The population of a bacteria colony doubles every 6 hours. For example, starting with a sample of 10 bacteria, after 6 hours there would be 20 bacteria and so on. After 12 hours there would be 40, and so on. Now consider a scientist who has collected a colony of 25 bacteria. Create an expression and approximate the number of bacteria after 3 hours.

Answer:

In Triangle FGH, m<F = 42 and an exterior angle at vertex H as a measure of 104. What is the measure of <G?

Step-by-step explanation:

Answer:

82 units

Step-by-step explanation:

look at the paper...

The graphs and their functions/equations are all illustrations of quadratic functions.

The zeros of a function of a graph are the points where the line or curve of the graph crosses the x-axis

The axis of symmetry of a graph is the line that divides the graph into equal  halves

The vertex of a function is the minimum or the maximum point on the graph

The vertex of a quadratic function is minimum if it opens upward, otherwise the vertex is maximum

Using the above definitions, the solutions to the worksheet are:

Graph 1

Graph 2

Graph 3

Graph 4

Graph 5

Graph 6

Graph 7

Graph 8

Graph 9

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Answer:

176 cubic cm

Step-by-step explanation:

[tex](2 \times 8 \times 2) + (3 \times 6 \times 8) = 32 + 144 = 176[/tex]

Answer:

580.4 cm^2 to the nearest tenth.

Step-by-step explanation:

If we draw a perpendicular line from the top right vertex to the base we split the figure into 2 triangles and a rectangle in the center.

Left side triangle:

base = √(28^2 - 20^2)    (using Pythagoras theorem

= 19.600

So its area = 1/2 * 19.6 * 20 = 196 cm^2.

Right side triangle:

Base = √(30^2 - 20^2) = 22.361

Area = 1/2 * 22.361 * 20 = 223.61 cm^2

Rectangle:

Base of rectangle = 50 - 19.6 - 22.361 = 8.039.

Area = 8.039 * 20 = 160.78.

So the area of the whole figure

= 196 + 223.61 + 160.78

= 580.39 cm^2.

Answer:

The Letter E has 1 line of symmetry. (Horizontal)

Step-by-step explanation:

Yes, because if you fold it in half (horizontally), both halves match up.

Answer:

First number = 9

Second number = 7

Step-by-step explanation:

Let x be the first number and y be the second.

2x + y = 25

3x - y = 20

1) Add them together.

5x = 45

x = 9

2) Solve for y.

2(9) + y = 25

y=7

3) Check your work on the other equation.

3(9) - (7) = 20

27 - 7 = 20

20 = 20

Therefore the first number is 9 and the second number is 7.

Answer:

a) growth

b) $500

c) 6% = 0.06

d) [tex]f(x)=500(1.06)^x[/tex]

e) $595.51

Step-by-step explanation:

Part (a)

Exponential GROWTH, since interest is applied to the account each year.

Part (b)

Initial amount = $500

Part (c)

Growth factor = 6% = 0.06 (in decimal form)

Part (d)

General form of exponential growth function:

[tex]f(x)=a(1+r)^x[/tex]

where:

Given:

[tex]\implies f(x)=500(1+0.06)^x[/tex]

[tex]\implies f(x)=500(1.06)^x[/tex]

Part (e)

when x = 3

[tex]\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}[/tex]

Answer:

4

Step-by-step explanation:

[tex](-1 (\frac{2}{3} - 4)) / (5/6)[/tex]

Let's solve for the numerator first:

PEMDAS says parenthesis first so...

2/3 - 4, we'll turn 4 into an improper fraction so it's easier

2/3 - 12/3 = -10/3

-1(-10/3) = (+)10/3

Now, we replace this as the numerator:

(10/3) / (5/6)

To divide, we multiply the first fraction by the reciprocal of the second:

(10/3) * (6/5) = 60/15

now simplify.....

60/15 = 4 or in other words, {15 * 4 = 60}

So, the answer is 4!

Answer:

Step-by-step explanation:

Since you did not include what the point is that you are trying to label, I can only tell you which quadrant is which. The quadrants go from 1 to 4 in a counterclockwise direction, starting from the top right quadrant (or the +,+ quadrant). One easy way to remember which direction the quadrants go in is the letter C, as they follow the same path as that letter.

I included a diagram to help.

Hope this helps! :)

Answer:

In radian :

[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]

In degree :

45° and 225°

Step-by-step explanation:

the x and y coordinate on the unit circle exactly the same at the angles :

In radian :

[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]

In degree :

45° and 225°

At those angles :

[tex]\left( x,y\right) =\left( \frac{\sqrt{2} }{2} ,\frac{\sqrt{2} }{2} \right) \ or\ \left( x,y\right) =\left( -\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} \right)[/tex]

Answer:

x = -17y/2+y

Step-by-step explanation:

Reorder the terms -7y = 2x + xy + 10y

Move the terms -7y = 2x + yx + 10y

Rewrite collect like terms -2x - yx = 10y + 7y

Divide both sides (-2 - y)x = 17y

simplify x = 17y/-2-y

Solution x = -17y/2+y

Have a good day <3

Mee

increase 31 kg by 100%

Write two ratios equal to each other :

12/5 = 8/x(second speed)

Cross multiply:

12x = 40

Divide both sides by 12:

X = 3.333 or 3 1/3 km/h

second speed = 3.33 ( as a decimal) or 3 1/3 ( as a fraction) km/h

x=2

_______

x= [tex]\frac{1}{3}[/tex]

Answer:

It is not symmetric and has a peak at $2.00

Step-by-step explanation:

$2.00 has 4 dots while the others have less

in order for it to be symmetric:

it is also not clustered from $1.00 to $5.00 because $1.00 has no amount

There are no gaps as $1.00 has no amount

Answer:

It is not symmetric and has a peak at $2.00

Step-by-step explanation:

hope i helped you very much

Answer:

Hence, the security camera be adjusted in order to have the lens aimed at point. P. on the ground at an angle of depression of. x∘=30∘

Step-by-step explanation:

Answer:

$15.00

Step-by-step explanation:

Just did the quiz

By evaluating the piecewise function, we will see that the brother owes $15.

