A scientist is working with a type of bacteria that duplicates itself every minute. He used the function f(b)=1 and the function g(b)=2^b to create the function h(b)=1×2^b, where b is the time in minutes.

After 5 minutes, how much bacteria should there be?

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

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Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

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Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

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If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

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In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

Answer:

Its's the letter B 24cm²

Answer:

b) 24 is the area

Explanation:

Formula area of triangle: (bxh)/2

Area of triangle:

A= 12 x 4= 48 ÷ 2= 24

Answer:

Volume of hemisphere =

[tex] \frac{2}{3} \pi \: r {}^{3} [/tex]

Given volume =

[tex]18\pi \: cube[/tex]

[tex] \frac{2}{3} \times \frac{22}{7} \: {r}^{3} = 18 \times \frac{22}{7} [/tex]

So pi is there on both the sides so it will be cut from both LHS and RHS

[tex] \frac{2}{3} \times r {}^{3} = 18[/tex]

[tex]2 \times r {}^{3 } = 18 \times 3[/tex]

[tex]2 \times r {}^{3} = 54[/tex]

[tex]r {}^{3} = \frac{54}{2} [/tex]

[tex]r {}^{3} = 27[/tex]

[tex]r = 3[/tex]

Therefore value of r=3 inches

If you are helped with my answer pls tag me brianliest I really want it... Plzz

THANK YOU

Answer:

13, 14, 13, 4.6, 48

Step-by-step explanation:

these are the x-values I have but I don't know hot to solve for th code.

Answer:

[tex]2f \: \alpha \: d \\ 2f = kd \\ : k \: is \: a \: constant \\ 2( \frac{3}{4} ) = k \times 1 \\ k = \frac{3}{2} \\ \therefore2f = \frac{3}{2} d \\ 4f = 3d \\ f = \frac{3}{4} d[/tex]

Answer:

3/1=1/3

Step-by-step explanation:

split the 60 ozs to 3

Answer: Cheeseburger

Real explanation:

Minimum: 28

Lower quartile: 32.5

Median: 39

Upper quartile: 49.5

Maximum: 56

Interquartile range: 23.5

Answer:

68 aliens

Step-by-step explanation:

Take the fraction of aliens that had 3 eyes and multiply by the number of aliens

17 / 40 * 160 =

17 * 160/40

17 *4

68

Answer:

x(x^2 + 6)

Step-by-step explanation:

We are to simplify -3x(x-4)-2x(x+3).  Begin by performing the indicated multiplication.  We get -3x^2 + 12x - 2x^2 - 6x.

Combining like terms, we get    -5x^2 + 6x, which is equivalent to

                                                       x(x^2 + 6)

Answer

=5x²+12x-6

Step-by-step explanation:

you multiply -3x(x-4)-2x(x+3)

=-3x²+12x-2x²-6

group like terms

=-3x²-2x²+12x-6

=-5x²+12x-6

Answer:

7.2 is your answer:)

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

Pythagorean Theorem = a² + b² = c²

6² + 8² = c²

36 + 64 = c²

100 = c²

c = 10

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

10

Step-by-step explanation:

pythagorean thereom

6^2 + 8^2 = c^2

100 = C^2

c = 10

Answer:

isosceles and obtuse

Step-by-step explanation:

We have 2 sides that are equal length - isosceles

We have an angle that is greater than 90 and less than 180 - obtuse

Answer:

B. Isosceles and Obtuse

Step-by-step explanation:

Two sides of the triangle have equal length, and one angle is more than 90 degrees.

Answer:

Step-by-step explanation:

You haven't given the choices but I believe the equation below could represent the area of the circle:

(pi ~ 3.14) * (18)^2

The area for a circle is pi * radius squared, so to find the radius divide the diameter by 2.

Step-by-step explanation:

In order to find the number of solutions, we have to expand both sides out first.

[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2)[/tex]

First, expand 3(x-2), which will obtain 3x-6.

Next, expand (1/2)(6x-2), which gives 3x - 1.

The result at this point should be as shown below:

[tex]3x - 6 + 7x = 3x - 1[/tex]

Now, we would shift all x terms to the left and all number terms to the right.

[tex]3x + 7x - 3x = - 1 + 6[/tex]

After simplifying, the final equation would be:

[tex]7x = 5[/tex]

This is a linear equation and it has one solution.

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

Answer:

x = 5/7

Step-by-step explanation:

Answer:

30k

Step-by-step explanation:

Answer:

The heavier boy would weigh 86 pounds.

Step-by-step explanation:

Let's say boy=b, the equation would be:

2b+34=138

This is because the boys would weigh the same, with an exception of 34 pounds.

But we need to find just one person's weight. So bring 34 to the other side:

2b=138-34

Solve:

2b=104

Now, we need to find b:

b=52

So one boy would weigh 52, and the other would weigh 52+34, which is 86.

The heavier boy would weigh 86 pounds.

Happy learning!

--Applepi101

Answer:

2√2

Step-by-step explanation:

< C = 180-15-45 = 120°

AC/sin 45° = AB/sin 120°

AC = 2√3 × sin 45° / sin 120°

= 2√3 × ½√2 / ½√3

= 2√2

Answer:

2√2

Step-by-step explanation:

Answer:

yes that is a statistical question

Step-by-step explanation:

Step-by-step explanation:

1st one

2nd

4th

Answer:

3. 31

4. 6

5. 7

6. No  because the frequency table shows only ranges of times.

Step-by-step explanation:

3. Add up the number of students in each section of your table:

6 + 2 + 8 + 6 + 9 = 31

4. Only the first group ran under 9 minutes.

5. 8 students ran 1 mile in under 10 minutes (the first two sections)

15 students took 11 or more minutes to run 1 mile (the last 2 sections)

15 - 8 = 7

6. No, because the frequency table shows only ranges of times.

There are 31 students in PE class, 6 students ran 1 mile in under 9​ minutes, 8 students are there who ran 1 mile in under 10 minutes than students who took 11 or more minutes to run that​ distance and no student ran a mile in exactly 12​ minutes.

A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data

A frequency distribution table is a method to organize the data given so that it makes it more meaningful and easier to understand.

The given frequency table

Time                  Number of students

8:00-8:59                     6

​9:00-9:59                     2

​10:00-10:59                  8

​11:00-11:59                    6

​12:00-12:59                  9

3. The number of students in the PE class

6+2+8+6+9

=31

4. Only the first group ran under 9 minutes which is 6 students

5.  8 students ran 1 mile in under 10 minutes

6+2=8

15 students took 11 or more minutes to run 1 mile

15 - 8 = 7

6. No, because the frequency table shows only ranges of times.

Hence there are 31 students in PE class, 6 students ran 1 mile in under 9​ minutes, 8 students are there who ran 1 mile in under 10 minutes than students who took 11 or more minutes to run that​ distance and no student ran a mile in exactly 12​ minutes.

To learn more on Statistics click:

https://brainly.com/question/23091366

#SPJ2

Answer:

4523.89m

So for a cylinder it is radius times two. Then multiply your answer by pie 3.14 then times high.

Answer:

bar bar bar bar bar barar bavr

Answer:

11.25

Step-by-step explanation:

Answer:

8 / 0.08888888888

Answer:

B

Step-by-step explanation:

hope it helps