Hannah weighed 7.2 pounds at birth. Her weight was recorded at each of her infant doctor visits. The records from her appointments from birth to six months are shown in the table below.

6a) Find the line of best fit:
10 points
Your answer
6b) Estimate Hannah’s weight at her one-year visit:
5 points
Your answer
7. The table below shows the average life expectancy (in years) based on certain birth years.

7a) Find the line of best fit:
10 points
Your answer
7b) Estimate the life expectancy for someone born in 2005

Step-by-step explanation:

Thereafter,

Distance :-

Time :-

Average Speed :-

Answer:

So, if the graph is a straight line,it is the graph of linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change of y with respect to x remains constant for a linear function.

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Step-by-step explanation:

Answer:

[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Integration

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

Trigonometric Integration

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Step 4: Integrate Pt. 3

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

x = 29

Step-by-step explanation:

These angles are vertical angles which mean that they're equal to each other:

2x - 24 = x + 5

2x - x = 5 + 24

x = 29

Percentage decrease is the amount by which a given number is decreased expressed as a percentage.

Reasons:

The percentage by which the number was decreased = 10%

The number is decreased by 10%

Let x represent the number, we have;

New remainder after first decrease = x -  10% × x = x - 0.1·x = 0.9·x

Decreasing the new number by 10% gives;

Second new number = 0.9·x - 0.09·x = 0.81·x

The percentage by which the number is decreased = x - 0.81·x = 0.19·x

The percentage by which the number is decreased = 19%

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Answer:

  x = 6

Step-by-step explanation:

12(x -2) +3x = 1/3(x +12) +10x

12x -24 +3x = 1/3x +4 +10x . . . . . eliminate parentheses

15x = (10 1/3)x +28 . . . . . . . . . . add 24, collect terms

(4 2/3)x = 28 . . . . . . . . . . . . . subtract 10 1/3

x = (3/14)(28) = 6 . . . . . . . . multiply by 1/(4 2/3) = 3/14

The value x=6 satisfies the equation.

Answer:

F =672

Step-by-step explanation:

joint variation is of the form

F = k *q1 * q2

Inversly means divide

F = k * q1 * q2

     -------------------

              d^2

We know  F=8 when q1=2, q2=8, and d=4  so we can solve for k

8 = k * 2*8

    -----------------

          4^2

8 = 16k

     ----

     16

8 = k

Substituting

F = 8 * q1 * q2

     -------------------

              d^2

Let q1=28, q2=12, and d=2

F = 8 * 28 * 12

   ----------------

    2^2

F = 2688

      -------

         4

F =672

We are given:

F varies jointly (directly) with q1 and q2, which means that F is proportional to both q1 and q2. also,

F varies inversely with d², so F is inversely proportional to the square to d

Finding a mathemetical experssion:

using the above information, we can say that:

F ∝ q₁

F ∝ q₂

F ∝ 1/(d²)

joining these together, we get:

F ∝ q₁q₂ / d²

let's say that 'k' is the constant of proportionality in this case,

F = k (q₁q₂ / d²)

First case:

F = 8, q₁ = 2, q₂ = 8, d = 4

we can use these values in our expression to find k

[tex]8 = k\frac{2*8}{4^2}[/tex]

[tex]8 = k\frac{16}{16}[/tex]

k = 8

Finding F in the second case:

q₁ = 28, q₂ = 12, d = 2, k = 8

[tex]F = k\frac{q_{1}*q_{2}}{d^2}[/tex]

[tex]F = 8(\frac{28*12}{2^2})[/tex]

[tex]F = 8(\frac{336}{4})[/tex]

[tex]F = 2(336)[/tex]

F = 672 N

Answer:

24 meters cubed

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Step-by-step explanation:

V=Bh

V=6*4

V=24

Answer:

Volume = 24 m³

Units is either cubic meters, m³ or something like that

BTW, am I a pro hacker know?

Step-by-step explanation:

Volume = B x h

Base = B = 6 m²

Height = h = 4 m

Volume = 6 m² * 4 m

Volume = 24 m³

-Chetan K (aka pro hacker)

Answer:

Part A:

1.40x+8.00=C

Part B:

1.40x+8=26

        -8   -8

1.40x=18

/1.40    /1.40

x=11 total rides

Step-by-step explanation:

An expression to represent this would be 1.40x+8.00=C (C is total cost).

