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harkovskaia [24]
3 years ago
5

Which of the following of x and y would make up the following expression represent a real number? (4+5i)(x+yi)

Mathematics
1 answer:
salantis [7]3 years ago
8 0

Answer:

x = 4 and y = - 5

Step-by-step explanation:

note that the product of a complex number and it's conjugate is real

That is

(a + bi)(a - bi) where a, b are real

= a² - abi + abi - b²i²

= a² + b² ← a real number

For (4 + 5i)(x + yi) to be real

we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i

(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5



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3 years ago
Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st
Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)  

b) n=523 rounded up to the nearest integer  

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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".  

\bar X=530 represent the sample mean for the sample  

\mu population mean

s=70 represent the sample standard deviation  

n=48 represent the sample size (variable of interest)  

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that z_{\alpha/2}=2.01  

Now we have everything in order to replace into formula (1):  

530-2.01\frac{70}{\sqrt{48}}=509.692  

530+2.01\frac{70}{\sqrt{48}}=550.308  

So on this case the 95% confidence interval would be given by (509.592;550.308)  

Part b

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (a)  

Assuming that \hat \sigma =s

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (b)  

The critical value for 95% of confidence interval is provided, z_{\alpha/2}=1.96, replacing into formula (b) we got:  

n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523  

So the answer for this case would be n=523 rounded up to the nearest integer  

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They're usually 365 days in each year every 4th year is call a leap year and has one extra day in February how many days are the
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Answer:

Total number of days in 8 years is 2,922 days.

Step-by-step explanation:

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Number of days in a  leap year  =  366 days

Also, Leap year comes exactly ONE TIME in every FOUR YEARS.

⇒ In every consecutive 4 years, 1 year is a leap year.

⇒ So, number of leap years in 8 years  =   2

Now, 8 Years  = 6 Normal years +  2 leap Years

<u>Number of days in 6 normal years</u>

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= 2 x ( Number of days in a leap year)

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So, Total number of days in 8 years

= Number of days in 6 regular years  + Number of days in 2 leap years

= 2,190 days  +  732 days

= 2,922 days

Hence, total number of days in 8 years is 2,922 days.

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The moon is about 240,000 miles from the earth what is the distance right now as a whole number multiplied by a power of 10
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