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3 years ago

Let a and b 2 positive real number such that a

Mathematics

1 answer:

lilavasa [31]3 years ago

7 0

Answer:

Proved

Step-by-step explanation:

Given

Integers: a and b

Where $a < b$

Required

Show that $a^n < b^n$

We start by writing out the given expression

$a < b$

Then, take nth root of both sides

$a^n < b^n$

For instance:

Let a = 2, b = 2 and n = 4

First

Since $2 < 3$

Then

$2^4 < 3^4$

$16 < 81$

Proved

<em>This is so for all positive values of a,b and n where a < b</em>

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Line segment AB has a midpoint, M at (2,6). If point B is located at (-3,10), what is location of point A?

Alex787 [66]

Answer is D.
As M is the midpoint of A and B; denote A(x,y); then x and y have to matched the two equations below:
(x- 3) : 2 = 2 <=> x = 7 and
(y +10) : 2 = 6 <=> y = 2
Conclusion : A (7,2)

4 0

3 years ago

Find the missing factor.<br> n(n-3)+2(n-3)=( )(n-3)

elena-s [515]

This is the concept of quadratic equations. We are required to find the missing factor in the partially factored quadratic equation given;
n(n-3)+2(n-3)=()(n-3)
here we proceed as follows;
n(n-3)+2(n-3)
when we factor this we get:
(n-3)(n+2)
this can be written as:
(n+2)(n-3)
The answer is (n+2)

3 0

3 years ago

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer

AlladinOne [14]

Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

Step-by-step explanation:

Previous concepts

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".

$\bar X=4$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=100 represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$

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

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

4 0

3 years ago

Company A had a loss of $255 in January. Company B had a profit of $162 in January. What was the difference between the profits

Julli [10]

Answer:

The difference of the profit of two companies is $ 417

Step-by-step explanation:

Given as :

The company A loss amount in January = $ 255

The company B profit amount in January = $ 162

Let the difference between there profits = x

So, x = company B profit - ( company A profit)

I.e x = company B profit - ( - company A loss)

Or, x = $ 255 + $162

∴ x = $ 417

Hence The difference of the profit of two companies is $ 417 . Answer

6 0

3 years ago

Jan has $245.50 to spend on home repairs. The repairman charges $75 for the initial visit and $35 per hour or any part of an hou

Murrr4er [49]

Answer:

Step-by-step explanation:

4 0

3 years ago