A bacterial colony starts with 120 cells and quadruples in size each day. Write an equation that relates the population of cells in this colony (P) at the start of each day and the number of days (d). Find the population on day 8.

Answers

Answer 1

Answer:

P = 120*([tex]2^{2d-2}[/tex])P(8) = 1, 966, 080

Step-by-step explanation:

Since the population quadruples each day, the population for the subsequent day would be 4*(population of the previous day).

Thus, the evolution of the population value takes the form of a geometric progression, with a common ratio, r = 4

The n-th term of a geometric progression is given by:

[tex]a_{n}[/tex] = [tex]ar^{n-1}[/tex]             (1)

Where a is the 1st term of the progression.

From (1), our population would generally take the form:

[tex]P_{d}[/tex] = [tex]P_0r^{d-1}[/tex]             (2)

In this case, the initial value (1st term) [tex]P_{0}[/tex] = 120.

So putting r and  [tex]P_{0}[/tex] into  (2):

P(d) = 120*([tex]4^{d-1}[/tex])

Noting that 4  = 2²:

P(d) = 120*([tex]2^{2(d-1)}[/tex])

P(d) = 120*([tex]2^{2d-2}[/tex])

FOR d = 8:

P(d) = 120*([tex]2^{2d-2}[/tex])

becomes:

P(8) = 120*([tex]2^{2(8)-2}[/tex])

P(8) = 120*([tex]2^{16-2}[/tex])

P(8) = 120*([tex]2^{14}[/tex])

P(8) = 120*(16,384)

P(8) = 1, 966, 080

Related Questions

what is the formula to find the circumference of a circle?

Answers

Answer:

C = 2 \pi r

Step-by-step explanation:

A function is a fifth-degree polynomial. how many turning points can it have? exactly four exactly five four or less five or less

Answers

A fifth-degree polynomial function can have five turning points in its graph.

What is a quintic function?In other terms, a polynomial of degree 5 defines a quintic function. When graphed, normal quintic functions resemble normal cubic functions since they have an odd degree, with the possible exception that they might contain an extra local maximum and/or local minimum. 9x5– 2x + 3x4– 2 – A leading term to the fifth degree and a term to the fourth degree are both included in this four-term polynomial. It is known as a polynomial of fifth degree.The given polynomial must be factored as much as feasible in order to solve a polynomial equation of degree 5. We can solve for the variable after factoring by equating factors to zero.Examples of polynomials with degrees include the following: The degree of the polynomial 5x5+4x2-4x+3 is 5

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Answer:

The correct is answer is option C: "four or less"

The answers to the next  part of the question on Edge are options A and C :)

Step-by-step explanation:

Hope this helped!

Brainliest would be greatly appreciated - Have a great day :3

a ladder 10 feet long rests against a vertical wall. let be the angle between the top of the ladder and the wall, and let be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast does change with respect to when ?

Answers

Rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex] is 5ft/s.

Since the ladder is 10ft long resting against a vertical wall.

Let the angle between the top of the ladder and the wall is [tex]\alpha[/tex] .

And let the distance from the bottom of the ladder to the wall is x.

Thus we need to find the rate of change of x with respect to [tex]\alpha[/tex]  when [tex]\alpha =\frac{\pi }{3}[/tex]

Consider L to be the length of the ladder.

Then, L = 10ft

Thus, we get the relation between the angle and distance x i.e.

x = L [tex]\sin \alpha[/tex]

On differentiating the above equation,

[tex]\frac{dx}{dt} =L \cos \alpha[/tex]

Now after putting the values [tex]\alpha =\frac{\pi }{3}[/tex] in above equation, we get,

[tex]=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5[/tex]

Therefore, [tex]\frac{dx}{dt} =5[/tex] ft/s

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what is - 8x-6y= -8 in slope- intercept form​

Answers

Answer:

y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

-8x - 6y = -8   Add 8x to both sides

-6y = 8x  - 8   Divide all the way through by -6

y = [tex]\frac{-8}{6}[/tex] c + [tex]\frac{8}{6}[/tex]  Simplify

y = [tex]\frac{-4}{3}[/tex] x + [tex]\frac{4}{3}[/tex]

A negative times a negative is a positive.

A negative times a positive is a negative.

I'm in a rush and need help on this one

Answers

4.

The volume of a cube equals its side cubed. Since the side of the cube is 12ft long, then its volume is given by:

[tex]V=(12ft)^3=1728ft^3[/tex]

Then, the volume of the cube, is:

[tex]1728ft^3[/tex]

5.

