Aubrey is putting flooring in a room that is 13 feet long and 10 feet wide. The flooring costs ​$4.00 per square foot. How much will the flooring for the room​ cost?

Answer:

[tex]\mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

[tex]g(n )= (05)2^n[/tex]

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

SOLUTION:

If we represent g(n) with  t;

Then

[tex]\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}[/tex]

Taking logarithm of both sides; we have :

[tex]\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}[/tex]

Answer:

(a) 11.64%

(b) 8.15%

Step-by-step explanation:

Airborne airlines has an annual interest of payment= $102

Principal payment= $1,000

Time to maturity= 20 years

Current price of the bond= $880

The formular for calculating the yield on maturity is

[ Annual interest payment+Principal payment-(price of the bond/number of years to maturity)] / 0.6(price of the bond) + 0.4(principal payment)

(a) [102+(1000-880)/20)]/ [0.6(880) + 0.4(1000)]

= [102+ (120/20)]/ [528+400]

= [102+6]/ 928

= 108/928

= 11.637%

= 11.64% ( to 2 decimal places)

(b) Kd= Yield(1-T)

Kd= 11.64(1-0.30)

Kd= 11.64×0.7

Kd= 8.145%

Kd= 8.15%( to 2 decimal places)

Hence the yield to maturity on the new issue is 11.64% and the aftertax cost of debt is 8.15%

Answer:

x-3

Step-by-step explanation:

f(x) = 3x-2

g(x) = 2x + 1

(f-g)(x) = 3x-2 - (2x+1)

Distribute the minus sign

          =3x-2-2x-1

Combine like terms

        = 3x-2x-2-1

        =x-3

Answer:

x = 20

Step-by-step explanation:

The angles are vertical angles and we know that vertical angles are equal

x+40 = 3x

Subtract x from each side

x+40-x = 3x-x

40 = 2x

Divide each side by 2

40/2 = 2x/2

20 =x

Answer:

The value of [tex]x[/tex]:

[tex]x = 20[/tex]

Step-by-step explanation:

-Since, one angle with the measure [tex]x + 40[/tex] and another angle with measure [tex]3x[/tex] are vertical angles, they equal each other. So, it will be written as:

[tex]x + 40 = 3x[/tex]

-After you have formed an equation, you switch the equation and you solve for the value of [tex]x[/tex]:

[tex]x + 40 = 3x[/tex]

[tex]x - x + 40 = 3x -x[/tex]

[tex]40 = 2x[/tex]

[tex]\frac{40}{2} = \frac{2x}{2}[/tex]

[tex]20 = x[/tex]

So, the final answer is [tex]20 = x[/tex] or [tex]x = 20[/tex] (They are both the same, you just switch them).

Answer:

18.2%

Step-by-step explanation:

The total number of trees in the wood = 420 + 160 + 300

                                                                = 880 trees

∴ The percentage of the oak trees = [tex]\frac{160}{880} * \frac{100}{1}[/tex]

                                                            = [tex]\frac{2 * 100}{11}[/tex]%

                                                            = [tex]\frac{200}{11}[/tex]%

                                                            = 18.181818...%

In 1 decimal place = 18.2%

Hope this helps!!

Answer:

ABE

DBC

CBE

Step-by-step explanation:

They all have B as the middle one, and B is the vertex

I think

Answer:

Step-by-step explanation:

5.volume=8×7×6=336 mi³

6.r=16/2=8 yd

volume=4/3×π×8³=2048/3 π yd³

≈2144.7 yd³

7.r=2.5/2=1.25 in

v=πr²h=π×1.25²×5

volume of 150 cups=7.8125 π×150=1171.875 π in³≈3681.6 in³

8. statement not visible.

Answer:

103.5 m²

Step-by-step explanation:

To find the area of a right trapezoid, you can decompose it into a rectangle and a triangle. The sum of the area of  the rectangle and the triangle gives the area of the trapezoid.

For the right trapezoid attached below, the area can be gotten by:

Area of rectangle = length × breadth = 9 × 8 = 72 m²

Area of triangle = 1/2(base × height) = 0.5 × 7 × 9 = 31.5 m²

Area of trapezoid = Area of rectangle + Area of triangle = 72 m² + 31.5 m² = 103.5 m²

Answer:

It is a gain.

