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3 years ago

If tan x = m, what is sin x in terms of m?

Mathematics

1 answer:

zubka84 [21]3 years ago

5 0

Answer: m/sqrt(m^2)+1

Step-by-step explanation: if tan x = m, then the opposite angle is m and the adjacent angle is 1 so 1 squared plus m squared equals c squared. c = sqrt (1 + m^2)

sin x = opposite/hypotenuse = m/sqrt(m^2)+1

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A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. T

CaHeK987 [17]

Answer:

We need to conduct a hypothesis in order to check if the mean is higher than 75, the system of hypothesis are :

Null hypothesis: $\mu \leq 75$

Alternative hypothesis: $\mu > 75$

A. One-Tailed

$z=\frac{82.2-75}{\frac{10.4}{\sqrt{10}}}=2.189$

$p_v =P(z>2.189)=0.0143$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

We have the following data: 84 94 80 88 77 68 90 74 96 71

We can calculate the sample mean with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X=82.2$ represent the sample mean

$\sigma=10.4$ represent the population standard deviation

$n=10$ sample size

$\mu_o =75$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z 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 check if the mean is higher than 75, the system of hypothesis are :

Null hypothesis: $\mu \leq 75$

Alternative hypothesis: $\mu > 75$

A. One-Tailed

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{82.2-75}{\frac{10.4}{\sqrt{10}}}=2.189$

P-value

Since is a ONE-TAILED test the p value would given by:

$p_v =P(z>2.189)=0.0143$

Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

5 0

3 years ago

one hose can fill a goldfish pond in 14 minutes, and the two hoses can fill the same pond in 10 minutes, find how long it takes

likoan [24]

Answer:

Step-by-step explanation:

$\frac{1}{14} +\frac{1}{t} =\frac{1}{10}$

Solving this ^^ would equal t=35.

4 0

4 years ago

an indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. on

frosja888 [35]

Here is the solution of the given problem above.
Bucket A: dumps every 16 minutes
Bucket B: dumps every 14 minutes
Last time they both dump water: 3:20p.m.
The first thing we need to do is to find the LCM.
14 and 16 / 2 = 7 and 8.
LCM: 2x7x8 = 112 minutes from the last time and this is equivalent to 1 hour and 52 minutes. So 3: 20 p.m + 1: 52 p.m = 4: 72
since there are only 60 minutes in an hour, the result would be 5: 12P.M.
So the first time that they dump water is at 5:12 P.M
Next, 5: 12 p.m + 1 hour and 52 minutes is 6:64 which gives us 7:04 pm. Therefore, the next two times that both buckets dump water at the same time are 5:12 P.M and 7:04 P.M. Hope this answer helps.

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3 years ago

What is 3/5 x 3 1/3 simpliest form

denpristay [2]

Answer:

Step-by-step explanation:

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3 years ago

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