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4 years ago

An isosceles trapezoid is a trapezoid with congruent bases True or false?

Mathematics

1 answer:

soldier1979 [14.2K]4 years ago

7 0

Answer:

<h2>False</h2>

Step-by-step explanation:

An isosceles trapezoid is a convex quadrilateral with a symmetric vertical axis, which means it can be divided in two congruent parts.

In other words, an isosceles trapezoid is defined by its congruent sides, not congruent bases.

The bases of a trapezoid doesn't have to be congruente to call it isosceles.

Therefore, the answer is false.

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3 years ago

Suppose that a college determines the following distribution for X = number of courses taken by a full-time student this semeste

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Answer:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$ In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$ And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

For this case we have the following distribution given:

X 3 4 5 6

P(X) 0.07 0.4 0.25 0.28

We can calculate the mean with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 3*0.07 +4*0.4 +5*0.25 +6*0.28= 4.74$

In order to find the variance we need to calculate first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 3^2*0.07 +4^2*0.4 +5^2*0.25 +6^2*0.28= 23.36$

And the variance is given by:

$Var(X) = E(X^2) +[E(X)]^2 = 23.36 -[4.74]^2 = 0.8924$

And the deviation would be:

$Sd(X) =\sqrt{0.8924} =0.9447$

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4 years ago

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4 years ago

The line plot shows the heights of the players on a basketball team, in inches.

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A: based on the given dot plot are: statements B, D, and E.

B: A. No. 74 is not an outlier because it is not different from the other heights in the dot plot.

In a dot plot, frequencies of each data point is represented as dots.

Thus, in the dot plot given:

Players of 70 1/2 in. tall and above are 7 in number. This is half of the number of the total players. (option B is true).

Players with height of 69 1/2 in. (3 players) are more than those that are 70 in. tall (1). (option A is not true).

One of the player is 68 1/2. (option C is not true).

Four of the players are 74 in. tall (option D is true).

The team has 6 different heights as shown in the dot plot given (option E is correct).

Therefore, the statements that are correct based on the given dot plot are: statements B, D, and E.

If a player of 73 in. tall replaces a player of 71 in, tall, 73 is close to 74.

Therefore, we can conclude that: A. No. 74 is not an outlier because it is not different from the otehr heights in the dot plot.

Learn more about dot plots on:

brainly.com/question/25957672

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