A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours​

Answer:

The rule depends on the scale factor.

Step-by-step explanation:

Hi there,

1) Many, I'd say mostly, dilations is centered at the origin (0,0) of the cartesian plane. Like the picture below.

2) So now, what's left to do is what is the scale factor? What coefficient that multiplies the original rectangle URST, will result the U'R'S'T'?

3) Since no coordinates, no options or any numerical value were given, then I've made one example.

Check below

If you do have the coordinates of each point then divide each coordinate this way

[tex]\frac{U'(x,y)}{U(x,y)}=\frac{R'(x,y)}{R(x,y)}=\frac{S'(x,y)}{S(x,y)}=\frac{T'(x,y)}{T(x,y)}=scale \:factor\\\frac{U'(-4,4)}{U(2,2)}\Rightarrow U'=2U\\(x,y)=D2(x,y)[/tex]

Answer:

you didn't put a picture

Step-by-step explanation:

The equation is c = 1.45 n

Total cost of 25 songs is $36.25

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

∵ The cost of downloaded one digital song is $1.45

∵ The cost of downloaded two digital song is $2.90

∵ The cost of downloaded five digital song is $7.25

- There is a linear relation between the cost of downloading

   the songs and the number of songs

∵ 2.90 = 2 × 1.45

∵ 7.25 = 5 × 1.45

∴ The total cost of downloaded songs is the product of the number

   of songs and the cost per song

∵ The cost per song is 1.45

∵ n is the independent variable

∴ n represents the number of songs

∵ c is the dependent variable

∴ c represents the total cost of n songs

- Now we can write the linear equation

∴ c = 1.45 n

The equation is c = 1.45 n

∵ 25 digital songs downloaded

∴ n = 25

∵ c = 1.45 n

∴ c = 1.45(25)

∴ c = 36.26

Total cost of 25 songs is $36.25

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Step-by-step explanation:

Given:

[tex] (x_1, \: y_1 ) =(2, \:3)\:\:\&\:\: (x_2, \: y_2) =(6, \:10)[/tex]

[tex]l(PQ) = \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2}} \\ \\ = \sqrt{ {(2 - 6)}^{2} + {(3 - 10)}^{2}} \\ \\ = \sqrt{ {( - 4)}^{2} + {( - 7)}^{2}} \\ \\ = \sqrt{16 + 49} \\ \\ = \sqrt{65} \\ \\ \therefore \purple{ \boxed{ l(PQ) = 8.06 \: units}}\\\\[/tex]

Let S be the mid-point of PQ.

[tex]\therefore S = \{\frac{x_1+x_2}{2}, \:\:\frac{y_1+y_2}{2}\} \\\\

= \{\frac{2 +6}{2}, \:\:\frac{3+10}{2}\} \\\\

= \{\frac{8}{2}, \:\:\frac{13}{2}\} \\\\

\therefore S= \{4, \:\:6.5\} \\\\[/tex]

Equation of line PQ is given as:

[tex] \frac{y-y_1}{y_1 - y_2}=\frac{x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-3}{3 - 10}=\frac{x-2}{2 - 6} \\\\

\therefore \frac{y-3}{-7}=\frac{x-2}{-4} \\\\

\therefore \frac{y-3}{7}=\frac{x-2}{4} \\\\

\therefore 4(y-3)=7(x-2)\\\\

\therefore 4y-12=7x-14\\\\

\therefore 7x-14 - 4y + 12=0\\\\

\red{\boxed {\therefore 7x-4y - 2 =0}} [/tex]

Answer:

length = square root of ((2-6)^2)+((3-10)^2) = square root (of) 16+49

square root of 65 =  8.062257748  = approx 8.1

midpoint = (x1+x2)/2  ,  (y1+y2)/2

= 2+6  /2  ,  3+10  /2

=8/2 , 13/2

= 4, 6.5 (midpoint)

equation= y=mx+c

m(gradient) = (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)

= so,  (3-10)/(2-6)  (y1-y2)/(x1-x2)- i normally use this one

= -7/-4 = 1.75

so y=1.75x+c

plug in the values from any one of them (2,3) or (6,10)

to get

for example:  3=1.75*2+c

3=3.5+c

-0.5=c

now we get the equation y=1.75x+(-0.5)

you always have to have a plus( +(-0.5)) since the equation is y=mx+c

Answer: 3600

Step-by-step explanation:

Answer:

not too sure sorry :(

Step-by-step explanation:

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark, get ready, start.

