Answer:
Think of even square roots close to 27: the closest is 25 which has a square root of 5. Now think of the number with an even square root after 25: 36 which has a square root of 6. Since 27 is between 25 and 36, the square root of 27 would be between 5 and 6.
To solve for the confidence interval for the population
mean mu, we can use the formula:
Confidence interval = x ± z * s / sqrt (n)
where x is the sample mean, s is the standard deviation,
and n is the sample size
At 95% confidence level, the value of z is equivalent to:
z = 1.96
Therefore substituting the given values into the
equation:
Confidence interval = 3 ± 1.96 * 5.8 / sqrt (51)
Confidence interval = 3 ± 1.59
Confidence interval = 1.41, 4.59
Therefore the population mean mu has an approximate range
or confidence interval from 1.41 kg to 4.59 kg.
Answer:
(#14 - supplementary) x = 10.5
(#15 - supplementary) x = 10
Explanation:
For these problems, we must know that a supplementary angle can be viewed as a sum of angles that add to 180 degrees. With this known, we can write our equations to find x.
(#14)
15x - 12 + 5x - 18 = 180
20x - 30 = 180
20x = 210
x = 10.5
(#15)
6x + 13 + 14x - 33 = 180
20x - 20 = 180
20x = 200
x = 10
Hope this helps.
Cheers.
Let, the length be l and breadth be b.
So, 2(l + b) = 26
Or, l + b = 13
Or, l = 13 - b
So, we may write like this,
Area = l * b
Or, l * b > 30
Or, l (13 - l) > 30
Or, 13l - l^2 > 30
Or, l^2 - 13l + 30 > 0
Or, l^2 - 3l - 10l + 30 > 0
Or, l(l - 3) - 10(l - 3) > 0
Or, (l - 3)(l - 7) > 0
Or, l - 7 > 0
Or, l > 7.
Now, putting the value of l,
We get, l * b > 30
Or, 7 * b > 30
Or, b > 30/7
➡️ Therefore, we get,
Length > 7
Breadth > 30/7
That's it..
