Your problem is missing the units after the numbers. It could be 4 cents and 32 cents, 4 dollars and 32 dollars, 4 cents and 32 dollars, 4 dollars and 32 cents, etc.
Assuming both are in dollars:
32 / 4 = 8
Deshaun can buy 8 pounds of candy.
Step-by-step explanation:
![a^{-n}=\dfrac{1}{a^n}\\\\\text{therefore}\ 10^{-5}=\dfrac{1}{10^5}=\dfrac{1}{100000}=0.00001\\\\1.23\cdot10^{-5}=1.23\cdot0.00001=0.0000123](https://tex.z-dn.net/?f=a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5C%5C%5C%5C%5Ctext%7Btherefore%7D%5C%2010%5E%7B-5%7D%3D%5Cdfrac%7B1%7D%7B10%5E5%7D%3D%5Cdfrac%7B1%7D%7B100000%7D%3D0.00001%5C%5C%5C%5C1.23%5Ccdot10%5E%7B-5%7D%3D1.23%5Ccdot0.00001%3D0.0000123)
- move the decimal point <em>n</em> place to the left
- move the decimal point <em>n</em> place to the right
Examples:
![1.2\cdot10^5=1\underbrace{20000}_{5\to}=120,000\\\\1.2\cdot10^{-5}=0\underbrace{.00001}_{\leftarrow5}2=0.000012](https://tex.z-dn.net/?f=1.2%5Ccdot10%5E5%3D1%5Cunderbrace%7B20000%7D_%7B5%5Cto%7D%3D120%2C000%5C%5C%5C%5C1.2%5Ccdot10%5E%7B-5%7D%3D0%5Cunderbrace%7B.00001%7D_%7B%5Cleftarrow5%7D2%3D0.000012)
1).50 students-100%
? Students who prefer cats-22%
First step: find the 1% of the students.
50/100=0.5
Second step: find the 22%
0.5x22=11students prefer cats
2.45 people (who chose yellow as their fav color)-15%
? People surveyed-100%
Find the 1%. 45/15=3
Now find the 100%. 3*100=300 person were surveyed.
3.141cookies-47%
? Cookies (she baked in total)-100%
Find the 1%.
141/47=3
Now find the 100%.
3*100=300 she baked 300 cookies in total.
It is going to be 2.95 because 79.65 divided by 27 equals 2.95
have a good day mate!
Answer:
![\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}](https://tex.z-dn.net/?f=%5Cfrac%7B%28n%2B4%29%2A%28n%2B3%29%2A%28n%2B2%29%2A%28n%2B1%29%2An%7D%7B120%7D)
Step-by-step explanation:
Given
5 tuples implies that:
![n = 5](https://tex.z-dn.net/?f=n%20%3D%205)
implies that:
![r = 5](https://tex.z-dn.net/?f=r%20%3D%205)
Required
How many 5-tuples of integers
are there such that![n\ge h\ge i\ge j\ge k\ge m\ge 1](https://tex.z-dn.net/?f=n%5Cge%20h%5Cge%20i%5Cge%20j%5Cge%20k%5Cge%20m%5Cge%201)
From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.
Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location
So, there are n + 4 items to make selection from
The selection becomes:
![^{n}C_r => ^{n + 4}C_5](https://tex.z-dn.net/?f=%5E%7Bn%7DC_r%20%3D%3E%20%5E%7Bn%20%2B%204%7DC_5)
![^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%21%7D%7B%28n%2B4-5%29%215%21%7D)
![^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%21%7D%7B%28n-1%29%215%21%7D)
Expand the numerator
![^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%21%28n%2B3%29%2A%28n%2B2%29%2A%28n%2B1%29%2An%2A%28n-1%29%21%7D%7B%28n-1%29%215%21%7D)
![^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%2A%28n%2B3%29%2A%28n%2B2%29%2A%28n%2B1%29%2An%7D%7B5%21%7D)
![^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%2A%28n%2B3%29%2A%28n%2B2%29%2A%28n%2B1%29%2An%7D%7B5%2A4%2A3%2A2%2A1%7D)
![^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}](https://tex.z-dn.net/?f=%5E%7Bn%20%2B%204%7DC_5%20%3D%20%5Cfrac%7B%28n%2B4%29%2A%28n%2B3%29%2A%28n%2B2%29%2A%28n%2B1%29%2An%7D%7B120%7D)
<u><em>Solved</em></u>