Suppose f(x) = x2 and g(x) = (4x)2. Which statement best compares the graph

The graph below shows two polynomial functions, f(x) and g(x): 6 f(x) 5 V -3 -2 2 3 4 g(x) -4 -5 -7 Which of the following state

olya-2409 [2.1K]

The function f(x) is a parabola. We can tell it is a even degree polynomial because the axis of reflection is a vertical line (it passes through the vertex).

In this case, f(x) has a double root at (0,1), but a parabola will have up to 2 roots.

It has a positive leading (quadratic in this case) coefficient, because it is concave up.

In the case of g(x), we can tell it is an odd degree polinomial, as it has a axis of reflection that is a line with slope m=-1. It is like it is reflected two times, one on an horizontal line and then on a vertical line.

The leading coefficient is positive because g(x) tends to infinity when x increases, and the leading coefficient is the one that has more weight for large values of x, so it has to be positive to have positive values of g(x).

Then, we can go through the statements.

O f(x) is an even degree polynomial with a negative leading coefficient. FALSE (the leading coefficient is positive)

O g(x) is an even degree polynomial with a negative leading coefficient. FALSE (it is an odd degree polynomial)

O f(x) is an odd degree polynomial with a positive leading coefficient. FALSE (it is an even degree polynomial).

O g(x) is an odd degree polynomial with a positive leading coefficient. TRUE

7 0

1 year ago

Write this number in expanded form using fractions and decimals 0.362

dalvyx [7]

0.362=

0.3+0.06+0.002
and
362/1000
and
0.362

3 0

3 years ago

Read 2 more answers

Item 4

olga nikolaevna [1]

Answer:

24

Step-by-step explanation:

5 0

3 years ago

What is the answer <br> 6*6^2

fomenos

The answer is 6^3 luvvvv

8 0

3 years ago

Read 2 more answers

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books check

Verdich [7]

Answer:

$n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11$

So the answer for this case would be n=11 rounded up to the nearest integer

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 (variable of interest)

$\sigma =150$ represent the population standard deviation

n represent the sample size

Solution to the problem

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

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

The confidence interval for this case is given by: (740, 920)

We can find the estimate for the mean and we got:

$\bar X = \frac{740+920}{2} = 830$

and the margin of error is given by :

$ME = \frac{920-740}{2}= 90$

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 =90 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (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:

$n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11$

So the answer for this case would be n=11 rounded up to the nearest integer

5 0

3 years ago