Theres no graphs but this is how the function looks like
The probability of losing per flip is 1/2. Multiply 1/2 by itself 6 times since the condition is asking for the probability for the person to lose 6 times in a row. 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64. The answer is 1/64.
Answer:

Step-by-step explanation:
Given that,
The radius of the sphere, r = 8 mm
We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

Put all the values,

So, the volume of the sphere is equal to
.
Using the area of a rectangle, it is found that her patio should have a width of 12 feet and a length of 27 feet.
<h3>What is the area of a rectangle?</h3>
The area of a rectangle of length l and width w is given by:
A = lw.
In this problem:
- She has enough tiles to cover 324 square feet, hence A = 324.
- She wants the length of the patio to be 15 feet longer than the width, hence l = 15 + w.
Thus:
324 = w(15 + w)
w^2 + 15w - 324 = 0
w = -27 or w = 12.
We take the positive value, hence l = 15 + w = 15 + 12 = 27 feet.
The dimensions should be a width of 12 feet and a length of 27 feet.
You can learn more about the area of a rectangle at brainly.com/question/10489198
Answer:
The simplified form of the expression is ![\sqrt[3]{2x}-6\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2x%7D-6%5Csqrt%5B3%5D%7Bx%7D)
Step-by-step explanation:
Given : Expression ![7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D-3%5Csqrt%5B3%5D%7B16x%7D-3%5Csqrt%5B3%5D%7B8x%7D)
To Simplified : The expression
Solution :
Step 1 - Write the expression
![7\sqrt[3]{2x}-3\sqrt[3]{16x}-3\sqrt[3]{8x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D-3%5Csqrt%5B3%5D%7B16x%7D-3%5Csqrt%5B3%5D%7B8x%7D)
Step 2- Simplify the roots and re-write as
and 
![7\sqrt[3]{2x}-3\times2\sqrt[3]{2x}-3\times2\sqrt[3]{x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D-3%5Ctimes2%5Csqrt%5B3%5D%7B2x%7D-3%5Ctimes2%5Csqrt%5B3%5D%7Bx%7D)
Step 3- Solve the multiplication
![7\sqrt[3]{2x}-6\sqrt[3]{2x}-6\sqrt[3]{x}](https://tex.z-dn.net/?f=7%5Csqrt%5B3%5D%7B2x%7D-6%5Csqrt%5B3%5D%7B2x%7D-6%5Csqrt%5B3%5D%7Bx%7D)
Step 4- Taking
common from first two terms
![\sqrt[3]{2x}(7-6)-6\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2x%7D%287-6%29-6%5Csqrt%5B3%5D%7Bx%7D)
![\sqrt[3]{2x}-6\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2x%7D-6%5Csqrt%5B3%5D%7Bx%7D)
Therefore, The simplified form of the expression is ![\sqrt[3]{2x}-6\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2x%7D-6%5Csqrt%5B3%5D%7Bx%7D)