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Snezhnost [94]
2 years ago
12

Which of the following is the difference of two squares

Mathematics
1 answer:
Roman55 [17]2 years ago
7 0

Answer:

2nd option

Step-by-step explanation:

A difference of squares has the general form

a² - b²

where the terms on either side of the subtraction ( the difference ) are both perfect squares.

The only one fitting this description is

16a² - 4y²

= (4a)² - (2y)² ← difference of squares

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What is the area of a circle with a radius of 2.1cm? Use 3.14 for π.
saul85 [17]

Answer: I got's you lol

A≈13.85cm²

And the radius is 2.1

Step-by-step explanation:

Hope this helps let me know :)

3 0
3 years ago
Read 2 more answers
Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old
DedPeter [7]

Answer:

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

Step-by-step explanation:

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=39 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=1 represent the population standard deviation

n=25 represent the sample size  

Solution to the problem

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

The margin of error is given by:

ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

And replacing we got:

ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392

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

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

7 0
3 years ago
Which is the better buy a 3 pound ham for $5.70 or 5 pounds for $8.75
tekilochka [14]

Answer:

The larger ham is the better buy.

Step-by-step explanation:

In order to determine the better buy, divide both of the prices by their weight to get the price per pound of ham.

5.70/3 = 1.90 per lb

8.75/5 = 1.75 per lb

Therefore the 5 pound of ham is a better buy.

7 0
3 years ago
Read 2 more answers
Solve for x: 7x + 15 = 38
oksano4ka [1.4K]
All you do is move all the terms that don't contain  " x " to the right side and solve. 

x = \frac{23}{7}


Hope that helps, Good luck! (:
8 0
3 years ago
Read 2 more answers
Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe
solmaris [256]

Answer:

a) 1/2

b) 250

Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for p such that 1000p(1-p) is maximized. Once we have that p, we can easily find the answer to part b.

Finding the value that maximizes 1000p(1-p) is the same as finding the value that maximizes p(1-p), just on a smaller scale. So, we really want to maximize p(1-p). To do this, we will do a trick called completing the square.

p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4.

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of p such that the inner part of the square term is equal to 0.

p-1/2=0\\p=1/2.

So, the answer to part a is \boxed{1/2}.

We can then plug 1/2 into the equation for p to find the answer to part b.

1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250.

So, the answer to part b is \boxed{250}.

And we're done!

3 0
2 years ago
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