Answer:
The result to your inquiry is 2 7/24.
Step-by-step explanation:
Data:
Hank's cows yield = 4 3/4 and 4 1/8
Debra's cows yield = 5 1/2 and 5 2/3
Process:
1.- Convert the mixed numbers into improper fractions:
For Hank: (16 + 3)/4 = 19/4 and (32 + 1)/8 = 33/8.
For Debra: (10 + 1)/2 = 11/2 and (15 + 2)/3 = 17/3.
2.- Add Hank's and Debra's milk quantities:
Hank: 19/4 + 33/8 = 38/8 + 33/8 = 71/8.
Debra: 11/2 + 17/3 = 33/6 + 34/6 = 67/6.
3.- Subtract Hank's total from Debra's total:
67/6 - 71/8 = (268 - 213)/24.
Thus, it simplifies to 55/24.
- Convert back to a mixed number:
2
24 55
7
Where 55/24 equals 2 7/24.
4.- Conclusion:
Debra produced 2 7/24 more milk than Hank.
Answer:
1. What are the amplitude and period of the sine function that indicates the positioning of the band members as they start performing?
Answer: The amplitude is 80 ft and the period is 60 ft.
2. Edna, seated in the stands, faces Darla and notices that the sine curve starts rising from the left edge of the field. What is the equation for the sine function representing the arrangement of band members at the beginning of their performance?
Answer: y = 80cos(x*π/30)+80
3. When the band starts playing, the members move away from the edges, and the sine curve changes to start decreasing at the far left. Darla remains in her position. Now the sine curve is half as tall as it originally was. What is the equation for the updated sine curve depicting the band members' positions?
Answer: y = 40cos(x*π/30)+80
4. Finally, the entire band shifts closer to the edge of the football field, causing the sine curve to now position itself in the lower half of the field from Edna’s perspective. What is the equation for this sine curve reflecting the band members' positions after these adjustments?
Answer: y = 40cos(x*π/30)+40
Step-by-step explanation:
x y
1 290
2 280
3 270
4 260
5 250
6 240
7 230
8 220
9 210
10 200
11 90
12 180
13 170
14 160
15 150
16 140
17 130
18 120
19 110
20 100
21 90
22 80
23 70
24 60
25 50
26 40
27 30
28 20
29 10
30 0
Response:
0.16 acres for each sheep
Explanatory steps:
With a total of 40 acres allocated to 250 sheep, you would calculate the area per sheep by dividing the total acres by the sheep count. This can be represented as:
40/250 =....
The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.
