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2 years ago

Which is a unit rate? 15 miles per gallon

Mathematics

1 answer:

Over [174]2 years ago

6 0

Step-by-step explanation:

Step:1

From given, the rate is

= 15 miles per gallon

= \frac{15}{1}115 = 15 miles.........................(1)

Step:2

Check for Option A,

= 30 miles per 3 gallons

= \frac{30}{3}330 = 10 miles.....................(2)

From the eqn (1) and (2),

Eqn (1) ≠ Eqn (2)

Step:3

Check for Option B and C are not match with given because, Miles provided first or top then the gallons provided the last or bottom.

Step:4

Check for Option D,

= 60 miles per 4 gallons

= \frac{60}{4}460 = 15 miles.........................(3)

From the eqn (1) and (3),

Eqn (1) ≠ Eqn (3)

Result:

The equivalent unit rate for 15 miles per gallon is 60 miles per 4 gallons (\frac{60 miles}{4 gallons}4gallons60miles ) .

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$\= x = 41. 795$

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

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 is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

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

=> $E = 1.96 * 2.5$

=> $E =4.9$

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$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

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=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

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$z = -1.282$

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