base, b = 45m
angle of elevation, aoe = 82deg
height at 86th floor, h1
height above 86th floor, h2 = 123m
total height, h = h1 + h2
using
tan (aoe) = h1/b
=》 h1 = tan (aoe) × b = tan 82 x 45 = 320.2
h = h1 +h2 = 320.2 + 123 = 443.2m
Answer:
1. D) 1 9/20
2. B) 7/12
4. D) $50.00
Step-by-step explanation:
The working is as follows :
1. Mrs. Lang bought 3/4 pound of red grapes and 7/10 pound of green grapes. To find out how many are in total we have to add both values total.
3/4 + 7/10
The LCM of 4 and 10 is 20.
3/4 * 5 = 15/20
7/10 * 2 = 14/20
15/20 + 14/20 = 29/20 = 1 9/20
2. 1/3 + 1/4
The LCM of 3 and 4 is 12
1/3 * 4 = 4/12
1/4 * 3 = 3/12
4/12 + 3/12 = 7/12
4. Sharon spent 2/3 of her clothing allowance; she was given $75. All we have to do is find 2/3 of $25 :
2/3 * $75 = $50.00
Although the number of new wildflowers is decreasing, the total number of flowers is increasing every year (assuming flowers aren't dying or otherwise being removed). Every year, 25% of the number of new flowers from the previous year are added.
The sigma notation would be:
∑ (from n=1 to ∞) 4800 * (1/4)ⁿ , where n is the year.
Remember that this notation should give us the sum of all new flowers from year 1 to infinite, and the values of new flowers for each year should match those given in the table for years 1, 2, and 3
This means the total number of flowers equals:
Year 1: 4800 * 1/4 = 1200 ]
+
Year 2: 4800 * (1/4)² = 300
+
Year 3: 4800 * (1/4)³ = 75
+
Year 4: 4800 * (1/4)⁴ = 18.75 = ~19 (we can't have a part of a flower)
+
Year 5: 4800 * (1/4)⁵ = 4.68 = ~ 5
+
Year 6: 4800 * (1/4)⁶ = 1.17 = ~1
And so on. As you can see, it in the years that follow the number of flowers added approaches zero. Thus, we can approximate the infinite sum of new flowers using just Years 1-6:
1200 + 300 + 75 + 19 + 5 + 1 = 1,600
Answer:
To find the scale factor, locate two corresponding sides, one on each figure. Write the ratio of one length to the other to find the scale factor from one figure to the other. In this example, the scale factor from the blue figure to the red figure is 1.6 : 3.2, or 1 : 2.
Step-by-step explanation:
