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TOTAL: 9 balls

Probability that first pick is black= 6/9=2/3

Probability that second pick is black (the first one is taken already, so subtract 1 from numerator and denominator.) = 5/8

Multiply both:5/8 x 2/3=5/12

Hint from another website:

\(5^3^k+1 + 1 = (5^3^k)^3 + 1 = (5^3^k+1)(5^2⋅3k − 5^3k+1)\)

-nerdiest.

Similar question, you can learn from it: https://web2.0calc.com/questions/how-many-terms-of-the-arithmetic-sequence-88-85-82

Relationships between shirts:

Pink= 198+W

24%=W

Total - Pink - W =114- RED.

To find pink, we need this: Total - 24% - 114= W+198.

76% - 114= W+198

Now you should be able to carry on.

-nerdiest.

я скажу какой 556-7-90 решите пример сам или посчитайте на калькуляторе 

Using logs properties:       \(alog(x)=log(x^a)\) and \(log(a)+log(b)=log(ab)\) yields:

\(log(a-3b)^2=log(ab) \iff (a-3b)^2=ab\)

Expanding the left-hand side:

\(a^2-6ab+9b^2=ab\)

Simplify:

\(a^2-7ab+9b^2=0\)

Now, we want \(\dfrac{a}{b}\),  so we divide this equation by \(b^2\) to get:

\((\dfrac{a}{b})^2-7(\dfrac{a}{b})+9=0\)

This is a quadratic in \(\dfrac{a}{b}\), which we can solve directly or by substitution as follows:

Let \(y=\dfrac{a}{b}\)

So our quadratic equation becomes:  \(y^2-7y+9=0\)

Using the quadratic formula: \(y=\frac{7\pm \sqrt{49-36}}{2}=\frac{7\pm \sqrt{13}}{2}\)

But recall: \(a>0 , b>0\), and \(a-3b>0 \implies a>3b \implies \frac{a}{b} > 3\)

Thus, we reject: \(y_2=\frac{7-\sqrt{13}}{2}\) as it is less than 3.

Therefore, \(y_1=\dfrac{a}{b}=\frac{7+\sqrt{13}}{2}\) is the only solution.

Hope this helps!

Simplify to get:

\(x^2-mx+20=0\)

Now, for this Quadratic to have no real solutions, it should not intersect the x-axis. 

So, the discriminant , which is: \(b^2-4ac\) must be less than zero.

So:
\(b^2-4ac<0\)

\(\iff m^2-80 <0\)  (Now we have to solve this Quadratic inequality for m).

The critical values:  \(m=\pm 4\sqrt{5}\)

Next, sketch (*) and place the critical points, you want the region below the x-axis (Hence, between the critical values):
Thus, \(-4\sqrt{5}

Since hte question is asking about the largest integer m, let us convert this to decimal:

\(-8.94427..

Therefore, the largest integer m, is: \(m=8\) is the desired solution.

Hope this helps!

\(\text{When two variables x and y, are inversely proportional, then: }\)

\(y=\dfrac{k}{x}\)  or \(x=\dfrac{k}{y}\) where k is a constant to be determined.

So, let us use: \(y=\dfrac{k}{x}\)

How to find k? Use the given:  \(x=2,y=4\)

\(4=\dfrac{k}{2} \implies k=8\)

Thus, \(y=\dfrac{8}{x} \)

Now, when y=1 then: \(1=\dfrac{8}{x} \implies x=8\)

Hope this helps!

Since  EF ll GH, then arcs  EH and FG are equal  .....so....

 x^2 - 2x =  65 - 3x

x^2 + x - 65   =  0 

x ≈ 7.58

So   arc EH = arc FG =  65 - 3(7.58)  =  42.26°

Then arc EPF  = 

360 - 2 * arc EH  - arc  GH

360  - 2(42.26) - 70   ≈ 205.5° 

In the realm of complex numbers, every number has two square roots, three cube roots, four fourth roots, five fifth roots and so on.

Do what you've done except put the angle in its multivalued form, 

\(\displaystyle 3\pi/4+2k\pi,\) where k is any integer.

For cube roots, (after you've divided by three), let k = 0, 1, 2.

(Try k = 3 if you want but you should find that it just duplicates k = 0, (and k = 4 duplicates k = 1 etc.).)

If you were calculating square roots you would (after the division by 2) let k = 0 or 1, if calculating fourth roots, k = 0,1,2,3 and so on. 

A=abs((30*5) - (5.5*20)), solve for A

A ==40 degrees

posted here. answered by EP. :https://web2.0calc.com/questions/help_78260

answered here: https://web2.0calc.com/questions/a-right-pyramid-has-a-square-base-with-area-288-square-cm 

-nerdiest.

nice job guest.

19 ==88  +  (-3 * N)

19 - 88 == - 3N

- 69 == - 3N

N ==- 69 / - 3 ==23 terms will appear before the 24th term, which will be 19

The above is with replacement. This is without replacement:

There are:

[10  C 2 ==45 combinations as follows:

( 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9) >>Total =  45 combinations

The probability is: 28 / 45

already posted here: https://web2.0calc.com/questions/help_85497

-nerdiest.

That's incorrect

The number of ways is 8!/2 = 20160.

The numerator:
[199 - 1] / 2 + 1==100>>>> n^2==100^2==10,000

The denominator:
[202 - 2] / 2 + 1==101>>>> n(n+1)=101*102==10,302

10,000 / 10,302==5000 / 5151

2 + 4 + 6 + 8 + 10 = 30

6/30 = 1/5 = 0.2

20%

She has \(40 \times 3x = 120x\)cents. 

Now, if the price was \(5x\) cents, how many oranges would she be able to buy?

\(3^{2c + 1} = 28 \times 3^c - 3^c\)

\(3^{2c + 1} = 27 \times 3^c\)

\(3^{2c + 1} = 3^3 \times 3^c\)

\(3^{2c+1} = 3^ {3 + c}\)

\(2c + 1 = 3 + c\)

\(c + 1 = 3\)

\(c = \color{brown}\boxed{2}\)