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baherus [9]
2 years ago
15

The square of a number consists of digits 0, 2, 3, 5. Find the number.

Mathematics
2 answers:
ladessa [460]2 years ago
7 0

Answer: 55

Square: 3025

55^2 = 3025

Fynjy0 [20]2 years ago
3 0

The required number is 55.

<u>SOLUTION: </u>

Given that, the Square of a number consists of digits 0, 2, 3, 5.  We have to find the number.

Now, 0 can’t be in ten thousands place, as if it is there, the square number will be 3 digits and we know that no 3 digit square has 2, 3, 5 together in them.

We know that first 4 digit square is 1024 that is square of 32 and until 44 square i.e. 1936 we have 1 in ten thousands place, but we don’t have 1 in our list.

So we have to consider numbers from 45.

Now, 0 can’t be in ones place also as if we have to keep 0 in once place, then it should a square of number whose units digit is 0, thereby if square a number with units place 0, the result will be having 2 zeros in units place and tens place.

Generally, our required number will be two digit number as its square is having 4 digits.

So, possibilities of units place of our number are 0 – 9, as we excluded 0, remaining possibilities are 1 – 9.

Now, we know that, unit digit of a square term will be based on the unit digit of the number.

So, let us see pairs of unit digits in number and its result in square terms.  

1 – 1, 2 – 4, 3 – 9, 4 – 4, 5 – 5, 6 – 6, 7 – 9, 8 – 4, 9 – 1. As we can see only 5 results in 5 but remaining all results in numbers that are not in our list.

So, units digit is 5, so we have to check 45, 55, 65, .... 95

Now, their squares are 2025, 3025, 4225, ….

Here, we got 3025 as square of 55, it has 0, 2, 3, 5 .

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Suppose a baker claims that the average bread height is more than 15cm. Several of this customers do not believe him. To persuad
laila [671]

Answer:

17-2.262\frac{1.9}{\sqrt{10}}=15.641    

17+2.262\frac{1.9}{\sqrt{10}}=18.359    

So on this case the 95% confidence interval would be given by (15.641;18.359)    

And since the lower limit for the confidence interval is higher than 15 we can conclude that at 5% of significance the true mean is higher than 15 cm

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=17 represent the sample mean

\mu population mean (variable of interest)

s=1.9 represent the sample standard deviation

n=10 represent the sample size  

Confidence interval

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=10-1=9

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that t_{\alpha/2}=2.262

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

17-2.262\frac{1.9}{\sqrt{10}}=15.641    

17+2.262\frac{1.9}{\sqrt{10}}=18.359    

So on this case the 95% confidence interval would be given by (15.641;18.359)    

And since the lower limit for the confidence interval is higher than 15 we can conclude that at 5% of significance the true mean is higher than 15 cm

4 0
3 years ago
Solve -1/2w-3/5=1/5w
elena55 [62]
Very easy:

Common denominator:
-5/10w - 3/5 = 2/10w

- 3/5 = 7/10w

-30 = 35w

-30/35 = w

-6/7 = w


That's how you do it mate ;)
8 0
2 years ago
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