Zoe planted a walnut tree. Every week, she measures the tree and records its
growth. On the first week, the tree was 27 1/2 inches tall. On the second week, it was
29 1/4 inches tall. On the third week, it was 31 1/3 inches tall. How much did the tree
grow from the first week until it was measured on the third week? Show your work.

Answer:

Step-by-step explanation:

We want to model the growth of a population of bacteria using an exponential function. We find it convenient to use an "exact" exponential function that relies directly on the numbers given in the problem statement. That function has the form ...

  p(t) = (initial population) × (growth factor)^(t/(growth period))

where the "growth factor" is the multiplying factor of the population in period "growth period."

__

Here, the "growth factor" is 4800/4000 = 1.2, and the corresponding "growth period" is 5 hours. Then the population function can be ...

  p(t) = 4000×1.2^(t/5)

__

The population after 15 hours is ...

  p(15) = 4000×1.2^(15/3) = 4000×1.728

  p(15) = 6912

__

To change this to the form ae^(kt), we find the value of k to be ...

  k = ln(1.2^(1/5)) = ln(1.2)/5 ≈ 0.036463

Then the desired form of the function for p is ...

  p(t) = 4000·e^(0.036463t)

_____

Additional comment

In the form p=ae^(kt) the value of k is often rounded to 3 or 4 decimal places. We believe that best accuracy is obtained if k has at least the number of significant digits expected in the answer. Here, the population of almost 7000 has 4 significant digits, so we choose to express k to 5 significant figures. That still gives a small error relative to the first formula that is only "corrected" by rounding the result to an integer.

Answer:

Step-by-step explanation:

View the attached graph for what your image should look like.

I hope this helps or gives you a picture of what it should look like, because it's quite a long process.

Hope this helps!

Answer:

The answer is (-4, 15/2)

Step-by-step explanation:

Let the Boone be x, Winston-Salem be y, Raleigh be z and Burlington be m.

We are given that Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh.

If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9).

We will use Midpoint Formula

[tex]( \frac{x _{1} + x _{2}}{2} , \frac{y _{1} + y _{2}}{2} ) \\ [/tex]

Where,

x₁ = (-1) and x₂ = (-5)

y₁ = 3 and y₂ = 9

Now, We will find Co-ordinates of y i.e., Winston-Salem.

So,

[tex] ( \frac{( - 1) + ( - 5)}{2} , \frac{3 + 9}{2} ) \\ [/tex]

[tex]( \frac{( - 1 - 5)}{2} , \frac{12}{2} ) \\ [/tex]

[tex]( \frac{ - 6}{2} , \frac{12}{2} ) \\ [/tex]

[tex]( - 3,6)[/tex]

Here, The coordinates of y i.e., Winston-Salem is (-3, 6).

Now, We will find Co-ordinates of m i.e., Burlington.

So,

Again, Using of Midpoint Formula;

Where,

x₁ = (-3) and x₂ = (-5)

y₁ = 6 and y₂ = 9

So,

[tex]( \frac{( - 3) + ( - 5)}{2} , \frac{6 + 9}{2} ) \\ [/tex]

[tex]( \frac{( - 3 - 5)}{2} , \frac{15}{2} ) \\ [/tex]

[tex]( \frac{( -8)}{2} , \frac{15}{2} ) \\ [/tex]

[tex]( - 4 , \frac{15}{2} ) \\ [/tex]

Thus, The coordinates of Burlington is (-4, 15/2).

Answer:

I'm confused with this, I dont understand what you are asking.

Step-by-step explanation:

2 is equivalent with a lot of things,

1+1

3-1

92-90

7×7-47

4÷2

the list goes on...

The cost of the mortgage is $81250

Interests are percentages of a principal

Given the following parameters

Principal = $65000

Rate = 7% = 0.07
Time = 5 years

I = PRT/100
I = 65000*0.07*25
I = 16,250

Cost of mortgage = Principal + Interest

Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250

Hence the cost of the mortgage is $81250

Learn more on mortgage here: https://brainly.com/question/22846480

Answer:

$72,823

Step-by-step explanation:

just took test

Answer:

(8, -2)

Step-by-step explanation:

While reflection over x-axis, the x-coordinate remains the same  and the y-coordinate changes to it's opposite.

