Answer:
10.25
Step-by-step explanation:
The slope of AC is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -1)/(3 -(-1)) = -5/4
Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-4) = 4/5(x -3) . . . . line CB
When y = 1 (to match the y-value of A), then ...
1 +4 = 4/5(x -3)
5(5/4) = (x -3) . . . . . multiply by 5/4
6.25 +3 = x = 9.25 . . . . add 3
Point B is (9.25, 1).
The length of the hypotenuse is ...
9.25 -(-1) = 10.25
Answer:
The other two angles are 75° and 125°.
Step-by-step explanation:
Let three angles are 2x, 3x and 5x.
The smallest angle is 50.
It means,
2x = 50
x = 25
So,
3x = 3(25) = 75°
5x = 5(25) = 125°
So, the other two angles are 75° and 125°.
Answer:
C. 44 cm, 30cm, and 16 cm
Step-by-step explanation:
Sana nakatulong
x=2 from cross multiplying.
Answer:
Test statistic,
(to 3 dp)
Step-by-step explanation:
Deviation, d = x -y
Sample mean for the deviation
![\bar{d} = \frac{\sum x-y}{n}](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%5Csum%20x-y%7D%7Bn%7D)
![\bar{d} = \frac{(28-6) + (31-27)+(20-26)+(25-25)+(28-29)+(27-32)+(33-33)+(35-34)}{8} \\\bar{d} = -0.625](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%2828-6%29%20%2B%20%2831-27%29%2B%2820-26%29%2B%2825-25%29%2B%2828-29%29%2B%2827-32%29%2B%2833-33%29%2B%2835-34%29%7D%7B8%7D%20%5C%5C%5Cbar%7Bd%7D%20%3D%20-0.625)
Standard deviation: ![SD = \sqrt{\frac{\sum d^{2} - n \bar{d}^2}{n-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20d%5E%7B2%7D%20-%20n%20%5Cbar%7Bd%7D%5E2%7D%7Bn-1%7D%20%20%7D)
![\sum d^{2} = (28-26)^2 + (31-27)^2 +(20-26)^2 +(25-25)^2 +(28-29)^2 +(27-32)^2 +(33-33)^2 +(35-34)^2\\\sum d^{2} = 63](https://tex.z-dn.net/?f=%5Csum%20d%5E%7B2%7D%20%20%3D%20%2828-26%29%5E2%20%2B%20%2831-27%29%5E2%20%2B%2820-26%29%5E2%20%2B%2825-25%29%5E2%20%2B%2828-29%29%5E2%20%2B%2827-32%29%5E2%20%2B%2833-33%29%5E2%20%2B%2835-34%29%5E2%5C%5C%5Csum%20d%5E%7B2%7D%20%20%3D%2063)
![SD = \sqrt{\frac{63 - 8 * (-0.625)^2}{8-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B63%20-%208%20%2A%20%20%28-0.625%29%5E2%7D%7B8-1%7D%20%20%7D)
SD =2.93
Under the null hypothesis, the formula for the test statistics will be given by:
![t_{s} = \frac{ \bar{d}}{s_{d}/\sqrt{n} } \\t_{s} = \frac{- 0.625}{2.93/\sqrt{8} }](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20%5Cfrac%7B%20%5Cbar%7Bd%7D%7D%7Bs_%7Bd%7D%2F%5Csqrt%7Bn%7D%20%20%7D%20%5C%5Ct_%7Bs%7D%20%3D%20%5Cfrac%7B-%200.625%7D%7B2.93%2F%5Csqrt%7B8%7D%20%20%7D)
![t_{s} = -0.6033](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20-0.6033)