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3 years ago

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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Answer:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

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

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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)

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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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