A teacher teaches 8 students how to fold an origami model. Each of these students goes on to teach 8
students of their own how to fold the same model. If this teaching process goes on for 6 generations,
how many people total will know how to fold the origami model

If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show

[tex]\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx[/tex]

Let [tex]f(x) = \sqrt{1 + x^3}[/tex]. Compute the inverse:

[tex]f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}[/tex]

and we immediately notice that [tex]f^{-1}(x+1)=\sqrt[3]{x^2+2x}[/tex].

So, we can write the given integral as

[tex]\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx[/tex]

Splitting up terms and replacing [tex]x \to x-1[/tex] in the first integral, we get

[tex]\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}[/tex]

Answer:

1)ur first answer is 12

2)Your median is 9

3)9

4) range 7

Step-by-step explanation:

it’s the most common number

The middle numbers are 8 and 10.9 is the number in between them which mean it is the median

4) you subtract the biggest number with the smallest one 12-5=7

Answer:

[1] 12

[2] 9

[3]  9

[4] 5

Step-by-step explanation:

[1] What is the mode for the following set of data?

5,7,8,10,12,12

Answer = 12

Explanation: Mode is what most appears in data set. Thus, we see that 12 is the mode.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[2] What is the median for the following set of data?

5,7,8,10,12,12

Answer = 9

Explanation:

Median is basically what in the middle.

5,7,8,10,12,12

5,7,8,10,12,12

Since there are two number in the middle: Add them up and then divide by 2. 8 + 10 = 18/2 = 9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[3] What is the mean for the following set of data?

5,7,8,10,12,12

Answer = 9

Explanation:

Mean is add all the number up and then divide by total number in data set

5 + 7 + 8 + 10 + 12 + 12 = 54

Total number in data set : 6

54/6 = 9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[4] What is the range for the following set of data?

5,7,8,10,12,12

Answer = 5

Explanation:

Range = IQR = Q3 - Q1

Knowing that;

Quartiles:

Q1 --> 7

Q2 --> 9

Q3 --> 12

Hence, 12 - 7 =5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Lenvy~

Answer:

Option B

Step-by-step explanation:

Numerator:

[tex]\dfrac{3}{x -1 }-4 =\dfrac{3}{x-1}-\dfrac{4*(x-1)}{x-1}\\\\[/tex]

                 [tex]=\dfrac{3- 4x -4*(-1)}{x-1}=\dfrac{3-4x+4}{x-1}\\\\\\=\dfrac{-4x+7}{x-1} \: \textbf{ [Combine like terms]}[/tex]

Denominator:

[tex]2-\dfrac{2}{x-1}=\dfrac{2*(x-1)}{x-1}-\dfrac{2}{x-1}\\[/tex]

                [tex]= \bf \dfrac{2x-2-2}{x-1}\\\\\\= \dfrac{2x-4}{x-1}\\\\= \dfrac{2*(x- 2)}{x-1}[/tex]

[tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\dfrac{-4x+7}{x-1}}{\dfrac{2*(x-2)}{x-1}}[/tex]

                 [tex]\bf = \dfrac{-4x+7}{x-1}*\dfrac{x-1}{2(x-2)} \ \ \ \textbf{ [(x-1) in the numerator and denominator will be cancelled]}\\\\\\=\dfrac{-4x+7}{2(x-2)}[/tex]

The distance between two cars comes to be 4412.06 feet.

Find the attached diagram to visualize it better.

From the attached diagram

The Distance between two cars is x+y

The angle of elevation for the first car = 22 degrees

The angle of elevation for the second car = 65 degrees.

Height of the Goodyear blimp = 1500 feet

The tangent of an angle is the ratio of the opposite side to the adjacent side of that angle.

So, tan 22° = 1500/x

So, x= 1500/tan 22°

x = 3712.63 feet

tan 65° = 1500/y

So, y = 1500/tan 65°

y = 699.46 feet

x+y = 4412.06 feet

So, the distance between two cars =  4412.06 feet

Therefore, the distance between two cars comes to be 4412.06 feet.