The piecewise function is:

y = 26,   if 0 < h < 4

y = 26 + 5*(h - 4),  if 4 < h < 8

y = 60, if 8 < h

Barbara uses it for 3 hours, so we only need to use the first part for her, so she needs to pay $26.

Then the brother uses it for 4 hours (and we need to add the 3 hours that Barbara used it, so we have h = 7).

Then for the 7 hours the two brothers need to pay:

y = $26 + $5*(7 - 4) = $41

If we subtract the part that Barbara needs to pay we get.

$41 - $26 = $15

This means that the correct option is $15.

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Answer:

14 pi

Step-by-step explanation:

Here,

Area = 49 pi

Pi r ^2 = 49 pi

r^2 = 49

r = 7m

Now,

Circumference = 2 pi r

=2*pi *7

=14 pi

Answer: 0.47 is equal to 47/100

Step-by-step explanation:

1.00=100 Is like pennies, if you have a hundred of them you have 1 dollar but since there’s only 47 it’s out of a hundred

Answer:

0.47 as a fraction equals 47/100

Step-by-step explanation:

Write 0.47 as  

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

[tex]\frac{0.47}{1}[/tex] = [tex]\frac{0.47 x 100 } {1x100}[/tex] = [tex]\frac{47}{100}[/tex]

So, 0.47 as a fraction  in simpliest form equals 47/100

Answer:

3,500

Step-by-step explanation:

700,000/200

7,000/2

3,500

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

Explanation:

The given statement is claiming something like [tex]P(X < 2)[/tex] produces a different result compared to [tex]P(X \le 2)[/tex]. The subtle difference of course is the "or equal to".

When talking about continuous random variables, the two values are the same. Why? Because probability of selecting *exactly* X = 2 is going to be zero. Think of a very very thin strip of height P(X = 2) and the width is approaching zero. The width is doing this because we're trying to pinpoint X = 2 itself. As you can see, this skinny rectangle will have its area approach 0. Ultimately, whether we compute [tex]P(X < 2)[/tex] or [tex]P(X \le 2)[/tex], it doesn't matter. They both produce the same result.

If you are a visual learner, consider the standard normal distribution. Now consider the task if shading to the left of z = 2. This area describes both probabiltiies mentioned above.

If X is a continuous random variable, then [tex]P(X < 2) = P(X \le 2)[/tex] and we can change the "2" to any number we want to have the same outcome.

Therefore, the original claim is false.

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

Extra info:

Now if X was discrete (say from the binomial distribution), then the two probabilities would be different. This is because

[tex]P(X < 2) = P(0) + P(1)\\\\P(X \le 2) = P(0) + P(1) + P(2)\\\\P(X < 2) \ne P(X \le 2) \ \text{only if X is discrete}[/tex]

We can see in this case that the second line has P(2) while the first one does not.

So the original claim would be true if we changed "continuous" to "discrete".

A geometric series is the sum of an unlimited number. The common ratio of the geometric sequence is 3.

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁ is 10, while the value of a₅ is 810, therefore, the common ratio can be written as,

[tex]\dfrac{a_5}{a_4} \times \dfrac{a_4}{a_3} \times \dfrac{a_3}{a_2}\times \dfrac{a_2}{a_1} = r \times r \times r \times r\\\\\\\dfrac{a_5}{a_1} = r^4\\\\\\dfrac{810}{10} = r^4\\\\\sqrt[4]{81} = r\\\\r = 3[/tex]

Hence, the common ratio of the geometric sequence is 3.

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Answer:

The answer with calculator would be 2.16096

Answer:

$3.50

Step-by-step explanation:

add up all the x's and distribute them starting from the outside until you get to the middle. if there is an odd number of x's (which there isn't), the last x to be placed will be on the spot that is the median. If there is an even number of x's, and they both land on the same spot, that spot will be the median, and if they are next to each other, the median will be between them.

Answer:

y = -3x -1

Step-by-step explanation:

Hi there!

We are given a line on a coordinate grid, with 2 marked points, (-1, 2) and (1, -4)

We can use these points to help find the equation of the line, which we can write in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope of the line
The formula for the slope calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to help avoid confusion.

[tex]x_1=-1\\y_1=2\\x_2=1\\y_2=-4[/tex]

Now substitute these values into the formula to find the slope

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

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

Simplify

m=[tex]\frac{-4-2}{1+1}[/tex]

m=[tex]\frac{-6}{2}[/tex]

Divide

m= -3

The slope of the line is -3

We can substitute this into the formula.
Here's our line so far:

y = -3x + b

Now we need to find b

As the equation passes through the points (-1, 2) and (1, -4), we can use either one to find the value of b

Taking (-1, 2) for example:

Substitute -1 as x and 2 as y.

2 = -3(-1) + b

multiply

2 = 3 + b

Subtract 3 from both sides

-1 = b

Substitute -1 as b.

y = -3x - 1

Hope this helps!

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Answer:

Permutation is an arrangement of things where order of arrangement matters. The position of each thing in a permutation matters. Thus, Permutation can be associated with Position.

Combination is grouping/selection of things where order does not matter. Permutation can be considered as an ordered combination.

Note the derivative rule

[tex]\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}[/tex]

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}[/tex]

[tex]\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})[/tex]

[tex]\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)[/tex]

Answer:

7 boxes

Step-by-step explanation:

16+19 is 35. divide 35 by 5 and you get 7 boxes