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igor_vitrenko [27]

3 years ago

15

Sarita showed the steps to solving the equation. 5 (x minus 3) + 7 (x + 4) = 73 Steps Sarita's Solution Sarita's Verification 1

5 x minus 15 + 7 x + 28 = 73 5 (5 minus 3) + 7 (5 + 4) = 73. 5 (negative 2) + 7 (9) = 73. Negative 10 + 63 = 73. 53 not-equal-to 73. 2 (5 + 7) x + (negative 15 + 28) = 73 3 12 x + 13 = 73 4 12 x + 60 5 x = 5 When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?

2 answers:

valentinak56 [21]3 years ago

4 0

Answer:

Sarita’s solution is correct. She made an error in her verification. Sarita was supposed to add the 5 and 7 in the first step.

Step-by-step explanation:

Given the following equation:

The steps to solve it are:

5(x-3)+7(x+4)-73

1. Apply the Distributive property:

5x-15+7x+28=73

2. Add the like terms:

12x+13=73

3. Subtract5 13 from both sides of the equation:

12x+13-(13)=73-(13

12x=60

4. Divide both sides of the equation by 12:

12r/12 = 60/12

x = 5

To verify it, let's substitute into the equation:

5(5-3)+7(5+4)=73

Evaluating, we get:

5(2)+7(9)=73

10+63=73

73=73

Based on this, we can determine that Sarita's solution is correct, but she made an error in her verification (Observe that 5-3 is not equal to -2 )

ladessa [460]3 years ago

4 0

Answer:

Sarita’s solution is correct. She made an error in her verification. Sarita was supposed to add the 5 and 7 in the first step.

Step-by-step explanation: i did it in edge

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Answer:

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,35)".And we see that $t_{\alpha/2}=2.03$

Now we have everything in order to replace into formula (1):

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

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