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[tex]\text{L.H.S}\\\\=4\sin(-x) \cos(-x)\\\\=-4\sin x \cos x\\\\=-2 \cdot 2 \sin x \cos x\\\\=-2 \sin 2x\\\\=\text{R.H.S}\\\\\text{The identity is true.}[/tex]

Answer:

Ans might be a+b+c

Step-by-step explanation:

Hope the picture will help

Step-by-step explanation:

as I don't see any equations or graphs here I can only answer in general :

f(x) is the patent function.

g(x) is the transformed function.

g(x) = -6f(x-7)

the "-" reflects the curve over the x-axis (what was positive is now negative and vice versa).

the factor 6 stretches the curve up and down by the factor 6 (everything is now 6 times larger or smaller).

and the argument "x-7" relates x (for the new function) with "x-7", meaning that now things are happening at x, that were originally happening at x-7, so they happen now "later" (more to the right on the x-axis) than before - hence a shift to the right.

Answer:

its D

Step-by-step explanation:

took the test :)

Answer:

$69.50

Step-by-step explanation:

As it was marked down 20%, this means the sale price would be 100-20=80%.  

When                   80%  ---- cost $55.60      

Therefore when 100% ---- cost = $55.60 * 100/80

So when we solve this, we get the final ans $69.50                                  

one shell stores CDs:6422/26

246

Answer:

0

Step-by-step explanation:

((3/5 ^0)^-2)

3/5^0=0

0^-2= 0

Try this option, all the details are in the attachment. Note the equation a) is performed with green, the equation b) with red line.

With break green line is the cureve y= -x²; with break red line is y=2x².

[tex]\left(2 + \sqrt 2 \right)\left(2-\sqrt 3 \right)\\\\=4- 2\sqrt 3 + 2 \sqrt 2 - \sqrt 6\\\\=0.91484.....[/tex]

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

An inequality is an expression that shows the non equal comparison between two or more numbers and variables.

A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Hence, if Grace plan as to spend a maximum of $7.50:

Volume (V) = (3x - 5)(2x)(x + 20) = 6x³ + 110x² - 200x

The inequality is:

6x³ + 110x² - 200x ≤ 15000

6x³ + 110x² - 200x - 15000 ≤ 0

x = 10

The maximum volume is at:

V' = 0

V' = 18x² + 220x - 200 = 0

x = 0.85 cm

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

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The amusement park employees who attend college have an average of 24 hours of homework per week, but we cannot conclude anything about the percent of the population who have homework.

The survey was to determine the average number of hours per week for employees that attended college. The result was that college students had an average of 24 hours of homework per week.

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Answer:

the last

answer

Step-by-step explanation:

Opie created facial features with simple geometric shapes and lines. Option A

Julian Opie is a known as a renowned British artist known for his distinctive depictions of figures, portraits, and landscapes.

His earliest works was the painted steel sculptures, domestic appliances, architectural structures and geometrical shapes showing the relationship between visual and spatial observation

He created distinct facial shapes and forms on a flat surface by means of lines, colors and shadings.

Thus, Opie created facial features with simple geometric shapes and lines. Option A

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#SPJ1

The bottle that holds more water has the larger volume

Beau's water bottle holds more water

The given parameters are:

Drew

Beau

The volumes of their bottles is calculated using:

V = πr^2h

So, we have:

Drew = 3.14 * (3/2)^2 * 7

Drew = 49.46

Beau = 3.14 * (2)^2 * 9

Beau = 113.04

By comparison, 113.04 is greater than 49.46

Hence, Beau's water bottle holds more water

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Answer:

when 12 pieces say =1/12

so 8 pieces say = 1/8

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

fraction of remaining part=8/12 (divided with 4)

=2/3

Answer:

Step-by-step explanation:

YES IS THE ANSWER BECAUSE X=9

AND 11+3=87

[tex]\sf y=50\left(1.8\right)^{x}[/tex]