Step-by-step explanation:

CLEAR STATEMENT:

Given that the fruit seller buys 10 apples for 45Rs each from wholesale market.

This implies her buys them for 10 × 45Rs = 450Rs.

UNCLEAR STATEMENT:

He packs them in a fruit basket for 40 and sells them each for 20 baskets Rs. 600.

ASSUMING:

What you are trying to say is that he bought baskets for 40Rs, and sold the apples for 600Rs.

Subtracting his expenses from this value, we have

600Rs - 450Rs - 40Rs = 110Rs

Since this amount is positive, we conclude that it is a gain of 110Rs.

Answer:

The answer is "Option C".

Step-by-step explanation:

In the given question attachment of the table is missing which can be defined as follows:

[tex]\left\begin{array}{cc}\bold{x} &\bold{f(x)}\\0 & 6 \\2 & 7\\4 & 0\\7 & 5 \end{array}\right[/tex]

In given table a method f(x) values corresponding to different values of x.  

We needed to try f(0) value  that is in this method, we have to calculate the f(x) value if x=0  

As we've seen from the table the f(x) value at x=0 is 6  

That's why the correct choice is option C that is 6.

Answer:

The answer would be C

Step-by-step explanation:

I just took the test !!

Answer: A (4, -7) B (9, -7)

Step-by-step explanation:

When it’s reflected over the x-axis, the y coordinates become negative but the x coordinates don’t change

x coordinates: 4, 9

y coordinates: 7, 7

Reflected over x-axis: (4, -7), (9, -7)

Answer:

First step=13x+7x=18+42

Step-by-step explanation:

13x-42=18-7x

First step

It is to collect like terms of the equation

13x+7x=18+42

20x=60

x=60/20

x=3

Answer:

12 trades

Step-by-step explanation:

Let's call 'x' the number of trades they will do.

After each trade, the number of cards Ian has increase by 1 (he gives 1 but receives 2), and the number of cards Jason has decrease by 1 (he receives 1 but gives 2), so after x trades, the number of cards Ian has is 20 + x, and Jason has 44 - x.

To find the number of trades when they will have the same amount of cards, we have that:

20 + x = 44 - x

2x = 24

x = 12 trades

The number of trades will Ian  and Jason each have an equal number of cards is 12 trades

Let's us assume the x' be the number of trades they will do.

20 + x = 44 - x

2x = 24

x = 12 trades

Learn more: brainly.com/question/16911495

Answer:

Go to me. Click on your profile picture then click on your profile picture again to change it

Answer:

x = 5, y = 9.

Step-by-step explanation:

8^x / 2^y = 64

3^4x * (1/9)^(y -1) = 81

From the first equation

2^3x / 2^y = 2^6

2^(3x-y) = 2^6

So 3x - y = 6  ..........(1)

From the second equation:

3^4x * 9^(-(y-1)) =  3^4

3^4x * 3^2(-(y-1)) = 3^4

3^(4x+ 2(1 - y)) = 3^4

So 4x + 2(1 - y) = 4

4x - 2y = 2

2x - y = 1   .............(2)

Subtract: (1) - (2):

x = 5.

and  2(5) - y = 1

so y = 9.

Solving the simultaneous equations we get x is 5  and y is 9 .

Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.

A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.

The two given equations can be simplified as:

[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]

And :

[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]

Now we can solve the two simultaneous equations :

3x - y = 6 and 2x - y = 1

Subtracting the equations we get:

x = 5

and

y = 9

Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .

To learn more about simultaneous equations visit:

brainly.com/question/16763389

#SPJ1

Answer:

(x)1.4=Y

Step-by-step explanation:

40% increase of memeber so ita 140% of X

Answer:

V of cylinder = V=πr^2h

V of rectangular prism = l*w*h

V of cylinder = 16 * 3.14 * 8

                      = 401.92

V of rectangular prism = 14 * 8 * 12

                                      = 1344

Add = 401.92 + 1344

       = 1,745.92

Answer:

Number of people in a room

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Its either 10 to the power of 6 or ten to the power of 5

Step-by-step explanation:

...

