If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?
1 answer:
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Well, we are starting with 100 servings, and we're trying to find the amount of ingredients necessary to create 25 servings. To do this, we must first simply divide 25 by 100 to see what the ratio would be, and when we do this, we can see that
25 / 100 =
= 
Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.
In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.
1.) 100 * = 
= 
= 
= 25
2.) 72 * = 
=
= 
= 18
3.) 14 * = 
= 
= 
= 3 
4.) 6 * = 
= 
= 
= <span>1 </span>
5.) 24 * = 
= 
= 
= 6
6.) 80 * = <span>
= 
= 
= <span>20</span>
</span>7.) 50 * = 
= 
= 
= 12
And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)
25 / 100 =
Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.
In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.
1.) 100 *
2.) 72 *
3.) 14 *
4.) 6 *
5.) 24 *
6.) 80 *
</span>7.) 50 *
And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)