Matthew wants to estimate the mean height of students attending his college. He records the heights of 100 randomly selected students attending the college. What is the population?
Select the correct answer below:


the mean height of the randomly selected students
the mean height of all students attending the college
the 100 randomly selected students
all the students attending the college
the heights of the randomly selected students

First, rewrite

[tex]\dfrac{x^2+5x+4}{x^2-3x+7} = \dfrac{(x^2-3x+7)+(8x-3)}{x^2-3x+7} = 1 + \dfrac{8x-3}{x^2-3x+7}[/tex]

Next, we have

[tex]\dfrac{x^2-3x+7}{8x-3} = \dfrac x8 - \dfrac{21}{64} + \dfrac{385}{512x-192}[/tex]

so we can further rewrite

[tex]\dfrac{x^2+5x+4}{x^2-3x+7} = 1 + \dfrac1{\frac x8 - \frac{21}{64} + \frac{385}{512x-192}}[/tex]

The idea behind all this is to get the limand into a form resembling the limit definition of the constant e, which is

[tex]\displaystyle e = \lim_{x\to\infty} \left(1+\frac1x\right)^x[/tex]

The next step is to make the substitution,

[tex]y = \dfrac x8 - \dfrac{21}{64} + \dfrac{385}{512x-192}[/tex]

Solving for x gives two solutions,

[tex]x = \dfrac{8y+3\pm\sqrt{64y^2+36y-19}}2[/tex]

but we want to have y approaching infinity, just like in the definition for e, which is achieved only by the solution with the positive square root. (You can check for yourself that the other solution instead approaches 3/4.)

So, our limit is equivalent to

[tex]\displaystyle \lim_{y\to\infty} \left(1+\frac1y\right)^{\frac{8y+3+\sqrt{64y^2+36y-19}}2}[/tex]

[tex]\displaystyle \lim_{y\to\infty} \left(1+\frac1y\right)^{\frac{8y+3+8y\sqrt{1+\frac{36}{64y}-\frac{19}{64y^2}}}2}[/tex]

[tex]\displaystyle \lim_{y\to\infty} \left(1+\frac1y\right)^{4y\left(1+\sqrt{1+\frac{36}{64y}-\frac{19}{64y^2}}\right)+\frac32}[/tex]

[tex]\displaystyle \lim_{y\to\infty} \left(\left(1+\frac1y\right)^y\right)^{4\left(1+\sqrt{1+\frac{36}{64y}-\frac{19}{64y^2}}\right)+\frac32}[/tex]

[tex]\displaystyle \lim_{y\to\infty} \left(\left(1+\frac1y\right)^y\right)^{4\left(1+\sqrt{1+\frac{36}{64y}-\frac{19}{64y^2}}\right)} \cdot \lim_{y\to\infty} \left(1+\frac1y\right)^{\frac32}[/tex]

Next, we use the fact that

[tex]\displaystyle \lim_{x\to\infty} f(x)^{g(x)} = \left( \lim_{x\to\infty}f(x)\right)^{\lim\limits_{x\to\infty}g(x)}[/tex]

Now, the "base" limit is e, while the "exponent" limit is

[tex]\displaystyle \lim_{y\to\infty} 4\left(1+\sqrt{1+\frac{36}{64y}-\frac{19}{64y^2}}\right) = 4(1+\sqrt{1+0+0}) = 8[/tex]

and the remaining limit is simply

[tex]\displaystyle \lim_{y\to\infty} \left(1+\frac1y\right)^{\frac32} = (1+0)^{\frac32} = 1[/tex]

So, we end up with

[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x^2+5x+4}{x^2-3x+7}\right)^x = e^8 \cdot 1 = \boxed{e^8}[/tex]

Answer:

Recipes 1 and 3 will make the same amount

Answer:

Step-by-step explanation:

you first have to find two points that pass directly through the graph in this case we have (1,4) and (4,-4)

Now we use y2-y1 divided by x2-x1

in this case -4 - 4 (y2-y1) and 4 - 1 (x2-x1)

giving you -8 and 3

so try putting -8/3 as your answer this is what i would put sorry if it is incorrect

Answer:

For 9., the answer is x = -6

For 10., the answer is x = 6

For 11., the answer is x = -7

For 12., the answer is x = -6

Answer:

-5.25

Step-by-step explanation:

There are 4 tick marks between every next integer, so you know that they are counting at a value of 0.25 per tick mark. D is at negative 5 plus negative 0.25, with D's position being at -5.25

Answer: 6 days

Step-by-step explanation:

if you make them into common denominators, it would be 6/8, so it would last 6 days

Answer:

6 days.

