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3 years ago

Write the rational number 2.13 repeating as the ratio of two integers

Mathematics

1 answer:

zmey [24]3 years ago

6 0

Let

x = 2.131313... Equation 1

Multiply both sides by 100 to get:

100x = 213.131313... Equation 2

Subtract equation 1 from equation 2.

99x = 211

x = 211/99

Answer: 211/99

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Use logarithmic differentiation to find the derivative of the function.y = x^8 sin(x)

givi [52]

$Answer: \frac{\partial y}{\partial x}=8x^{8sinx}(cosx.logx+\frac{sinx}{x})$

Step-by-step explanation:

Since we have given that

$y=x^{8sinx}$

By using logarithmic on both sides we get,

$log y= 8 sinx. logx$

(∵ $log(a^m)=m.loga$ )

Now, differentiating on both sides ,we get,

$\frac{1}{y}.\frac{\partial y}{\partial x}=8(\frac{\partial sinx}{\partial x}.logx+sinx \frac{\partial logx}{\partial x})$

$\\\frac{1}{y}\frac{\partial y}{\partial x}=8(cosx.logx+sinx.\frac{1}{x})$

$\\\frac{\partial y}{\partial y}=8y(cosx.logx+\frac{sinx}{x})\\\\\frac{\partial y}{\partial x}=8x^{8sinx}(cosx.logx+\frac{sinx}{x})$

6 0

2 years ago

A consulting firm had predicted that 35% of the employees at a large firm would take advantage of a new company Credit Union, bu

m_a_m_a [10]

Answer:

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Step-by-step explanation:

a. Find the standard deviation of the sample proportion based on the null hypothesis

Based on the null hypothesis:

$p_{0}$ : 0.35

and the standard deviation σ = $\sqrt{p_{0} *(1-p_{0}) }$ = $\sqrt{0.35 *0.65 }$ ≈0.4770

b. Find the z statistic

z-statistic is calculated as follows:

z= $\frac{X-p_{o} }{\frac{s}{\sqrt{N} } }$ where

X is the proportion of employees in the survey who take advantage of the Credit Union ( $\frac{138}{300}=0.46$ )
$p_{0}$ is the proportion in null hypothesis (0.35)
s is the standard deviation (0.4770)
N is the sample size (300)

putting the numbers in the formula:

z= $\frac{0.46-0.35} }{\frac{0.4770}{\sqrt{300} } }$ = 3.9945

c. Does the z statistic seem like a particularly large or small value?

z-statistics seem a large value, which will cause us to reject the null hypothesis.

4 0

3 years ago

The maximum speed an animal can walk in feet per second is a 5.7VI, where l is the animal's leg length in feet. What is the maxi

ad-work [718]

Answer:

Maximum walking speed of camel is 31.749V feet per second

Step-by-step explanation:

Walking speed of an animal is given by :

Speed = 5.7VI (in feet per second) where l is the animal's leg length.

For a camel, leg length is 5.7feet.

So maximum walking speed of camel will be:

Speed of camel = 5.7V * 5.7 = 5.7² V feet per second

Speed of camel = 31.749V feet per second

hence, maximum walking speed of camel is 31.749V feet per second

7 0

3 years ago

The graph represents the speed at which Pete's marble travels.

fiasKO [112]

Answer:b

Step-by-step explanation:

5 0

3 years ago

Which one of these grids is shaded red and blue in the ratio 5 : 7?

trasher [3.6K]

Answer:

Step-by-step explanation:

there are 5 red boxes and 7 blue boxes

8 0

3 years ago

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