Based on the information provided, it follows that there are 1,728 possible seating arrangements.
<h3>How can we find the number of possible arrangements?</h3>
To find the number of arrangements in this problem situation we must take into account the following key factors:
- Chris only has 1 possible seat.
- Jo has 2 possible seats.
- Dave, Alex, and Barb have 3 possible seats.
- Gareth, Fred, and Eddie have 3 possible seats.
- There are 4 other adults who do not have a preference in seats but have the possibility of using 4 seats.
According to the above, we must use the factorization of these numbers to find out the number of possibilities we have to seat them.
<h3>What is factoring?</h3>
A factorial function is a mathematical tool that is characterized by using the exclamation mark “!” behind a number. The factorial function is used to express that the number accompanied by the symbol must be multiplied by all positive integers between that number and 1.
In accordance with the above, in the problem situation that we must solve, we must use the factorial function with the possibilities of:
- Dave, Alex and Barb: 3! = 3 × 2 × 1 = 6
- Gareth, Fred and Eddie: 3! = 3 × 2 × 1 = 6
- Other 4 adults: 4! = 4 × 3 × 2 × 1 = 24
Subsequently, to calculate the number of total possibilities of the entire group we must multiply the possibilities of each group and individual as shown below:
- Number of possibilities = 1 × 2 × 6 × 6 × 24
- Number of possibilities = 1728
Learn more about the factorial function in: brainly.com/question/16674303
Answer:
10 ft away
Step-by-step explanation:
do pythagorean theorum
24^2 + b^2 = 26^2
576 + b^2 = 676
*subtract 576 from both sides*
b^2 = 100
*find square root of 100*
b = 10
since we have the area of the front side, to get its volume we can simple get the product of the area and the length, let's firstly change the mixed fractions to improper fractions.
![\stackrel{mixed}{23\frac{2}{3}}\implies \cfrac{23\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{71}{3}} ~\hfill \stackrel{mixed}{4\frac{7}{8}}\implies \cfrac{4\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{39}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{3}\cdot \cfrac{39}{8}\implies \cfrac{71}{8}\cdot \cfrac{39}{3}\implies \cfrac{71}{8}\cdot 13\implies \cfrac{923}{8}\implies 115\frac{3}{8}~in^3](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B23%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B23%5Ccdot%203%2B2%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B71%7D%7B3%7D%7D%20~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B7%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%208%2B7%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B39%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B71%7D%7B3%7D%5Ccdot%20%5Ccfrac%7B39%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B71%7D%7B8%7D%5Ccdot%20%5Ccfrac%7B39%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B71%7D%7B8%7D%5Ccdot%2013%5Cimplies%20%5Ccfrac%7B923%7D%7B8%7D%5Cimplies%20115%5Cfrac%7B3%7D%7B8%7D~in%5E3)
Answer:
Step-by-step explanation:
Starting at 5 on the number line, 5 + (-3) is 3 units to the left of 5; that is, you are at 2 on the number line.
