Answer: The probability that the diameter of a selected bearing is greater than 109 millimeters is 0.047
Step-by-step explanation:
Since the diameters of ball bearings are distributed normally, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the diameters of ball bearings.
µ = mean diameter
σ = standard deviation
From the information given,
µ = 104 millimeters
σ = 3 millimeters
The probability that the diameter of a selected bearing is greater than 109 millimeters is expressed as
P(x > 109) = 1 - P(x ≤ 109)
For x = 109,
z = (109 - 104)/3 = 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.953
Therefore,
P(x > 109) = 1 - 0.953 = 0.047
Answer:
circle a: 3.14x36= 113.04
circle b: 3.14 x 64 = 200.96
circle c: 3.14 x 121= 379.94
circle d : 3.14 x 81 = 254.34
Step-by-step explanation: circle a is 6cm, circle b is 8 cm, circle c is 11 cm and circle d is 9cm.
and (Area = π r²) example: circle a 6²=36 and π=3.14 so 3.14x36=113.04
Answer:
maximum value at (- 1, 6 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then minimum value
• If a < 0 then maximum value
y = - (x + 1)² + 6
with (h, k) = (- 1, 6 ) and a = - 1
Thus vertex = (- 1, 6 ) and is a maximum
Answer:
D. Yes by SAS Similarity Postulate
Step-by-step explanation:
This is the answer because if you flip triangle LNM around to shape the DEF. Then you will see that:
1. angle D is congruent to angle L
2. angle E is congruent to angle N
3. angle F is congruent to angle M
4. angle E and N are both 90 degrees
Because (DE and LN) and (MN and FE) are similar and (E and N) are 90 degrees, then we do not need (FD and ML) to tell if triangle DEF and triangle LNM is similar or not. They are similar.
We next need to figure out if the triangles are similar by SSS (Side-side-side) Similarity Postulate or SAS (side-angle-side) Similarity Postulate. The SAS Similarity Postulate states that if you have 2 similar sides and 1 congruent angle, then the two shapes are similar. Right now we have 2 similar sides in (DE and LN) and (MN and FE) and 1 congruent angle that are both 90 degrees. This follows all the rules of the SAS Similarity Postulate, so that means that these two triangles are similar by SAS Similarity Postulate.
Answer:
30 meters per second
Step-by-step explanation:
