1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Papessa [141]
2 years ago
5

How to solve 6x - 9 - 2 (1 - x) = x + 9​

Mathematics
1 answer:
Likurg_2 [28]2 years ago
7 0

x = 2.857

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}

6x - 9 - 2(1 - x) = x + 9 \\ ⇢ 6x - 9 - 2 + 2x = x + 9 \\ ⇢ 8x - x = 9 + 11 \\ ⇢ 7x = 20 \\ ⇢  x =  \frac{20}{7}  \\ ⇢ x = 2.857

{ \bf{ \underbrace{To\:verify:}}}

6 \times 2.857 - 9 - 2(1 - 2.857) = 2.857 + 9 \\ ➪ \: 17.142 - 9 - 2 \times(  - 1.857) = 11.857 \\➪ \: 8.142 + 3.714 = 11.857 \\➪ \: 11.856 = 11.857 \\  ➪ \: 11.86 = 11.86 \\ ➪ L.H.S.=R. H. S

Hence verified.

\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}

You might be interested in
Ten percent of the engines manufactured on an assembly line are defective.
antoniya [11.8K]

Answer:

a) the probability that the first non-defective engine will be found on the second trial is 0.09

b) probability that the third non-defective engine will be found on the fifth trial is 0.00486

c) the Mean is 1.1111  and Variance is 0.1235  

d) the Mean is 3.3333and Variance is 0.3704  

Step-by-step explanation:

Firstly;

Let x be the number of trail on which the rth defective occurs

Also let the probability that an occurrence of a defective be p = 0.10

Here, x follows negative binomial distribution with parameters r and p

The probability mass function of X is as follows:

P(X = x) = [ x -1  p^r ( 1 - p)^(x-r)       ; x = r, r + 1, r + 2, ...

                 r - 1 ]

=   [ x -1  (0.10)^r ( 1 - 0.10)^(x-r)

     r - 1 ]

= [ x -1  (0.10)^r ( 0.9)^(x-r)  ..........n 1..... let this be equatio

    r - 1 ]

This represents the probability that the rth success occurs on the xth trail.  

a)

probability that the first non-defective engine will be found on the second trial?

Substitute r = 1 and x = 2 in equation 1  

P(X = 2)  = [ 2 - 1   (0.10)¹ ( 0.90 )²⁻¹

                   1 - 1 ]

= (0.10) × (0.90)

= 0.09

Therefore, the probability that the first non-defective engine will be found on the second trial is 0.09

b)

probability that the third non-defective engine will be found on the fifth trial?

So we substitute r = 3 and x = 5 in equation 1  

P(X = 5) = [ 5 - 1  (0.10)³ ( 0.90)⁵⁻³

                  3 - 1 ]

=    [ 4    (0.10)³ ( 0.9)²

      2 ]

= 0.00486

Therefore, probability that the third non-defective engine will be found on the fifth trial is 0.00486

Now the formula for the mean of the negative binomial distribution is as follows:  

Mean u = r / p    ------- let this be equation 2

The formula for the variance of the negative binomial distribution also is as follows:  

Variance α² = rq / p²   ---------- let this be equation 3

so

c)

the mean and variance of the number of trials on which the first non-defective engine is found.  

First, let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10  

Now we substitute r = 1, p = 0.90 and q = 0.10 in equation 2 & 3simultaneously,

the mean and variances are as follows;

Mean = r/p = 1/0.90 = 1.1111

Variance = rq/p² = (1)(0.10) / (0.90)² = 0.1235  

Therefore the Mean is 1.1111  and Variance is 0.1235  

d)

the mean and variance of the number of trials on which the third non-defective engine is found  

Let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10

Now we substitute r = 3, p = 0.90 and q = 0.10 in equation (2) and (3) simultaneously,

the mean and variances are;

Mean = r/p = 3/0.90 = 3.3333

Variance = rq/p² = (3)(0.10) / (0.90)² = 0.3704

Therefore the Mean is 3.3333 and Variance is 0.3704    

5 0
3 years ago
How many 1/2s are in 2
Delvig [45]

Answer:

4

Step-by-step explanation:

Easy

1/2+1/2=1 or 2/2

2/2+1/2= 3/2

3/2+1/2= 2

1/2*4=2

1/2+1/2+1/2+1/2=2

there are 4 halves in 2

Hope this helps

4 0
2 years ago
Does anyone know how to solve this?
Margarita [4]

Answer:

The correct option is c.

Step-by-step explanation:

Given that,

u = 7i+4j and v = 2i-3j

We need to find the product of u and v. The dot product of two vectors is given by :

u{\cdot}v=(7i+4j){\cdot} (2i-3j)\\\\=(7i)(2i)+(4j)(-3j)\\\\=14-12\\\\=2

So, the dot product of u and v is equal to 2.

4 0
3 years ago
1
irina [24]

Answer:

0.530 (the 0 is not required)

Step-by-step explanation:

this is because another combination would be .35 which is less than .53 so this what i think the answer is.

--hope this helped :))

7 0
3 years ago
Help plz Find y when x = 15 if y = 6 when x = 30
lutik1710 [3]

Answer:Y=3

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Can someone please help me with this plss and thanks
    15·1 answer
  • Ethan makes $6 per hour mowing lawns and $7.50 per hour bagging groceries. last week, he made a total of $129. The difference be
    10·1 answer
  • What ordered pair is a solution of the equation?<br> y=-2x-5
    10·1 answer
  • Can you have an isolceles triangle withsides of 3cm, 8cm, and 8cm?
    13·1 answer
  • What is the greatest common factor of 35y^4, 14y^4, and 63y^4 ?
    5·1 answer
  • The probability that a person chosen at random is at least 15 years old is
    10·1 answer
  • Plot a point at the y-intercept pf the following function on the graph provided. 3y= -5^x+7
    15·1 answer
  • What is 12+45(3-8) because I’m confused plz help
    7·2 answers
  • Share 7.20 naira between Tayo and Visit,so that Tayo gets 70 Kobo more than Bisi. how much does Tayo get?​
    15·1 answer
  • -(3g + 5h -2j - 5 + 4g - 5<br><br> What is this simplified <br><br> (Giving out brainiest )
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!