The volume of the prism equals the product of each of its dimensions. Then:

[tex]V=(7m)(2m)(3m)=42m^3[/tex]

Then, the volume of the rectangular prism, is:

[tex]42m^3[/tex]

Find the inverse of the given function.
5. f= {(1,3), (2,-5), (3,6)} ​

Answers

Check the picture below.

Please help, i really need help

Answers

Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees

Step-by-step explanation:

Since m<2 and m<4 are vertical angles, they will be equal to each other.

By using straight lines, we can easily find out that m<1 = 180-34 = 146

Since m<1 and m<3 are vertical angles, they are equal to each other.

Hope this helped :))

Angle 4: is 34 degrees since angle 2 and angle 4 are vertical angles and congruent (equal)
Angle 1: is 146 degrees. Since angle 4 and angle 1 are linear angles they are equal to 180. So subtract 180 and 34 to get 146
Angle 3: is 146 because angles 1 and 3 are vertical and congruent.
Hope this helps :)

NEEED HELP PLSSSS . Find x in triangles Geometry.

Answers

Answer:

10) x = 76,12) x = 8, Perimeter = 77 units

=========================

Question 10

The triangle is isosceles as marked.

The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.

Use angle sum of the triangle:

2x + 28 = 1802x = 152x = 76

Question 12

Same as previous question, we have an isosceles triangle. Equal sides are:

3x + 5 = 5x - 115x - 3x = 5 + 112x = 16x = 8

Find the perimeter by substituting the value of x:

P = 3*8 + 5 + 5*8 - 11 + 2*8 + 3 = 77 units

what do you divide by 15 to get to 9

Answers

Answer:

aproamitly 1.66666666667

Step-by-step explanation: 15/9=1.66666666667 thus

15/1.66666666667=9

Answer: it's 135 the other dude used a calculator probs

Even though I already got the question right,I need someone to show the work on how to get the answer for this question.

Answers

Given

Answer

[tex]\begin{gathered} \sin x=\frac{P}{H} \\ \sin x=\frac{5}{8.3} \\ x=\sin ^{-1}(\frac{5}{8.3}) \end{gathered}[/tex]

Which is triangle 2

The function g(x) is defined as g(x) = -2x^2 - 4x + 2 The value of g(-3)

Answers

[tex]g(x)=-2x^2-4x+2[/tex][tex]\begin{gathered} g(-3)=-2(-3)^2-4(-3)+2 \\ g(-3)\text{ =-(2}\times\text{9) + (4}\times3)+2 \\ g(-3)\text{ =-18 + 12}+2\text{ =-18+14} \end{gathered}[/tex][tex]g\text{ (-3) =-4}[/tex]

In the figure shown below, all the corners form right angles. What is the area of the figure?
15 ft
B.
44 ft²
17 ft
215 ft2
5 ft
7 ft

Answers

Based on the dimensions of the shape, the area of the figure can be found to be 215 ft².

How to find the area of the figure?

To find the area of the figure, you can divide the shape into two different shapes and then find the area of those shapes, and then sum them up to find the area of the entire figure.

As shown in the attached photo, you can divide the figure into two rectangles with the dimensions:

15 ft and 12 ft (17 - 5)7 ft and 5 ft

The areas are:

= 15 x 12

= 180 ft²

Second rectangle:

= 7 x 5

= 35ft²

The area of the figure is:

= 35 + 180

= 215 ft²

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someone please help me!!!

Answers

Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel

Write two hundred thousand and
Seventeen in figures

Answers

Answer:

200,017

Step-by-step explanation:

2 at the front for 200,000 , and then you have 17 which are the last 2 digits

Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. Calculate the amount of money that Vince receives

Answers

workout:

19+21=40

2000÷40=50

Vince=50×19=950

Wendy=50×21=1050

-u can check by adding 950+1050=2000 (which means the ratio is correct)

Answer:

(vince:wendy)= 950:1050

Answer:

V:W

19:21

19 + 21 = 40

19 over 40 × 200

Vince received $950

Find the area of ABC with verticles A(4,-3), B(9,-3) and C(10,-11)

Answers

Answer:

Step-by-step explanation:

The  area of the triangle when the vertices of the triangle are given can be calculated by the following formula:

Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|  where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)

Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)

Therefore,

By applying the formula and substituting the given values, we get

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Area = 0.5 * |44|

Area = 22

Hence, the area of triangle ABC with the given vertices is 22 square units

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Let f(x) = 2x + 8, 9(x) = x2 + 2x – 8, and h(x) = 3x - 6. Perform the indicated operation. (Simplify as far as possible.) (h. f)(3) = =

Answers

[tex]\begin{gathered} (3x-6)\cdot(2x+8) \\ 6x^2+24x-12x-48 \\ 6x^2+12x-48 \\ \end{gathered}[/tex]

x=3

[tex]\begin{gathered} 6\cdot3^2+12\cdot3-48 \\ 6\cdot9+36-48 \\ 54+36-48=42 \end{gathered}[/tex]

A survey was given to people who own a sertain car. What percent of the people surveyed were completely satisfied with the car

Answers

The percent of the people surveyed were completely satisfied with the car is 55%.

