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2 years ago

What is the justification for each step in the solution of the equation?

Mathematics

1 answer:

Reil [10]2 years ago

8 0

Step 1 : (5x-4)/2 = 2x-1 [Given]

Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1) [Multiplicative Property of Equality i.e. by multiplying both sides of the equation by same number]

Step 3 : (5x-4) = 4x-2 [By Distributive Property]

Step 4 : 5x - 4 + 4 = 4x - 2 + 4 [By addition property of equality i.e. by adding both sides of the equation by same number]

⇒ 5x = 4x + 2

Step 5 : 5x - 4x = 4x + 2 - 4x [By subtraction property of equality i.e. by subtracting both sides of the equation by same number]

⇒ x = 2

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June served 4/9 of 18 liters of fruit punch. How many liters does she have left?

victus00 [196]

She has 10 liters left. Find 4/9 of 18 by multiplying 4/9 and 18. 4/9 of 18 is 8, so she served 8 of the 18, leaving 10 liters.

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3 years ago

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The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

Viefleur [7K]

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

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.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then

$n = 1537, \pi = \frac{353}{1537} = 0.2297$

95% confidence level

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

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507$

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

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2 years ago

Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twe

alina1380 [7]

Just to remove ambiguities, the bar over the expression means it's repeating itself to infinity.

$\bf 2.888\overline{8}\impliedby \textit{now say, let's make }x=2.888\overline{8}
\\\\\\
\textit{and multiply it by 10, to move over the 8 to the left}
\\\\\\
\begin{array}{llll}
10x&=&10\cdot 2.888\overline{8}\\
&&28.88\overline{8}\\
&&26+2.888\overline{8}\\
&&26+x
\end{array}\implies 10x=26+x
\\\\\\
9x=26\implies x=\cfrac{26}{9}$

notice, the idea being, you multiply it by 10 at some power, so that you move the "recurring decimal" to the other side of the point, and then split it with a digit and "x".

now, you can plug that in your calculator, to check what you get.

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2 years ago

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The function f(x) is the cost of renting a car where x represents the number of miles driven.

Ghella [55]

Answer:

The correct option is the third: All positive real numbers

Step-by-step explanation:

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x> 0

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2 years ago

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Vitek1552 [10]

I'm not sure if it's 10x or 10 times a number

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3 years ago

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