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stepan [7]
2 years ago
6

The annual salaries of all employees at a financial company are normally distributed with a mean= $34,000 and a standard deviati

on= $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?
Mathematics
2 answers:
Goshia [24]2 years ago
7 0
The question ask the z score of the company having a mean of 34000 and standard deviation of 4000 and the answer would be -1.5. I hope you are satisfied with my answer and feel free to ask for more if you have further question and clarifications
Alexandra [31]2 years ago
7 0

The <em>correct answer</em> is:

-1.5.

Explanation:

The formula for a z-score is

z=\frac{X-\mu}{\sigma}, where X is our test value, μ is the mean, and σ is the standard deviation.

Using our information, we have:

z=\frac{28000-34000}{4000}=\frac{-6000}{4000}=-1.5

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Set up, but do not evaluate, the integral that represents the length of the curve given by x = 1 + 3t^2, y = 4 + 2t^3 over the i
kherson [118]

L

=

∫

t

f

t

i

√

(

d

x

d

t

)

2

+

(

d

y

d

t

)

2

d

t

. Since  

x

and  

y

are perpendicular, it's not difficult to see why this computes the arclength.

It isn't very different from the arclength of a regular function:  

L

=

∫

b

a

√

1

+

(

d

y

d

x

)

2

d

x

. If you need the derivation of the parametric formula, please ask it as a separate question.

We find the 2 derivatives:

d

x

d

t

=

3

−

3

t

2

d

y

d

t

=

6

t

And we substitute these into the integral:

L

=

∫

√

3

0

√

(

3

−

3

t

2

)

2

+

(

6

t

)

2

d

t

And solve:

=

∫

√

3

0

√

9

−

18

t

2

+

9

t

4

+

36

t

2

d

t

=

∫

√

3

0

√

9

+

18

t

2

+

9

t

4

d

t

=

∫

√

3

0

√

(

3

+

3

t

2

)

2

d

t

=

∫

√

3

0

(

3

+

3

t

2

)

d

t

=

3

t

+

t

3

∣

∣

√

3

0

=

3

√

3

+

3

√

3

=6The arclength of a parametric curve can be found using the formula:  

L

=

∫

t

f

t

i

√

(

d

x

d

t

)

2

+

(

d

y

d

t

)

2

d

t

. Since  

x

and  

y

are perpendicular, it's not difficult to see why this computes the arclength.

It isn't very different from the arclength of a regular function:  

L

=

∫

b

a

√

1

+

(

d

y

d

x

)

2

d

x

. If you need the derivation of the parametric formula, please ask it as a separate question.

We find the 2 derivatives:

d

x

d

t

=

3

−

3

t

2

d

y

d

t

=

6

t

And we substitute these into the integral:

L

=

∫

√

3

0

√

(

3

−

3

t

2

)

2

+

(

6

t

)

2

d

t

And solve:

=

∫

√

3

0

√

9

−

18

t

2

+

9

t

4

+

36

t

2

d

t

=

∫

√

3

0

√

9

+

18

t

2

+

9

t

4

d

t

=

∫

√

3

0

√

(

3

+

3

t

2

)

2

d

t

=

∫

√

3

0

(

3

+

3

t

2

)

d

t

=

3

t

+

t

3

∣

∣

√

3

0

=

3

√

3

+

3

√

3

=

6

√

3

Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.    

Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.

8 0
3 years ago
a fair dice is rolled. work out the probability of getting a number more than 2. give your answer in its simplest form​
Amanda [17]

Answer:

67% (rounded)

Step-by-step explanation:

Since there is 1-6,

There is 3,4,5,6 which is 4/6 chance being above 2.

2/3 = 66.6%  

5 0
3 years ago
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Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with
Nadusha1986 [10]

Answer:

Step-by-step explanation:

Given that a particular detection system has a 0.83 probability of detecting a missile attack.

Also each system is independent of the other to detect missile attack.

a)  the probability that a single detection system will detect an attack=0.83

b) the probability that at least one of the systems will detect the attack given two systems= 1-Prob no system detects

=1-(1-0.83)(1-0.83)\\\\=1-0.0289\\=0.9711

c)  If three systems are installed,  the probability that at least one of the systems  will detect the attack

= 1- none of the three systems detect attack

= (1-0.17^3)\\=1-0.004913\\=0.995087

d) We find that probability of detecting is more if we increase the system form 1 to 2 and 2 to 3.

Hence for safety and defence purpose multiple detection system is recommended.

7 0
3 years ago
Number System
Pie
C is the correct answer
4 0
2 years ago
A. Identify all pair of parallel in the diagram.
12345 [234]

Answer:

Parallel: G and F

perpendicular: G & H, F & H

Step-by-step explanation:

G and F are parallel because they will never cross, where as both are perpendicular to H because they intersect at 90°

4 0
3 years ago
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