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svlad2 [7]
3 years ago
7

The formula F=9/5C+32 converts temperatures from Celsius C to Fahrenheit F. A. Solve the formula for C b. The boiling point of w

ater is 212 degrees F. What is the temperature in Celsius? C. If a house thermostat is set at 80 degrees F, what is the setting in Celsius? Round your answer to the nearest tenth.
Mathematics
1 answer:
liraira [26]3 years ago
7 0

Answer:

(a) \therefore C=\frac59(F-32)

(b)The boiling point of water in Celsius scale is 100°C.

(c)The setting in Celsius scale is 26.7°C.

Step-by-step explanation:

Given that,the formula is

F=\frac95 C+32......(1)

(a)

Given that,

F=\frac95 C+32

\Rightarrow F-32=\frac95 C+32-32     [ subtracting 32  from both sides]

\Rightarrow F-32=\frac95 C

\Rightarrow \frac95 C=F-32

\Rightarrow C=\frac59(F-32) ......(2)         [Multiplying \frac59  ]

\therefore C=\frac59(F-32)

(b)

Given that, the boiling point of water is 212°F.

Putting F=212 in equation (2)

\therefore C=\frac59(212-32)

\Rightarrow C=\frac59\times 180

\Rightarrow C=5\times 20

\Rightarrow C=100

The boiling point of water is 100°C.

(c)

Given that, a house thermostat is set at 80 degree.

Putting F=80 in equation (2)

\therefore C=\frac59(80-32)

\Rightarrow C=\frac59\times 48

\Rightarrow C\approx26.7

The setting in Celsius scale is 26.7°C.

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Norma-Jean [14]

Answer:

The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.

7 0
3 years ago
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

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Answer:

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Therefore, the expected revenue of an airline ticket sold by this travel website is;

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Therefore, the expected revenue of an airline ticket sold by this travel website is $408

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Answer:

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Step-by-step explanation:

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A designer builds a model of a sports car. The finished model is exactly the same shape as the original, but smaller. The scale
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Answer:

Ratio = 2 : 15

Step-by-step explanation:

Given

k = 2 : 15 --- scale factor

Required [missing from the question]:

The ratio of width of the model to the original

From the question, we understand that the scale factor is: 2 : 15

The ratio of the width of the model to the original equals the given scale factor i.e.

Ratio = 2 : 15

8 0
3 years ago
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