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Sonja [21]
3 years ago
14

This is Josh’s work and solution for the equation x^2-6x-7=0:

Mathematics
2 answers:
inn [45]3 years ago
7 0

Answer:

Step-by-step explanation:

the solution is right

x^2-6x-7=0:

x^2-6x-7=0 (add 7 to both sides)

x^2-6x=7

x^2-6x+9=7+9  (the coefficient of x² will be used to divide all sides)for here its 1, it will remain same ,

then we get the coefficient of x, divide it by 2 and square it and add it to both sides

which is like these

x²-6x=7

the coefficient of x is -6

-6/2 = -3, square it (-3)² = 9

then add 9 to both sides

x^2-6x+9=7+9

simplifiy the squares on the left hand side

x²+9 = (x-3)²

(x-3)^2=16

√(x-3)^2 )=±√16

x-3=± 4

x=-3±4

then simplify each sign

x=-3+4            x=-3-4

x=1                   x=-7

ozzi3 years ago
3 0

Answer: his solution was incorrect.

Step-by-step explanation:

The given equation is expressed as

x² - 6x - 7 = 0

Josh was applying the method of completing the square. Since the coefficient of the first term is 1, the next step he took was to add the square of the coefficient of x to the left hand side and the right hand side of the equation which is correct.

After adding, he took the square root of the left hand side and the right hand side of the equation which is also correct.

Finally, he made a mistake by adding - 3 instead of 3 to the left hand side and the right hand side of the equation. Therefore, his solution is incorrect

The right step is

x - 3 = ± 4

x = 3 ± 4

x = 3 + 4 or x = 3 - 4

x = 7 or x = - 1

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Step-by-step explanation:

Because -7.045 is closer to 0

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A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCI/L of radon. The resulting reading
valkas [14]

Answer:

Null hypothesis:\mu = 100  

Alternative hypothesis:\mu \neq 100  

t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921  

p_v =2*P(t_{11}  

Step-by-step explanation:

1) Data given and notation  

Data: 105.6, 90.9, 91.2, 96.9, 96.5, 91.3, 100.1, 105.0, 99.6, 107.7, 103.3, 92.4

We can calculate the sample mean and deviation for this data with the following formulas:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}

The results obtained are:

\bar X=98.375 represent the sample mean  

s=0.6.109 represent the sample standard deviation  

n=12 sample size  

\mu_o =100 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to 100pCL/L, the system of hypothesis are :  

Null hypothesis:\mu = 100  

Alternative hypothesis:\mu \neq 100  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921  

4) P-value  

First we need to find the degrees of freedom for the statistic given by:

df=n-1=12-1=11

Since is a two sided test the p value would given by:  

p_v =2*P(t_{11}  

5) Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significant different from 100 at 5% of significance.  

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Answer:

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