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2 years ago

What is the leading coefficient of the polynomial function? y=-x^4+4x^2

Mathematics

1 answer:

attashe74 [19]2 years ago

6 0

<h3>Answer: -1</h3>

Explanation:

The given equation is the same as y = -1x^4+4x^2

The leading term is the term with the largest exponent, so it's -1x^4

The leading coefficient is the coefficient of the leading term.

In short, we circle the first coefficient we see. This is assuming that the polynomial is in standard form where the exponents decrease when going from left to right.

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What are considered measures of variability

shusha [124]

Statisticians use summary measures to describe the amount of variability or spread in a set of data. The most common measures of variability are the range, theinterquartile<span> range (</span>IQR<span>), </span>variance<span>, and standard deviation. This is from google btw</span>

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3 years ago

A wire 30 feet long is stretched from the top of a flagpole to the ground at a point 15 feet from the base of the pole. How high

sweet-ann [11.9K]

Answer:

28.3

Step-by-step explanation:

Use the Pythagorean Theorem to solve for the answer. 10^2 + x^2 = 30^2

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3 years ago

Read 2 more answers

Identify the property that the statement illustrates

oksian1 [2.3K]

Answer:

6 units away from 0.

Step-by-step explanation:

when move to 6 you count the units.

5 0

3 years ago

According to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on ave

ki77a [65]

Answer:

The value of test statistics is 1.06.

Step-by-step explanation:

We are given that according to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on average. A random sample of 11 American teenagers was surveyed and the mean amount of time per month each teenager watched social media posts was 15.6. This data has a sample standard deviation of 2.5.

We have to test if the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year or not.

Let, NULL HYPOTHESIS, $H_0$ : $\mu$ = 14.8 hours {means that the mean amount of time American teenagers watch social media posts per month is same as the mean amount of time last year}

ALTERNATE HYPOTHESIS, $H_1$ : $\mu$ > 14.8 hours {means that the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year}

The test statistics that will be used here is One-sample t-test;

T.S. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean amount of time per month each teenager watched social media posts = 15.6 hours

$s$ = sample standard deviation = 2.5 hours

n = sample of teenagers = 11

So, <u>test statistics</u> = $\frac{15.6 - 14.8}{\frac{2.5}{\sqrt{11} } }$ ~ $t_1_0$

= 1.06

Hence, the value of test statistics is 1.06.

5 0

3 years ago

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

3 years ago