All categories

2 years ago

Which is the rationalized form of the expression sqrtx/sqrtx+sqrt5

Mathematics

1 answer:

adoni [48]2 years ago

3 0

$\dfrac{\sqrt x}{\sqrt x + \sqrt 5}\\\\\\\\= \dfrac{\sqrt x(\sqrt x - \sqrt 5)}{(\sqrt x + \sqrt 5)(\sqrt x - \sqrt 5)}\\\\\\= \dfrac{\left(\sqrt x \right)^2 - \sqrt{5x}}{\left(\sqrt x \right)^2 - \left(\sqrt 5)^2}}\\\\$

$=\dfrac{x - \sqrt{5x}}{x -5}$

You might be interested in

By law, an industrial plant can discharge not more than 500 gallons of waste water per hour, on the average, into a neighboring

Alisiya [41]

Answer:

We conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

Step-by-step explanation:

We are given that an industrial plant can discharge not more than 500 gallons of wastewater per hour, on average, into a neighboring lake.

Four one-hour periods are selected randomly over a period of one week. The following are observed:

1384, 683, 1534, 405

Let $\mu$ = population average gallons of wastewater discharged per hour

So, Null Hypothesis, $H_0$ : $\mu \leq$ 500 gallons {means that not more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

Alternate Hypothesis, $H_A$ : $\mu$ > 500 gallons {means that more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = $\frac{\sum X}{n}$ = 1001.5 gallons

s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }$ = 543.79

n = sample of periods = 4

So, the test statistics = $\frac{1001.5-500}{\frac{543.79}{\sqrt{4} } }$ ~ $t_3$

= 1.844

The value of t-test statistics is 1.844.

Since in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the t table gives a critical value of 2.353 at 3 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.844 < 2.353, so we have insufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

4 0

3 years ago

A sample chosen by stratified random sampling involves a. randomly selecting one of the first k elements in an ordered populatio

Pavlova-9 [17]

Answer:

The answer is (d)= Selecting a simple random sample from each of a given number of strata formed from the elements in the population.

Stratified random sampling is a sampling method where the population has a number of distinct categories. The population can be organized into separate strata and each stratum is then sampled as an independent sub-population out of which individual elements can be randomly selected. In this case, each unit in a stratum, that is, each element in a group has the chance of being selected into the sample and there is adequate representation of minority sub-groups. With Stratified sampling, the best result occurs when elements within strata are internally homogeneous.

Step-by-step explanation:

5 0

3 years ago

How do I do this? It is a regular hexagon with a height of 30. We have to find the perimeter of it.

Sliva [168]

Answer:

The radius of a hexagon is called the apothem, which in this case is 15.

We need to know the side length which is found by the equation:

side length = apothem * 2 * (tan (180 / #sides))

side length = apothem * 2 * (tan (180 / 6))

side length = 15 * 2 * (tan (30 degrees))

side length = 30 * .57735

side length = 17.3205

We need the perimeter of the hexagon which equals the side length times six.

perimeter = 6 * 17.3205 = 103.923

Source: https://www.1728.org/polygon.htm

Step-by-step explanation:

8 0

4 years ago

If the total unit cost of manufacturing Product Y is currently $36 and the total unit cost after modifying the style is estimate

luda_lava [24]

The question is incomplete. The question is asking whether the given statement is TRUE or FALSE.

Answer:

The given statement is FALSE.

Step-by-step explanation:

Given:

Total unit cost of manufacturing product Y is, $C_{man}=\$36$

Total unit cost after modifying the style is, $C_{mod}=\$48$

So, the differential cost for this situation is given as the difference of the modifying cost and manufacturing cost.

Therefore, the differential cost is given as:

$\textrm{Differential cost}=C_{mod}-C_{man}\\\textrm{Differential cost}=\$48-\$36=\$12$

Hence, the given statement is false and the correct value for differential cost for this situation is $12.

7 0

3 years ago

Talia took the bus from her home to the bank and then walked back to her home along the same route. The round trip took 0.9 hour

larisa [96]

The rate of trip 2 is 5 km/h

The time of trip 1 is 0.9-x hours

3 0

3 years ago