A typical container of orange juice concentrate holds 12 fluids ounces (fl oz). The standard recipe is "Mix one can of concentra

te with three cans of cold water".
Olivia has one gallon container to fill with orange juice. She uses the standard recipe. How much concentrate does she need? (One gallon 128 fl oz)

Mathematics

1 answer:

dangina [55]4 years ago

7 0

$The\ standard\ recipe\ is:\\\ 12\ fl\ oz\of\ orange\ juice\ concentrate\\ and\ 3\cdot 12=36\ fl\ oz\ of cold\ water\\so\ is\ 12+36=48\ fl\ oz\ of\ mix\\\\128:48=2 \frac{2}{3} \\\\Ans.\ Olivia\ need\ \ 2 \frac{2}{3}\ cans\ of\ orange\ juice\ concentrate.$

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Find the recursive rule, explicit rule, and f(20)

DiKsa [7]

Answer:

Recursive:

$f(1)=35, f(n)=f(n-1)+10$

Explicit:

$f(n)=35+10(n-1)$

And the 20th term is 225.

Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

$f(n)=a, f(n)=f(n-1)+d$

Where a is the initial term and d is the common difference.

From our sequence, we know that a the initial term is 35.

And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

$f(1)=35, f(n)=f(n-1)+10$

Explicit Rule:

The standard format for the explicit rule is:

$f(n)=a+d(n-1)$

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

$f(n)=35+10(n-1)$

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

$f(20)=35+10(20-1)$