Step-by-step explanation:

First, make each fraction have a like denominator

3/4 × 2/2 = 6/8

Then, subtract the 1/8 for each day

6/8 - 1/8 = 5/8

You can either write this out can count how many times you do this, or since were subtracting 1/8 every time, and we have 6/8, you can see that there is enough food to feed the dog for 6 days.

Answer:

I'm assuming the answer is 400, I'm not quite sure

Answer:

Y = 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is an isosceles triangle, since XY and ZY are the same length. That means by the Isosceles Triangle Theorem, angle X and angle Z are congruent. Since the measures of a triangle by the Triangle Angle-Sum Theorem have to add up to equal 180 degrees, then angle Y, the vertex angle, measures

180 - 34 - 34 which is 112, choice A.

the answer is A. 112 hope this helps

Answer:

2 hours 6 minutes

Step-by-step explanation:

40% of 315 is 126 [miles]

126 miles = 126 minutes, since he went at 60 miles per hour [one mile per minute]

126 minutes = 2 hours 6 minutes

So, 2 hours 6 minutes, or 126 minutes.

Answer:

mn

Step-by-step explanation:

Step-by-step explanation:

In pictures answered .

Answer:

1,200

Step-by-step explanation:

3x2=6 and 6x200=1,200

Answer:

Step-by-step explanation:

Geometric sequence.

Each term is obtained by multiplying 2. So, it is geometric sequence

2 = 1*2

4 = 2*2

8 = 4 *2

16 = 8 *2

Answer:

9^-4 + 2^-3

Step-by-step explanation:

It can't be broken down anymore under the law of indices.

ANSWER

this answer is 33 pls picke me brainliest

Answer:

a is 2-1= 1  b is 1-2=1   c is 1 its simple "liahthegoddest'

9514 1404 393

Answer:

Step-by-step explanation:

The translation of a parent function f(x) by (h, k) gives the function ...

  g(x) = f(x -h) +k . . . . . h units right, k units up

Reflection across the x-axis multiplies the function value by -1.

__

a) The square root function is translated 4 left and 2 down. The equation of the graph is ...

  y = √(x +4) -2

__

b) The equation of the parabola is reflected across the x-axis and translated right 2 and down 3.

  y = -(x -2)^2 -3

Answer:

Well I'm not sure what your answer choices are but based on the question I can tell you this:

If you have 4 wood and 5 other materials then you have 9 total materials.

So if you have 4 wood then you have a 4/9 chance of choosing wood.

And you have a 5/9 chance of choosing another material

So based on that, you would be more likely to choose another material, that is not wood.

Answer:

It will take 4 hours and 20 minutes to hike the rest of the 7 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x be the number of hours worked

Let C = the charge made by the first company

Let c  = the charge made by the second company

You want to know when the costs will be =.

Equations

C = 376 + 12x

c = 280 + 15x

Solution

Make the two right sides equal

376 + 12x = 280 + 15x            Subtract 12x from both sides

376 = 280 + 15x - 12x             Combine like terms on the right

376 = 280 + 3x                       Subtract 280 from both sides

376 - 280 = 3x                        Combine

96 = 3x                                    Divide both sides by 3

32 = x

Each company would have to work 32 hours to get the same amount to be charged.

C = 376 + 12x

C = 376 + 12*32

C = 376 + 384

C = 760

The amount each would charge is 760

Answer:

2062 4/11

Step-by-step explanation:

Okay so assuming 2003 4/11 is a mixed number, we just add:

2003 4/11 + 59 = 2062 4/11

Hope this helps:)

Answer:his mom sounds like a push over

Step-by-step explanation: she’s limiting his video games dude

Answer:

2556 feet squared

Step-by-step explanation:

Area is calculated by multiplying length times width. 71x36=2556

Answer:

(-7)*(-8)

Step-by-step explanation:

Two negatives make a postive so 7*8=56 and 4*6=24.

Hello! The missing number is -1.

Notice that we add 1 every time:

-3+1=-2

-2+1=-1

-1+1=0

Hope this helps!

~Just a felicitous girlie

#HaveAnAwesomeDay

[tex]SilentNature :)[/tex]