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3 years ago

Bill and Ben each have three cards, numbered 4, 5 and 6.

Mathematics

1 answer:

trapecia [35]3 years ago

5 0

Answer:

a) Probability = 4/9

b) Probability = 6/9

Step-by-step explanation:

<h3>Data Given:</h3>

Bill and Ben each have three cards 4,5 and 6. They each take one of their own cards. Then they add together the two numbers on the cards.

<h3>Find all the possibilities:</h3>

Bill = {4, 5, 6}

Ben = {4, 5, 6}

If both of them take one card, all possibilities are:

{ (4,4) , (4,5) , (4,6) , (5,4) , (5,5) , (5,6) , (6,4) , (6,5) , (6,6) }

Total No. of possibilities = 9

<h3 /><h3>a) What is the probability that their answer is an odd number?</h3>

We see from the all possibilities listed above that which one of them has a sum of odd number. We get:

{ (4,5) , (5,6) , (5,6) , (6,5) }

Total No. of Desired outcomes = 4

Total No. of possibilities = 9

Probability = Total No. of Desired outcomes/Total No. of possibilities

Probability = 4/9

<h3>b) What is the probability that their answer is a number less than 11?</h3>

We see from the all possibilities listed above that which one of them has a sum less than 11. We get:

{ (4,4) , (4,5) , (4,6) , (5,4) , (5,5) , (6,4) }

Total No. of Desired outcomes = 6

Total No. of possibilities = 9

Probability = Total No. of Desired outcomes/Total No. of possibilities

Probability = 6/9

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Answer:

Step-by-step explanation:

A 2 - sided counter ; (red, yellow)

A spinner (1,2,3,4,5,6)

Number of trials = 80

P(red and number > 3) :

P(red) = 1/2 ;

P(number >3) : numbers greater Than 3 = (4, 5, 6)

Hence, P(number <3) = 3 /6 = 1/2

Theoretical probability = 1/2 *1/2 = 1/4

Expected number of outcomes :

1/4 * number of trials

1/4 * 80 = 20

Experimental outcome :

Relative frequency = number of outcomes / number of trials

Relative frequency = 2/5

Hence,

2/5 = number of outcomes / 80

Cross multiply :

160 = number of outcomes * 5

Number of outcomes = 160 /5 = 32

Actual outcomes = 32

Difference between actual and expected :

32 - 20 = 12

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3 years ago

Which of the following is the result of the equation below after completing the square and factoring?

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Answer:

D) $(x + \frac{5}{2})^{2} = \frac{9}{4}$

Step-by-step explanation:

Given equation

⇒ $x^{2} + 2 X \frac{5}{2} x + (\frac{5}{2} )^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

<u><em>Step(ii):</em></u>-

By using (a + b)² = a² + 2 a b + b²

⇒ $(x + \frac{5}{2})^{2} - (\frac{5}{2} )^{2}+ 8 = 4$

⇒ $(x + \frac{5}{2})^{2} = 4 + (\frac{5}{2} )^{2} -8$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25}{4} ) -4$

⇒ $(x + \frac{5}{2})^{2} = (\frac{25-16}{4} )$

⇒ $(x + \frac{5}{2})^{2} = \frac{9}{4}$

<u><em>Final answer:-</em></u>

$(x + \frac{5}{2})^{2} = \frac{9}{4}$

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