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Ahat [919]
2 years ago
7

Does the equation t degree straight C equals left parenthesis 32 plus 1.8 t right parenthesis degree straight F work for any rat

ional number? Check that it does with t equals 8 2 over 3 and t equals negative 8 2 over 3.
Evaluate the right side of the equation when t equals 8 2 over 3.



Do not include units (degrees Fahrenheit) in your answer.





x =?
Mathematics
1 answer:
lorasvet [3.4K]2 years ago
5 0

Answer:

  • 16.4 for t = -8 2/3
  • 47.6 for t = 8 2/3

Step-by-step explanation:

We assume you want to evaluate the equation ...

  T = 32 +1.8t

for t = -8 2/3 and t = 8 2/3

The evaluation involves addition and multiplication, both of which are closed for all real numbers, which includes all rational numbers. The equation works for any rational numbers.

Your examples:

  T = 32 +1.8(-8 2/3) = 32 -15.6 = 16.4 . . . . the equation works

  T = 32 +1.8(8 2/3) = 32 +15.6 = 47.6 . . . . the equation works

_____

<em>Additional comment</em>

Some calculators play nicely with decimals and mixed numbers.

The product 1.8(8 2/3) can be found as ...

  (1.8)(8 2/3) = 1.8(26/3) = 0.6(26) = 15.6

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A number increased by 4 is the same as 19 minus 2 times the number
ElenaW [278]

Hello from MrBillDoesMath!

Answer:

n = 5


Discussion:

Let the original number be "n"  Translating the problem  statement to mathematical symbolism:

n + 4 = 19 - 2n                   =>  add 2n to both sides

n + 2n + 4 = 19 - 2n + 2n  =>  combine like terms

3n + 4 = 19                        => subtract 4 from both sides

3n = 19 -4  = 15                 => divide both sides by 3

n = 15/3 =5


Check: Does 5 +4 = 19 - 2(5)? Does 9 = 9? Yes. so the value for n is confirmed correct.


Thank you,

MrB

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The formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0°C, or 32°F a
BlackZzzverrR [31]

Answer:

The formula y = mx + b sometimes appears with

different symbols.

For example, instead of x, we could use the

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Then the equation becomes

F = mC + b.

All temperature scales are related by linear

equations. For example, the temperature in

degrees Fahrenheit is a linear function of degrees Celsius.

Water freezes at: 0°C, 32°F

Water Boils at: 100°C, 212°F

Hope this helps!

4 0
3 years ago
Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his
Fudgin [204]

Answer:

a

  The point estimate of the population mean is  \= x  =  56

b

  The 80% confidence level is  50.57 <  \mu  < 61.43

c

  There is  80% confidence that the true population mean lies within the confidence interval.

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  18

   The  standard deviation is  \sigma  =  18 \ L

   The  sample mean is  \= x  =  56

Generally the point estimate of the population mean is equivalent to the sample mean whose value is  \= x  =  56

Given that the confidence interval is 80% then the level of significance is mathematically represented as

      \alpha  =  100 -  80

      \alpha =  20 \%

      \alpha = 0.20

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table

 The  value is   Z_{\frac{ \alpha }{2} } =  1.28

 Generally the margin of error is mathematically evaluated as

          E =  Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }

=>       E =  1.28 * \frac{18 }{\sqrt{18} }

=>       E =  5.43

     Generally the 80% confidence interval is mathematically represented as

    \= x  - E  <  \mu  < \= x  + E

=>    56  - 5.43  <  \mu  < 56  + 5.43

=>   50.57 <  \mu  < 61.43

The  interpretation is that there is  80% confidence that the true population mean lies within the limit

3 0
3 years ago
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