7% of 80 is what number

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

Erin created a scale drawing for a garden that will be 10 ft by 5 ft. She plans to include a section in the garden for herbs, wh

Elanso [62]

Answer:

The dimensions of the herb garden in the scale drawing are 2.4 in. by 6 in

Step-by-step explanation:

we know that

The dimensions of the garden in the actual are 10 ft by 5 ft

The dimensions of the garden on the scale drawing are 12 in. by 6 in

step 1

Find the scale factor

To find the scale factor divide the corresponding side on the scale drawing by the corresponding side in the actual

so

$\frac{12}{10}\ \frac{in}{ft}$

simplify

$1.2\ \frac{in}{ft}$

That means

1.2 inches in the drawing represent 1 foot in the actual

step 2

Find out the dimensions of the herb garden on the scale drawing

we know that

The dimensions of the herb garden in the actual are 2 ft by 5 ft

Multiply by the scale factor

so

$2\ ft=2(1.2)=2.4\ in$

$5\ ft=5(1.2)=6\ in$

therefore

The dimensions of the herb garden in the scale drawing are 2.4 in. by 6 in

5 0

2 years ago

A new car sells for $27,500. The value of the car decreases by 14% annually. You want to sell the car when it's worth about $400

NemiM [27]

Answer: 13 years.

Step-by-step explanation:

The price decreases by 14% anually

To find the decimal form, you have 14%/100% = 0.14

So, the year zero, the price is $27,500

After one year, the price is:

P = $27,500 - 0.14*$27500 = $27,500*(0.86)

After the second year, the price is:

P = $27,500*(0.86)^2

and so on, so we want to find x such that:

P = $27,500*(0.86)^x = $4000

0.86^x = $4000/$27,500

Now, using the natural logaritm rule:

a^x = b

x = ln(a)/ln(b)

x = ln($4000/$27,500)/ln(0.86) = 12.8

We can round it up to 13, so after 13 years the price of the car is about $4000

7 0

2 years ago

The antibiotic clarithromycin is eliminated from the body according to the formula A(t) = 500e−0.1386t, where A is the amount re

PolarNik [594]

Answer:

Time(t) = 11.61 hours (Rounded to two decimal place)

Step-by-step explanation:

Given: The antibiotic clarithromycin is eliminated from the body according to the formula:

$A(t) = 500e^{-0.1386t}$ ......[1]

where;

A - Amount remaining in the body(in milligram)

t - time in hours after the drug reaches peak concentration.

Given: Amount of drug in the body is reduced to 100 milligrams.

then,

Substitute the value of A = 100 milligrams in [1] we get;

$100= 500e^{-0.1386t}$

Divide both sides by 500 we get;

$\frac{100}{500}=\frac{ 500e^{-0.1386t}}{500}$

Simplify:

$\frac{1}{5} = e^{-0.1386t}$

Taking logarithm both sides with base e, then we have;

$\log_e (\frac{1}{5})= \log_e (e^{-0.1386t})$

$\log_e (\frac{1}{5})=-0.1386t$ [ Using $\log_e e^a =a$ ]

or

$\log_e (0.2)=-0.1386t$

$-1.6094379124341 = -0.1386t$

[using value of $\log_e (0.2) = -1.6094379124341$ ]

then;

$t = \frac{-1.6094379124341}{-0.1386}$

Simplify:

t ≈11.61 hours.

Therefore, the time 11.61 hours(Rounded two decimal place) will pass before the amount of drug in the body is reduced to 100 milligrams

6 0

2 years ago

I have 10 apples, I give away 2, how many apples do I have left

Volgvan

This would be 10-2 which would equal 8

5 0

3 years ago

Read 2 more answers