A culture of bacteria has an initial population of 470 bacteria and doubles every 8 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t ​ =P 0 ​ ⋅2 d t ​ , where P_tP t ​ is the population after t hours, P_0P 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?

Answer: 8 pie

Step-by-step explanation:

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The length of the given arc is determined as 2π.

option B is the correct answer.

The length of the arc EF is calculated by applying the formula for the length of an arc as shown below;

EF = θr

where;

From the given diagram, the radius of the arc = 4, and the angle subtended by the arc = π/2

The length of the arc is calculated as follows;

EF = ( π/2 ) x 4

EF = 2π

Thus, the length of the given arc is determined by applying the formula for length of an arc.

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Answer: 187.5 gallons of gas

Step-by-step explanation:

He travels 30000 miles per year, and each gallon lets him travel 16 miles. Divide 30000 by 16 to get the amount of gas he uses in a year, which amounts to 187.5 gallons of gas.

Answer:

answer is C

the slope is 3 and the intercept is (0,2) which is 2

Answer:49.5

Step-by-step explanation:so if 1 inch equal to 3 yards then 7.5 will be 21.5  and 6 inchs will be 18 so if you all together you will get 49.5

Answer:

36

Step-by-step explanation The answer would be  36 because A=a2=62=36 and the math added to 36 hope this helped.

The image of the labeled spinner isn't attached

Answer:

Kindly check explanation

Step-by-step explanation:

Answering hypothetically ;

First create a sample space using the label of the two spinners ;

Each space will be the sum of the possible number that shows up on each turn of the spinner.

From the sample space, count the number of spaces where, the sun is greater than 4, that is the required outcome ; = x

Then the total number of samples in the sole space = total possible outcomes = y

Hence,

P(obtaining a sum greater than 4) = required outcome / Total possible outcomes

= x / y

B  128 divide 8 = 16

took test

Answer:

128 / 8 = 16

Step-by-step explanation:

Answer:

not a straight line

Step-by-step explanation:

Linear has the word "line" in it. A linear relation has a graph shaped like a straight line.

Nonlinear means "not like a straight line".

Answer: not a straight line

Answer:

Due south and due west form a right angle, and the shortest distance between any two points is a straight line. Therefore, we can apply the Pythagorean theorem and write:

3.12+2.82=x2

Here, you will need to use a calculator to simplify the left-hand side:

17.45=x2

Now use your calculator to take the square root. You will likely need to round your answer.

x=17.45−−−−√≈4.18 miles

As you can see, it will be up to you to determine that a right angle is part of the situation given in the word problem. If it isn’t, then you can’t use the Pythagorean theorem.

Step-by-step explanation:

this is my explanation

Answer:

n=6

Step-by-step explanation:

i used math-way :P

Answer:

Limaçon

Step-by-step explanation:

In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal, is defined as a roulette formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.

The name of the shape depicted in the graph below is a. Limacon.

Polar curves are the curves which are formed using the polar coordinate system.

The distance of the points from the origin will be varying depending on the angle from the positive X axis.

The given curves in the option Limacon, Rose, Cardioid, Lemniscate are types of polar curves.

Limacon is the curve which is also known as Pascal's snail. It is formed by following the path by a fixed point to a circle when this circle rolls another circle's of equal radius outside.

The given shape is the limacon with inner loop.

Lemniscate will always be a 8 shaped curve.

Hence the correct option is a, limacon.

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Answer:

I think the answer is letter B

Answer:

4π yd²

Step-by-step explanation:

Area of a circle = πr²

πr²=4π

r²=4

r=2

Circumference of a circle = 2πr = 2π(2) =4π

Answer:

2x^2 + 7x + 3 is the area of the rectangular piece of wood.

Step-by-step explanation:

Here,

Length ( l ) = x + 3

Breadth ( b ) = 2x + 1

Formula : -

Ar ( rectangle ) = lb

lb

= ( x + 3 ) ( 2x + 1 )

= x ( 2x + 1 ) + 3 ( 2x + 1 )

= 2x^2 + x + 6x + 3

= 2x^2 + 7x + 3

Answer:

oc2

Step-by-step explanation:

because

Answer:

x = 2

Step-by-step explanation:

H(x) = 64x - 16x²

Find the value of x when the ball reaches its maximum height.

