Answer: C) Today's soup will taste the same
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Explanation:
The usual recipe has 9 tomatoes for every 12 bowls. This forms the ratio 9:12.
Divide both parts of the ratio by 12 to end up with 0.75:1
The ratio 0.75:1 means that there are 0.75 tomatoes for each bowl.
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Then the restaurant updates the recipe to involve 6 tomatoes for every 8 bowls, leading to the ratio 6:8. Divide both parts by 8
The ratio 6:8 is the same as 0.75:1
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We get the same ratio (0.75:1) each time we turn that second number into a 1, which means that each bowl involves the same number of tomatoes. Therefore, the taste should be the same.
Of course the concept of taste is subjective, meaning that the taste could easily vary over time even if you involved the same number of tomatoes. Also, the taste may vary from person to person. However, there should be an objective way to measure the "tomato"ness of each bowl.
Answer:
![v\sqrt[28]{v^{13}}](https://tex.z-dn.net/?f=v%5Csqrt%5B28%5D%7Bv%5E%7B13%7D%7D)
Step-by-step explanation:
The exponent rules that apply are ...
![(a^b)(a^c)=a^{b+c}\\\\a^{\frac{b}{c}}=\sqrt[c]{a^b}](https://tex.z-dn.net/?f=%28a%5Eb%29%28a%5Ec%29%3Da%5E%7Bb%2Bc%7D%5C%5C%5C%5Ca%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Csqrt%5Bc%5D%7Ba%5Eb%7D)
Using these rules for your product, we have ...
![v^{\frac{3}{4}}\times v^{\frac{5}{7}}=v^{\frac{3}{4}+\frac{5}{7}}\\\\=v^{\frac{41}{28}}=v\cdot v^{\frac{13}{28}}=v\sqrt[28]{v^{13}}](https://tex.z-dn.net/?f=v%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%5Ctimes%20v%5E%7B%5Cfrac%7B5%7D%7B7%7D%7D%3Dv%5E%7B%5Cfrac%7B3%7D%7B4%7D%2B%5Cfrac%7B5%7D%7B7%7D%7D%5C%5C%5C%5C%3Dv%5E%7B%5Cfrac%7B41%7D%7B28%7D%7D%3Dv%5Ccdot%20v%5E%7B%5Cfrac%7B13%7D%7B28%7D%7D%3Dv%5Csqrt%5B28%5D%7Bv%5E%7B13%7D%7D)
I can't see the graph but let's use logic
hmm, more than 10 cubic feet of topsoil so the first and 2nd options are wrong
let's ee the costs
3rd option
10*1=10
2*12=24
10+24=34 and 34<50, that is fine
4th option
3*10=30
2*12=24
30+24=54
54>50, nope, that is over cost
answer is 3rd one
the one with 1 cubic yard compost and 12 cubic yard topsoil
