Estimate the square root to the nearest (a) integer and (b) tenth.

15x-7=2+12x I need help with this

Amanda [17]

Answer:

$\huge{ \boxed{ \bold{ \tt{x = 3}}}}$

<h3>♁ Question : Solve for x</h3>

15x - 7 = 2 + 12x

<h3>♁ Step - by - step explanation</h3>

$\text{15x - 7 = 2 + 12x}$

Move 12x to L.H.S ( Left Hand Side ) and change it's sign

➛ $\sf{15x - 12x - 7 = 2}$

Move 7 to R.H.S ( Right Hand Side) and change it's sign

➛ $\sf{15x - 12x = 2 + 7}$

Subtract 12x from 15x

Remember that only coefficients of like terms can be added or subtracted.

➛ $\sf{3x = 2 + 7}$

Add the numbers : 2 and 7

➛ $\sf{3x = 9}$

Divide both sides by 3

➛ $\sf{ \frac{3x}{3} = \frac{9}{3}}$

➛ $\boxed{ \bold{ \sf{x = 3}}}$

The value of x is $\boxed{ \sf{3}}$

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☄ Now, let's check whether the value of x is 3 or not!

<h3>☥ Verification :</h3>

$\sf{15x - 7 = 2 + 12x}$

$\dashrightarrow{ \sf{15 \times 3 - 7 = 2 + 12 \times 3}}$

$\dashrightarrow{ \sf{45 - 7 = 2 + 36}}$

$\dashrightarrow{ \sf{38 = 38}}$

L.H.S = R.H.S ( Hence , the value of x is 3 ).

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<h3>✒ Rules for solving an equation :</h3>

If an equation contains fractions ,multiply each term by the L.C.M of denominators.
Remove the brackets , if any.
Collect the terms with the variable to the left hand side and constant terms to the right hand side by changing their sign ' + ' into ' - ' and ' - ' into ' + ' .
Simplify and get the single term on each side.
Divide each side by the coefficient of variable and then get the value of variable.

Hope I helped!

Have a wonderful time ! ツ

~TheAnimeGirl

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A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard d

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The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

<h3>
How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>

Suppose that we have:

Sample size n > 30
Sample mean = $\overline{x}$
Sample standard deviation = s
Population standard deviation = $\sigma$
Level of significance = $\alpha$

Then the confidence interval is obtained as

Case 1: Population standard deviation is known

$\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}$

Case 2: Population standard deviation is unknown.

$\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}$

For this case, we're given that:

Sample size n = 90 > 30
Sample mean = $\overline{x}$ = 138
Sample standard deviation = s = 34
Level of significance = $\alpha$ = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).

At this level of significance, the critical value of Z is: $Z_{0.1/2}$ = ±1.645

Thus, we get:

$CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]$

Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

Learn more about confidence interval for population mean from large samples here:

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The mean time from prescription drop-off to medicine pickup for a customer served at Heisenberg's Pharmacy is 64 minutes, with a

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Step-by-step explanation:

Given : The mean time : $\mu=64\text{ minutes}$