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pogonyaev
3 years ago
6

Three years ago, Jolene bought $525 worth of stock in a software company. Since then the value of her purchase has been increasi

ng at an average rate of 12 2/5
% per year. How much is the stock worth now? (Round each money calculation you make to the nearest cent.)
Mathematics
1 answer:
hram777 [196]3 years ago
8 0

Answer:

Is there multiple choice or just calculations?

Step-by-step explanation:

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Factor y2 + 8y + 15
vovangra [49]
Y² + 8y + 15
since 8 and fifteen are positive, that means your factors are going to be positive
(y + )(y + )
What are the factors of 15 that add up to 8?
8 0
3 years ago
A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours
qaws [65]

Answer:

  • The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.
  • Below are all the steps explained in detail.
  • The graph is attached.

Explanation:

<u />

<u>1. Name the variables:</u>

  • x: number of smaller lifts
  • y: number of larger lifts

<u></u>

<u>2.  Build a table to determine the number of hours each lift requires from each department:</u>

<u></u>

Number of hours

                                        small lift    large lift   total per department

Welding department            1x             3y                x + 3y

Packaging department        2x             1y                2x + y

<u></u>

<u>3. Constraints</u>

  • 150 hours available in welding:         x + 3y ≤ 150
  • 120 hours available in packaging:   2x + y ≤ 120
  • The variables cannot be negative:    x ≥ 0, and y ≥ 0

Then you must:

  • draw the lines and regions defined by each constraint
  • determine the region of solution that satisfies all the constraints
  • determine the vertices of the solution region
  • test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

<u></u>

<u>4. Graph</u>

See the graph attached.

Here is how you draw it.

  • x + 3y ≤ 150
  • draw the line x + 3y = 150 (a solid line because it is included in the solution set)
  • shade the region below and to the left of the line

  • 2x + y ≤ 120
  • draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
  • shade the region below and to the left of the line

  • x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

  • the solution region is the intersection of the regions described above.

  • take the points that are vertices inside the solutoin region.

<u>5. Test the profit function for each vertex</u>

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

  • (0,0)
  • (0,50)
  • (42,36)
  • (60,0)

The profits with the vertices are:

  • P(0,0) = 0
  • P(0,50) = 25(0) + 90(50) = 4,500
  • P(42,36) = 25(42) + 90(36) = 4,290
  • P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

3 0
3 years ago
K(a)= 4a-4, Find k(-9)
FromTheMoon [43]

We simply replace a with -9

k(-9) = 4 * -9 - 4

k(-9) = -40

:)

5 0
3 years ago
A certain brand of coffee costs $2.99 for 11.3 ounces. What is the unit rate? Enter your answer, rounded to the nearest cent, in
Marysya12 [62]
To find the unit rate, you would do 2.99 / 11.3 and get about 26 cents. So the unit rate would be 26 over 1 ( 26/1 ).


Hope I helped! 

Marsh
8 0
3 years ago
Read 2 more answers
Solve: 2 + = 2. Give solutions in interval [0, 2)
Dovator [93]
\because\cos 2x+\sin x=\sin 2x\because\sin 2x=2\sin xcosx\because\cos 2x=\cos ^2x-\sin ^2x

→ Substitute cos 2x and sin 2x by their expressions

\therefore\cos ^2x-\sin ^2+\sin x=2\sin x\cos x

→ Subtract both sides by sin x

\cos ^2x-\sin ^2x=2\sin xcosx-\sin x

→ Take sin x as a common factor in the right side

\therefore\cos ^2x-\sin ^2x=\sin x(2\cos x-1)

From the graph, the equation has 4 solutions, the intersection points between the 2 graphs

7 0
1 year ago
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