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3 years ago

Use the substitution method to solve these simultaneous equations.

Mathematics

1 answer:

Amanda [17]3 years ago

4 0

Answer:

Step-by-step explanation:

a) 3x+2(41-5x)=33 as y=41-5x is given

3x+82-10x=33

-7x+82=33

-7x=33-82

-7x=-49 cut the negative signs as its LHS and RHS

x=49/7=7

b)-5x+3(3x-3)=3 as y=3x-3 is given

-5x+9x-9=3

4x-9=3

4x=3+9

x=12/4=3

c)4x+11-5x=9

-x+11=9

-x=9-11

-x=-2 cut the negative signs as its LHS and RHS

x=2

d) 5y+ -5-2y=-11 as x=-5-2y is given

3y+-5=-11

3y=-11+5

3y=-6

y=-6/3=-2

e)-5x-4(2x+1)=35 as y=2x+1

-5x-8x+4=35

3x+4=35

3x=35-4

3x=31

x=31/3

x=10.3

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Find the diameter of a sphere with a surface area of 196π square centimeters

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2 years ago

What is the formula for a confidence interval?

ikadub [295]

Answer:

a) The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) $\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean $\bar X$ is given by:

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Part a

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Part b

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$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

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