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3 years ago

سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x

Mathematics

1 answer:

harina [27]3 years ago

3 0

Step-by-step explanation:

Given: $y = -\dfrac{2}{x}$

Derivative of a power function $x^n$ :

$\dfrac{d}{dx}(x^n) = nx^{n-1}$

Therefore,

$\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}$

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Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

Aleks04 [339]

Answer:

a) $\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) $P(\bar X \leq 77)=P(Z$

d) See figure attached

Step-by-step explanation:

Previous concepts

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".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

$E(X) = 75$

$sd(X) = 7$

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X \leq 77)=P(Z$

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

8 0

3 years ago

What is the measure of m<1 will ensure that the rail is parallel to the bottom of the staircase?

cricket20 [7]

You can observe that angle 1 and angle with 47° are inside a parallelogram.

Consider that the sum of the internal angles of a parallelogram is 360°.

Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.

Consider that angle down right side is congruent with angle 1, then, they have the same measure.

You can write the previous situation in the following equation:

47 + 47 + ∠1 + ∠1 = 360 simplify like terms

94 + 2∠1 = 360 subtract both sides by 94

2∠1 = 360 - 94

2∠1 = 266 divide by 2 both sides

∠1 = 266/2

∠1 = 133

Hence, the measure of angle 1 is m∠1 = 133°

6 0

1 year ago

HELP PLEASE!!!!!!!!!

Rudiy27

Answer:

15 hight and 6 langth

Step-by-step explanation:

its just u measure the hight and the langht is half of 12

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3 years ago

Simplify 3^2 + 1 * 2

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Answer:

3×3+1×2

9+2

11 is the answer

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Step-by-step explanation:

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سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x​

سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x