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3 years ago

Solve the simultaneous Equation using the two methods4m=n +73m+ 4n+9=0

Mathematics

1 answer:

GrogVix [38]3 years ago

5 0

Elimination method:

4m = n + 7

3m + 4n + 9 = 0

First, let's get the equations in the same form.

4m - n - 7 = 0

3m + 4n + 9 = 0

Now let's make multiply the first equation by 4 so we can eliminate n.

16m - 4n - 28 = 0

+3m + 4n + 9 = 0

Now we can add the equations.

16m + 3m - 4n + 4n - 28 + 9 = 0

19m + 0n - 19 = 0

19m - 19 = 0

19m = 19

m = 1

Now we put m back into one (or both) of the original equations.

4(1) = n + 7

4 = n + 7

n = -3

If you plug m into the other equation, you get the same result.

Substitution method:

4m = n + 7

3m + 4n + 9 = 0

With this method, we plug one of the equations into the other one. I'm going to use m in the second equation as a substitute for m in the second equation.

3m + 4n + 9 = 0

3m = -4n - 9

m = (-4/3)n - 3

Now I can substitute the right side into the first equation like so:

4[(-4/3)n - 3] = n + 7

(-16n)/3 - 12 = n + 7

(-16n)/3 = n + 19

-16n = 3(n + 19)

-16n = 3n + 57

0 = 16n + 3n + 57

0 = 19n + 57

0 = 19n/19 + 57/19

0 = n + 3

-3 = n

And then we put that back into one of the original equations.

4m = n + 7

4m = -3 + 7

4m = 4

m = 1

Hopefully you learned something from this.

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Step-by-step explanation:

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3 years ago

What is the distance between Harry’s home and his office?

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Answer:

The distance between Harry’s home and his office? is 15 miles.

Step-by-step explanation:

The speed, distance time formula is:

$Speed(s)=\frac{Distance(d)}{Time(t)}$

Given:

Speed (s) = 30 miles/hour

Then the relation between distance and time is:

$s=\frac{d}{t} \\30=\frac{d}{t}\\d=30t...(i)$

If Speed was 60 miles/hour the time taken is $(t-\frac{1}{4})$ hours.

Then the relation between distance and time is:

$s=\frac{d}{t} \\60=\frac{d}{(t-\frac{1}{4}) }\\d=60t-15...(ii)$

Use the value of d = 30t in (ii)

$d=60t-15\\30t=60t-15\\30t=15\\t=\frac{1}{2} hour$

Determine the distance as follows:

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3 years ago

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next j

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Complete Question

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks with a sample standard deviation of the time unemployed is 6.7 weeks.

1 Which of the following statements is the correct alternative hypothesis?

2 The test statistic for testing the hypothesis is

a. -2.64

b. -2.32

c. -2.11

d. -1.28

e. none of these are correct

Answer:

The alternative hypothesis $H_a : \mu < 15.9$

The test statistics $z = -2.64$

Step-by-step explanation:

From the question we are told that

The population mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The sample size is n = 50

The sample standard deviation is 6.7 weeks.

The sample mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The null hypothesis is $H_o : \mu \ge 15.9$

The alternative hypothesis $H_a : \mu < 15.9$

Generally test statistics is mathematically represented as

$z = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }$

=> $z = \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}$

=> $z = -2.64$

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3 years ago

You work a part-time job at $7.85/hr for 10 hours per week. Your deductions are FICA (7.65%), federal tax withholding (9.8%), an

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Here, My initial salary = 7.85

FICA deduction amount = 7.85 * 7.65% = 7.85 * 0.0765 = 0.60
Federal Tax amount = 7.85 * 9.8% = 7.85 * 0.098 = 0.77
State tax amount = 7.85 * 5.5% = 7.85 * 0.055 = 0.43

So, Total deducted amount = 0.60 + 0.77 + 0.43 = 1.80
Net hourly wage = 7.85 - 1.80 = 6.05

In short, Your Answer would be $6.05

Hope this helps!

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3 years ago

Solve the simultaneous Equation using the two methods4m=n +73m+ 4n+9=0​

Solve the simultaneous Equation using the two methods4m=n +73m+ 4n+9=0