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Taya2010 [7]
3 years ago
15

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

t to x from the first equation is substituted into the second equation.
x + 4y = −9
2x + 5y = −6

A. 2x + 5(4y − 9) = −6
B. 2x + 5(−4y − 9) = −6
C. 2(4y − 9) + 5y = −6
D. 2(−4y − 9) + 5y = −6
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
5 0
The answer would be D.
The only you thing you have to do is alter the first equation to isolate the x. You do that by moving the 4y to the other side, giving you:
x=(-4y-9)
Then you simply insert your new value for x into the second equation.
Hope this helps. :)
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A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a
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SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}

Hence the answer is 0.1157

(ii) None is defective becomes

\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}

hence the answer is 0.4823

(iii) All are defective

\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}

(iv) At least one is defective

This is 1 - probability that none is defective

\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}

Hence the answer is 0.5177

3 0
10 months ago
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solniwko [45]

Step-by-step explanation:

Here we are given that , the Value of

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And we need to find the prove that ,

  • xy = 4

We know a identity as ,

  • (a-b)^3 = a^3-b^3-3ab(a-b)

On cubing both sides of the given equation,

  • (3x-2y)^3 = 9^3

Simplify and then substitute ,

  • 27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729

  • 1377 - 18xy (9) = 729

  • 162xy = 1377-729

  • xy =\dfrac{648}{162}

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Hence Proved !

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Answer:

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7/8- 1/2 which is equivilient to 4/8 is 3/8

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