3 and 4 only
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
3 and 4 only
![PERFORMANCE TASK (MELC 19-21 ):
PROBLEM SOLVING
Direction: Solve the following problems involving sampling distribution of the sample mean
correctly and accurately
1. The average number of milligrams (mg) of cholesterol in a cup of a certain brandof
1ce cream is 660 mg, the standard deviation is 35 mg. Assume the variable is normally
distributed.
a. If a cup of ice cream is selected, what is the probability that the cholesterol
content will be more than 670 mg?
b. Ifa sample of 10 cups of ice cream is selected, what is the probability thatthe
mean of the sample will be larger than 670 mg?
2. In a study of the life expectancy of 400 people in a certain geographic region, the
mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample
of 50 people from this region is selected, what is the probability that the mean life
expectancy will be less than 68 years?
3. The average cholesterol content of a certain canned goods is 215 milligrams, andthe
standard deviation is 15 milligrams. Assume that the variable is normally distributed.
If a sample of 25 canned goods is selected, what is the probability that the mean of
the sample will be greater than 220 milligrams?
4. The average public elementary school has 468 students with a standard deviationof 87. If a
random sample of 38 public elementary schools is selected, what is theprobability that the
number of students enrolled is between 445 and 485?
SIGNATURE OF PARENTS:
IGNATURE OF STUDENT
RUBRIC FOR PERFORMANCE TASK
12 POINTS
10 POINTS
8 POINT
6 POINT
Category
15 POINTS
The answer to
the problem is
correct but the
solution is not
detailed and
clear
Solved all the
The answer to
the problem is
almost correct
and solution is
detailed and
clear
Solved 3
The answer to
the problem is
not correct and
solution is not
detailed and
clear
Solved 2
The answer to
the problem is
not correct and
solution is not
The answer to
Accuracy of the problem is
correct and
solution is
detailed and
clear
Solved all the
Solution
present.
Completeness problems
completely
problems but 1 problem
is not
problems but
is not
Tried to solve
1 the problem
completely.
completed
completed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55ec9327-23f3-442f-a7ad-671c4dfc9b13%2F8a9b6be4-827a-4db0-ad77-2f2d0a3668d7%2Flsllw7_processed.jpeg&w=3840&q=75)
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