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A drilling machine can drill 12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill ______ holes in 25 minutes.

Numerical Answers Expected!

Answer for Blank 1:

help

The last ratio is correct 1:4, for every 1 mile A, B travels 4 times as long

(x+1)(x^2-x+1) - x^2 (x+4)=0

The probability is 0, as ? is not a digit.

Since 1 us dollar is 1.4167 NYZ then 1 nyz is 1/1.4167 or 0.7USD

So it follows that 900 NYZ = 900*0.7=630 USD.

Note that I've rounded to one decimal point so there's a slight deviation the exact rate is 0.7058... and exact USD amount 635.2791.

Cheers

I don't know exactly what you mean by this, please elaborate on you question if you want exact answers. But I will assume that you want to write a fraction in latex. In that case, here is an example: \frac{x}{y} gives us \(\frac{x}{y}\). Hope this helps :)

45 dollAR   

answer is nine 9

By the way, your pattern works! If you looked at the link, there is a solution similar to yours.

Although If it asked for proof (In competitions etc..) using mods is a must and not just patterns. 

Hello, 

I found this may help you: 

https://www.quora.com/What-is-the-remainder-when-2019-2019-is-divided-by-2020 from Quora. 

If you place a 40 foot ladder against the top of a 24 foot building how many feet will the bottom of the ladder be from the bottom of the building?

Hello Guest!

\(s^2+ h^2=l^2\\ s=\sqrt{l^2-h^2}=\sqrt{(40ft)^2-(24ft)^2}=\color{blue}32ft\)

32 feet will the bottom of the ladder be from the bottom of the building.

  !

31.50 / 3.5 = $9 per pound

$9 * 5 = 45 bucks.

The rectangle ABCD has vertices at A = (1, 2, 3), B = (3, 6, −2), and C = (0, 2, −6).

Determine the coordinates of vertex D.

\(\begin{array}{|rcll|} \hline \mathbf{\vec{B}-\vec{A}} &=& \mathbf{\vec{C}-\vec{D}} \\\\ \left( \begin{array}{r} 3 \\ 6 \\ -2 \end{array}\right) - \left( \begin{array}{r} 1 \\ 2 \\ 3 \end{array}\right) &=& \left( \begin{array}{r} 0 \\ 2 \\ -6 \end{array}\right) - \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) \\\\ \left( \begin{array}{r} 3-1 \\ 6-2 \\ -2-3 \end{array}\right) &=& \left( \begin{array}{r} 0 \\ 2 \\ -6 \end{array}\right) - \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) \\\\ \left( \begin{array}{r} 2 \\ 4 \\ -5 \end{array}\right) &=& \left( \begin{array}{r} 0 \\ 2 \\ -6 \end{array}\right) - \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) \\\\ \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) &=& \left( \begin{array}{r} 0 \\ 2 \\ -6 \end{array}\right) - \left( \begin{array}{r} 2 \\ 4 \\ -5 \end{array}\right) \\\\ \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) &=& \left( \begin{array}{r} 0-2 \\ 2-4 \\ -6-(-5) \end{array}\right) \\\\ \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) &=& \left( \begin{array}{r} 0-2 \\ 2-4 \\ -6+5 \end{array}\right) \\\\ \left( \begin{array}{r} x_D \\ y_D \\ z_D \end{array}\right) &=& \left( \begin{array}{r} -2 \\ -2 \\ -1 \end{array}\right) \\ \hline \end{array}\)

\(\mathbf{\vec{D} =} \left( \begin{array}{r} \mathbf{-2} \\ \mathbf{-2} \\ \mathbf{-1} \end{array}\right)\)

You don't have to make an account.

On the farm, rather than use money, they exchange animals.
The exchanges are as follows: 4 bunnies = 3 chickens, 5 chickens = 2 pigs, 3 pigs = 2 donkeys.
How many bunnies would you have to trade for a donkey?

\(\begin{array}{|rcll|} \hline && \dfrac{4 ~\text{bunnies} }{3 ~\text{chickens} }\times \dfrac{5 ~\text{chickens} }{2 ~\text{pigs} }\times \dfrac{3 ~\text{pigs} }{2 ~\text{donkeys} } \\\\ &=& \dfrac{4\times 5\times 3}{3\times 2 \times 2} \dfrac{\text{bunnies} } {\text{donkeys} } \\\\ &=& 5\dfrac{\text{bunnies} } {\text{donkeys} } \\ \hline \end{array}\)

5 bunnies   = 1 donkey

His chance is 9/22 or 40,91%. Simply write the equation as follows and solve for x.

x*0.4091=50

x=50/0.4091

x=122

A slightly different solution:

\((-5):(2\sqrt{7})=cos(\beta):sin(\beta) )\)

                                            \(sin(\beta)=\sqrt{1-cos^2(\beta)}\)        

\((-5)/(2\sqrt{7})=cos(\beta)/\sqrt{1-cos^2(\beta)}\\ \frac{25}{28}=\frac{cos^2(\beta)}{1-cos^2(\beta)}\)

\(28cos^2(\beta)=25-25cos^2(\beta)\)

\(53cos^2(\beta)=25\\ cos^2(\beta)=\frac{25}{53}\)

\(cos(\beta)=\pm\sqrt{\frac{25}{53}}=\pm \frac{5}{\sqrt{53}}\)

\(cos(\beta\ [-5;2\sqrt{7}])=- 0.686802819743\)      

\([\beta =133^022'39'']\)

  !

The rectangle ABCD has vertices at A = (1, 2, 3), B = (3, 6, −2), and C = (0, 2, −6). Determine the coordinates of vertex D.

The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2sqrt7) .
What is the value of cosβ ?
Enter your answer, in simplest radical form

Hello Guest!

\(tan(\alpha)=\frac{2\sqrt{7}}{5}\\ \alpha=arctan(\frac{2\sqrt{7}}{5})\\ \beta=180^0-\alpha=180^0-arctan(\frac{2\sqrt{7}}{5})=180^0-46.622^0\\ \beta=133.378^0 \)

\(cos(\beta)=-0.6868\)

  !

What is the measure of the central angle of a circle if the radius is 18 centimeters. Assume that it intercepts a 12pi centimeter arc. I would prefer the answer in degrees if you dont mind.

Hello John!

\(b=\frac{\pi r \alpha}{180^0}\\ \alpha=\frac{b\cdot 180^0}{\pi r}=\frac{12cm\cdot \pi \cdot180^0}{\pi\cdot18cm}\)

\(\alpha=120^0\)

  !