How to calculate the percentage?

Number of people completely satisfied = 1155

Number of people somewhat satisfied = 755

Number of people not satisfied = 190

Total number of people = 1155 + 755 + 190 = 2100

Therefore, the percent of the people surveyed were completely satisfied with the car will be:

= Number of people completely satisfied / Total number of people × 100

= 1155 / 2100 × 100

= 55%

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Solve the following equation: 5(n + 2) = 3(1 + 2n)​

Answers

Answer: n=7

Step-by-step explanation:

First distribute the numbers to get 5n+10=3+6n

Next Subtract 6n from both sides to get -n=10=3

Finally divide both sides my -1 to get rid of the -n to get n=7

Hope this helps :)

Alysa buys 23 boxes of toothpicks. There are 255 toothpicks in each box. Which equation and solution show the number toothpicks, t, in all the boxes?

Answers

Answer:

255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.

Please help!! Math is not my cup of tea and I’m really struggling!! ASAP

Given the function:

f(x)=x²-3x - 4

Find the following values.

a) f(2)
f(2)=

b) f(4)
ƒ(4)=

c) f(-3)
ƒ(-3) =

Answers

The values of f(2), f(4) and f(-3) for the function, f(x) = [tex]x^{2} -3x-4[/tex], are -6, 0 and 14 respectively.

According to the question,

We have the following information:

f(x) = [tex]x^{2} -3x-4[/tex]

Now, to find the values of each function we will put the values in place of x.

We will find the value of f(2) by putting 2 in place of x.

f(2) = [tex](2)^{2} -3(2)-4[/tex]

f(2) = 4-6-4

f(2) = -2-4

f(2) = -6

(We know that the numbers with negative sign are added but the result always remains in negative.)

We will find the value of f(4) by putting 4 in place of x:

f(4) = [tex](4)^{2} -3(4)-4[/tex]

f(4) = 16-12-4

f(4) = 4-4

f(4) = 0

Now, we will find the value of f(-3) by putting -3 in place of x:

f(-3) = [tex](-3)^{2} -3(-3)-4[/tex]

f(-3) = 9+9-4

f(-3) = 18-4

f(-3) = 14

Hence, the values of f(2), f(4) and f(-3) are -6, 0 and 14 respectively.

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There are 125 people in a sport centre.
59 people use the gym.
70 people use the swimming pool.
55 people use the track.
25 people use the gym and the pool.
30 people use the pool and the track.
17 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?

Answers

Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.

Probability of an event

The probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.

We shall determine the answer to the question as follows;

People in the sport centre = 125

People who used the 3 facilities = 6

People who accessed only gym = 59 - (6 + 11 + 19) = 26

People who accessed only track event = 55 - (6 + 11 + 24) = 14

People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21

People who accessed only gym and swimming pool events = 29 - 6 = 19

People who accessed only gym and track events = 17 - 6 = 11

People who accessed only swimming pool and track events = 30 - 6 = 24

Total number of people who accessed at least any one of the facilities = 121

The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.

Therefore, the probability that the person selected doesn't use any facility = 1/4

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Which of the following statements is true about the graph shown?

The equation y = 4.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (3, 13.5).
The graph is incorrect and the line should go through the point (4.5, 4.5).
The graph does not show a proportional relationship

Answers

Answer: A

Step-by-step explanation:

what is the doubling timefor this population of alligators ?

Answers

Answer:

3 years

Explanations:

The given function representing the population of alligators is:

[tex]P(t)\text{ = (}319)2^{\frac{t}{3}}[/tex]

Find the intial population at t = 0

[tex]\begin{gathered} P(0)\text{ = 319 }\times2^0 \\ P(0)\text{ = 319 }\times\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}[/tex]

The population will double when:

P(t) = 319 x 2

P(t) = 638

The doubling time is the value of t at which P(t) = 638

[tex]\begin{gathered} P(t)\text{ = 319 }\times2^{\frac{t}{3}} \\ 638\text{ = 319 }\times2^{\frac{t}{3}} \\ \frac{638}{319}=2^{\frac{t}{3}} \\ 2\text{ }=2^{\frac{t}{3}} \\ 2^1=2^{\frac{t}{3}} \\ 1\text{ = }\frac{t}{3} \\ t\text{ = 3} \end{gathered}[/tex]

The population will double after 3 years.