If you had $26.00 you would first spend $8.00 on the entry leaving you with $18.00. Then you would divide the $18 by $1.40 for each ride to get 12.8... It doesn't make sense to go on a fraction of a ride so you just round down to 11 rides

An expression that represent this situation would be 1.40x+8.00=C (C is total cost).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that The amusement park charges $8.00 for entry and $1.40 for each ride.

Part A:

An expression to represent this scenario where r represents the number of rides.

1.40x + 8.00 = C

Part B:

An equation to determine how many rides Kolby can ride if his parents gave him $26.00.

1.40x + 8 = 26

1.40x = 18

x = 11 total rides

An expression that represent this situation would be 1.40x+8.00=C (C is total cost).

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6 and 10. 6*10=60 10-6=4

0.70 ft

Step-by-step explanation:

The volume V of a cone is given by

[tex]V = \dfrac{\pi}{3}r^2h[/tex]

where r is the radius of the base and h is the height of the cone. Since the radius is half the diameter D, we can rewrite V as

[tex]V = \dfrac{\pi}{3}\left(\dfrac{D}{2}\right)^2h = \dfrac{\pi}{12}D^2h[/tex]

But since the base diameter D is always equal to the cone's height, we can write the volume in terms of the height h as

[tex]V = \dfrac{\pi}{12}h^3[/tex]

Now gravel is being added to the conical pile at a rate of 35 cubic ft per minute so to find the rate at which the height of the pile is increasing, we are going to take the derivative of V with respect to time:

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}\left(\dfrac{\pi}{12}h^3\right)[/tex]

[tex]\:\:\:\:\:\:\:= \dfrac{\pi}{12}\cdot 3h^2\dfrac{dh}{dt} = \dfrac{\pi}{4}h^2\dfrac{dh}{dt}[/tex]

Rearranging the variables and solving for dh/dt, we get

[tex]\dfrac{dh}{dt} = \dfrac{4}{\pi h^2}\dfrac{dV}{dt}[/tex]

[tex]\:\:\:\:\:\:\:\:= \dfrac{4}{\pi(8\:\text{ft})^2}(35\:\text{ft}^3\text{min})[/tex]

[tex]\:\:\:\:\:\:\:=0.70\:\text{ft/min}[/tex]

Step-by-step explanation: −913−(−113)

=−913−(−113)

=−913+113

=−800

Answer:

1/6

Step-by-step explanation:

prob. that first spin will land on blue = 1/4

prob. that the second spin will land on yellow = 2/8

= 1/4 * 2/8 = 1/16  

Answer:

multiply them by a a number that allows the denominators to be the same

Step-by-step explanation:

example

1/2-1/6

I would multiply 1/2 by 3 to get 3/6 which i could then subtract from 1/6

3/6-1/6 = 2/6

Answer:

y = - 1/7x - 7

Step-by-step explanation:

Given equation ,

=> y = -1/7 - 2

On comparing to slope intercept form of the line we get the slope as -1/7

Now as we know that the slope of two parallel lines are same . So the slope of parallel line will be -1/7 .

Using point slope form ,

=> y - 6 = -1/7( x -7)

=> y -6 = -1/7x +1

=> y -7 = -1/7x

=> y = -1/7x -7

Answer:

under

Step-by-step explanation:

B D E

Okay, suppose your income is about $100.

You might spend $70 & save $30.

Now, suppose your income remains constant at $100 but your expenses go up to, say, $90. You can see that your savings will reduce or decrease. Now, you'll only have about $10 to save.

=》 So, if your income is constant, then your savings will 'decrease' when your expenses increase.

_______

RainbowSalt2222 ☔

Answer:

it is a b and c

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

It crosses on the y axis at the point (0,4)

Answer:

4

Step-by-step explanation:

The y-intercept of the line shown is 4.

Hope this helps :)

Answer:

[tex](10x - 14) = (7x - 8) \\ \\ 10x - 7x = 14 - 8 \\ \\ 3x = 6 \\ \\ x\frac{6}{3} \\ \\ x = 2[/tex]

it was equal to each other

Answer:

Option B) 13 is correct

Step-by-step explanation:

Answer:

The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.

Answer:

it is bigger then because 4/12 is in 72 Step-by-step explanation:

Answer:

what

Step-by-step explanation:

Answer:

Appologies but Why do you have pOn open?

Step-by-step explanation:

umm that is inapropriate but idrc

Hi how u doin ?

[tex] log( \frac{x}{x + 1} ) = \\ [/tex]

[tex] log(x) - log(x + 1) [/tex]

Have a great day ❤