Archive for the ‘Analysis’ Category

Problem 1050

Write the negation of the statement.

Some panthers do not have claws.

 

Solution:-

 

Use the following diagram to help remember the negation of qualified statements.

n1

Notice that the given statement “Some panthers do not have claws

” is in the form “Some are not.” Using the diagram, follow the arrows to see the negation of “Some are not.”

Since the statement “All are.” is the negation of “Some are not,” the negation of the given statement will be in the form “All are.” Thus, the  statement “All panthers have claws.” is the correct negation statement.

 

 

Problem 418

Find expressions for the Revenue, Cost, and Profit from selling x thousand items.

Item Price Fixed Cost Variable Cost

7.00, 195,503, -3x^{2} +3480x -100

 

Solution

 

R= 7000x (7 dollars per 1000x items)

C = 195503 – 3x^{2} + 3480x – 100 (fixed cost + variable cost)

C = -3x^{2} + 3480x + 195,403

P = 7000x –(195403 – 3x^{2} + 3480x)

= 7000x – 195403 + 3x^{2} – 3480x

= 3x^{2} – 3520x – 195,403