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Bogdan [553]
2 years ago
14

Solve for x ~

3 \: (14 - 5x) =16 - 12x" alt="3 \: (14 - 5x) =16 - 12x" align="absmiddle" class="latex-formula">

thankyou ~​
Mathematics
2 answers:
lesya692 [45]2 years ago
6 0

3(14 - 5x) = 16 - 12x

Distribute 3 throught the parentheses

42 - 15x = 16-12x

Move the variable to the left-hand side and change its sign

42 - 15x + 12x = 16

Move the constant to the right-hand side and change its sign

- 15x+12x=16 - 42

Collect like terms

- 3x =  - 26

Divide both sides of the equation by -3

\boxed{x =  \frac{26}{3} }

Andrews [41]2 years ago
3 0

  • \sf \: 3(14 - 5x) = 16 - 12x

  • \sf \: 42 - 15x = 16 - 12x

  • \sf \:  - 15x + 12x = 16 - 42

  • \sf \:  - 3x =  - 26

  • \sf x =  \frac{ \cancel -26}{  \cancel- 3}

  • \large   \boxed{\sf \underline{ \color{green}x =  \frac{26}{ 3} }}

<h3>Hope Helps~</h3>
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a. The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

b. Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

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Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.

This means that n = 1664, \pi = \frac{939}{1664} = 0.5643

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So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

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\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 + 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.588

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(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?

Yes, because the confidence interval is entirely above 0.5.

Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

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