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oksian1 [2.3K]
2 years ago
8

X + 4 = x2? Assume x greater-than 0

Mathematics
1 answer:
inysia [295]2 years ago
6 0

Answer:

The  value comes out to be  

x=\frac{1}{2}+\frac{\sqrt{17}}{2}

Step-by-step explanation:

The quadratic equation is an equation containing a single variable of degree 2. Its general form is ax^{2} +bx + c=0.

The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

The equation we are given is :x+4=x^{2} \\x^{2} -x-4=0\\

We know the formula as :

x=[-b±\sqrt{b^{2}-4ac}] ×\frac{1}{2a}

x=[-(-1)±\sqrt{(-1)^{2} -4(1)(-4)}]×\frac{1}{2(1)}

x=\frac{1}{2} ±\frac{\sqrt{17} }{2} }

Since x≥0

Other negative option is neglected

x=\frac{1}{2}+\frac{\sqrt{17}}{2}

Learn more about quadratic equations - brainly.com/question/1214333

#SPJ10

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Answer:

Step-by-step explanation:

Hello!

The variables of interest are:

X₁: Number of cases of polio observed in kids that received the placebo vaccine.

n₁= 201299 total children studied

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X₂: Number of cases of polio observed in kids that received the experimental vaccine.

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You have to test if the population proportions of children who contracted polio in both groups are different: p₂ ≠ p₁

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H₀: p₂ = p₁

H₁: p₂ ≠ p₁

α: 0.05

Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

Sample proportion placebo p'₁= x₁/n₁= 110/201299= 0.0005

Sample proportion vaccine p'₂= x₂/n₂= 33/200745= 0.0002

Pooled sample proportion p'= (x₁+x₂)/(n₁+n₂)= (110+33)/(201299+200745)= 0.0004

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Z_{\alpha/2}= Z_{0.025}= -1.96

Z_{1-\alpha /2}= Z_{0.975}= 1.96

Then if Z_{H_0} ≤ -1.96 or if Z_{H_0} ≥ 1.96, the decision is to reject the null hypothesis.

If -1.96 < Z_{H_0} < 1.96, the decision is to not reject the null hypothesis.

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b)

H₀: p₂ = p₁

H₁: p₂ ≠ p₁

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Z= \frac{(p'_2-p'_1)-(p_2-p_1)}{\sqrt{p'[\frac{1}{n_1} +\frac{1}{n_2} ]} }

The value of Z_{H_0}= -4.76 doesn't change, since we are working with the same samples.

The only thing that changes alongside with the level of significance is the rejection region:

Z_{\alpha /2}= Z_{0.005}= -2.576

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Then if Z_{H_0} ≤ -2.576or if Z_{H_0} ≥ 2.576, the decision is to reject the null hypothesis.

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⇒ Z_{H_0}= -4.76, the decision is to reject the null hypothesis.

c)

Remember the level of significance (probability of committing type I error) is the probability of rejecting a true null hypothesis. This means that the smaller this value is, the fewer chances you have of discarding the true null hypothesis. But as you know, you cannot just reduce this value to zero because, the smaller α is, the bigger β (probability of committing type II error) becomes.

Rejecting the null hypothesis using different values of α means that there is a high chance that you reached a correct decision (rejecting a false null hypothesis)

I hope this helps!

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