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3 years ago

How do we find an equation of a linear function by giving two points

Mathematics

1 answer:

aleksley [76]3 years ago

4 0

Answer:

the right side of the image is truncated,

but "A" seems to be the answer....

take (2,3) and (3,4)

#1) y2-y2/x2-x1 ... 4-3/3-2 = 1 ... slope = 1

#2 ) y = 1x + b

#3 plug in (2,3) ... 3 = 1(2) + b ... B=1

#4 Y= 1 x + 1

Step-by-step explanation:

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What is the value of x so that l is parallel to m (5x+18) (12x+9)

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2 years ago

Dannette and Alphonso work for a computer repair company. They must include the time it takes to complete each repair in their r

olga55 [171]

Answer:

(a):

Dannette Alphonso

$\bar x_D = 4.33$ $\bar x_A = 5.17$

$M_D = 2.5$ $M_A = 5$

$\sigma_D = 3.350$ $\sigma_A = 1.951$

$IQR_D = 7$ $IQR_A = 1.5$

(b):

Measure of center: Median

Measure of spread: Interquartile range

(c):

There are no outliers in Dannette's dataset

There are outliers in Alphonso's dataset

Step-by-step explanation:

Given

See attachment for the appropriate data presentation

Solving (a): Mean, Median, Standard deviation and IQR of each

From the attached plots, we have:

IQR_A = 1.5 ---- Dannette

$A = \{3,4,4,4,4,5,5,5,5,6,6,11\}$ ---- Alphonso

n = 12 --- number of dataset

Mean

The mean is calculated

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x_D = \frac{1+1+1+1+2+2+3+7+8+8+9+9}{12}$

$\bar x_D = \frac{52}{12}$

$\bar x_D = 4.33$ --- Dannette

$\bar x_A = \frac{3+4+4+4+4+5+5+5+5+6+6+11}{12}$

$\bar x_A = \frac{62}{12}$

$\bar x_A = 5.17$ --- Alphonso

Median

The median is calculated as:

$M = \frac{n + 1}{2}th$

$M = \frac{12 + 1}{2}th$

$M = \frac{13}{2}th$

$M = 6.5th$

This implies that the median is the mean of the 6th and the 7th item.

So, we have:

$M_D = \frac{2+3}{2}$

$M_D = \frac{5}{2}$

$M_D = 2.5$ ---- Dannette

$M_A = \frac{5+5}{2}$

$M_A = \frac{10}{2}$

$M_A = 5$ ---- Alphonso

Standard Deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}$

So, we have:

$\sigma_D = \sqrt{\frac{(1 - 4.33)^2 +.............+(9- 4.33)^2}{12}}$

$\sigma_D = \sqrt{\frac{134.6668}{12}}$

$\sigma_D = 3.350$ ---- Dannette

$\sigma_A = \sqrt{\frac{(3-5.17)^2+............+(11-5.17)^2}{12}}$

$\sigma_A = \sqrt{\frac{45.6668}{12}}$

$\sigma_A = 1.951$ --- Alphonso

The Interquartile Range (IQR)

This is calculated as:

$IQR =Q_3 - Q_1$

Where

$Q_3 \to$ Upper Quartile and $Q_1 \to$ Lower Quartile

$Q_3$ is calculated as:

$Q_3 = \frac{3}{4}*({n + 1})th$

$Q_3 = \frac{3}{4}*(12 + 1})th$

$Q_3 = \frac{3}{4}*13th$

$Q_3 = 9.75th$

This means that $Q_3$ is the mean of the 9th and 7th item. So, we have:

$Q_3 = \frac{1}{2} * (8+8) = \frac{1}{2} * 16$ $Q_3 = \frac{1}{2} * (5+6) = \frac{1}{2} * 11$

$Q_3 = 8$ ---- Dannette $Q_3 = 5.5$ --- Alphonso

$Q_1$ is calculated as:

$Q_1 = \frac{1}{4}*({n + 1})th$

$Q_1 = \frac{1}{4}*({12 + 1})th$

$Q_1 = \frac{1}{4}*13th$

$Q_1 = 3.25th$

This means that $Q_1$ is the mean of the 3rd and 4th item. So, we have:

