Write a conjecture using the information provided.

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

6 0

An integer has to be either even or odd

Even numbers are numbers divisible by 2, while odd numbers are not

Let us represent the 2 even numbers like this

ax+1

bx+1

When you add the two numbers together, you get

2a + 1 + 2b + 1

This can be simplified using the inverse of distributive property

2(a+b) + 2

2(a+b+1)

This is the sum, which is divisible by 2

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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

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

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

1 year ago

Match each description when z = 9 + 3i. 1. Real part of z 2. Imaginary part of z 3. Complex conjugate of z 4. 3i - z 5. z - 9 6.

sergey [27]

$1)\quad \Re(9+3i)=9\qquad\text{F}\\\\
2)\quad \Im(9+3i)=3\qquad\text{E}\\\\
3)\quad \overline{(9+3i)}=9-3i\qquad\text{D}\\\\
4)\quad 3i-(9+3i)=3i-9-3i=-9\qquad\text{A}\\\\
5)\quad 9+3i-9=3i\qquad\text{B}\\\\
6)\quad 9-(9+3i)=9-9-3i=-3i\qquad\text{C}\\\\$