Select the factors of 10ax 5bx − 8ay − 4by.

Mathematics

2 answers:

Yakvenalex [24]3 years ago

4 0

10ax + 5bx - 8ay - 4by = 5x(2a + b) - 4y(2a + b) = (5x - 4y)(2a + b)
option d is the correct answer.

PolarNik [594]3 years ago

3 0

Answer:

Factors are (2a+b) and (5x-4y)

Option D is correct.

Step-by-step explanation:

Given: $10ax+5bx-8ay-4by$

Here we are four term to factor it.

First we make two group and factor each group.

$(10ax+5bx) + (-8ay-4by)$

$\text{Group 1: }10ax+5bx$

Taking 5x common from both term

$10ax+5bx\Rightarrow 5x(2a+b)$

$\text{Group 2: }-8ay-4by$

Taking -4y common from both term

$-8ay-4by\Rightarrow -4y(2a+b)$

Factor is:

$\Rightarrow 5x(2a+b)-4y(2a+b)$

$\Rightarrow (2a+b)(5x-4y)$

Hence, Factors are (2a+b) and (5x-4y)

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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

zavuch27 [327]

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