check the solution in both equation

-x+4 = -15

-3 +4 = -15

1 does not equal -15 so it is not a solution

-2x-3y = -8

-2(3)+-3(-5) = -8

-6 +15 = -8

9 = -8

It is not a solution to either equation

Answer:

77

Step-by-step explanation:

Currently:

Talk to 8 customers per hour, work 8 hours, so:

Talk to 8*8 = 64 customers.

With the increase:

Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then

64*1.2 = 76.8

Rounding up, 77 is the answer.

Answer:

The answer is 5 units.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

the answer is regular octagon

i think

Answer:

90 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here's how you convert:

[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}[/tex]  The little number outside the radical, called the index, serves as the denominator in the rational power, and the power on the x inside the radical serves as the numerator in the rational power on the x.

A couple of examples:

[tex]\sqrt[3]{x^4}=x^{\frac{4}{3}[/tex]

[tex]\sqrt[5]{x^7}=x^{\frac{7}{5}[/tex]

It's that simple. For your problem in particular:

[tex]\sqrt[3]{7}[/tex] is the exact same thing as [tex]\sqrt[3]{7^1}=7^{\frac{1}{3}[/tex]

Answer:

there are infinite solutions

Step-by-step explanation:

if you add y-3 to both sides of the first equation, you will see that it is equal to the second equation, so they are the same line. Therefore, there are infinite solutions to this system

Answer:

x=0,5/2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The period is stretched by 30 and divided by pi, meaning that the wheel rotates does a full rotation every 60 seconds. But the most important part is vertical stretch of 47 and shift up of 52. At the peak it would be 99 since the peak is 47 with the stretch but add 52 from the shift and it would be 99.

Answer:

A= π ( 3.8)^2

A= 45.36

OAmalOHopeO

Step-by-step explanation:

area is 2xr(times your answer)

Answer:

Option B, AAS

Option C, HA

Option E, ASA

these three options applies

Step-by-step explanation:

-4b-24-2b+8b2

8b2-6b-24=0

Answer:

5:10

6 (-2,0)

7 (-5,6)

8 (5,3)

9 No, ab=8 CD=6

Step-by-step explanation:

60 mL=55% alcohol

?mL=85% alcohol

85×60÷55

=92.727 mL

I think do like this....I'm not sure

Hope this help you

9514 1404 393

Answer:

  120 mL

Step-by-step explanation:

Let x represent the amount of 85% solution needed. Then the total amount of alcohol in the mix is ...

  0.55(60) +0.85(x) = 0.75(60 +x)

  33 + 0.85x = 45 +0.75x . . . . . . . eliminate parentheses

  0.85x = 12 +0.75x . . . . . . . . . .subtract 33

  0.10x = 12 . . . . . . . . . . . . . . subtract 0.75x

  x = 120 . . . . . . . . . . . . . . multiply by 10

You will need 120 mL of the 85% solution.