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alina1380 [7]
2 years ago
5

Will factor the express 36xyz + 24xy − 16x by dividing each term by a common fact

Mathematics
2 answers:
sesenic [268]2 years ago
6 0

\\ \bull\tt\longmapsto 36xyz+24xy-16x

  • Divide by 4

\\ \bull\tt\longmapsto \dfrac{36xyz}{4}+\dfrac{24xy}{4}-\dfrac{16x}{4}

\\ \bull\tt\longmapsto 9xyz+6xy-4x

  • Divide by x

\\ \bull\tt\longmapsto \dfrac{9xyz}{x}+\dfrac{6xy}{x}-\dfrac{4x}{x}

\\ \bull\tt\longmapsto 9yz+6y-4

MrMuchimi2 years ago
4 0

Answer:

4x(9yz + 6y - 4)

Step-by-step explanation:

36xyz + 24xy - 16x ← factor out 4x from each term

= 4x(9yz + 6y - 4)

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A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective
andriy [413]

Answer:

(a) P(X \leq 20) = 0.9319

(b) Expected number of defective light bulbs = 15

(c) Standard deviation of defective light bulbs = 3.67

Step-by-step explanation:

We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.

Firstly, the above situation can be represented through binomial distribution, i.e.;

P(X=r) = \binom{n}{r} p^{r} (1-p)^{2} ;x=0,1,2,3,....

where, n = number of samples taken = 150

            r = number of success

           p = probability of success which in our question is % of bulbs that

                  are defective, i.e. 10%

<em>Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.</em>

So, Let X = No. of defective bulbs in a box

<u>Mean of X</u>, \mu = n \times p = 150 \times 0.10 = 15

<u>Standard deviation of X</u>, \sigma = \sqrt{np(1-p)} = \sqrt{150 \times 0.10 \times (1-0.10)} = 3.7

So, X ~ N(\mu = 15, \sigma^{2} = 3.7^{2})

Now, the z score probability distribution is given by;

                Z = \frac{X-\mu}{\sigma} ~ N(0,1)

(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X \leq 20) = P(X < 20.5)  ---- using continuity correction

    P(X < 20.5) = P( \frac{X-\mu}{\sigma} < \frac{20.5-15}{3.7} ) = P(Z < 1.49) = 0.9319

(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = n \times p = 150 \times 0.10 = 15.

Standard deviation of defective light bulbs is given by = S.D. = \sqrt{np(1-p)} = \sqrt{150 \times 0.10 \times (1-0.10)} = 3.67

8 0
3 years ago
What is y greater then or equal to 2x on a graph
Juliette [100K]

Answer:

The minimal number for the objective function P =20x+16y is: 780

The value of x then is: 15

and the value of y then is : 30

Step-by-step explanation:

We are given a system of inequalities as:

y is less than or equal to 2x

i.e.          y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e.      x+y ≥ 45  ------------(2)    

and    x is less than or equal to 30.    

i.e.               x ≤ 30 -----------(3)    

On plotting these inequalities we get the boundary points as:

        (15,30) , (30,60) and (30,15)    

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

 Minimize  P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

 P= 1560

at (30,15) we get:

P= 840

This  means that the minimal value of the function is 780

and the value exist at (15,30)

5 0
3 years ago
What is the place value of the number 8 in the number 814,295
VLD [36.1K]
The place value is a hundred thousand, as there are 5 digits following the eight.
3 0
3 years ago
I got disconnected from my tutor, can't reconnect. need an explanation ​
kherson [118]

The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.

|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x

For the equation

-3 + 4 |2<em>x</em> - 5| = 14

rearrange terms to get

|2<em>x</em> - 5| = 17/4

Now,

• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then

2<em>x</em> - 5 = 17/4

• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that

-(2<em>x</em> - 5) = 17/4, or

2<em>x</em> - 5 = -17/4

In the first case,

2<em>x</em> - 5 = 17/4

2<em>x</em> = 17/4 + 5 = 37/4

<em>x</em> = 37/8

In the second case,

2<em>x</em> - 5 = -17/4

2<em>x</em> = -17/4 + 5 = 3/4

<em>x</em> = 3/8

5 0
2 years ago
What two numbers add up to equal 6, but multiply to equal 13?
KatRina [158]
4 and 2 equal up to be 6
4 0
2 years ago
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