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Darina [25.2K]
3 years ago
8

Some four​-digit ​numbers, such as 3003 and 6226​, read the same forward and backward. If a boy selects a number from all four​-

digit ​numbers, find the probability that it will read the same forward and backward.
Mathematics
1 answer:
Norma-Jean [14]3 years ago
3 0

<u>Answer:</u>

The probability of selecting such number =\frac{90}{9000} = \frac{1}{100}

<u>Explanation:</u>

4-digit numbers start from 1000 and ends at 9999

So, there are 9000 4-digit numbers present

There are 90 palindrome numbers (which reads the same forward and backward) present between 1000-9999. They are 1001; 1111; 1221; 1331; ... 1001; 1111; 1221; 1331; ... to 9669; 9779; 9889; 9999; 9669; 9779; 9889; 9999

Therefore, the probability of selecting such number =\frac{90}{9000} = \frac{1}{100}

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Answer:

no it is not

Step-by-step explanation:

3x+9y=1 simplified is

9y=-3x+1

y=-1/3x+1/9

this is the exact same equation as 3x+9y=1, so you cannot find another line thats parallel to it and passes through that same point (it'll always be that point)

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Which shows the location of the point (2,-5) after being reflected across the y-axis?
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2 years ago
A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose
Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

Step-by-step explanation:

Notation and definitions  

n=50 represent the sample size  

\bar X= 27.2 represent the sample mean  

s=5.83 represent the sample standard deviation  

m represent the margin of error  

Confidence =88% or 0.88

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".  

Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by \alpha=1-0.88=0.12 and \alpha/2 =0.06. The degrees of freedom are given by:  

df=n-1=50-1=49  

We can find the critical values in R using the following formulas:  

qt(0.06,49)

[1] -1.582366

qt(1-0.06,49)

[1] 1.582366

The critical value tc=\pm 1.582366  

Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

m=t_c \frac{s}{\sqrt{n}}  

m=1.582366 \frac{5.83}{\sqrt{50}}=14.613  

With R we can do this:

m=1.582366*(5.83/sqrt(50))

m

[1] 1.304639

Calculate the confidence interval  

The interval for the mean is given by this formula:  

\bar X \pm t_{c} \frac{s}{\sqrt{n}}  

And calculating the limits we got:  

27.02 - 1.582366 \frac{5.83}{\sqrt{50}}=25.715  

27.02 + 1.582366 \frac{5.83}{\sqrt{50}}=28.325

Using R the code is:

lower=27.02-m;lower

[1] 25.71536

upper=27.02+m;upper

[1] 28.32464

The 95% confidence interval is given by (25.71536 ;28.32464)  

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)  

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