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4 years ago

2x^4+x^3+6x+3>0 solve the system of inequalities

1 answer:

8 0

Solve for where it equals 0
use grouping

(2x^4+x^3)+(6x+3)=0
(x^3)(2x+1)+(3)(2x+1)=0
(x^3+3)(2x+1)=0
set equal to zero

x^3+3=0
x^3=-3
x=-∛3

2x+1=0
2x=-1
x=-1/2

now see where the inequality is true

evaluate for x=0
we get 3>0, true
so it it outside the range from -∛3 to -1/2

basically

x<-∛3 or x>-1/2
those are the solutionsets

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(1 point) A noted psychic was tested for ESP. The psychic was presented with 180 cards face down and was asked to determine if t

Luba_88 [7]

Answer:

a) $z=\frac{0.239 -0.2}{\sqrt{\frac{0.2(1-0.2)}{180}}}=1.308$

b) $p_v =P(z>1.308)=0.0954$

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=43 represent the correct guesses

$\hat p=\frac{43}{180}=0.239$ estimated proportion correct guesses

$p_o=0.2$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the ture proportion is higher than 0.2 or no.:

Null hypothesis: $p=0.2$

Alternative hypothesis: $p > 0.2$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Part a: Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.239 -0.2}{\sqrt{\frac{0.2(1-0.2)}{180}}}=1.308$

Part b: Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>1.308)=0.0954$

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Since that tangent line is drawn, this is really asking, "What's the slope of that line?"

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Answer:

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Step-by-step explanation:

7 squared is 49

8 squared is 64

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