Answer:

the answer is to 72 divided by 1/3 is 216

The result of the division 72 divide by 1/3 is : 216.

Here, we have,

given that,

What is 72 divide by 1/3

we know that,

72 divide by 1/3 is the same thing as 72 times 3/1.

i.e. 72 ÷ 1/3

=> 72 × 3/1

now, we know that,

So 72 x 3 = 216

=> 216/1

And 216 divided by 1 is 216.

so, we get,

Hence, The result of the division 72 divide by 1/3 is : 216.

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Answer:help with mine ples

Step-by-step explanation: beause i need it orther wise i fail

Lateral surface area is given as the area of all sides of a figure excluding the area of the base where as surface area is the sum of the areas of all faces of the solid.

Step-by-step explanation:

Lateral surface area is given as the area of all sides of a figure excluding the area of the base where as surface area is the sum of the areas of all faces of the solid.

If given total surface area, you can find lateral surface area by subtracting the area of the base from the surface area of the solid.

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Lateral surface area refers to the area of the sides only, while total surface area includes the area of all faces. To compute the lateral surface area from the total surface area, subtract the areas of the bases. This process isolates the lateral surface area.

The difference between lateral and surface area is critical in understanding geometric shapes. In contrast, the total surface area includes the area of all the faces, including the bases. For example, in a cylinder, the lateral surface area is the area of the side rolled out into a rectangle, while the total surface area includes the areas of the upper and lower two circular bases.

If you are given the total surface area of a cylinder and need to determine the lateral surface area, you can use the following steps:

Answer:

y = 30

Step-by-step explanation:

If y varies directly with x, then you can make a ratio:

24/8

Simplify the ratio:

3/1

Y is always the first number/ on top in a ratio, that's where I get 24 over 8

3/1 means that y is triple x

so 10 * 3 is 30

Brandus bought a total of 7/12 pounds of meat by adding together 1/3 pound of ground turkey and 1/4 pound of ground beef.

To find out how much meat Brandus bought, you need to add the weights of the ground turkey and the ground beef. Brandus bought 1/3 pound of ground turkey and 1/4 pound of ground beef.

Convert the fractions to have a common denominator:

1/3 = 4/12 (multiply both the numerator and the denominator by 4)

1/4 = 3/12 (multiply both the numerator and the denominator by 3)

Add the two amounts:

4/12 + 3/12 = 7/12

Hence, Brandus bought 7/12 pounds of meat in total to make sausages.

Answer:

The ordered pair (6,3) can not be a solution for the problem situation.

Step-by-step explanation:

Marcus has total 50 tokens to spend at the carnival.

Now, given that the Ferris wheel costs 7 tokens and  the carousel costs 5 tokens.

So, if Marcus play the Ferris wheel for x times and the carousel for y times, the total expenditure will be given by

7x + 5y = 50 ............ (1)

Now, the ordered pair (6,3) i.e. x = 6 and y = 3 does not satisfy the above relation equation (1).

So, the ordered pair (6,3) can not be a solution for the problem situation. (Answer)

The angles of a triangle always add to 180°. In the triangle with 35°, we know that the other angle is 55° since 180 - 90 - 35 = 55. Know we know that 55° angle, 60° angle and the unknown angle will add to 180° because they form a flat line. So 180 - 60 - 55 = 65. Next, we subtract 65° and 90° from 180° to get the last unknown angle, which is 25°. Lastly we subtract 25° from 180 because the x angle and the 25° angle form a a flat line. 180 - 25 = 155.

I believe the measure of angle x is 155°.

The required value of the exterior angle x = 155°

A figure of angle in triangles is shown in which the value of x is to be determined.

The angle can be defined as the one line inclined over another line.

From the image attached below From the orange triangle,
The sum of the interior angle of a triangle is 180°,
35 + 90 + z =180
z = 180 -90 - 35
z = 55
Now, the sum of the angle
z + y + 60 = 180
55 + y + 60 = 180
y = 180 -60 - 55
y = 65

Now angle x can be given as the sum of the remote angle is equal to exterior angle x.
35 + z + y = x
35 + 55 + 65 = x
x = 155

Thus, the required value of the exterior angle x = 155°

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Answer:

B) GREATEST POSSIBLE PROBABILITY in any experiment is 1.

Step-by-step explanation:

The probability of any event E is given as:

[tex]\textrm{Probability of any event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}}[/tex]

Let us assume the the number of TOTAL OUTCOMES of any event E  = n

Now, if the event is a SURE EVENT, then all outcomes are favorable events.

