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3 years ago

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?

Mathematics

2 answers:

ryzh [129]3 years ago

7 0

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4. x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

jeyben [28]3 years ago

7 0

Answer:

The graph touches, but does not cross, the x–axis at x = .4

The graph of the function crosses the x–axis at x = .0

Step-by-step explanation:

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Does this set of ordered pairs represent a function? Why or why not?

belka [17]

Answer:

Step-by-step explanation:

Recall that for a function to be valid, each input value of x must give us one and only one unique output value for y.

in this case we can see that one of the data sets is (3,-1)

which means that an input of 3 gave an output of -1

but we also see that another data set (3,1)

in this case an input of 3 gave an output of 1.

Because the same x input gives 2 different y outputs, this is not a function.

the answer is A

3 0

3 years ago

(1 point) Suppose we want a 95% confidence interval for the average amount spent on books by freshmen in their first year at col

Ne4ueva [31]

Answer:

a) $n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

b) For this case if we see the formula for the margin of error

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

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean

$\sigma=16$ represent the population standard deviation

n represent the sample size

Solution to the problem

Part a

The margin of error is given by this formula:

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

And on this case we have that ME =5 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 now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

Part b

For this case if we see the formula for the margin of error

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

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

5 0

3 years ago

A box of oranges weighs 4 kg. if one orange weighs 80 g how many oranges are in the box

stepladder [879]

There would be 20 oranges in each box

6 0

3 years ago

Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if hi

charle [14.2K]

64,000 I believe. What I did was find the area so 4*4 =16. 1000/16 = 62.5 earthworms per square foot. So if the side is 8 times longer then 8*4= 32 feet per side and to find the area of that it's 32*32 = 1024 feet squared. So 62.5 * 1024 =64,000

6 0

3 years ago

Read 2 more answers

Can someone please answer this question please answer it correctly and please show work please help me I need it

I am Lyosha [343]

Answer:

the answer to this question is the number 8

5 0

3 years ago