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postnew [5]
3 years ago
15

PROBLEM #1

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer:

  • 500 - 25w ≥ 200

Explanation:

Translate every verbal statement into an algebraic statement,

<u>1. Keith has $500 in a savings account at the beginning of the summer.</u>

  • Initial amount: 500

<u>2.  He wants to have at least $200 in the account by the end of summer. </u>

<u />

  • Final amount ≥ 200

<u>3. He withdraws $25 a week for his cell phone bill.</u>

<u />

  • Call w the number of weeks
  • Withdrawls = 25w

<u>4. Write an inequality that represents Keith's situation.</u>

  • Create your model: Final amount = Initial amount - withdrawals ≥ 500

  • 500 - 25w ≥ 200

With that inequality you can calculate how many week will pass before his account has less than the amount he wants to have in the account by the end of summer:

  • 500 - 200 ≥ 25w
  • 300 ≥ 25w
  • 300/25 ≥ w
  • 12 ≥ w
  • w ≤ 12

That represents that he can afford spending $ 25 a week during 12 weeks to have at least $ 200 in the account.

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Answer:

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When you add all the angles, you get 360.

Angle a and b would measure the same and so would angle d and c. So you double the measure for one of those angles and subtract it from 360.

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Triangle DEF, shown below, is reflected over the y-axis to form triangle D'E'F'. What are
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Type the correct answer in each box. Use numerals instead of words. Any non-integer answers in this problem should be entered as
ladessa [460]

Answer:

The interquartile range of the data set is 5

The mean absolute deviation of the data set is 3.6

Step-by-step explanation:

* Lets explain how to find the interquartile range and the mean absolute

  deviation (MAD)

- The steps to find the interquartile range is:

1- Arrange the values from the smallest to the largest

∴ The values are 5 , 6 , 10 , 11 , 12 , 13 , 14 , 15 , 18 , 20

2- Find the median

- The median is the middle value after arrange them

* If there are two values in the middle take their average

∵ The values are 10 then the 5th and the 6th are the values

∵ The 5th is 12 and the 6th is 13

∴ The median = \frac{12+13}{2}=12.5

∴ The median is 12.5

3- Calculate the median of the lower quartile

- The lower quartile is the median of the first half data values

∵ There are 10 values

∴ The first half is the first five values

∴ The first half values are 5 , 6 , 10 , 11 , 12

∵ The middle value is 10

∴ The median of lower quartile = 10

- Similar find the median of the upper quartile

- The upper quartile is the median of the second half data values

∵ There are 10 numbers

∴ The second half is the last five values

∴ The second half values are 13 , 14 , 15 , 18 , 20

∵ The middle value is 15

∴ The median of upper quartile = 15

4- The interquartile range (IQR) is the difference between the upper

    and the lower medians

∴ The interquartile range = 15 - 10 = 5

* The interquartile range of the data set is 5

* Lets talk about the mean absolute deviation

- Mean absolute deviation (MAD) of a data set is the average distance  

 between each data value and the mean

- To find the mean absolute deviation of the data, start by finding

   the mean of the data set.  

1- Find the sum of the data values, and divide the sum by the  

   number of data values.  

∵ The data set is 5 , 6 , 10 , 11 , 12 , 13 , 14 , 15 , 18 , 20

∵ Its sum = 5 + 6 + 10 + 11 + 12 + 13 + 14 + 15 + 18 + 20 = 124

∵ The mean = the sum of the data values/the number of the data

∵ The set has 10 numbers

∴ The mean = 124/10 = 12.4

2- Find the absolute value of the difference between each data value  

   and the mean ⇒ |data value – mean|

# I5 - 12.4I = 7.4

# I6 - 12.4I = 6.4

# I10 - 12.4I = 2.4

# I11 - 12.4I = 1.4

# I12 - 12.4I = 0.4

# I13 - 12.4I = 0.6

# I14 - 12.4I = 1.6

# I15 - 12.4I = 2.6

# I18 - 12.4I = 5.6

# I20 - 12.4I = 7.6

3- Find the sum of the absolute values of the differences.

∵ Their sum = 7.4 + 6.4 + 2.4 + 1.4 + 0.4 + 0.6 + 1.6 + 2.6 + 5.6 + 7.6

∴ Their sum = 36

4- Divide the sum of the absolute values of the differences by the

    number of data values  to find MAD

∴ MAD = The sum of the absolute values/number of the values

∵ The sum = 36

∵ The data set has 10 values

∴ MAD = 36/10 = 3.6

* The mean absolute deviation of the data set is 3.6

6 0
2 years ago
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