So, the total number of maximum  favorable events   = n

[tex]\textrm{Probability of event E} = \frac{\textrm{Number of favorable events}}{\textrm{Total Number of outcomes}} = \frac{n}{n} = 1[/tex]

Hence, the GREATEST POSSIBLE PROBABILITY in any experiment is 1.

Answer:

          [tex]\large\boxed{-7\text{ }dollars\text{ }per\text{ }hour}[/tex]

Explanation:

The average rate of change is the ratio of the change in the dependent variable (Money Earned) to the change in the independent variable (Hour).

Thus, the average rate of change for the data from the 5th hour to the 8th hour is calculated using the points (5, 96) and (8, 75) from the graph. This is, what happens in the middle does not affect the average rate of change.

          [tex]Rate\text{ }of\text{ }change=(\$75-\$96)/(8hour-5hour)[/tex]

          [tex]Rate\text{ }of\text{ }change=(-\$21)/(3hour)=-7\text{ }dollars\text{ }per\text{ }hour[/tex]

Answer:

−7 dollars per hour per hour

Step-by-step explanation:

took test

Answer:

32 cups of water is needed to fill a 2 gallon water tank.

Step-by-step explanation:

Here, the amount of water to be filled in the fish tank = 2 gallons

The utensil to measure water   =  a measuring cup

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

Hence, 32 cups of water is needed to fill a 2 gallon water tank.

The best scenario for an exponential function is Option B, as it describes a consistent percentage decrease annually, which is characteristic of exponential decay.

The situation that is best modeled by an exponential function is Option B, which describes the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually. This exemplifies an exponential decay scenario where the rate of change of a quantity is directly proportional to its current value. Over time, the substance decreases by a consistent percentage, which is characteristic of exponential decay functions.

A key feature of exponential relationships is that they describe processes where the change at any given point is proportional to the current amount, which fits the description of a substance decreasing by a consistent percentage each year.

Answer:

x=98,217

Step-by-step explanation:

936 + 97281 = x

x=98217

Answer:

936 + 97281 = 98,217‬

x = 98,217‬

You just need to add to find x

Answer:

A. 2x/3

Step-by-step explanation:

4xsqrt5-2xsqrt5/3sqrt5

4x-2xsqrt5/3sqrt5

2xsqrt5/3sqrt5

2x/3

Answer:

The percent in increase is 18%.

Step-by-step explanation:

Given:

The price of gasoline rose from $2.45 in May to $2.89 in August.

Now, to find the percent of increase.

The price of gasoline in May = $2.45.

The price of gasoline in August = $2.89.

So, we get the price of increase:

[tex]2.89-2.45=\$0.44.[/tex]

Now, to get the percent increase:

[tex]\frac{0.44}{2.45} \times 100[/tex]

[tex]=0.179\times 100[/tex]

[tex]=17.9\%.[/tex]

The increase in percent nearest to whole = 18%.

Therefore, the percent in increase is 18%.

To find the percent increase in gasoline prices, you subtract the initial price from the final price, divide this difference by the initial price, and then multiply by 100 to get a percentage. In this case, the increase in price was about 18%.

The first step to finding the percent of increase in the price is to subtract the initial price from the final price. So, $2.89 - $2.45 equals $0.44. This is the amount of the increase in price. Then, to find the percentage of this increase, we divide the increase by the initial price, and multiply by 100 to convert it into a percentage. So, ($0.44 / $2.45) * 100 equals about 18%. So the percent of increase in the price of gas from May to August is 18%.

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Answer:

  a linear equation with a solution of m = 7

Step-by-step explanation:

The equation is a linear equation in m.

Perhaps you want the value of m that is the solution to the equation.

  10m -6m +27 = 9m -9 +1 . . . . . eliminate parentheses

  4m +27 = 9m -8 . . . . . . . . . . . . collect terms

  35 = 5m . . . . . . . . . . . . . . . . . .  add 8-4m to both sides

  7 = m . . . . . . . . .  divide by the coefficient of m

The solution is m = 7.

Answer:

4 units

Step-by-step explanation:

Distance formula:

[tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

[tex]length \: of \: line \: xy \\ = \sqrt{(3 - 3 )^{2} + (1 - ( - 3))^{2} } \\ = \sqrt{(1 + 3)^{2} } \\ \ = \sqrt{4^{2} } \\ = 4 \: units[/tex]

Or since both coordinates lie at x=3, the line is a vertical line so you can simply count the increase in y to find the distance of the line.

