To find the time Jack takes to cross Swan Lake, his average speed is required:
The time it will take Jack to cross Swam Lake is <u>0.5 hours</u>
Reason:
Time it took Jack to paddle 6.4 km upstream, t = 2 hours
Distance Jack paddled, d = 6.4 km
The given speed of the Black River, <em>v₂</em> = 1.8 km/h
The width of the lake, w = 2.5 km
The time it will take Jack to cross Swan Lake
Let <em>v₁</em>, represents Jack's speed, we have;
Therefore;
v₁ = 3.2 + 1.8 = 5
The time it will take Jack to cross Swan Lake, = <u>0.5 hours</u>
Learn more here:
Answer: 86.64%
Step-by-step explanation:
Let x be a random variable that represents the diameter of metal samples.
Given : Population mean :
Standard deviation:
Specified tolerance on the diameter is 0.75 mm.
i.e. range of diameter = 10-0.75< x <10+0.75 = 9.25< x< 10.75
Formula to find the z-score corresponds to x:
At x= 0.75,
Using standard normal table for z-value,
P-value :
∴ Percentage of samples manufactured using this process satisfy the tolerance specification = 86.64%
A diagram can be helpful.
When triangles have the same altitude, their areas are proportional to their base lengths.
The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...
... BC : EC = (1+5) : 5 = 6 : 5
so ABDC will be 6/5 times AEDC.
... ABDC = (6/5)×(5 in²)
... ABDC = 6 in²
_____
The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...
... AABD : ABDC = AD : DC = 4 : 3
so AABD will be 4/3 times ABDC.
... AABD = (4/3)×(6 in²)
... AABD = 8 in²
_____
Of course, AABC is the sum of the areas of the triangles that make it up:
... AABC = AABD + ABDC = 8 in² + 6 in²
... AABC = 14 in²
