A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 with a standard deviation of 12. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than 160. use the P-value method of testing hypotheses.

Answers

Answer 1

Answer:

[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

And the p value would be:

[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]  

Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160

Step-by-step explanation:

Information provided

[tex]\bar X=183[/tex] represent the sample mean

[tex]s=12[/tex] represent the sample standard deviation

[tex]n=25[/tex] sample size  

[tex]\mu_o =160[/tex] represent the value to test

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 160, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 160[/tex]  

Alternative hypothesis:[tex]\mu > 160[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

And the p value would be:

[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]  

Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160


Related Questions

Which is required for sexual reproduction?

Answers

Answer:

2 parents are required

Step-by-step explanation:

Answer:

semen.............

Find the missing side. Round to
the nearest tenth.
x
9
28°
x = [?]

Answers

Answer:

19.2

Step-by-step explanation:

It's right on Acellus.

The required value of x nearest to tenth is 19.17

What is hypotenuse?

The longest side of the right angled triangle is called hypotenuse

By the Pythagoras theorem in the right angled triangle

h^2 = b^2 + p^2

where h = hypotenuse, b = base, p = perpendicular

How to calculate hypotenuse?

Here we have given perpendicular p = 9

and an angle = 28°

Using sin for the given angle we have

sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]

0.46947 = [tex]\frac{9}{x}[/tex]

x = [tex]\frac{9}{0.46947}[/tex]

x =  19.17

Hence the required length of the side hypotenuse = x = 19.17

This is the conclusion to the answer.

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Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)

Answers

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

[tex]\frac{dV}{dt}=15ft^3/min[/tex]

We have to find the increasing rate of change of height of pile  when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r=[tex]\frac{d}{2}=\frac{h}{2}[/tex]

Volume of pile=[tex]\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3[/tex]

[tex]\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}[/tex]

h=12 ft

Substitute the values

[tex]15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}[/tex]

[tex]\frac{dh}{dt}=0.13ft/min[/tex]

The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard deviation 7.6 mm.(a)What is the probability that defect length is at most 20 mm

Answers

Answer:

14.69% probability that defect length is at most 20 mm

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 28, \sigma = 7.6[/tex]

What is the probability that defect length is at most 20 mm

This is the pvalue of Z when X = 20. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 28}{7.6}[/tex]

[tex]Z = -1.05[/tex]

[tex]Z = -1.05[/tex] has a pvalue of 0.1469

14.69% probability that defect length is at most 20 mm

A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).

Answers

Answer:

x=2

Step-by-step explanation:

Original width = 6

New width 6+x+x

Orignal length 12

New length  12+x+x

A = l*w

160 = ( 6+2x) ( 12+2x)

Factor

160 = 2( 3+x) 2(6+x)

Divide each side by 4

40 = (3+x) (6+x)

FOIL

40 = 18+ 6x+3x+ x^2

40 = 18 +9x+x^2

Subtract 40 from each side

0 = x^2 +9x -22

Factor

0 = (x +11) (x-2)

Using the zero product property

x +11 =0   x-2 =0

x= -11   x=2

Since we cannot have a negative  sidewalk

x =2

Answer:

2

Step-by-step explanation:

Original width = 6

New width = 6 + x + x = 6 + 2x

Orignal length = 12

New length = 12 + x + x = 12 + 2x

A = l * w

160 = (6 + 2x)(12 + 2x)

160 = 2(3+x) * 2(6+x)

160 = 4 * (3 + x)(6 + x)

160/4 = (3 + x)(6 + x)

40 = 18 + 6x + 3x + x^2

40 = 18 + 9x + x^2

x^2 + 9x - 22 = 0

= x^2 + 11x - 2x - 22 = 0

= x(x + 11) - 2(x + 11) = 0    

= (x + 11) (x - 2) = 0

x = - 11, 2

Since we cannot have a negative width because it's a dimension,

x = 2 is right

Twice the length of the rectangle exceeds three times the width of the rectangle by one centimeter and if one-third of the difference of the length and the width is one centimeter.find the dimension.​

Answers

The length of rectangle is twice the width

The dimensions of the rectangle are given as 4cm and 1cm respectively.

What is a rectangle?

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

Suppose the length of rectangle be x.

And, the width be y.

Then, the following equations can be written as per the information given as,

2x - 3y = 1               (1)

And, 1/3(x - y) = 1

⇒ x - y = 3              (2)

Multiply equation (2) by 2 and subtract from (1) to get,

2x - 3y - 2(x - y) = 1 - 2 × 3

⇒ -5y = -5

⇒ y = 1

Substitute y = 1 in equation (2) to get,

x - 1 = 3

⇒ x = 4

Hence, the dimensions are 4cm and 1cm respectively.

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1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998

(a) Find the common difference d

(b) Find the value of n.​


pls help...

Answers

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

--------------

(b)

Given

[tex]a_{n}[/tex] = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

------------------

Please answer this correctly

Answers

Answer:

20 total

Shelves 3 shelves /20 total=0.15=15%

Signs 2/20=0.10=10%

Benches 6/20=0.30=30%

Tablet Holders 9/20=0.45=45%

Step-by-step explanation:

Answer:

Shelves: 15%

Signs: 10%

Benches: 30%

Tablet Holders: 45%

Step-by-step explanation:

Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%

Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%

Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%

Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%

Find the value of z Subscript alpha divided by 2 that corresponds to a confidence level of​ 89.48%.

Answers

Answer:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

Step-by-step explanation:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the​ mean, or between 96.36degreesF and 100.02degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degrees​F?

Answers

Answer:

a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.

Step-by-step explanation:

For this case we know that the distribution of the temperatures have the following parameters:

[tex] \mu = 98.19, \sigma =0.61[/tex]

Part a

From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

Part b

We can calculate the number of deviations from the mean with the z score with this formula:

[tex]z=\frac{X -\mu}{\sigma}[/tex]

And using this formula we got:

[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.

What is the value of log625^5 converted to a fraction

Answers

Answer:

1/4

Step-by-step explanation:

625^x = 5

x = 1/4

i need help in homework no guess

Answers

Answer:

No

Step-by-step explanation:

Use the vertical line test. If the line intercepts more than one point, it is not a function. Since there are two points where the value of 'x' is two, the line will pass both points. The graph is not a function.

ANSWER:
Use the vertical line test .If the line intersepts more than one point ,it is not a function .Since there are two points where the value of 'x' is two the line will pass both points.Therefore the graph is not a function.
HOPE IT HELPS!!!!!

The function​ s(t) represents the position of an object at time t moving along a line. Suppose s (1 )equals 62 and s (5 )equals 102. Find the average velocity of the object over the interval of time [1 comma 5 ].

Answers

Answer:

v = 10

the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time

Step-by-step explanation:

Given;

function​ s(t) represents the position of an object at time t moving along a line.

s(1) = 62 at t1 = 1

s(5) = 102 at t5 = 5

Velocity v = distance/time

Average velocity v over time t is;

v = ∆s/∆t

v = [s(5) - s(1)]/[t5 - t1]

Substituting the given values;

v = (102 - 62)/(5 - 1)

v = 10

the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time

Please answer this correctly

Answers

Answer:

3.14

Step-by-step explanation:

We find the total circumference of a circle with radius 2 to be

2 * pi * r

= 2 * 3.14 * 2

= 12.56

We divide by 4 to get the perimeter of the quarter circle

12.56/4 = 3.14

Which steps can be used to solve for the value of y?
(2013
(y +57) = 178​

Answers

Answer: [tex]y = 121[/tex]

[tex](y+57) = 178[/tex]

[tex]y+57= 178[/tex]

[tex]y = 178 -57[/tex]

[tex]y = 121[/tex]

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Answers

Answer:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Step-by-step explanation:

Information given

[tex]\bar X=25.5[/tex] represent the sample mean

[tex]s=1[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =26[/tex] represent the value to verify

[tex]\alpha=0.06[/tex] represent the significance level  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to est

We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25.5[/tex]  

Alternative hypothesis:[tex]\mu < 25.5[/tex]  

The statistic for this case is given by;

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Please help me with this problem

Answers

Answer:

10

-5

Step-by-step explanation:

5 - -5

Subtracting a negative is like adding

5+5 = 10

-9 - -4

-9+4

-5

Answer:

Step-by-step explanation:

5+5 = 10

-9+4 = -5

Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?

Answers

Answer:one would get 12 one would get 20

Step-by-step explanation:just plug it in to the equation

Answer

Someone would get 12 and the other would get 20 beads

Solve: x - 1 < 3 help me plssss

Answers

Answer:

x =2

Step-by-step explanation:

becaue 2-1 is smaller than 3

Answer:

Hello!

I believe your answer is:

x=2

If this is not correct, please let me know and I will try again!

Step-by-step explanation:

A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $200. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $905, the value reported for all college students with credit cards

Answers

Answer:

Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Step-by-step explanation:

We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=905\\\\H_a:\mu< 905[/tex]

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=825.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=500-1=499[/tex]

This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-8.94)=0[/tex]

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Pamela is a college student. She pays tuition every semester and rent every month, and she uses cash daily for food. The expression 2x+12y+365z represents her yearly expenses. Which variable represents her rent?

Answers

Answer:

Variable y represent the rent of Pamela

Step-by-step explanation:

Given

Pamela pays tuition every semester and rent every month, and she uses cash daily for food.

lets understand what constitute semester ,  month and day in a year.

A semester consist of 6 months.

As a year has 12 months , a year will have 2 semester.

If one pays  x for one semester then in a year one has to pay 2x .

As a year has two semester

Similarly

A year has 12 months .

If one pays  y for one month then in a year one has to pay 12y .

As a A year has 12 months .

A year has 365 days

If one pays  z for each month then in a year one has to pay 365z .

As a A year has 365 days.

__________________________________________

Based on above discussion , we can now safely assume that the we have to look at the coefficient of  expression 2x+12y+365z to find the which variable represent which type of bill.

As we have to find variable for rent and rent is paid monthly.

so for a year total bill will have 12 months and hence going by expression variable y represent the rent of Pamela.

What sit he shape of the cross section formed when’s. Cone intersects a plane as shown in the drawing?
Give me a reason why tok

Answers

Answer: Option D.

Step-by-step explanation:

Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.

As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)

So the correct option is D.

PLEASE HELP

Compare the number of x intercepts of f(x)=x^2 and g(x)= (x-4)^2. Tell me the transformations involved and how g(x) moves from the parent graph.

Answers

Answer

g(x) moves 4 spaces to the left compared to f(x),  

when g(4)=0  when f(0)=0

when g(3)=1   when f(-1)=1

...

and so on

what is the least common denominator of 4 7/9 and 2 2/3

Answers

Answer:

9

Equivalent Fractions with the LCD

4 7/9 = 43/9

2 2/3 = 24/9

For the denominators (9, 3) the least common multiple (LCM) is 9.

Therefore, the least common denominator (LCD) is 9.

4 7/9 = 43/9 × 1/1 = 43/9

2 2/3 = 8/3 × 3/3 = 24/9

Hope this helps :)

The least common denominator of 4 7/9 and 2 2/3 is 9.

Given data:

To find the least common denominator (LCD) of 4 7/9 and 2 2/3, we need to first convert both fractions to their equivalent forms with a common denominator.

The given fractions are:

4 7/9 = 4 + 7/9

2 2/3 = 2 + 2/3

To find a common denominator, we need to find the least common multiple (LCM) of the denominators 9 and 3, which is 9.

Now, let's convert the fractions to their equivalent forms with a denominator of 9:

4 7/9 = (4 * 9)/9 + (7/9) = 36/9 + 7/9 = 43/9

2 2/3 = (2 * 9)/9 + (2/3) = 18/9 + 2/3 = 20/9

The fractions 4 7/9 and 2 2/3 are now expressed with a common denominator of 9.

Hence, the least common denominator (LCD) of 4 7/9 and 2 2/3 is 9.

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A marketing analyst randomly surveyed 150 adults from a certain city and asked which type of tooth paste they were currently using - Extra Whitening or Regular. 96 said they were currently using Extra Whitening while the rest said they were using Regular. The analyst wants to determine if this is evidence that more than half of the adults in this city are using Extra Whitening. Suppose a​ p-value from the correct hypothesis test was 0.0003. Which of the following is a correct interpretation of this​ p-value?
A. HA: p_extra White > p_Regular.
B. HA: p > 0.5, where p = the proportion of all adults in this city using Extra Whitening.
C. HA: p = 0.64, where p = the proportion of all adults in this city using Extra Whitening.
D. HA: p=0.5, where p = the proportion of all adults in this city using Extra Whitening.

Answers

the answer to this question is A.

А
What is the measure of ZDAB?
&
B
Enter your answer in the box.
D
96°
C
Next​

Answers

Answer:

  84°

Step-by-step explanation:

Adjacent angles in a parallelogram are supplementary:

  ∠A = 180° -96°

  ∠A = 84°

Order the numbers from least to greatest based on their absolute values.

|23|, |−37|, |−6|, |18|, |−24|, |2|

Answers

Answer:

/-37/, /-24/, /-6/, /2/, /18/, /23/

what is 2n+3n +1 +8n+4

Answers

How do you need this answered?
If you need it simplified it would be 13n+5

Please tell me or you need it solved

Answer:

13n + 5

Step-by-step explanation:

2+3+8 = 13n

1+4 = 5

13n+5

Please help me please I’m stuck please

Answers

[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer:

9

Step-by-step explanation:

The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.

[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex]   Starting equation

[tex]\frac{5}{8} =\frac{15}{15+x}[/tex]   Simplify

[tex]5(15+x)=8*(15)[/tex]   Cross multiply

[tex]75+5x=120[/tex]   Distributive Property on left and simplify on right

[tex]5x=45[/tex]   Isolate the variable

[tex]x=9[/tex]   Divide both sides by 5 (Division Property of Equality)

−2.73(m+4)=−6m−4.38.

Answers

Answer:

m=2

Step-by-step explanation:

-2.73m-10.92=-6m-4.38

3.27m=6.54

m=2

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