A rectangular swimming pool has a length twice as long as its width. The pool has a sidewalk around it that is 2 feet wide. Writ
e an expression that would help you find the area of the pool and its sidewalk.
1 answer:
Answer:
Step-by-step explanation:
Functions and Geometry
Sometimes we need to express areas, volumes, and distances in terms of unknown quantities (or variables). When we can find such expressions, they can be referred to as functions. Let's recall the area of a rectangle is A=wl, being w its wide and l its length
Please refer to the image below. The length of the swimming pool is l and its width is w. Its area is
We know the length is twice as long as its width, l=2w, so
The sidewalk is 2 feet wide. The length of the pool and its sidewalk is
Similarly, the width of the pool+sidewalk is
The area of the pool+sidewalk is
We know that l=2w, so
The area of the sidewalk alone is the subtraction of both areas
Simplifying
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The complete question is:
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend. You expect to purchase at least 3 pounds of hamburgers.
- Write a system of inequalities to represent this situation.
- Graph the system of inequalities on the grid.
- Give three possible combinations for buying hamburgers and chicken for your summer bash.
Justify your answers
Answer:
A) System of inequalities:
- 2x + 3y ≤ 30
- x ≥ 3
- x ≥ 0
- y ≥ 0
B) Graph: see the picture attached
C) Three possible combinations:
- 3 pounds of hamburgers and 8 pounds of chicken
- 3 pounds of hamburgers and 0 pounds of chicken
- 15 pounds of hamburgers and 0 pounds of chicken
Explanation:
<u>A) Write the system of inequalities to represent this situaction.</u>
<u>1. Variables:</u>
- x: number of pound of hamburgers
- y: number of pound of chicken
<u>2. Costs:</u>
- x pounds of hamburgers at $2 per pound: 2x
- y: pounds of chicken at $3 per pound: 3y
- total cost: 2x + 3y
<u>3. First constraint:</u>
- You have no more than $ 30 to spend: means that the cost of what you buy can be at most (less than or equal to) $ 30.
- 2x + 3y ≤ 30
<u>4. Second constraint:</u>
- You expect to purchase at least 3 pounds of hamburgers: means that the number of pounds of hamburgers may be greater than or equal to 3.
- x ≥ 3
<u>5. Additional constraints:</u>
- Both, x and y cannot be negative: x, y ≥ 0
<u>6. System of equations:</u>
- 2x + 3y ≤ 30
- x ≥ 3
- x ≥ 0
- y ≥ 0
<u>B) Graph </u>
You have to graph all the constraints in a x-y coordinate system.
<u>1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30</u>
- Choose the y-intercept and x-intercept.
- x = 0 ⇒ 3y = 30 ⇒ y = 10 ⇒ point (0, 10)
- y = 0 ⇒ 2x =30 ⇒ x = 15 ⇒ point (15, 0)
- With two points you can draw the line
- Clear y: y ≤ 10 - 2x/3. Since, the symbol is ≤ you shade the region below the line, and the line is included, so you draw it as as solid line.
<u>2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).</u>
<u>3. The constraints x ≥ 0 and y ≥ 0 </u>mean that the region is restricted to the first quadrant (including the positive axis).
<u>4. The feasible solutions</u> are the set of points inside the common regions (intersection).
With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).
<u>C) Give 3 possible combinations.</u>
You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:
- (3, 8) ⇒ 3 pounds of hamburgers and 8 pounds of chicken
- (3,0) ⇒ 3 pounds of hamburgers and 0 pounds of chicken
- (15,0) ⇒ 15 pounds of hamburgers and 0 pounds of chicken
You could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.
This is how you prove it:
- 5 ≥ 0
- 5 ≥ 3
- 4 ≥ 0
- 2(5) + 3(4) = 10 + 12 = 22 ≤ 30
And you can do the same for any pairs to verify whether they are solution or not.
Answer:
The probability that the average score of a group of n = 4 people is between 70 and 75=0.13591
Step-by-step explanation:
We are given that
n=4
We have to find the probability that the average score of a group of n = 4 people is between 70 and 75.
Hence, the probability that the average score of a group of n = 4 people is between 70 and 75=0.13591