Answer:
74º
Step-by-step explanation:
- Ray TV bisects ∠RTS, so ∠RTV=∠STV=(16x-6)º
- We also know that ∠RTS=(26x+18)º
- So, (16x-6)º+(16x-6)º=(26x+18)º
- We don't need parenthesis, 16x-6+16x-6=26x+18
- Combine like terms, 32x-12=26x+18
- Add, 32x=26x+30
- Subtract, 6x=30
- Divide, x=5
- ∠RTV now is [16(5)-6]º=(80-6)º=74º
Assuming a normal distribution we find the standardized z scores for a:-
z1 = (80 - 180) / 25 = = -100/25 = -4
z2 = (280-180) / 25 = 4
Required P( -4 < z < 4) from the tables is >99.9%
b
z1 = 130-180 / 25 = -2
z2 = 230-180 / 25 = 2
from tables probability is 2* 0.4773 = 95.46 %
Answer:
-4600
Step-by-step explanation:
Answer:
circle area = 1963.495 ft²
Step-by-step explanation:
<u>Given</u>
A rectangle 550 ft by 350 ft packed with circles on a rectangular grid
<u>Find</u>
the area of the largest circle that can be packed this way
<u>Solution</u>
The diameter of the circle must be a factor of both 350 and 550. We want the diameter to be the largest such factor. We can write the factors of 350 and 550 as ...
- 350 = 50 × 7
- 550 = 50 × 11
The largest factor common to both numbers is 50, so that will be the diameter of the largest circle that will fit on a square grid.
The area of a circle is commonly given by the formula ...
A = πr² . . . . . where r represents the radius of the circle.
The radius is half the diameter, so will be (50 ft)/2 = 25 ft. And the area of the circle is ...
A = π(25 ft)² = 625π ft² ≈ 1963.495 ft²
The area of one circle is about 1963.495 square feet.
_____
The total number of circles is 11×7 = 77. Their total area is 77×1963.495 ft² ≈ 151,189 ft². This is 151,189/192,400 ≈ 78.54% of the total area of the rectangle.
Answer:
Adam's total cost: $9.20
Cindy's total cost: $9.20
Step-by-step explanation:
Since Adam and Cyndi's total bill costs $16, evenly splitting the cost means that each of them has to pay $8, not including the tip.
To find out the dollar value of their 15% tip, multiply $8 by 0.15:
$8 × 0.15 = $1.20.
Adam and Cindy will have to pay $8 (lunch cost) + $1.20 (tip) = $9.20 separately.
