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1 year ago

Is this equation an identity? (2x+1)^2-(x+1)^2=3(x+1)^2-1

Mathematics

1 answer:

sergey [27]1 year ago

6 0

Answer:

See below, please

Step-by-step explanation:

Left side

${(2x + 1)}^{2} - {(x + 1)}^{2}$

$= (4 {x}^{2} + 4x + 1) - ( {x}^{2} + 2x + 1)$

$= (4 {x}^{2} - {x}^{2} ) + (4x - 2x) + (1 -1 )$

$= 3 {x}^{2} + 2x$

Right side

$3 \times {(x + 1)}^{2} - 1$

$= 3 \times ( {x}^{2} + 2x + 1) - 1$

$= 3 {x}^{2} + 6x + 3 - 1$

$= 3 {x}^{2} + 6x + 2$

After compared with both sides, we can make a conclusion that

This equation isn't an identity.

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A researcher surveyed 150 high school students and found that 68% played a musical insturment. What would be a reasonable range

maria [59]

Answer:

The reasonable range for the population mean is (61%, 75%).

Step-by-step explanation:

The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.

The mean of the sampling distribution of sample proportion is, $\hat p$ .

One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Given:

n = 150

$\hat p$ = 0.68

The critical value of <em>z</em> for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for proportion as follows:

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)$

Thus, the reasonable range for the population mean is (61%, 75%).

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3 years ago

a swimming pool is 30 feet long 20 feet wide and 6 feet deep .There are 7.5 gallons of water in 1 cubic foot.How many gallons wi

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In this problem it is asking how many gallons the pool holds. It gives you a method of exchange from cubic feet to this however, so in order to solve for this, we first have to solve for how many cubic feet is in the swimming pool, or how much volume the swimming pool has. The formula for the volume of a rectangle is Length*Width*Depth=Volume. Plugging in what we have we get 30*20*6=Volume, or Volume = 3600. As there are 7.5 gallons of water in each cubic foot, we simply multiply 7.5 times 3600 to get the answer. This is 27000.

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3 years ago

If Charlotte spent 25% more on furniture than she will on flooring, how much did she spend on furniture?

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Answer:

Charlotte spent $x + 0.25x$ on furniture

Step-by-step explanation:

Given:

Charlotte spent 25% more on furniture than she will on flooring

To Find:

Amount spent on furniture = ?

Solution:

Let the amount spent on flooring be x

and the amount spent on furniture be y

25% more on furniture than she spent on flooring can be written as

=>25% of x

So the cost spent on furniture will be

=>y= cost spent on flooring + 25% of cost spent on flooring

=>y= x + 25% of x

=>y= $x + \frac{25}{100} \times x$

=> y= $x + 0.25x$

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3 years ago