−2x+5y=10 −3x+9y=6 −3x+9y=6 −2x+5y=10

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Illusion [34]

Answer:

x = 4

Step-by-step explanation:

Step 1: Subtract 4 from both sides.

5x+4−4=24−4

5x=20

Step 2: Divide both sides by 5.

5x

5

=

20

5

x=4

you welcome love

6 0

3 years ago

Read 2 more answers

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:

1a

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

1b

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

1c

$\= x = 41. 795$

2

$n = 25$

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

$P( Z< - 2.4 ) = 0.0081975$

So

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

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

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

3 years ago

What is the surface are of the cylinder pictured below

Elina [12.6K]

Surface area of the cylinder is 294π in².

Step-by-step explanation:

Step 1: Surface area of a cylinder = 2πrh + 2πr² Here, r = 7 in, h = 14 in

⇒ Surface Area = 2 × π × 7 × 14 + 2 × π × 7 × 7

= π (196 + 98) = 294π in²

4 0

3 years ago

What is completely factored form of d^4-81

romanna [79]

Answer:

(d − 3) (d + 3) (d² + 9)

Step-by-step explanation:

d⁴ − 81

Factor using difference of squares.

(d² − 9) (d² + 9)

Factor using difference of squares again.

(d − 3) (d + 3) (d² + 9)

5 0

3 years ago

Solve for x. X +5 4x + 15 x = [?]

Darina [25.2K]

Answer:

The answer is 70x

Step-by-step explanation:

simplify step-by-step.

x+54x+15x

Combine Like Terms:

=x+54x+15x

=(x+54x+15x)

=70x

Answer:

=70x

8 0

2 years ago

−2x+5y=10 −3x+9y=6 ​ −3x+9y=6 −2x+5y=10 ​

−2x+5y=10 −3x+9y=6 −3x+9y=6 −2x+5y=10