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3 years ago

Solve for x.... -4+13x=12x+4

Mathematics

2 answers:

svetlana [45]3 years ago

6 0

-4 + 13x = 12x + 4
+4 +4

13x = 12x + 8
-12x -12x

1x=8 or x=8

Sav [38]3 years ago

5 0

You put all x on left side and numercial on the right side

13x-12x = 4+4

x = 8

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The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

$P(39 < X < 48 ) = 0.8767$

95% of all sample means will fall between $40.1 < \mu < 49.9$

$\= x = 41. 795$

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

5 0

2 years ago

If Acot theta + Bcot theta =4 and

geniusboy [140]

Answer is: B

Step-by-step explanation: correct answer is B

−a

Given, acotθ+bcscθ=p

bcotθ+acscθ=q

⇒p

−q

=(p−q)(p+q)

=[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

=[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

=(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

=(a

−b

)(cot

θ−csc

θ)

=(−1)(a

−b

)[∵csc

θ−cot

θ=1]

=(b

−a

)

7 0

2 years ago

¿Qué entiendes por propiedad distributiva?

yan [13]

La propiedad distributiva es una propiedad de las matemáticas de “distribuir” un múltiplo a una expresión.
La propiedad distributiva es lo opuesto a factorizar.
Para que quede más claro, aquí dejo algunos ejemplos:

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3 years ago

If 9% of the bar’s weight is iron, how much does the iron weigh

Leya [2.2K]

Answer:

15 pounds

Step-by-step explanation:

7 0

3 years ago

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Solve.

OleMash [197]

Answer:

x< -1.8

Step-by-step explanation:

-12x+13>35

We leave the variable alone passing the 13 with opposite sign to the other side and subtracting it from 35.

-12x>22

We divide both by the variable, -12x, and it gives x > -1.8. Since the sign of x changed, we flip the sign and the final result is x < -1.8

4 0

3 years ago

Read 2 more answers