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Does this table represent a proportional relationship?<br><br> A) Yes<br> B) No

Nonamiya [84]

Answer:

a

Step-by-step explanation:

it is all doubles

7 0

3 years ago

Read 2 more answers

What is 10x and a negative 15 over 10 plus one half

eimsori [14]

Answer:

-29/2

Step-by-step explanation:

3 0

3 years ago

HELP I NEED THIS DONE

Bogdan [553]

Answer:

22

Step-by-step explanation:

since q is given as r + 10 we can add 10 to 12 in the missing place and find the value

5 0

3 years ago

A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quar

kotykmax [81]

Answer:

a

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

b

The 95% confidence interval is $0.224 < \mu_1 - \mu_2 < 2.776$

Step-by-step explanation:

From the question we are told that

The sample size is n = 36

The first sample mean is $\= x_1 = 11.4$

The first standard deviation is $s_1 = 2.5$

The second sample mean is $\= x_2 = 9.9$

The second standard deviation is $s_2 = 3.0$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 0$

Generally the test statistics is mathematically represented as

$z = \frac{ (\= x_1 - \= x_2 ) - (\mu_1 - \mu_2 ) }{ \sqrt{ \frac{s_1^2 }{n} + \frac{s_2^2 }{ n} } }$

=> $z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }$

=> $z = 2.3$

From the z table the area under the normal curve to the left corresponding to 2.3 is

$P( Z > 2.3 ) = 0.010724$

Generally the p-value is mathematically represented as

$p-value = 2 * P( Z > 2.3 )$

=> $p-value = 2 * 0.010724$

=> $p-value = 0.02$

From the value obtained we see that $p-value < \alpha$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

Considering question b

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 margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{s_1^2 }{n } + \frac{s_2^2}{n}}$

=> $E = 1.96 * \sqrt{ \frac{2.5^2 }{ 36 } + \frac{ 3^2}{36}}$

=> $E = 1.276$

Generally 95% confidence interval is mathematically represented as

$( \= x_1 - \= x_2) -E < \mu_1 - \mu_2 < ( \= x_1 - \= x_2) + E$

=> $( 11.4 - 9.9 ) -1.276 < \mu_1 - \mu_2 < ( 11.4 - 9.9 ) + 1.276$

=> $0.224 < \mu_1 - \mu_2 < 2.776$

4 0

3 years ago

A building feet tall has a shadow that is feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree

lina2011 [118]

Answer:

The angle of elevation of the sun to the nearest hundredth of a degree is 44.07°

Step-by-step explanation:

Here is the complete question:

A building 86.53 feet tall has a shadow that is 89.39 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree.

Step-by-step explanation:

Please see the attachment below for an illustrative diagram:

From the diagram

/AC/ is the height of the building

/CB/ is the length of the shadow

/AC/ = 86.53 feet

/CB/ 89.39 feet

θ is the angle of elevation

Consider triangle ABC

/AC/ is the opposite

and /CB/ is the adjacent

From

tanθ = $\frac{Opposite}{Adjacent}$

Then,

tanθ = $\frac{/AC/}{/CB/}$

tanθ = $\frac{86.53}{89.39}$

tanθ = 0.9680

∴θ = tan⁻¹(0.9680)

θ = 44.0686°

θ = 44.07° (to the nearest hundredth of a degree)

Hence, the angle of elevation of the sun to the nearest hundredth of a degree is 44.07°

8 0

3 years ago