Answer:
514/4
Step-by-step explanation:
128 1/4
= (128×4+1)/4
= 514/4
Answer:
51.69 hours (see explanation)
Step-by-step explanation:
This question is simple once you break it down:
84 boxes in 312 hours is a rate, so it can be shown in fraction form:
84 boxes / 312 hours
Now to figure out how long it takes to unpack those 192 boxes, just multiply:
192 x 84/312
(192 x 84) / 312
16128 / 312
Now, just divide the numbers:
16128 ÷ 312 = 51.69 hours
Answer:
He solved 75% of the puzzles!
Step-by-step explanation:
Okay, let's look at our fraction 18 out of 24. We can see that they are both even numbers, so at worst, we can divide the entire fraction by two. However, they have a GCF of six, so we will use that.
18 3
---- divided by 6 = ----
24 4
Now that we have the fraction 3/4, we can turn that into a percentage!
3/4 is 0.75. To get the percentage, we multiply that by 100--now we have 75%.
Answer: 4.5 miles
Explanation:
When you draw the situation you find two triangles.
1) Triangle to the east of the helicopter
a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°
b) hypotensue = distance between the high school and the helicopter
c) opposite-leg to angle 20° = heigth of the helicopter
d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x
2) triangle to the west of the helicopter
a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°
b) distance between the helicopter and the elementary school = hypotenuse
c) opposite-leg to angle 62° = height of the helicopter
d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x
3) tangent ratios
a) triangle with the helicpoter and the high school
tan 20° = Height / x ⇒ height = x tan 20°
b) triangle with the helicopter and the elementary school
tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°
c) equal the height from both triangles:
x tan 20° = (5 - x) tan 62°
x tan 20° = 5 tan 62° - x tan 62°
x tan 20° + x tan 62° = 5 tan 62°
x (tan 20° + tan 62°) = 5 tan 62°
⇒ x = 5 tant 62° / ( tan 20° + tan 62°)
⇒ x = 4,19 miles
=> height = x tan 20° = 4,19 tan 20° = 1,525 miles
4) Calculate the hypotenuse of this triangle:
hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²
hipotenuse = 4.46 miles
Rounded to the nearest tenth = 4.5 miles
That is the distance between the helicopter and the high school.
