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3 years ago

Solve the system of equations using the substitution method.

Mathematics

1 answer:

Delicious77 [7]3 years ago

8 0

Answer:

$x = 14$

$y = -3$

Step-by-step explanation:

Given

$2x + 8y =4$

$x = -3y + 5$

Required

Solve

Substitute $x = -3y + 5$ in $2x + 8y =4$

$2(-3y + 5) + 8y =4$

Open bracket

$-6y + 10 + 8y =4$

Collect like terms

$-6y + 8y =4-10$

$2y =-6$

Divide both sides by 2

$y = -3$

Substitute $y = -3$ in $x = -3y + 5$

$x = -3 * -3 + 5$

$x = 9+ 5$

$x = 14$

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3 years ago

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

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

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

=> $n = 5^2$

=> $n = 25$

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2 years ago

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The answer would be B

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3 years ago

Read 2 more answers

2 questions here:

solmaris [256]

<span>1. Make y the subject
a) 4y=12x+18
y = 3x + 4.5

b) 2x=7-3y
3y = -2x + 7
y = -2/3x + 7/3

2.
a) what is the equation of the line which passes through both (-2,-4) and (6,16)

slope = (16 + 4)/(6 +2) = 20/8 = 2.5
y = mx + b
-4 =2.5(-2) +b
-4 = -5 +b
b = 1

equation
y = 2.5x + 1

b) what is the equation of the line perpendicular to y= 1/2X + 7 passing through point (3,9)

</span>y= 1/2X + 7
slope = 1/2

slope of line perpendicular = -2

passing through point (3,9)

y = mx + b
9 = -2 (3) + b
b = 15

equation

y = -2x + 15

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3 years ago

Read 2 more answers