1-(-3)= 4 units

Answer:

[tex]f(5)=2.048*10^{-7}[/tex]

Step-by-step explanation:

We have that [tex]f(x)=2x^{-10}[/tex], we want to find [tex]f(5)[/tex].

We can rewrite this function with positive index to get:

[tex]f(x)=\frac{2}{x^{10}}[/tex]

We need to substitute [tex]x=5[/tex] into the given function to get:

[tex]f(5)=\frac{2}{5^{10}}[/tex]

This implies that:

[tex]f(5)=\frac{2}{9765625}[/tex]

In scientific notation:

[tex]f(5)=2.048*10^{-7}[/tex]

Second graph.

Hello! You haven't provided any relationship, but I found it on the internet and it is the table attached below. The point-slope form of the equation of a line is given by:

[tex]y=mx+b[/tex]

So:

[tex]y-Intercept: \\ \\ (0,b) \\ \\ \\ From \ the \ table: \\ \\ (0,b)=(0,46) \\ \\ So: \\ \\ b=46[/tex]

Finding the slope:

[tex]m=\frac{39-46}{1-0} \\ \\ m=-7[/tex]

So the equation of the line is:

[tex]y=-7x+46[/tex]

From the graphs, only option 2 and 4 have negative slope and only option 2 passes through [tex](0,46)[/tex]

Conclusion: Correct option is second graph.

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Answer:

Step-by-step explanation:

203 miles in 3.5 hrs....and 243 miles in 4.5 hrs

totaling : (203 + 243) miles in (3.5 + 4.5) hrs = 446 miles in 8 hrs

speed = distance / time

speed = 446 / 8

speed = 55.75 mph <==

Yo sup??

cot(7π/6)=cot(π+π/6)

=cot(π/6)

=√3

Hope this helps

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the trigonometric identity

cot x = [tex]\frac{1}{tanx}[/tex]

Consider tan([tex]\frac{7\pi }{6}[/tex] )

[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant where tan > 0

Thus tan([tex]\frac{7\pi }{6}[/tex] ) = tan([tex]\frac{7\pi }{6}[/tex] - π ) = tan([tex]\frac{\pi }{6}[/tex] ) = [tex]\frac{1}{\sqrt{3} }[/tex]

Hence

cot([tex]\frac{7\pi }{6}[/tex] ) = [tex]\frac{1}{\frac{1}{\sqrt{3} } }[/tex] = [tex]\sqrt{3}[/tex]

The height of the redwood tree can be determined through trigonometry, using the tangent of the angles given and the distances provided. The height of the tree from point B is found to be 1.8 feet, and the total height of the tree from point A is found to be approximately 30.9 feet.

In this question, we can use trigonometry to solve the problem. From point B, we see two angles. The smaller angle, 85.8°, is the angle from the line extending to the tree and line AB, and the greater angle is 90°. Therefore, the angle between the line extending to the top of the tree and line AB is (90-85.8)= 4.2°.

Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle, we can solve for h. Tan 4.2° = h/24.8 feet. Solving for h gives us h = 24.8 feet * tan 4.2°. Using a calculator, we find that h is approximately 1.8 feet.

Similarly, let's calculate the height from point A. From point A, the angle of elevation to the top of the tree is 10.4°. The distance from the tree to point A is the sum of the length of AB (24.8 feet) and the length from B to the tree (h/tan 85.8°). So, the total height of the tree is h (from point B) + distance from A to the tree * tan 10.4°. This calculation gives us h = 1.8 feet + (24.8 feet + 1.8 feet/tan 85.8°)*tan 10.4°. After doing the calculations, we find that the height of the tree is approximately 30.9 feet when rounded to one decimal place.

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Answer:

Option $152.19

Step-by-step explanation:

Data provided in the question:

Previous balance = $152.35

Finance charge = $1.78

New purchases of $45.23 and $15.67

Payment = $50.00

Credit = $12.84

Now,

New Balance

= [Previous balance + Finance charge + New purchases ] - [ Payments + Credits ]

= [ $152.35 + $1.78 + ($45.23 + $15.67) ] - [$50.00 + $12.84 ]

= $215.03 - $62.84

= $152.19

Hence,

Option $152.19

Answer:

131.04

Step-by-step explanation:

I did it and got it right.

Tommy have to pay $133.2

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Price of book = $180

Discount= 30% off

and, tax = 4%

So, the total discount will be = 30- 4= 26%

Then, price after 26% discount

= 180 - 26% of 180

= 180 - 46.8

= 133.2

Hence, Tommy have to pay $133.2

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