Answer:
\frac{1}{230230}
Step-by-step explanation:
Given that in a certain lottery, an urn contains balls numbered 1 to 26
From this urn, 6 balls are chosen randomly, without replacement.
Bet amount 1 dollar and he selects a set of six numbers.
If these match with those chosen from the urn he wins (order does not matter)
Total ways of choosing 6 out of 26 = 
The way he selects = 1
Hence probability of winning =
with one ticket
Answer:
Step-by-step explanation:
We'll take this step by step. The equation is
![8-3\sqrt[5]{x^3}=-7](https://tex.z-dn.net/?f=8-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-7)
Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:
![-3\sqrt[5]{x^3}=-15](https://tex.z-dn.net/?f=-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-15)
The goal is to isolate the term with the x in it, so that means that the -3 has to go. Divide it away on both sides:
![\sqrt[5]{x^3}=5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E3%7D%3D5)
Let's rewrite that radical into exponential form:

If we are going to solve for x, we need to multiply both sides by the reciprocal of the power:

On the left, multiplying the rational exponent by its reciprocal gets rid of the power completely. On the right, let's rewrite that back in radical form to solve it easier:
![x=\sqrt[3]{5^5}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B5%5E5%7D)
Let's group that radicad into groups of 3's now to make the simplifying easier:
because the cubed root of 5 cubed is just 5, so we can pull it out, leaving us with:
which is the same as:
![x=5\sqrt[3]{25}](https://tex.z-dn.net/?f=x%3D5%5Csqrt%5B3%5D%7B25%7D)
Height would be 21 inches, depth would be 5.
Answer:
Sometimes, but not always.
Step-by-step explanation:
A parallelogram is a quadrilateral with two pairs of parallel sides, but there are no requirements for its interior angles. A rectangle, on the other hand, <em>must</em> have four interior 90 degree angles. So a rectangle is always a parallelogram, but a parallelogram is not always a rectangle.