Where are the asymptotes of f(x) = tan (4x-pi) from x=0 to x= pi/2

Miguel and his brother Ario are both standing 3 meters from one side of a 25 meter pool when they decide to race. Miguel offers

nalin [4]

Since both of them are 3 meters from one side of the 25 meter pool, the distance that they have to cover is actually only 22 meters only. To answer this item, we let x be the distance covered by Ario and 22-x be his remaining distance. Such that,
x/(22-x) = 1/4
The value of x from the equation is 4.4.

Therefore, the distance that Ario had covered is 4.4 m.

3 0

3 years ago

Read 2 more answers

Gloria earns 1.5 times her normal hourly pay for each hour that she works over 40 hours in a week. Here normal pay is $9.70 per

svetoff [14.1K]

She earns ($9.70x40) for a 40 hour week=$388
She earned $489.85-$388 extra= $101.85
She gets paid $9.7x1.5 for every extra hour=$14.55
She worked $101.85/$14.55 hours extra=7hours
She worked 7+40 hours that week=47 hours

5 0

3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 180180 engin

tiny-mole [99]

Answer:

$z=\frac{4.6-4.8}{\frac{0.9}{\sqrt{180}}}=-2.98$

$p_v =P(Z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=4.6$ represent the sample mean

$\sigma=0.9$ represent the population standard deviation

$n=180$ sample size

$\mu_o =4.8$ represent the value that we want to test

$\alpha=0.1$ 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 thetrue mean is below the specifications, the system of hypothesis would be:

Null hypothesis: $\mu \geq 4.8$

Alternative hypothesis: $\mu < 4.8$

If we analyze the size for the sample is > 30 and we know the population deviation so 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:

$z=\frac{4.6-4.8}{\frac{0.9}{\sqrt{180}}}=-2.98$

P-value

Since is a one sided test the p value would be:

$p_v =P(Z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis,and we have enough evidence to conclude that the true mean is significantly lower thn 4.8 at 10% of signficance.

4 0

3 years ago

The temperature is 45°F. The temperature will decrease by 2°F each hour. Let h be the number of hours.

Varvara68 [4.7K]

45 - 2t < 32 ( where t is time and you can replace it with x or h if you prefer)
Solving for t you get:
45 - 2t - 32 < 0
45 - 32 < 2t
13 < 2t
13/2 < t
Or the temperature will drop below 32F after 6 and a half hours

8 0

3 years ago

4) Choose the correct inequality for this situation.

Ksenya-84 [330]

Answer:

B. 21x + 40 ≤ 124

Step-by-step Explanation:

Maximum amount budgeted = $124 (this means they can't spend more than this)

x = number of people

Cost per head = $21

Given that Mr Walter already spent $40, which is part of the money budgeted, the number of people that can go canoeing cam be expressed with the following inequality:

21x + 40 ≤ 124

(note: the amount total to be spent will either be equal to or greater than $124, because it's the maximum amount budgeted for spending).

6 0

4 years ago