Answer:
0.6710
Step-by-step explanation:
The diameters of ball bearings are distributed normally. The mean diameter is 107 millimeters and the population standard deviation is 5 millimeters.
Find the probability that the diameter of a selected bearing is between 104 and 115 millimeters. Round your answer to four decimal places.
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 107 mm
σ is the population standard deviation = 5 mm
For x = 104 mm
z = 104 - 107/5
z = -0.6
Probability value from Z-Table:
P(x = 104) = 0.27425
For x = 115 mm
z = 115 - 107/5
z = 1.6
Probability value from Z-Table:
P(x = 115) = 0.9452
The probability that the diameter of a selected bearing is between 104 and 115 millimeters is calculated as:
P(x = 115) - P(x = 104)
0.9452 - 0.27425
= 0.67095
Approximately = 0.6710
Answer:
Step-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
- AB = 50*2 = 100 km
- AC = 70*2 = 140 km
The angle between AB and AC is:
- 60 + 50 = 110 degrees (opposite directions from south)
We are looking for the distance BC, which can be found by using the law of cosines:
- BC² = AB² + AC² - 2AB*AC*cos ∠BAC
- BC² = 100² + 140² - 2*100*140*cos 110°
- BC² = 39176.56 (rounded)
- BC = √39176.56 = 197.93 km (rounded)
The distance between the boats is 197.93 km.
Answer:
First get the formula for your pattern in the form of TN. Where d represents your difference and a represents your first term. Then equate the -401 to your formula and solve for n
Answer:
17.5 for perpendicular triangle
Step-by-step explanation:
A= 1/2 ( b*h )
A= 1/2 ( 7*5)
A= 1/2 ( 35)
A= 17.5
Answer:
(x + 6)(x + 13)
Step-by-step explanation:
Given
x² + 19x + 78
Consider the factors of the constant term (+ 78) whuch sum to give the coefficient of the x- term (+ 19)
The factors are + 6 and + 13 , since
6 ×13 = + 78 and 6 + 13 = + 19 , then
x² + 19x + 78 = (x + 6)(x + 13) ← in factored form
