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3 years ago

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Mags and Vector are playing a board game. They use a spinner to determine if they should move forward or backward. They roll a n

umber cube with the numbers 1-6 on it to determine how many Mags and Vector are playing a board game. They use a spinner to determine if they should move forward or backward. They roll a number cube with the numbers 1-6 on it to determine how many spaces to move. What is the probability of moving backward an even number of spaces?
Answers- 1/6 1/4 1/2 1/3

1 answer:

padilas [110]3 years ago

5 0

Answer: 1/4

Step-by-step explanation:

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Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

$RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}$

$ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}$

$TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}$

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$QR = \frac{9 + 1}{2 + 3} = \frac{10}3$

$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

$ST = \frac{5+5}{-4 + 7} = \frac{10}3$

$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

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2 years ago

A student takes an exam containing 1414 multiple choice questions. The probability of choosing a correct answer by knowledgeable

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Answer:

0.0082 = 0.82% probability that he will pass

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 14, p = 0.3$ .

If the student makes knowledgeable guesses, what is the probability that he will pass?

He needs to guess at least 9 answers correctly. So

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{14,9}.(0.3)^{9}.(0.7)^{5} = 0.0066$

$P(X = 10) = C_{14,10}.(0.3)^{10}.(0.7)^{4} = 0.0014$

$P(X = 11) = C_{14,11}.(0.3)^{11}.(0.7)^{3} = 0.0002$

$P(X = 12) = C_{14,12}.(0.3)^{12}.(0.7)^{2} = 0.000024$

$P(X = 13) = C_{14,13}.(0.3)^{13}.(0.7)^{1} = 0.000002$

$P(X = 14) = C_{14,14}.(0.3)^{14}.(0.7)^{0} \cong 0$

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0066 + 0.0014 + 0.0002 + 0.000024 + 0.000002 = 0.0082$

0.0082 = 0.82% probability that he will pass

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