All Answers 358087 Answers

There should be more to the question :)

Write (2√3)(5√27^3) as a single exponent

\((2\sqrt3)(5(\sqrt{27})^3)\\ =(2\sqrt3)(5(\sqrt{9*3})^3)\\ =(2\sqrt3)(5(3\sqrt{3})^3)\\ =(2\sqrt3)(5(3^3(\sqrt{3})^3)\\ =(2\sqrt3)(5(3^3(3\sqrt{3}))\\ =2*\sqrt3*5*3^3*3\sqrt{3}\\ =2*5*3^3*3\sqrt{3}*\sqrt3\\ =10*3^3*3*3\\ =10*3^5\\ \)

The following data shows the weight (in kg) of 13 crabs found in a restaurant on a particular evening: 3.4 1.2 1.7 2.4 2.4 1.1 0.9 0.8 1.2 1.3

(i) Compute the mean and median

3.4      1.2     1.7      2.4      2.4    1.1    0.9    0.8    1.2     1.3         I onlu count 10 crabs,

For the median I must put them in order.

0.8      0.9      1.1     1.2     1.2     1.3     1.7    2.4      2.4    3.4      

There are 2 middle ones so the median is    (1.2+1.3)/2= 1.25Kg

For the mean, add them all up and divide by 10 (because there are 10 crabs)

(0.8+0.9+1.1+1.2+1.2+1.3+1.7+2.4+2.4+3.4)/10 = 1.64Kg                       

(ii) Determine the shape of the distribution based on the sample data. Explain your conclusion

3/4x - 1/3y = 2 and 1/2x + 2/3 y = 4

\(\frac{3}{4}x-\frac{1}{3}y=2\\\frac{1}{2}x+\frac{2}{3}y=4\) 

\(\frac{6}{4}x-\frac{2}{3}y=4\)

\(\frac{6}{4}x-4=\frac{2}{3}y\\4-\frac{1}{2}x=\frac{2}{3}y\)

\(\frac{6}{4}x-4=4-\frac{1}{2}x\\\frac{6}{4}x+\frac{2}{4}x=8\\2x=8\)

\(x=4\)

\(\frac{1}{3}y=\frac{3}{4}x-2\\y=\frac{9}{4}x-6=\frac{9}{4}\cdot 4-6\)

\(y=3\)

  !

Is 3.5%<7.6*10^-3<3.8*10^-1 true?

lets see

3.5% = 0.035

\(7.6*10^{-3}=0.0076\)

0.035 is not less than 0.0076 so the statement is not true. 

Well here is your graph :)

Solve the following system:
{(3 x)/4 - y/3 = 2 | (equation 1)
x/2 + (2 y)/3 = 4 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:
{(3 x)/4 - y/3 = 2 | (equation 1)
0 x+(8 y)/9 = 8/3 | (equation 2)

Multiply equation 1 by 12:
{9 x - 4 y = 24 | (equation 1)
0 x+(8 y)/9 = 8/3 | (equation 2)
Multiply equation 2 by 9/8:

{9 x - 4 y = 24 | (equation 1)
0 x+y = 3 | (equation 2)

Add 4 × (equation 2) to equation 1:
{9 x+0 y = 36 | (equation 1)
0 x+y = 3 | (equation 2)

Divide equation 1 by 9:
{x+0 y = 4 | (equation 1)
0 x+y = 3 | (equation 2)

Collect results:
Answer: | x = 4      and          y = 3

I have no idea what you are asking.

(+1)+x i  = 1+xi

How would you graph y=a(7)^x.

\(y=a\times 7^x\)

\(f(x)\\\color{purple}=10\times 7^x\\\color{green}=3\times 7^x\\\color{blue}=2\times 7^x\\\color{red}=7^x\)

  !

7/10 divided by 5

\(\frac{7}{10}:5=\frac{7}{10\cdot 5}=\frac{7}{50}\color{blue}=0.14\)

  !

transformation (3,1),(0,-5),(-4,-2)

Parable of three points

\(y=ax^2+bx+c\)

A ) \(1=a\cdot 3^2+3b+c\\9a+3b+c=1\)

B)  \(-5=0a+0b+c\\c=-5\)

C)  \(-2=16a-4b+c\\16a-4b-5=-2\) 

A)  \(9a+3b-5=1\\a=\frac{6-3b}{9}\)

C)  \(16a-4b=3\\a=\frac{4b+3}{16}\)

A)&C)  \(\frac{6-3b}{9}=\frac{4b+3}{16}\\96-48b=36b+27\\84b=69\\b=\frac{69}{84}=\frac{3\cdot23}{2\cdot2\cdot21}\\b=0.821\)

A)&C)⇒A) \(a=\frac{6-3\cdot \frac{69}{84}}{9}=\frac{6}{9}-\frac{3\cdot69}{9\cdot84}\\a=0.393\)

\(\color{blue}{y=ax^2+bx+c\\y=0.393x^2+0.821x-5}\)

  !

What is this? sqrt(64*x^6*y^3)
I feel like it is (8)(x^(6/2))(y^(3/2))

\(\sqrt{64x^6y^3}=8x^3 y\times\sqrt{y}\)

\(8\times x^{\frac{6}{2}}\times y^{\frac{3}{2}}\)   \(Your \ solution \ is \ correct.\)

  !

A bicycle travels 20 m in 4 seconds. Calculate the speed of the bicycle, in km/h.

\(v=\frac{s}{t}=\frac{20m}{4sec}\times\frac{3600sec}{h}\times\frac{km}{1000m}=18\ km/h\)

  !

what the descride transformation (3,1),(0,-5),(-4,-2)

A graph through the three points may be a circle or a second-degree parabola, 3rd degree or higher degree.

Circle:

\(x_M=\frac{x_1+x_2+x_3}{3}=\frac{3+0-4}{3}\\x_M=\frac{7}{3}\)

\(y_M=\frac{y_1+y_2+y_3}{3}=\frac{1-5-2}{3}\\y_M=-2\)

\(r=\sqrt{(x_M-x_1)^2+(y_M-y_1)^2}\)

\(r=\sqrt{(\frac{7}{3}-3)^2+(-2-1)^2}\)

\(r=\sqrt{(-\frac{2}{3})^2+(-3)^2}=\sqrt{\frac{4}{9}+9}=\sqrt{\frac{85}{9}}\)

\(r=\frac{\sqrt{85}}{3}\) 

Circular function

\(x^2+y^2=r^2\)

\(x^2+y^2=\frac{85}{9}\)

  !

But in the original problem it doesnt ever say that its equal to zero though???

I think the cafeteria workers want to know what flavor of ice cream is the student body's favorite...so they should ask the second option: "What is your favorite flavor of ice cream?"