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3 years ago

Which expression is equivalent to (X^1/4 y^16)^1/2?

Mathematics

1 answer:

lawyer [7]3 years ago

3 0

Answer:

$x^{\frac{1}{8} } y^{8}$

Step-by-step explanation:

Given :

$(x^\frac{1}{4} y^{16} )^{1/2}$

Now,

$(x^\frac{1}{4} y^{16} )^{1/2}\\x^{\frac{1}{8} } y^{8}$

Therefore, expression is equivalent to $x^{\frac{1}{8} } y^{8}$

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What kind of triangle does it form?

Gwar [14]

Answer:

It forms a scalene triangle

Step-by-step explanation:

This is because scalene triangle does not have any of its sides equal.

$\sqrt{111}$ is also 10.54.And looking at the measurements none of it are equal to each other so therefore it is a scalene triangle

7 0

3 years ago

Q.23 Prove that: (sin4A - cos4A + 1) = 2sin2A

FrozenT [24]

Answer:

Step-by-step explanation:

I think you have the question incomplete, and that this is the complete question

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

To do this, we can start my mirroring the equation.

x² + y² = (x + y)² - 2xy,

This helps us break down the power from 4 to 2, so that we have

(sin²a)² + (cos²a)² = (sin²a + cos²a) ² - 2(sin²a) (cos²a)

Recall from identity that

Sin²Φ + cos²Φ = 1, so therefore

(sin²a)² + (cos²a)² = 1² - 2(sin²a) (cos²a)

On expanding the power and the brackets, we find that we have the equation proved.

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

4 0

3 years ago

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the

Andre45 [30]

Answer:

Step-by-step explanation:

A direct variation equation is of the form

y = kx,

where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.

We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is

d = kw and we need to find k in order to have the model for dosing the animals.

$\frac{3}{5} =k(30)$

Divide both sides by 1/30 to get k alone.

$(\frac{1}{30})(\frac{3}{5})=k$ and

$k=\frac{1}{50}$

Our model then is

$d=\frac{1}{50}w$

This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.

7 0

3 years ago

Read 2 more answers

5) Lee's model airplane flies at 18 miles per hour. Lee took the plane to a field in windy weather. It took six minutes to fly 2

kap26 [50]

The wind is blowing at the rate of 4 miles per hour

<h3>Speed and distances</h3>

The formula for calculating speed is expressed as:

Speed = Distance/Time

Given the following parameters

Speed of airplane = 18 miles per hour

Speed in wind = 2.2 * 10 = 22 miles/hr

Speed of the wind = 22 - 18

Speed of the wind = 4mi/hr

Hence the wind is blowing at the rate of 4 miles per hour

Learn more on speed here: brainly.com/question/4931057

7 0

2 years ago

) The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday

Vsevolod [243]

Answer:

a) The standard deviation of this sampling distribution is 2.07.

b) The missing number is 4.14.

c) The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

Step-by-step explanation:

To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Central Limit Theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

$\mu = 272, n = 840, \sigma = 60$

(a) If we take many samples, the sample mean x⎯⎯⎯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution?

Using the Central Limit Theorem:

$s = \frac{\sigma}{\sqrt{n}} = \frac{60}{\sqrt{840}} = 2.07$

The standard deviation of this sampling distribution is 2.07.

(b) According to the 95 part of the 68-95-99.7 rule, 95% of all values of x⎯⎯⎯ fall within _______ on either side of the unknown mean μ. What is the missing number?

Within 2 standard deviations of the mean.

So, 2*2.07 = 4.14

The missing number is 4.14.

(c) What is the 95% confidence interval for the population mean score μ based on this one sample?

Within 4.14 of the mean

272 - 4.14 = 267.86

272 + 4.14 = 276.14

The 95% confidence interval for the population mean score μ based on this one sample is between 267.86 and 276.14.

6 0

3 years ago