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3 years ago

Which statement best describes the graph of this polynomial function f(x)=x^4+x^3-2x^2

Mathematics

1 answer:

jenyasd209 [6]3 years ago

3 0

Answer:

See below description.

Step-by-step explanation:

The function $f(x) = x^4+x^3-2x^2$ has the following characteristics:

Factors: $x^2(x+2)(x-1)$
Zeros/roots: x=0, x=-2, amd x=1
Positive leading coefficient
Graph starts up, curves down through -2 on the x-axis and back up to 0 where it touches and curves down and back up again again. It comes down back through 1 and crosses.
Its graph s the shape of a W.
It has minimum values at -2.83 and -0.397

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A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decre

Dmitry [639]

Using the t-distribution, it is found that since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

At the null hypothesis, it is tested if the consumption is not different, that is, if the subtraction of the means is 0, hence:

$H_0: \mu_1 - \mu_2 = 0$

At the alternative hypothesis, it is tested if the consumption is different, that is, if the subtraction of the means is not 0, hence:

$H_1: \mu_1 - \mu_2 \neq 0$

Two groups of 22 patients, hence, the standard errors are:

$s_1 = \frac{45.1}{\sqrt{22}} = 9.6154$

$s_2 = \frac{26.4}{\sqrt{22}} = 5.6285$

The distribution of the differences is has:

$\overline{x} = \mu_1 - \mu_2 = 52.1 - 27.1 = 25$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{9.6154^2 + 5.6285^2} = 11.14$

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{25 - 0}{11.14}$

$t = 2.2438$

The p-value of the test is found using a two-tailed test, as we are testing if the mean is different of a value, with t = 2.2438 and 22 + 22 - 2 = 42 df.

Using a t-distribution calculator, this p-value is of 0.0302.

Since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

A similar problem is given at brainly.com/question/25600813

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Step-by-step explanation:

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3 years ago

Read 2 more answers

What is the solution of the equation when solved using the quadratic formula?<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B

Artemon [7]

Answer:

$x=\pm2i\sqrt{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

Imaginary Numbers: √-1 = i

Step-by-step explanation:

Step 1: Define Equation

x² + 20 = 0

Step 2: Identify Variables

a = 1

b = 0

c = 20

Step 3: Find roots x

Substitute: $x=\frac{-0\pm\sqrt{0^2-4(1)(20)} }{2(1)}$
Exponents: $x=\frac{-0\pm\sqrt{0-4(1)(20)} }{2(1)}$
Multiply: $x=\frac{-0\pm\sqrt{0-80} }{2}$
Subtract: $x=\frac{\pm\sqrt{-80} }{2}$
Factor: $x=\frac{\pm\sqrt{-1} \sqrt{80} }{2}$
Simplify: $x=\frac{\pm4i\sqrt{5} }{2}$
Divide: $x=\pm2i\sqrt{5}$

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3 years ago

chubhunter [2.5K]

MNOP is similar to QRST with ratio of 5:4. That means the MP:QT ratio would also be 5:4

The length of QT would be
MP/QT = 5/4
85mm/QT=5/4
85mm*4= 5*QT
5QT= 340
QT=68mm

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vovikov84 [41]

The answer is in the attachment.

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