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2 years ago

In the above diagram, you see a standard deck of cards. Answer each of the following questions using this deck of cards.

Mathematics

1 answer:

Novay_Z [31]2 years ago

7 0

Answer:

See below.

Step-by-step explanation:

52 as there is a total of 52 in the pack.

Probability (drawing a red card) =26/52 = 1/2.

4 aces.

Probability(drawing an ace) = 4/52 = 1/13.

Probability(drawing a numbered card) = 40/52 = 10/13.

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Answer:

First image attached

The error was done in Step E, because student did not multiply $2\cdot x -8$ by the negative sign in numerator. Step E must be $\frac{2\cdot x -5}{(x+4)\cdot (x-4)}$ .

Second image attached

The error was done in Step C, because the student omitted the $2\cdot a \cdot b$ of the algebraic identity $(a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}$ . Step C must be $5\cdot x = x^{2}+4\cdot x + 4$

Step-by-step explanation:

First image attached

The error was done in Step E, because student did not multiply $2\cdot x -8$ by the negative sign in numerator. The real numerator in Step E should be:

$3-(2\cdot x -8)= 3-2\cdot x+8 = 11-2\cdot x$

Hence, Step E must be $\frac{2\cdot x -5}{(x+4)\cdot (x-4)}$ .

Second image attached

The error was done in Step C, because the student omitted the $2\cdot a \cdot b$ of the algebraic identity $(a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}$ . Step C must be $5\cdot x = x^{2}+4\cdot x + 4$

And further steps are described below:

Step D

$x^{2}-x+4 = 0$

Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: ( $a = 1$ , $b = -1$ , $c = 4$ )

$D = b^{2}-4\cdot a\cdot c$

$D = (-1)-4\cdot (1)\cdot (4)$

$D = -17$ (Conjugated complex roots)

Step E

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Step F

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m = -2/3 ⇒ y = (-2/3)x +n

A(-4, 6) ∈ d ⇒ 6 = (-2/3)·(-4) +n ⇒ 6 = 8/3 +n ⇒

⇒ n = 6 - 8/3 ⇒ n = 10/3

Now, we have:

y = (-2/3)x +10/3

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