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Use   arctan (26/53) =

nCr =20C3 =20! / {[20 - 3]!. 3!} =1,140 to 1 of matching 3 white balls.

1,140 x 10 =11,400 to 1 of matching 3 white balls and 1 SuperBall.

The probability of selecting a king is 4/52 which is just 1/13 because there are 4 kings in a 52 card deck. 

The probability of selecting a black card is 1/2 because half of the cards are black. 

The probability of selecting a black king is 2/52 which is just 1/26 because there are 2 black kings in a 52 card deck.

Kirsty needs to hire a plumber to fix her house. The plumber charges $242_5$ dollars for every hour of labor and $367_{8}$ dollars for equipment. If the plumber works for $3.5_{10}$ hours, how many dollars (in base ten) will Kirsty owe the plumber?

Are you an English-speaking student? Don't you know how to write dollars and cents? The numbers I have highlighted don't make sense!! If you want to write "One hundred and twenty-five dollars and sixty-seven cents", this is how it is written: $125.67.  You should change your numbers so that people understand what you want calculated.

Solve:

Between 1 and 999 =189 zeros and 300 "1s"
Between 1,000 and 9,999 =2,700 zeros and 3,700 "1s"
Between 10,000 and 99,999 =36,000 zeros and 46,000 "1s"
100,000 =5 zeros and one "1". So, the total will be:
189 + 2,700 + 36,000 + 5 =38,894 "zeros", and:
300 + 3,700 + 46,000 + 1 =50,001 "ones"

23 old spaces + 4 new spaces =27 parking spaces.

27 spaces x 8 rows =216 parking spaces after exapansion.

94% = 100% x (1/2)^(n/5730), where n = Number of years

.94 = 1 x (1/2)^(n/5730)      take the log of both sides

n/5730 =Log(0.94) / Log(1/2)

n/5730 =0.089267.......        cross multiply

n =5730 x 0.089267

n =511.5 =~512 years ago.

Note: It is NOT necessary to find r and t, since the above formula works EXACTLY the same.

If your weekly allowance is $5, then, for Christmas week, your allowance was $15, then your allowance went up by: $15 / $5 =3 - 1 = 2 x 100 =200%.

Let log base 4 of 3 = x. Then log base 2 of 27 = kx. Find k.

k = 6

You changed the question !!!

Solve:

What is the value of pi? Of course, it is =3.141592.........

200 x 3.141592......=628.318............ drop the fraction and you have:

628 positive integers LESS than 200pi.

22 old chairs + 5 new chairs =27 chairs per row.

8 rows x 27 chairs =216 chairs - after the work is done.

A wood, rectangular box, with no top, is constructed with five panels that are each one centimeter thick. The external dimensions of the base are 16 cm by 24 cm, and the external height is 10 cm. When the box is totally submersed in paint, how many square cm of painted surface will there be?

The straight lines around 1-y mean "take the absolute value of".  The absolute value of 1-y is the same as that of y-1, so, as Max noted, ln(|y-1|) is the same as ln(|1-y|).

A box is to be made out of a 10 by 14 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L , width  W, and height H  of the resulting box that maximizes the volume. (Assume that  ). 

L=

W=

H=

Hello Sloan!

\(V=(10-2x)*(14-2x)*x\\ =(140-20x-28x+4x^2)x\\ =4x^3-48x^2+140x \) 

\(f(x)=4x^3-48x^2+140x\\ f'(x)=12x^2-96x+140=0\)

\(x = {{-b \pm \sqrt{b^2-4ac}} \over 2a}\\ x = {{96 \pm \sqrt{9216-4*12*140}} \over 2*12}\\ x=\frac{96\pm \sqrt{2496}}{24}=\frac{96\pm 49.95}{24}\\ x_1=6.082\ (inadmissible)\\ \color{blue}x_2=1.918\)

L = 14 - 2 * 1.918 = 10.163

W = 10 - 2 * 1.918 = 6,163

H = 1.918

Greetings

  !

See the answer here: https://web2.0calc.com/questions/some-help-with-one-problem-would-be-nice-c

How do you solve
$i^{-100}+i^{-99}+i^{-98}+\cdots+i^{-1}+i^0+i^1+\cdots+i^{99}+i^{100}$

\(\small{ \begin{array}{|rcll|} \hline && i^{-100}+i^{-99}+i^{-98}+i^{-97}+\cdots+i^{-2}+i^{-1}+i^0+i^1+i^2+i^3+i^4\cdots+i^{99}+i^{100} \\ &=& i^{-100}(1+i)+i^{-98}(1+i) +\cdots+i^{-2}(1+i)+i^0+i^1(1+i)+i^3(1+i)+\cdots+i^{99}(1+i) \\ && \boxed{\color{red}1+i =1-1=0} \\ &=& i^{-100}\times 0+i^{-98}\times 0 +\cdots+i^{-2}\times 0+i^0+i^1\times 0+i^3\times 0+\cdots+i^{99}\times 0 \\ &=&0+i^0+0 \\ &=& i^0 \\ &\mathbf{=}& \mathbf{1} \\ \hline \end{array} }\)

To make it less confusing, first know that: \(1-y = -(y-1)\).

Then, using the property of absolute value function, we have: \(|-x| = |x|\)

It is supposed to be \(-\ln|1-y| + C\), however, \(-\ln|1-y| = -\ln|-(y-1)| = -\ln|y-1|\).

Both \(-\ln|1-y| + C\) and \(-\ln|y-1| + C\) are correct answers.

Let \(\phi\) be the reference angle of \(\theta\).

\(\sin \theta = \dfrac{\sqrt3}{2}\\ \therefore \sin \phi = \dfrac{\sqrt3}{2}\\ \text{As }\phi\text{ is a reference angle, it always lies in Quadrant I.}\\ \therefore \phi = 60^{\circ}\\ \theta\text{ lies in Quadrant IV}\\ \therefore \theta = 360^{\circ}-60^{\circ} = 300^{\circ}\\\)

Triangle.

Imagine a clay(?) cone is cut into half from the top to the bottom. If you look at where you cut it into half, there should be a triangle.

Like this:

There you see the answer is triangle.

(a) and (f)