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Scenario

The average income in thousands of dollars for a single Hispanic family in the United States t years since 2000 can be estimated by using the expression:
1.5t+42

The number of Hispanic families in millions in the United States t years since 2000 can be estimated by using the expression:
0.3t+8.4



QUESTION 1

Read the instructions carefully. If we want to find information about the year 2015 from the expressions in the instructions, what number would we use for t? Hint: don't just put in 2015! Read the scenario in the instructions.
t=________

QUESTION 2

Find the average income of a single Hispanic family in the United States in 2010. Remember that your answer should be in the range of thousands of dollars (type in a number in standard notation, without commas or dollar signs).
$_____________

QUESTION 3

Find the number of Hispanic families in the United States in 2010. Remember that your answer should be in the range of millions of families (type in a number in standard notation, without commas).
_________________________

QUESTION 4

Express your answer from question 3 in scientific notation.
____×10^___

QUESTION 5

Use the given expressions to write a new expression for the total income of all Hispanic families in the United States (your answer to this problem should be a polynomial – type in the coefficients for the polynomial you found below).
_____t^2+_____t +______

QUESTION 6

Explain how you found your answer to question #5.

Respuesta :

Question 1:
Because we start with the year 2000, we must subtract 2000 from 2015 giving us t= 15 years.  
Question 2:
Like Question 1, we must subtract 2000 from 2010, giving us t=10 years.  We then plug t=10 into the first equation, giving 1.5*10+42, which equals 57.  Then because this number is in thousands of dollars, we know that the average income is equal to 57,000 dollars.  
Question 3:  
For this problem, we can use the same value for t as we used in Question 2, t=10 years, because we are dealing with the same date, 2010.  We then plug this value of t into the second equation, giving 0.3*10+8.4, which equals 11.4.  We then multiply this number by 1 million because this number is in millions of people giving an answer of 11,400,000 Hispanic people in 2010.
Question 4:
We must take the number 11,400,000. from Question 3 and put this into scientific notation by moving the decimal point to the left until there is only one number of the left side of the decimal point and multiplying our result of that by 10 to the power of how many places we moved the decimal point, giving us 1.14*10^7(^ means to the power).  
Question 5:
The total income of all Hispanic families is going to be equal to the number of total Hispanic families (0.3t+8.4) times the income of one average Hispanic family (1.5t+42).  However, we first must recognize that the formula for the number of Hispanic families is in millions, but the formula for the average income of one Hispanic family is in thousands.  Since thousands is less than millions we will change both will change the formula for the number of Hispanic families to thousands by multiplying the first equation by 1000.  This gives us an a new equation of 300t+8400 for the number of Hispanic families in thousands.  Now we can multiply the two equations together using the FOIL Method (First, Outer, Inner, Last).  This gives us a resulting equation of (1.5t*300t+42*8400+42*300t+8400*1.5t).  When we multiply out these terms, we get (450t^2+352800+12600t+12600t).  Since there are multiple terms with the same power of t, we can combine like terms and condense the equation to 450t^2+352800+25200t.  Since there are some pretty big numbers in this equation, we can divide the whole equation, which is in thousands, by one thousand, which in turn will make the equation in millions.  This yields (.45t^2+352.8+25.2t) in millions.  This is the equation for the total income of all Hispanic families in a given year after the year 2000 where t is equal to the current year minus 2000.   
Question 6:
Explained in Question 5.
fichoh

The evaluation is performed by substituting the appropriate value of time, t into the expressions given. The solutions are outlined thus :

Using the equations given :

1.)

Since, t = number of years since the year 2000; the value of t would be calculated thus;

  • t = 2015 - 2000 = 15

2.)

Average income of a single Hispanic Family in 2010:

  • t = 2010 - 2000 = 10

Substitute the value t = 10 into the equation :

Average income = 1.5(10) + 42 = $57000

3.)

Number of Hispanic Families in 2010:

  • t = 2010 - 2000 = 10

Substitute the value t = 10 into the equation :

Average income = 0.3(10) + 8.4 = 11400000

4.)

Expressing 11400000 using scientific notation

Since 0's are to the right, power of 10 would be positive ;

Number of Hispanic Families = [tex] 1.14 \times 10^{7}[/tex]

5.)

Total income earned = (total number of Hispanic families × Average earning per family)

(1.5t + 42) × (0.3t + 8.4)

0.45t² + 12.6t + 12.6t + 352.8

Total income earned in $ billions = 0.45t² + 25.2t + 352.8

Learn more : https://brainly.com/question/25274329

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