A surveyor must divert her path from point C by proceeding due south for 300 ft to point A. The
surveyor determines that point B, which is due east of point C, is N49°E from point A. What is the distance
from point C to point B?
A. 350 ft
B. 375 ft
C. 360 ft
D. 370 ft
1. What is 57% of 11? (1 point)
11 = 0.57 • n; 19.3
n = 57 • 11; 627
n = 0.57 • 11; 6.27
11 = 57 • n; 0.19
2. 224 is 25% of what number? (1 point)
224 • 0.25 = w; 560
224 = 0.25 • w; 896
224 • 0.25 = w; 56
224 = 0.25 • w; 90
3. What is 45% of 10? (1 point)
450
45
4.5
0.45
Find the percent of increase.
4. 50 to 70 (1 point)
20%
30%
40%
50%
Find the percent of decrease. Round your answer to the nearest tenth of a percent where necessary.
5. 75 to 60 (1 point)
20%
30%
40%
50%
Find the percent markup. Round to the nearest whole percent.
6. Store's cost: $100.00
Selling price: $160.00 (1 point)
50%
60%
70%
80%
Find the sale price. Round to the nearest cent.
7. Regular price: $57.63
Percent of discount: 10% (1 point)
$63.39
$5.76
$51.87
$57.53
Find the sale price. Round to the nearest cent.
8. Regular price: $56.00
Percent discount : 40% (1 point)
$50.00
$22.40
$40.00
$33.60
9. Find the interest earned in an account with $600.00 invested at 4.5% annual simple interest for 2 years. (1 point)
$540.00
$5,400.00
$54.00
$13.50
10. Find the interest earned by an account with $1,200 of simple interest of 4% for 3 years. (1 point)
$144.00
$244.00
$44.00
$88.00
To solve this problem, we can use the concept of vector addition. We know that the direction from point B to point A is N49°E, which means it is 49 degrees clockwise from north.
First, let's break down the given information:
- The surveyor moves due south from point C to point A for a distance of 300 ft.
- Point B is due east (90 degrees clockwise from north) of point C, and it is N49°E from point A.
We need to find the distance from point C to point B. To do this, we can consider the vectors from each point:
1. The vector from point C to point A is 300 ft due south.
2. The vector from point A to point B is the combination of two vectors: from point A to the direction of N49°E, and then from that point to point B.
To calculate the distance from C to B, we need to add the vectors from C to A and from A to B.
Let's break it down step by step:
1. Start at point C and move south for 300 ft.
2. Now, you are at point A.
3. From point A, move in the direction of N49°E.
- Since N49°E is 49 degrees clockwise from north, you will need to turn 49 degrees to the right.
- After turning, move straight in that direction until you reach point B.
4. Measure the distance between point C and point B. This will give you the answer.
Now that we have the steps, let's evaluate the options:
A. Move due south for 300 ft from C, then move in the direction of N49°E for the given distance. If the distance between C and B matches the option (i.e., 350 ft), then A is the correct answer.
B. The same process as option A, but the distance between C and B should be 375 ft for this option to be correct.
C. The distance between C and B should be 360 ft if this option is correct.
D. The distance between C and B should be 370 ft if this option is correct.
By following the steps and considering which option matches the calculated distance, you can determine the correct answer.