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2 years ago

What is the median number for the numbers 4 8 10 5 & 9

2 answers:

6 0

List the numbers from lease to greatest:

4 5 8 9 10

Find the number in the middle .

Since there are 5 numbers, the 3rd one is the median, which would be 8.

PolarNik [594]2 years ago

4 0

I think the answer is 10.

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5 0

2 years ago

Consider the following function.

Kryger [21]

Answer:

See below

Step-by-step explanation:

I assume the function is $f(x)=1+\frac{5}{x}-\frac{4}{x^2}$

A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, $x=0$ is the only vertical asymptote.

B) Set the first derivative equal to 0 and solve:

$f(x)=1+\frac{5}{x}-\frac{4}{x^2}$

$f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}$

$0=-\frac{5}{x^2}+\frac{8}{x^3}$

$0=-5x+8$

$5x=8$

$x=\frac{8}{5}$

Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:

$f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}$

$f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3$

Therefore, the function increases on the interval $(0,\frac{8}{5})$ and decreases on the interval $(-\infty,0),(\frac{8}{5},\infty)$ .

C) Since we determined that the slope is 0 when $x=\frac{8}{5}$ from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, $f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}$ , meaning there's an extreme at the point $(\frac{8}{5},\frac{41}{16})$ , but is it a maximum or minimum? To answer that, we will plug in $x=\frac{8}{5}$ into the second derivative which is $f''(x)=\frac{10}{x^3}-\frac{24}{x^4}$ . If $f''(x)>0$ , then it's a minimum. If $f''(x)$ , then it's a maximum. If $f''(x)=0$ , the test fails. So, $f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}$ , which means $(\frac{8}{5},\frac{41}{16})$ is a local maximum.

D) Now set the second derivative equal to 0 and solve:

$f''(x)=\frac{10}{x^3}-\frac{24}{x^4}$

$0=\frac{10}{x^3}-\frac{24}{x^4}$

$0=10x-24$

$-10x=-24$

$x=\frac{24}{10}$

$x=\frac{12}{5}$

We then test where $f''(x)$ is negative or positive by plugging in test values. I will use -1 and 3 to test this:

$f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34$ , so the function is concave down on the interval $(-\infty,0)\cup(0,\frac{12}{5})$

$f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0$ , so the function is concave up on the interval $(\frac{12}{5},\infty)$

The inflection point is where concavity changes, which can be determined by plugging in $x=\frac{12}{5}$ into the original function, which would be $f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}$ , or $(\frac{12}{5},\frac{43}{18})$ .

E) See attached graph

5 0

2 years ago

What is the slope of the line represented by the equation y =-1/2x + 1/4?

jarptica [38.1K]

The slope is -1/2x in this case because it is always next to a variable y=mx+b.

4 0

2 years ago

the perimeter of the triangle shown to the right is 154 meters. find the lenght of each side. (4x)m (7x+2)m (7x+8)m

yaroslaw [1]

The first to find the length of each side, we have to find the value of x :
$(4x) + (7x + 2) + (7x+8) = 154$

$4x + 7x + 7x + 2+8 = 154$

$18x +10 = 154$

$18x = 154 - 10$

$18x = 144$

$x = \frac{144}{18}$

$\boxed{x=8}$

Solution First side :
 $(4x)m = (4 \cdot 8)m = 32\ m$ 

Solution Second Side :
 $(7x+2)m = (7(8)+2)m = 58\ m$ 

Solution Third Side :
 $(7x+8)m = (7(8)+8)m = 64\ m$

6 0

2 years ago

Read 2 more answers

I need HELPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! please

Alja [10]

Step-by-step explanation:

you simplify your answer and write it as proper fraction

6 0

3 years ago