Answer:
a = 0.5 or 1/2
b = 19/4 or 4.75
Step-by-step explanation:
Step 1: Isolate <em>x</em>'s
x² - x = -5
Step 2: Complete the Square
x² - x + 1/4 = -5 + 1/4
(x - 1/2)² = -19/4
Step 3: Move everything to one side
(x - 0.5)² + 4.75
For this case what we should do is use the given equation:
F = mg sin (theta)
And replace the following values:
m = 0.01 kg
g = 9.8m / s ^ 2
theta = 22.5 degrees
Substituting we have:
F = (0.01) * (9.8) * sin (22.5)
F = 0.037502976 N
Answer:
The force pulling on the pendulum when it makes a 22.5 degree angle with the vertical is:
F = 0.037502976 N
1+4p
the answer cant be simplified any further than this.
Answer:
the probability that the woman is taller than the man is 0.1423
Step-by-step explanation:
Given that :
the men's heights are normally distributed with mean
68
standard deviation
= 3.1
And
the women's heights are normally distributed with mean
65
standard deviation
= 2.8
We are to find the probability that the woman is taller than the man.
For woman now:
mean
= 65
standard deviation
= 2.8

![\\ 1 -p \ P[(x - \mu ) / \sigma < (68-25)/ 2.8]](https://tex.z-dn.net/?f=%5C%5C%201%20-p%20%20%5C%20P%5B%28x%20-%20%5Cmu%20%29%20%2F%20%5Csigma%20%3C%20%2868-25%29%2F%202.8%5D)
= 1-P (z , 1.07)
Using z table,
= 1 - 0.8577
= 0.1423
Thus, the probability that the woman is taller than the man is 0.1423
Answer:
At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.
Step-by-step explanation:
Hello!
Considering the dependent variable:
Y: Ductility in steel.
And the independent variable:
X: Carbon content of the steel.
The linear regression was estimated and a prediction interval was calculated.
The prediction interval is calculated to predict a value that the variable Y (response variable) can take for a given value of the variable X (predictor variable) in the definition range of the linear regression line. Symbolically [Y/X=
]
In this case 95% prediction interval for Y/X=0.5
At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.
I hope it helps!