Therefore, the doubling-time for this population of alligators is 3 years

Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb. How much does each weight now?

Answers

Using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.

What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.as in 3x + 5 = 15, for example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the weight of Sean and Brad.

Let, Brad, be 'x'.Then Sean be '2x + 10'

So, the equation will become:

x + 2x + 10 = 230

Now, solve this equation for 'x' as follows:

x + 2x + 10 = 2303x = 230 - 103x = 220x = 220/3x = 73.33

Rounding off: 73 lbs

Then,

Brad weights ⇒ 73 lbsSean weights ⇒ 2(73) + 10 = 156 lbs

Therefore, using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.

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Can someone please help answer the attached?

Answers

The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].

The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.

[tex]12s+16k=105.64[/tex][tex]3k+16k=105.64[/tex][tex]k=5.56[/tex] per knife.
Answer:  5.56 pounds

===================================================

Explanation:

k = cost of one knife

s = cost of one spoon

costs are in pounds

12s = cost of 12 spoons

16k = cost of 16 knives

12s+16k = 105.64 pounds is the total cost

We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.

So,

12s+16k = 105.64

12s+16(4s) = 105.64

12s+64s = 105.64

76s = 105.64

s = 105.64/76

s = 1.39 pounds is the cost of one spoon

k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife

----------------------

Check:

1 spoon = 1.39 pounds

12 spoons = 12*1.39 = 16.68 pounds

1 knife = 5.56 pounds

16 knives = 16*5.56 = 88.96 pounds

12 spoons + 16 knives = 16.68+88.96 =  105.64 pounds total

This fully verifies the answer.

Your mom Paid $8 for 10 Granny Smithapples and bought 15 Golden Delicious at60 cents an apple. What is her average costper apple?

Answers

First, let's find the total cost of all the apples:

[tex]8+(0.6\cdot15)=17[/tex]

Now, we divide this by the total amount of apples bought. In our case, we know that there were 10 Granny Smith apples and 15 Golden Delicious, for a total of 25 apples.

[tex]\frac{17}{25}\rightarrow0.68[/tex]

Therfore, we can conclude that the average cost per apple was $0.68

The midpoint of AB is M(0, -7). If the coordinates of A are (-2,-6), what arethe coordinates of B?Answer:Submit AnswerPASSA

Answers

Explanation:

The coordinates are given below are

[tex]\begin{gathered} A(-2,-6) \\ M(0,-7) \\ B=(x,y) \end{gathered}[/tex]

The image is given below as

To calculate the coordinate of A,we will use the formula below

[tex]M=\frac{(x_1+x_2}{2},\frac{y_1+y_1}{2})[/tex]

By substituting the values, we will have

[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\frac{y_{1}+y_{1}}{2} \\ (0,-7)=\frac{-2+x)}{2},(\frac{-6+y}{2}) \\ \frac{-2+x}{2}=0,\frac{6+y}{2}=-7 \\ -2+x=0,6+y=-14 \\ x=2,y=-14+6 \\ x=2,y=-8 \end{gathered}[/tex]

Hence,

The coordinate of B will be

[tex]B=(2,-8)[/tex]

in the diagram below , the measure of arc SQ is 160 degrees and the measure of arc PR is 102 degrees . find the value of x .

Answers

Given:

The measure of angle of arrc SQ is 160°.

The measure of angle of arc PR is 102°.

The objective is to find the measure of angle x.

Since, the angle x is away from te center of the circle.

Then, the formula to find the value of angle x is,

[tex]x=\frac{PR+SQ}{2}[/tex]

Now, substitute the given values in the above formula.

[tex]\begin{gathered} x=\frac{102+160}{2} \\ =\frac{262}{2} \\ =131\degree \end{gathered}[/tex]

Hence, the value of x is 131°.

How many cups will stack to the top of the door frame?
Explain why...

Answers

Answer:

157 cups

Step-by-step explanation:

First, convert in to cm

83.375 in  * 2.54   Cm/in = 211.77 cm

Each cup adds 1.3 cm to the (9.2 - 1.3 cm) base     (Base is 7.9)

211.77  =  7.9  + 1.3  x          X is the number of cups

         X = 156.9 = ~ 157 cups

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