We know that,
In a right-angled triangle,
Hypotenuse ² = Base ² + Height ²
1 – 10 ² = 6 ² + X ²
Or, X ² = 10 ² – 6 ²
Or, X ² = 100 – 36
Or, X ² = 64
Or, X = √ 64
Or, X = 8 Units
2– X² = 7² + 3²
Or, X² = 49 + 9
Or, X² = 58
Or, X = √58
Or, X = 7.61 Units ( Approx )
3 – 15 ² = EF ² + 9
Or, EF² = 15 ² – 9 ²
Or, EF ² = 225 – 91
Or, EF ² = 134
Or, EF = √ 134
Or, EF = 11.6 Inches ( Approx)
.II} 1 – Here the length of the ladder will be the hypotenuse.
Hence, Hypotenuse = 13 Metre
.Now, The vertical wall will be the height.
Hence, Height = 12 Metre
Distance of the foot of the ladder to the wall will be the base.
Let base be B.
Now, Hypotenuse ² = Base ² + Height ²
Or, 13² = B² + 12²
Or, B² = 13² – 12²
Or, B² = 169 – 144
Or, B² = 25
Or, B = √25
Or, B = 5 Metre
Hence, the distance of the foot of the ladder from the wall is 5 metre apart.
Answer:
Answer for the question:
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 69 and standard deviation 2.7.
a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?
b. If the acceptable range of hardness is (69-C, 69+C), for what value of C would 95% of all specimens have acceptable hardness?
c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?
d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than 72.84(HINT Y=number among the ten specimens with hardness less than72.84 is a binomial variable; what is p?)
is given in the attachment.
Step-by-step explanation:
Answer:
x=-3
Y=-5
Step-by-step explanation:
2x-y=-1 ×2
3x-2y=1. ×1
4x-2y= -2
3x-2y=1
eliminate y by subtracting
I think the answer would be -8^4