Percent change = (new number - old number)/(old number) * 100
A positive percent change is a percent increase.
A negative percent change is a percent decrease.
In this problem, we have:
The new number is 15 laps.
The old number is 12 laps.
percent change = (15 - 12)/(12) * 100
percent change = 3/12 * 100
percent change = 25
Since the percent change is positive, +25, it is a percent increase.
Answer: The percent increase is 25%
Answer:
the correct choice is A. At the gas station
Step-by-step explanation:
Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;
PG=4;
GH=5;
∠P=90°.
The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer:
The area of the region between the two curves by integration over the x-axis is 9.9 square units.
Step-by-step explanation:
This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:
Given that resulting expression is a second order polynomial of the form 
, there are two real and distinct solutions. Roots of the expression are:
and 
.
Now, it is also required to determine which part of the interval 
is equal to a number greater than zero (positive). That is:
and 
.
Therefore, exists two sub-intervals: ![[-5, -4.899]](https://tex.z-dn.net/?f=%5B-5%2C%20-4.899%5D)
and ![\left[4.899,5\right]](https://tex.z-dn.net/?f=%5Cleft%5B4.899%2C5%5Cright%5D)
. Besides, 
in each sub-interval. The definite integral of the region between the two curves over the x-axis is:
![A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E%7B-4.899%7D_%7B-5%7D%20%5B%7B1%20-%20%28x%5E%7B2%7D-24%29%5D%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B4.899%7D_%7B-4.899%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B5%7D_%7B4.899%7D%20%5B%7B1%20-%20%28x%5E%7B2%7D-24%29%5D%7D%20%5C%2C%20dx)
The area of the region between the two curves by integration over the x-axis is 9.9 square units.
Answer:
a) 23.76%
b) 7.8%
Step-by-step explanation:
a) probability that a failure is due to loose keys.
loose key failure (27%) comes under mechanical failure(88%)
hence, probability that a failure is due to loose keys= 0.27×0.88= 0.2376= 23.76%
b) probability that a failure is due to improperly connected wire which comes under electrical failure = 0.12×0.13
probability that a failure is due to poorly welded wires which comes under electrical failure= 0.52×0.12
now, the probability that a failure is due to improperly connected or poorly welded wires. = 0.12(0.52+0.13)= 0.078= 7.8%
