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Varvara68 [4.7K]
1 year ago
10

Question B,C and D I need answers to these parts.

Mathematics
1 answer:
Alik [6]1 year ago
5 0
Explanation<h2>Part b</h2>

So in part (b) we must give the annual growth factor. For any quantity that increases annualy, this factor is the number by which the quantity multiplies itself every year. For a given quantity that increases at a rate of p% its growth factor is given by:

1+\frac{p}{100}

In this case the production of ethanol increases at a rate of 5.5% per year which means that the growth factor is:

1+\frac{5.5}{100}=1.055

Then the growth factor and answer to part (b) is 1.055.

In part (c) we must write an equation that models the increase in the ethanol production. Given an initial qunatity Q and an annual growth factor k the quantity after x years is given by multiplying the initial quantity by the growth factor raised to the x. Then we get:

C(x)=Q\cdot k^x

In this case we need a function for the amount of ethanol produced E, x years after 1990. The 0.9 billion gallons produced that year compose our initial quantity and knowing that the annual growth factor is 1.055 we have the desire equation:

E(x)=0.9\cdot1.055^x

And that's the answer to part (c).

In part (d) we have to compare the actual production of ethanol in 2008 to the one predicted by the equation of part (c). Remember that x represents the years passed after 1990 so for the year 2008 the value of x is given by:

x=2008-1990=18

So the number we are looking for is E(18):

E(18)=0.9\cdot1.055^{18}=2.359

So the production estimated for 2008 is 2.359 billions of gallons. Then the actual production of 9 billion gallons is higher than the one predicted by our equation.

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2 years ago
Solve for each expression by writing the solution in unit form and in standard form.
Sonja [21]

Answer:

<em>Unit Form:</em>

  • <em>3 hundreds, 0 tens, 0 ones</em>
  • <em>5 thousands, 0 hundreds, 0 tens, 0 ones</em>
  • <em>9 thousands, 0 hundreds, 0 tens, 0 ones</em>
  • <em>7 ten thousands, 0 thousands, 0 hundreds, 0 tens, 0 ones</em>

<em>Standard Form:</em>

  • <em>300</em>
  • <em>5,000</em>
  • <em>9,000</em>
  • <em>70,000</em>

Step-by-step explanation:

Here is how to write solutions to expressions in unit form:

Its important to note that unit form expands a standard form number into ones, tens, hundreds, and so on.

Take your first expression for example.

10 × 3 tens

Re-write this expression so that all terms are in standard form. The second term is <em>3 tens,</em> which can be represented as thirty.

10 × 3 tens

10 × 30

Solve this expression. Multiply ten by thirty.

10 × 30

300

The expression is now represented in its simplest form. We can start to write it in unit form. Break up three hundred into its hundreds, tens, and ones.

300

3 hundreds, 00

3 hundreds, 0 tens, 0

3 hundreds, 0 tens, 0 ones

This shows that the solution to the first expression written in unit form is <em>3 hundreds, 0 tens, 0 ones.</em>

We can continue to solve the following expressions in the same manner. Just in case you still need some help. Here is how you find the remaining three solutions in unit form.

<em>Problem Two</em>

5 hundreds × 10

500 × 10

5,000

<em>5 thousands, 0 hundreds, 0 tens, 0 ones</em>

<em>Problem Three</em>

9 ten thousands ÷ 10

90,000 ÷ 10

9,000

<em>9 thousands, 0 hundreds, 0 tens, 0 ones</em>

<em>Problem Four</em>

10 × 7 thousands

10 × 7,000

70,000

<em>7 ten thousands, 0 thousands, 0 hundreds, 0 tens, 0 ones</em>

Here's how to solve the second part of the problem:

This portion says we need to write the solution in standard form. It is important to remember that a number written in standard form will looks like an ordinary number, i.e. 76, 902, 474.

This means that under the category titled '<em>standard form'</em> we must write the answer as the ordinary solution.

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The 9th term of an arithmetic sequence is 29 and the 27th term is 83 find a and d
bixtya [17]

Answer:

Hope you understand

a=5 and d=3

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3 years ago
sarah earns $3,120 every month her monthly expenses total to $2,130 determine how much money will be spent on rent
stealth61 [152]

3120-2130=990
Hence 990 remaining for rent

However I do believe the question may be quite unclear or not telling enough information, otherwise ^
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3 years ago
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Hunter-Best [27]
The answer to your questions is 224. I hope this helped! Good luck on anymore tests and questions.
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3 years ago
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