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KIM [24]
3 years ago
5

Determine whether the conjecture is true or false. Give a counter example for any false conjecture. Given points R, S, and T. Co

njecture: R, S, and T and coplanar
Mathematics
2 answers:
dybincka [34]3 years ago
5 0

Answer:

  True

Step-by-step explanation:

Three points define a plane.

If two or more of the points are coincident, the points define an infinite number of planes. In any event, there is at least one plane that will contain all three points.

statuscvo [17]3 years ago
5 0

Answer:

<h2>b. True.</h2>

Step-by-step explanation:

Choices for this question are

a. False; the points do not have to be in a straight line.

b. True.

c. False; the points do not have to form right angles.

d. False; one point may not be between the other two.

If R, S, and T are ponts, that menas they are in the same plane.

Remember that coplanar means "in the same plane". So, when points, segments or lines are coplanar, it means they are placed in the same plane.

For example, if you put three glasses on the surface of your table, you can side that the points marked by the bottom of each glass are coplanar, because the surface of the table is a plane, and all glasses are in the same one.

Therefore, the answwe is true.

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If two of these shapes are randomly chosen, one after the other without replacement, what is the probability that the first will
aleksandrvk [35]

Answer:

P(T\ n\ S) = \frac{1}{14}

Step-by-step explanation:

*Missing Part of the Question*

4 stars

5 triangles

3 circles

3 squares

Required

Determine the probability of triangle being first then square being second

Total = 4 + 5 + 3 + 3

Total = 15

Represent the triangle with T and square with S

So, we're solving for P(T n S)

P(T\ n\ S) = P(T) * P(S)

Solving for P(T)

P(T) = \frac{n(T)}{Total}

P(T) = \frac{5}{15}

Solving for P(S)

The question implies a probability without replacement;

Hence Total has now been reduced by 1

Total = 14

P(S) = \frac{n(S)}{Total}

P(S) = \frac{3}{14}

Recall that

P(T\ n\ S) = P(T) * P(S)

P(T\ n\ S) = \frac{5}{15} * \frac{3}{14}

P(T\ n\ S) = \frac{15}{15 * 14}

P(T\ n\ S) = \frac{1}{14}

Hence, the required probability is

P(T\ n\ S) = \frac{1}{14}

3 0
3 years ago
In​ Marissa's calculus​ course, attendance counts for 15​% of the​ grade, quizzes count for 20​% of the​ grade, exams count for
Alexandra [31]

Answer:

Her average was 87.35% on this course.

Step-by-step explanation:

In order to determine Marissa's average we need to take the average she has on each of the cattegories and find how much that relates to the weight of the  cattegory on the final grade. We have:

Attendance counts for 15% of the grade and she has 100% average on that. So we have:

attendance = weight*(Marissa's average)

attendance = 15%*(100/100) = 15%

Quizzes counts for 20% of the grade and she has a 93% average on that. So we have:

Quizzes = weigth*(Marissa's average)

Quizzes = 20%*(93/100) = 18.6 %

Exams counts for 50% of the grade and she has a 82% average on that. So we have:

Exams = weigth*(Marissa's average)

Exams = 50%*(82/100) = 41%

The final exam counts for 15% of the grade and she has a average of 85% on that so we have:

Finals = 15%*(85/100) = 12.75%

So her grade is the sum of all the cattegories:

Course's average = 15+18.6+41+12.75 = 87.35 %

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