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8. Amount invested in savings account A = $950.

Amount invested in savings account B = $550.

9. Students must sell 16 scarves to break-even.

Step-by-step explanation:

8. Let A be the amount invested in savings account A and B be the amount invested in savings account B.

We have been given that amount invested in two savings account is  $1500. We can represent this information as:

We are also told that after 1 year, we have earned a total of $69.50 in interest. We can represent this information as:

We will use substitution method to solve our system of equations. From equation (1) we will get,

Upon substituting this value in equation (2) we will get,

Therefore, the amount invested in savings account B is $550.

Upon substituting B=550 in equation (1) we will get,

Therefore, the amount invested in savings account A is $950.  

9. Let x be the number of scarfs.

We are told that the yarn to make a scarf costs $4. So the cost of yarn for making x scarves will be 4x.

The booth at craft show cost $160 and the cost of a pair new knitting needles is $16. So the total cost of making x scarves will be:

Since we are told that each scarf sells for $15. So the revenue earned from selling x scarves will be:

Since we know that break-even point is the point, where total costs are equal to total revenue and total profit at break-even equals 0.

To find the break-even point we will equate total costs to total revenues as:

Let us solve for x.  

Therefore, the student need to sell 16 scarves to break-even.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: