How long does each phase of the moon (exactly) take long to complete?

21-35a<br>Factor the following expression

erica [24]

Answer:

7x(3-5a)

Step-by-step explanation:

21-35a =

to find a minimum common multiply you have to rationalize the number with the same numer, and this number must be a whole, this will help you to write the expression easier, if you notice that 21 and 35 are familiar of 7, then you can find a common factor, to multiply your expression

4 0

3 years ago

For f(x)=4x+1 and g(x)=x^2-5, find (g/f)(x)

ddd [48]

Answer:

$(g/f)(x) = \frac{g(x)}{f(x)} = \frac{ {x}^{2} - 5 }{4x + 1}$

I hope I helped you^_^

3 0

3 years ago

GRE Test: The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores o

Zepler [3.9K]

Answer:

a) $\bar X=144.3$

b) The 95% confidence interval would be given by (138.846;149.754)

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

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

$\bar X=144.3$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=8.8$ represent the population standard deviation

n=10 represent the sample size

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

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

$\bar X=144.3$

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$144.3-1.96\frac{8.8}{\sqrt{10}}=138.846$

$144.3+1.96\frac{8.8}{\sqrt{10}}=149.754$

So on this case the 95% confidence interval would be given by (138.846;149.754)

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (5) we got:

$n=(\frac{1.960(8.8)}{3})^2 =33.05 \approx 34$

So the answer for this case would be n=34 rounded up to the nearest integer

Part d

$n=(\frac{1.960(8.8)}{1})^2 =297.493 \approx 298$

So the answer for this case would be n=298 rounded up to the nearest integer

Part e

$n=(\frac{1.960(8.8)}{0.5})^2 =1189.97 \approx 1190$

So the answer for this case would be n=1190 rounded up to the nearest integer

7 0

3 years ago

the admission fee to an amusement park is $27.it cost an additional p dollars to rent a locker to hold your belongings. the tota

Mademuasel [1]

$6.00 for one person to rent a locker.

6 0

3 years ago

Help! If u get it i will mark brainliest!

konstantin123 [22]

Answer:

Lead-the-market pay strategies. An employer may choose to establish an internal compensation strategy that is in excess of the pay rates in the prevailing marketplace. This compensation strategy may increase the supply of candidates, increase selection rates of qualified applicants, decrease employee turnover, increase morale and productivity, or prevent unionization efforts. However, prior to implementing a lead compensation strategy, an organization should carefully consider what benefits it expects to realize from such a strategy, keeping in mind that this type of structure has the greatest propensity of increasing overall labor costs.

Step-by-step explanation:

6 0

3 years ago

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