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Norma-Jean [14]
2 years ago
6

Next

Mathematics
1 answer:
AveGali [126]2 years ago
8 0

Answer:

C. Robbie's glider

Step-by-step explanation:

P.S -The exact question is -

Given - Melissa and Robbie are flying remote control gliders.

The altitude of Melissa's glider, h(s), in feet, is modeled by this function, where sis time, in seconds, after launch.

m(s) = 0.4(s³ - 11s² + 31s – 1)

The altitude of Robbie's glider is modeled by function r, where sis time, in seconds, after launch.

To find - Which glider reaches the greater maximum altitude in the first 6 seconds after launch?

A. Neither glider reaches a maximum altitude on the given interval.

В. Melissa's glider

C. Robbie's glider

D. Both gliders reach the same altitude on the given interval.

Proof -

At t = 6 sec,

Melisa glider is

h(6) = 0.4((0.6)³ - 11(0.6)² + 31(0.6) – 1)

      = 0.4( 0.216 - 3.96 + 18.6 - 1 )

      = 0.4(13.856) = 5.5424

⇒h(6) = 5.5424

∴ we get

At t = 6 seconds, Melissa glider is at the altitude of 5.54 feet

Now,

From the figure, we can see that,

At t = 6 seconds, Robbie's glider is approximately at an altitude of 13 feet

Now,

As 13 > 5.5

So,

Robbie's glider is at maximum height in 6 seconds after the launch.

So,

The correct option is - C. Robbie's glider

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Answer:

p_v =P(Z>4.146)=0.0000169  

Based on the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .  

Step-by-step explanation:

1) Data given and notation  

n=170 represent the random sample taken  

X=58 represent the student's who belief that such software unfairly targets students

\hat px=\frac{58}{170}=0.341 estimated proportion of students who belief that such software unfairly targets students

\hat p=\frac{112}{170}=0.659 estimated proportion of students who NOT belief that such software unfairly targets students

p_o=0.50 is the value that we want to test  

\alpha=0.05 represent the significance level (no given)  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

p= proportion of student's who belief that such software unfairly targets students

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that a majority of students at the university do not share this belief. :  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p>0.5

We assume that the proportion follows a normal distribution.  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}    (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly (different,higher or less) from a hypothesized value p_o.  

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =170*0.5=85>10

n(1-p_o)=170*(1-0.5)=85>10

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{170}}}=4.146  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided is \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a one right side test the p value would be:  

p_v =P(Z>4.146)=0.0000169  

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