$Q_1 = \frac{1}{2}(1+1) = \frac{1}{2} * 2$ $Q_1 = \frac{1}{2}(4+4) = \frac{1}{2} * 8$

$Q_1 = 1$ --- Dannette $Q_1 = 4$ ---- Alphonso

So, the IQR is:

$IQR = Q_3 - Q_1$

$IQR_D = 8 - 1$ $IQR_A = 5.5 - 4$

$IQR_D = 7$ --- Dannette $IQR_A = 1.5$ --- Alphonso

Solving (b): The measures to compare

Measure of center

By observation, we can see that there are outliers is the plot of Alphonso (because 11 is far from the other dataset) while there are no outliers in Dannette plot (as all data are close).

Since, the above is the case; we simply compare the median of both because it is not affected by outliers

Measure of spread

Compare the interquartile range of both, as it is arguably the best measure of spread, because it is also not affected by outliers.

Solving (c): Check for outlier

To check for outlier, we make use of the following formulas:

$Lower =Q_1 - 1.5 * IQR$

$Upper =Q_3 + 1.5 * IQR$

For Dannette:

$Lower = 1 - 1.5 * 7 = -9.5$

$Upper = 8 + 1.5 * 7 = 18.5$

Since, the dataset are all positive, we change the lower outlier to 0.

So, the valid data range are:

$Valid = 0 \to 18.5$

From the question, the range of Dannette's dataset is: 1 to 9. Hence, there are no outliers in Dannette's dataset

For Alphonso:

$Lower = 4 - 1.5 * 1.5 =1.75$

$Upper = 5.5 + 1.5 * 1.5 =7.75$

So, the valid data range are:

$Valid = 1.75\to 7.75$

From the question, the range of Alphonso's dataset is: 3 to 11. Hence, there are outliers in Alphonso's dataset

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3 years ago

I also need help with this quick!

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Answer:

I think its 5

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3 years ago

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Dan took out a 24-year loan for $111,000 at an APR of 7.7%, compounded

Gekata [30.6K]

Dan would save more by paying off his loan 13 years early

Step-by-step explanation:

The formula for compound interest, including principal sum, is:

$A=P(1+\frac{r}{n})^{nt}$ where:

A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial deposit or loan amount)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per unit t
t is the time the money is invested or borrowed for

Dan took out a 24-year loan for $111,000 at an APR of 7.7%,

compounded monthly

∴ P = $111,000

∴ r = 7.7% = (7.7/100) = 0.077

∴ n = 12 ⇒ compounded monthly

∵ The loan is paid in 13 years

∴ t = 24 - 13 = 11 years ⇒ 13 years early

- Substitute these values in the formula above

∴ $A=111,000(1+\frac{0.077}{12})^{(12)(11)}$

∴ A = $258,223.20

If it paying in 24 years

∴ $A=111,000(1+\frac{0.077}{12})^{(12)(24)}$

∴ A = $700,382.38

∴ Dan saves = 700,382.38 - 258,223.20 = $442,159.18

Forrest took out a 24-year loan for $96,000 at an APR of 7.7%,

compounded monthly

∴ P = $96,000

∴ r = 7.7% = (7.7/100) = 0.077

∴ n = 12 ⇒ compounded monthly

∵ The loan is paid in 13 years

∴ t = 24 - 13 = 11 years ⇒ 13 years early

- Substitute these values in the formula above

∴ $A=96,000(1+\frac{0.077}{12})^{(12)(11)}$

∴ A = $223,328.17

If it paying in 24 years

∴ $A=96,000(1+\frac{0.077}{12})^{(12)(24)}$

∴ A = $605,736.11

∴ Forrest saves = 605,736.11 - $223,328.17 = $382.407.94

∵ Dan saves $442,159.18

∵ Forrest saves $382,407.94

∴ Dan would save more by paying off his loan 13 years early

Dan would save more by paying off his loan 13 years early

Learn more:

You can learn more about interest in brainly.com/question/8280736

#LearnwithBrainly

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