Answer:
T = 36
Step-by-step explanation:
T = 5(4.2)-6(-2.5)
T = 21 + 15
T = 36
Answer:
1) Yes, it is a right angle triangle
2)Yes, it is a right angle triangle
3) No, they are not similar.
Step-by-step explanation:
Dimension of triangle A = 48, 55 & 73
Dimension of triangle B = 36, 77 & 85
For any of the triangles to be a right angled one, then;
c = √(a² + b²)
Where a,b & c are side dimensions of a triangle.
Thus;
Triangle A: c = √(48² + 55²)
c = √5329
c = 73
This tallies with what we are given and so it is a right angled triangle.
Triangle B: c = √(36² + 77²)
c = √(7225)
c = 85
Similar to the third side dimension of 85, thus it is true.
For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.
Thus, we have;
48/36 = 1.5
55/77 = 5/7
73/85 = 73/85
Since the ratios are not similar, then we can say that the triangles are not similar.
5/2 because 5/2 is greater than 1, an improper fraction that does not take a piece of 1 but rather considers whole numbers as that origin
Answer: (143.07, 158.93)
Step-by-step explanation:
The formula to find the confidence interval is given by :-
![\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z%5E%2A%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
where n= sample size
= Sample mean
z* = critical z-value (two tailed).
= Population standard deviation
We assume that the underlying population distribution is normal.
As per given , we have
n= 108
![\sigma=32](https://tex.z-dn.net/?f=%5Csigma%3D32)
Critical value for 99% confidence level = 2.576 (By using z-table)
Then , the 99% confidence interval for the population mean hours spent watching television per month :-
![151\pm (2.576)\dfrac{32}{\sqrt{108}}](https://tex.z-dn.net/?f=151%5Cpm%20%282.576%29%5Cdfrac%7B32%7D%7B%5Csqrt%7B108%7D%7D)
![151\pm (2.576)\dfrac{32}{10.3923048454}](https://tex.z-dn.net/?f=151%5Cpm%20%282.576%29%5Cdfrac%7B32%7D%7B10.3923048454%7D)
![151\pm (2.576)(3.07920143568)](https://tex.z-dn.net/?f=151%5Cpm%20%282.576%29%283.07920143568%29)
![151\pm (7.93202289831)\approx151\pm7.93\\\\=(151-7.93,\ 151+7.93)\\\\=(143.07,\ 158.93 )](https://tex.z-dn.net/?f=151%5Cpm%20%287.93202289831%29%5Capprox151%5Cpm7.93%5C%5C%5C%5C%3D%28151-7.93%2C%5C%20151%2B7.93%29%5C%5C%5C%5C%3D%28143.07%2C%5C%20158.93%20%29)
Hence, the required 99% confidence interval for the population mean hours spent watching television per month. = (143.07, 158.93)
Ratio of Cake Donuts to Total Donuts = 15/36
Let, the number of people with Cake donuts = x
Then, 15/36 = x/12
x = 12/36 * 15
x = 1/3 * 15
x = 5
In short, Your Answer would be: 5
Hope this helps!