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2 years ago

A hot air balloon rose from a height of 100 m to 400 m in 3 minutes what was the ballons rate of change

Mathematics

2 answers:

Volgvan2 years ago

8 0

Answer:

100 m/minute

Step-by-step explanation:

We are given that

Initial height of balloon=100 m

Final height of balloon=400 m

Time taken =3 minute

We have to find the rate of change of balloon height.

Change in height of balloon=Final height-initial height=400 -100= 300 m

Rate of change of balloon height= $\frac{300}{3}=100 m/minute$

Hence, the rate of change of balloon height is 100 m/minute.

Marina86 [1]2 years ago

3 0

Each minute 100 meters would go by so the answer is 100 meters per minute

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Natali5045456 [20]

Answer:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

$p_v =P(t_{13}$

If we compare the p value and a significance level assumed for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.

Step-by-step explanation:

Data given and notation

$\bar X=71.86$ represent the sample mean

$s=17.52$ represent the standard deviation for the sample

$n=14$ sample size

$\mu_o =78$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is less than 78, the system of hypothesis would be:

Null hypothesis: $\mu \geq 78$

Alternative hypothesis: $\mu < 78$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

Calculate the P-value

First we need to find the degrees of freedom given by:

$df=n-1=14-1=13$