Answer:

0.3° = 0.3π/180

8° = 2π/45

Multiplying both

0.3π/180×2π/45

3/10π/180 × 2π/45

You will get

π/300 × π/45

= π²/13500 where a = π² b= 13500

Hope this helps.

Answer:

Step-by-step explanation:

The graph of a function and its inverse will always reflect through the line

y = x.

This is because a function has a specific set of coordiates, (x, y). That function's inverse has a set of coordinates that flips the x and y coordinates. For example, if a function has a set of coordinates (0, 1), (2, 3), (4, 5) then its inverse will have the coordinates (1, 0), (3, 2), (5, 4). If you plot the function's points and then the inverse's points in the same plane (meaning on the same graph) and connect the dots, you will see that the function and its inverse are reflections of each other through y = x. Below is an example of this. The dotted purplish line is the line y = x.

Answer: b. (6,27)

Step-by-step explanation:

y=5x- 3     x=6<---- put in the equation

y=5(6)-3 <------- mulitply 5 and 6

y=30-3 <---- subtracted

y= 27. <---- y value.

Answer being (6,27)

Hope it helps :)

Answer:

x = -2

Step-by-step explanation:

-5x - 7 = 3

-5x = 10

x = 10/-5

x = -2

Answer: D. (I, II, and III)

Step-by-step explanation:

having a ticket doesn't necessarily mean you will win the lottery, but you must have a ticket to win

not all numbers divisible by 3 are divisible by 6, but all numbers divisible by 6 are also by 3 (since 3 goes into 6 twice)

if a quadrilateral is a square, it is also a rhombus

Answer:

It is D.

Step-by-step explanation:

If you win the lottery, then you will need a ticket. But, if you have a ticket, it doesn't mean that you'll win the lottery.

If a number is divisible by 3. it is not necessarily divisible by 6. For example, 9 ÷ 3 = 3, but 9 ÷ 6 will not equal a whole number.

All squares are rhombuses, but not all rhombuses are squares (they need to have all interior right angles).

Answer:  [tex]\bold {1)\ \cos\ \theta}=\dfrac{\sqrt2}{2}\qquad 2)\ \tan \theta =\dfrac{1}{3}\qquad 3)\ \cos\ \theta=\dfrac{3\sqrt{13}}{13}\qquad 4)\ \cos\ \theta = \dfrac{2\sqrt5}{5}}[/tex]

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c², where "c" is the hypotenuse

[tex]1)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt2}\quad =\large\boxed{\dfrac{\sqrt2}{2}}[/tex]

Note: 2² + 2² = hypotenuse²  →  hypotenuse = 2√2

[tex]2)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{2}{2\sqrt2}\quad =\dfrac{5}{15}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]

Note: hypotenuse not needed for tan θ

[tex]3)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3}{\sqrt{13}}\quad =\large\boxed{\dfrac{3\sqrt{13}}{13}}[/tex]

Note: 2² + 3² = hypotenuse²  →  hypotenuse = √13

[tex]4)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{2\sqrt5}\quad =\large\boxed{\dfrac{2\sqrt5}{5}}[/tex]

Note: hypotenuse given in problem

Answer:

10% = 1/10

20% = 1/5

100% = 3/3

75% = 3/4

Step-by-step explanation:

Answer:

Awnser is down below

Step-by-step explanation:

75= 3/4

20= 1/5

10 = 1/10

100= 3/3

Hope this helps :)

Answer:

d = 0.0175n    ---> required equation

Billy can buy 285.714 gram nut with $5

Step-by-step explanation:

cost of 100g loose nut = $1.75

dividing LHS and RHS by 100

cost of 100/100g loose nut = $1.75

Thus, cost of 1 gm loose nut = $0.0175

let the weight of loose nut be n gm

Multiplying LHS and RHS by n

cost of x g loose nut = $0.0175*n =  $0.0175n

It is given that Billy spent d dollars to buy n gm nuts

thus,

d = 0.0175n    ---> required equation

________________________________________________

He spent $5 to buy nuts

substituting value of d as 5 we have

0.0175n = 5

=>n = 5/0.0175 = 285.714

Thus, Billy can buy 285.714 gram nut with $5.

Answer:

False, it could be.