On Saturday, Simone’s volleyball team will be having a family picnic. Hot dogs are sold at the local store with 10 hot dogs in a package. Hot dog buns, however, are only sold in packages of 8 hot dog buns. Simone’s team wants to buy the exact same number of packages for hot dogs as hot dog buns. What is the least number of packages of hot dogs and hot dog buns that Simone’s team should buy to have exactly the same number of hot dogs as hot dog buns? Show your work.

The correct answer is 4 packages of hot dogs and 5 packages of hot dog buns

Explanation:

To find the least number of packages of each item the team has to buy, it is necessary to find the Least Common Multiple of the two numbers (10 and 8), which is the lowest integer that is multiple of both 10 and 8, and therefore represents the least number of hot dogs and hot dog buns the team has to buy to get the same number of the two items. Now, to find the LCM follow this process:

1. List the two numbers

10

8

2. Now, find the multiplies of each number

10 x 1 = 10 / 10 x 2= 20/ 10 x 3= 30 / 10 x 4 = 40...

8 x 1= 8/ 8 x 2 = 16 / 8 x 3 = 24 / 8 x 4 = 32 / 8 x5 = 40...

3. Notice the first common number in both, in this case, 40 because 10 x 4 = 40 and 8 x 5= 40.

This means the Least Common Multiple is 40, and therefore the team should buy 40 of each item. Additionally, this means they need to buy 4 packages of hot dogs (each package contains 10 units) and 5 packages of hot dog buns (each package contains 8 units).

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2