So,

Rx-axis =>  = (8, -2)

Answer:

C. 56.42

Step-by-step explanation:

56 is a whole number and .42 is 42 hundredths

Answer: 18:4

Step-by-step explanation:

Ez

Answer:

9 : 2

Step-by-step explanation:

length : Width = 18 : 4

                       [tex]\sf = \dfrac{18 \ \div \ 2}{4 \ \div \ 2}\\\\=\dfrac{9}{2}[/tex]

                       = 9 : 2

Answer:

529/55 and 57/2

Step-by-step explanation:

Step-by-step explanation:

let's first convert feet to inches

4 ft = 48 inches ( width )

6.5 ft = 78 inches ( length )

12.5 ft = 150 inches ( height )

each cube is 1/4 x 1/4 x 1/4

x-axis ( length )

78 ÷ 1/4 = 78 x 4 = 312 cubes

y-axis ( width )

48 x 4 = 192 cubes

z-axis ( height )

150 x 4 = 600 cubes

the total number of cubes fit in the closet is :

312 x 192 x 600 = 35,942,400 cubes

Answer:

Length: 20 feet
Width: 8 feet

Step-by-step explanation:

20 is 12 feet longer than 8

20 x 8 = 160

Answer:

volume = lenght x width x height

v= 12x20x14

v=3,360 in³

Answer:

91.3 and 0913

Step-by-step explanation:

91 + 91 + 91 is an expression that can be simplified into a multiplication problem, because there is a number being added by itself a certain amount of times. So we have to look for a multiplication problems within our answers.

Leading us up to 91(3) and (91)(3), these are both examples of multiplcation.

91.3 would happen if you were adding .3 to 91

And 0913 would happen if you added 91 and 822

Answer:

I think it's D. All rectangles are always parallelogram

Step-by-step explanation:

Please mark me brainliest if correct

Step-by-step explanation:

4cm×2cm×1/2=4cm³

4cm³×8=32cm³

I think the answer is 176

Step-by-step explanation:

please tell me if I'm wrong

The doctoral degree educational level has the highest median income

Education level refers to the years of formal instruction received and successfully completed.

From research in 2017 for those with the highest levels of educational level (doctoral and professional degrees) income is more than triple those with the lowest level (high school diploma)

Find out more on educational level at: https://brainly.com/question/2987151

Answer: Bachelor's Degree, and Male

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

well it's says for a its 35° and B is 100° to find x it would be 180-(35+110)=x

Step-by-step explanation:

180-(35+110)=180-145=35. so x=35°

Answer:

2

Step-by-step explanation:

→ Find the scale factor

12 ÷ 7.5 = 1.6

→ Form an equation

x + 6 = 1.6 ( 2x+ 1 )

→ Solve

x = 2

Answer:

40%

Step-by-step explanation:

Givens and Formula

% Good = (number good / total number) * 100

% Good = ?

Number Good = 32

Total Number = 80

Solution

% Good = (32 / 80) * 100

% Good = 2/5 * 100

% Good = 40%

Answer:

Step-by-step explanation:

According to coordinates on the graphs and numbers in the tables we have the following relationship:

As we see B, C and E have same relationship, matching the target.

Step-by-step explanation:

hope it's help you this answer

Answer:

Step-by-step explanation:

We would like to calculate the centre and the radius of the circle . The given equation is ,

[tex]\longrightarrow (x - 4)^2+(y+3)^2=74 [/tex]

As we know that the Standard equation of circle is given by ,

[tex]\longrightarrow (x - h)^2+(y-k)^2=r^2[/tex]

where ,

We can rewrite the equation as ,

[tex]\longrightarrow (x-4)^2+\{ y -(-3)\}^2=(\sqrt{74})^2\\ [/tex]

Now on comparing to the standard form , we have ;

Graph :-

[tex] \setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\circle*{0.2}}\put(0.2, - .1){(4,-3)}\put(-1.2,0){\vector(0,1){5}}\put(-1.2,0){\vector(0, - 1){5}}\put(-1,0.7){\vector(1,0){5}}\put(-1,0.7){\vector( - 1,0){5}}\put(0,0){\line(-1,0){2.3}}\put( - 1.2,-0.7){$\sf \sqrt{74}$}\put(2,6){$\boxed{\sf \textcopyright \: RISH4BH }$}\end{picture} [/tex]

And we are done !

We are given the equation of circle (x - 4)² + (y + 3)² = 74 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-4)^{2}+(y+3)^{2}=74}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf (x-4)^{2}+\{y-(-3)\}^{2}=({\sqrt{74}})^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

Answer:

25

Step-by-step explanation:

[tex]1^2=1\\\\2^2=4\\\\3^2 = 9\\\\4^2=16\\\\\text{So the next number should be}~ 5^2=25[/tex]

Hello!

To solve this exercise, we must use the formula below:

[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]

Knowing these values, let's replace them in the formula to obtain r:

[tex]\mathrm{62.8=2\cdot\ 3.14\cdot r}\\\mathrm{62.8=6.28r}\\\mathrm{6.28r=62.8}\\\\\mathrm{r=\dfrac{62.8}{6.28}}\\\\\boxed{\mathrm{r=10}}[/tex]

So, the radius of this circle is 10cm.

Hope this helps!

Answer:

5 and 6.

Step-by-step explanation:

7*8 is 56. 56 divided by 10 is 5 6/10

Answer:

3

Step-by-step explanation:

Answer: The correct answer is 3

Step-by-step explanation:

:) it should be correct have a good day!