Since the largest degree in this equation is two, this function represents a parabola. We can find the maximum height of the ball at the vertex of the quadratic.

In H(x) = 64x - 16x², rearrange the powers from greatest to least:

Vertex: [-b/2a, f(-b/2a)]

Substitute a and b into the x-value of the vertex: -b/2a.

The vertex of the parabola is at x = 2, with a maximum height of H(2).

Answer:

c

Step-by-step explanation:

Is is right?

Read the procedural text.

Plain Taffy

3.5 lbs. white sugar

2 cups water

1 teaspoon cream of tartar

Put the sugar and water in a clean pan. Heat mixture over medium-high heat, stirring occasionally until melted. Continue heating to a slow boil.

Add the cream of tartar and put a lid on the pan. Allow mixture to boil in this way for ten minutes.

Remove the lid and immerse a candy thermometer in the boiling liquid. Boil to 310 degrees.

Quickly remove pan from heat and pour contents into oiled frames, tins, or onto a pouring slab.

Cut into bars or squares with a knife or taffy cutter while still warm.

Allow taffy to cool before eating.  so the answer is A

[1] … … 2x₁ + 0x₂ + 3x₃ = 3

[2] … … 4x₁ - 3x₂ + 7x₃ = 5

[3] … … 8x₁ - 9x₂ + 15x₃ = 10

Since [1] is already free of x₂, you might as well start by eliminating x₂ from the other two equations. Add -3 times [2] to [3] :

-3 (4x₁ - 3x₂ + 7x₃) + (8x₁ - 9x₂ + 15x₃) = -3 (5) + 10

-12x₁ + 9x₂ - 21x₃ + 8x₁ - 9x₂ + 15x₃ = -15 + 10

-4x₁ - 6x₃ = -5

[4] … … 4x₁ + 6x₃ = 5

Now eliminate x₃ in [1] and [4]. Add -2 times [1] to [4] :

-2 (2x₁ + 3x₃) + (4x₁ + 6x₃) = -2 (3) + 5

-4x₁ - 6x₃ + 4x₁ + 6x₃ = -6 + 5

0 = -1

which is a contradiction. This means the system has no solution.

Answer:

The Answer is 12 - 15= 129

Step-by-step explanation:

x2−15=129

Step 1: Add 15 to both sides.

x2−15+15=129+15

x2=144

Step 2: Take square root.

x=±√144

x=12

Answer:

4(x+8) OR 4x+32

Step-by-step explanation:

4x+(4*3.75)+(4*4.25)

There are four people, so there are four tickets, four drinks, and four pieces of candy, so everything must be multiplied by four. Next, you need to either factor or simplify the equation.

If you want to factor it, the answer would be 4(x+8)

If you want it simplified, it would be 4x+32

Answer:

f(6) = -22, and g(-3) = 49

Step-by-step explanation:

f(x) = -4x + 2

f(6) = -4(6) + 2

f(6) = -24 + 2

f(6) = -22

I assume the 3 in g(x) = -2x3 -5 is cubed

g(-3) = -2(-3)^3 - 5

g(-3) = -2(-27) - 5

g(-3) = 54 - 5

g(-3) = 49

Answer:

[tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

Step-by-step explanation:

In order to solve this we can start by drawing a sketch of the problem (see attached picture)

So fist, let's take the general form of a sinusoidal movement:

[tex]y=Asin(\omega x+\phi)+b[/tex]

where:

A= amplitude

[tex]\omega[/tex]= angular frequency

x= time

[tex]\phi[/tex] = horizontal shift

b= vertical shift.

In this case, the amplitude will be the maximum distance between the center of the wheel and the highest or lowest point of the trajectory, in this case:

A= 13in - 0.5in =12.5 in

The angular frequency is how many radians the wheel will turn in a minute, so we get:

[tex]\omega=\frac{90 rev}{min}*\frac{2\pi rad}{1 rev}[/tex]

[tex]\omega=180\pi rad/min[/tex]

Generally, the sin function will start at the center of the circular movement. In this case, since it starts on the lowest point, we can say that the graph moves right by [tex]\frac{\pi}{2} rad[/tex], so in this case:

[tex]\phi=-\frac{\pi}{2}[/tex]

and finally, the vertical shift is the distance between the center of the circular movement and the ground so in this case:

b=13in

so when putting it all together we get our equation to be:

 [tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

Step-by-step explanation: