Explain how you know which terms to combine when combining like terms.

The mean cost of a meal for two in a mid-range restaurant in Tokyo is $40 (Numbeo.com website, December 14, 2014). How do prices

NNADVOKAT [17]

Answer:

a) $Me=2.02 \frac{6.827}{\sqrt{42}}=2.13$

b) So on this case the 95% confidence interval would be given by (30.53;34.79)

c) On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices for mid range restaurants in Tokyo at 5 % of significance.

Step-by-step explanation:

1) 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Part a

The margin of error is given by:

$Me=t_{\alpha/2}\frac{s}{\sqrt{n}}$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that $t_{\alpha/2}=2.02$

$Me=2.02 \frac{6.827}{\sqrt{42}}=2.13$

3) Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=32.66$

The sample deviation calculated $s=6.827$

Now we have everything in order to replace into formula (1):

$32.66-2.02\frac{6.827}{\sqrt{42}}=30.532$

$32.66+2.02\frac{6.827}{\sqrt{42}}=34.788$

So on this case the 95% confidence interval would be given by (30.532;34.788)

4) Part d

On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices in mid range restaurants in Tokyo at 5 % of significance.

8 0

4 years ago

Which equation describes a line perpendicular to y=8x-9 that passes through the point (9,-9)?

Margaret [11]

The answer is G. Perpendicular lines have opposite reciprocal slopes

6 0

3 years ago

Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her

Art [367]

For this case we have the following equation:

$y + 1 = 2 (x - 3)$

That can be rewritten in the form $y = mx + b$

Where:

m is the slope of the line

b is the cut point

So, we have:

$y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7$

Where:

$m = 2$ is the slope

$b = -7$ is the cut point

Carlota has the following points:

(-1, 3) and (2, 9)

To know if the line $y = 2x-7$ passes through these points, we must replace them in the equation and the equality must be fulfilled. So:

Point (-1, 3):

Substituting:

$3 = 2 (-1) -7\\3 = -2-7$

$3 = -9$ It's false, equality is not met. The point (-1, 3) does not go through the line.

The equation written by Carlota is erroneous, the procedure to follow is:

Given $(x1, y1) = (- 1, 3)$ and $(x2, y2) = (2, 9)$ , we find the slope:

$m=\frac{(y2-y1)}{(x2-x1)}$

$m=\frac{(9-3)}{(2-(-1))}$

$m=\frac{6}{3}$

$m=2$

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:

$y = 2x + b$

Substituting (2,9) we have:

$9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5$

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is $y = 2x + 5$

Answer:

The correct equation of the line that passes through the given points is $y = 2x + 5$

Carlota's mistake was at the cutoff point

5 0

3 years ago

The diagram shows a scale drawing of a playground. In the scale drawing the playground has a length of 16 cm and a width of 8 cm

kicyunya [14]

Answer:

3 m : 4 cm, 3 m/4 cm, 3 m to 4 cm

Step-by-step explanation:

The actual playground will have an area of 72 m², and have one side be double the other, because the scale drawing does so too.

We can make a system of equations: l * w = 72, l = 2w

Substitute: 2w * w = 72

Simplify: 2 * w² = 72

Divide: w² = 36

Square root: w = 6 m (no negatives due to distances always > 0)

Substitute: l = 2 * 6 m

Simplify: l = 12 m

This means that the relations of one side is 6 m : 8 cm. That can be simplified to 3 m : 4 cm.

8 0

4 years ago

Y = 3x + 8 8x + 4y = 12

kolbaska11 [484]

Answer: good luck

Step-by-step explanation:Step 1) Because the first equation is already solved for

y

we can substitute

3

x

+

8

for

y

in the second equation and solve for

x

:

8

x

+

4

y

=

12

becomes:

8

x

+

4

(

3

x

+

8

)

=

12

8

x

+

(

4

⋅

3

x

)

+

(

4

⋅

8

)

=

12

8

x

+

12

x

+

32

=

12

(

8

+

12

)

x

+

32

=

12

20

x

+

32

=

12

20

x

+

32

−

32

=

12

−

32

20

x

+

0

=

−

20

x

=

−

20

x

20

=

−

20

x

20

=

−

1

x

=

−

1

Step 2) Substitute

−

1

for

x

in the first equation and calculate

y

:

y

=

3

x

+

8

becomes:

y

=

(

3

⋅

−

1

)

+

8

y

=

−

3

+

8

y

=

5

The solution is:

x

=

−

1

and

y

=

5

or

(

−

1

,

5

)

7 0

3 years ago