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

the first term : 50

crosses point : (0, 50), (1, 90)

solve for y,

[tex]\sf y=50\left(1.8\right)^{1}[/tex]

[tex]\sf y=90[/tex]

Graph:

[tex] \qquad\begin{gathered} \begin{array}{ ||c|| c} \hline \\ \textsf { \huge{ \underline{lets\: \: solve}}} \\ \\ \: \: \sf6. \: \underline{ find \: measure \: of \: angle \: TSR}\: \: \\ \\ \textsf {As we know, diameter subtends 90° } \\ \textsf{ at an arc of same circle.} \\ \textsf{ hence we can conclude that :} \\ \\ \rm{ \therefore\angle \:TSR = 90 \degree } \\ \\ \\ \sf7. \: \underline{ find \: measure \: of \: angle \: subtended }\\ \: \underline{ \sf by \: arc \: ST \: at \: the \: centre \: of \: circle}\: \\ \\ \\ \textsf{Angle subtended by an arc at centre} \\ \textsf{ of the circle is double the angle} \\ \textsf{ subtended by the same arc on other } \\ \textsf{ part of circle, hence we can} \\ \textsf{conclude that :} \\ \\ \sf\angle SOT =2 \angle SRT \\ \\ \angle \sf SOT =2 \times 41\degree \\ \\ \sf \therefore\angle SOT = 82 \degree \\ \\ \\ \\ \hline \end{array} \end{gathered}[/tex]

Answer:

Step-by-step explanation:

1 2/3 -(-1/2)

=5/3+1/2

[tex]=\frac{10+1}{6} \\=\frac{11}{6} \\=1\frac{5}{6}[/tex]

The number of stickers John and Ken have in the end is 6 and 18 respectively.

let

New stickers

x + x - 12 = 3x + 5x

2x - 12 = 8x

-12 = 8x - 6x

-12 = -2x

x = 12/2

x = 6

So,

Ken stickers = x

= 6 stickers

John stickers = 3x

= 3 × 6

= 12 stickers

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Answer:

B. Multiply each term in the 1st equation by 3

Step-by-step explanation:

Step-by-step explanation:

step 1

Multiply each term in the second equation with 4

step 2

Add equation 1 to equation 2

step 3

make x subject of formula and obtain value of X

step 4

substitute value of X in equation 1 and find Y

Answer:

3(C + 5) = 7

Step-by-step explanation:

Let C = unknown number

The sum of a number and 5:

C + 5

Three times the sum of a number and 5:

3(C + 5)

Three times the sum of a number and 5 is 7:

3(C + 5) = 7

To solve

Use the distributive law:  a(b + c) = ab + ac

⇒ 3C + 15 = 7

Subtract 15 from both sides:

⇒ 3C = -8

Divide both sides by 3:

⇒ C = -8/3

So

The expression is

On solving

Answer:

D. would be the correct answer

Using it's concept, it is found that the relative frequency of landing on heads is 0.48 and of landing on tails is 0.52.

A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 50 flips, 24 landed on heads and 26 on tails, hence:

Fh = 24/50 = 0.48.

Ft = 26/50 = 0.52.

The relative frequency of landing on heads is 0.48. The relative frequency of landing on tails is 0.52.

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Explanation:

First we need the slope

[tex](x_1,y_1) = (-4,2) \text{ and } (x_2,y_2) = (3,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 2}{3 - (-4)}\\\\m = \frac{-5 - 2}{3 + 4}\\\\m = \frac{-7}{7}\\\\m = -1\\\\[/tex]

Then we can find the y intercept using the coordinates of (x,y) = (-4,2)

y = mx+b

2 = -1(-4)+b

2 = 4+b

2-4 = b

-2 = b

b = -2

Alternatively, you can use the other point (x,y) = (3,-5) and m = -1.

Because m = -1 and b = -2, we go from y = mx+b to y = -1x+(-2) which simplifies to y = -x-2

Answer:

1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder (or each of those is a counting number that can be multiplied by another counting number to make 12).

Step-by-step explanation:

hope this helps.