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Marta_Voda [28]
3 years ago
5

The gasoline gauge on a van initially read one fourth14 full. when 1010 gallons were added to the​ tank, the gauge read two thir

ds23 full. how many more gallons are needed to fill the​ tank?
Mathematics
1 answer:
antoniya [11.8K]3 years ago
7 0
First, have common denominators.
1/4 = 3/12
2/3 = 8/12
8/12 - 3/12 = 5/12 or 1,010 gallon
1,010/5 gallon = 1/12 full
202 gallons = 1/12 full
7/12 needed until full  ⇒ 7*202 = 1,414 gallons
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A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be c
Anna [14]

Answer:

The interval from the sample of size 400 will be approximately <u>One -half as wide</u> as the interval from the sample of size 100

Step-by-step explanation:

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the 95% confidence interval is dependent on the value of the margin of error at a constant sample mean or sample proportion

Generally the margin of error is mathematically represented as

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

Here assume that Z_{\frac{\alpha }{2} } \ and \  \sigma \ is constant so

     E =  \frac{k}{\sqrt{n} }

=>  E \sqrt{n} = K

=>   E_1 \sqrt{n}_1 =  E_2 \sqrt{n}_2

So  let  n_1 = 400 and n_2 =  100

=>   E_1 \sqrt{400} =  E_2 \sqrt{100}

=>  E_1 =  \frac{\sqrt{100} }{\sqrt{400} } E_2

=>  E_1 =  \frac{1}{2 } E_2

So From this we see that  the confidence interval for a sample size of 400 will be half that with a sample size of 100

   

     

   

7 0
3 years ago
Richard and Teo have a combined age of 37. Richard is 4 years older than twice​ Teo's age. How old are Richard and​ Teo?
valkas [14]

Answer:

Teo is 11 years old and Richard is 26 years old.

Step-by-step explanation:

Let R be the age of Richard and T be the age of Teo.

<u><em>First set up the equations:</em></u>

The combined age of Teo and Richard is 37:

R+T=37

Richard is four years old than twice Teo's age:

R=2T+4

<u><em>Then, solve the equations:</em></u>

Substitute (2) to (1) and solve for T:

(2T+4)+T=37

3T=11

T=11

Solve for R using (2):

R=2(11)+4

R=22+4

R=26

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