Answer:
Step-by-step explanation:
Weekly wages at a certain factory are
normally distributed. The formula for normal distribution is expressed as
z= (x - u)/s
Where
u = mean
s = standard deviation
x = weekly wages
From the given information,
u = 400
s = 50
The probability that a worker
selected at random makes between
$350 and $400 is expressed as
P(350 lesser than or equal to x lesser than or equal to 400)
For x = 350
z = (350 - 400)/50 = -50/50 = -1
z = -1
From the normal distribution table, the corresponding z score is 0.1587
For x = 400
z = (400 - 400)/50 = 0/50 = 0
z = 0
From the normal distribution table, the corresponding z score is 0.5
P(350 lesser than or equal to x lesser than or equal to 400)
= 0.5 - 0.1587 = 0.3413
The angle relationship and their reasons are:
- m∠HED = m∠FEJ ---> Vertical angles theorem
- m∠KFE = m∠DEH ---> Alternate interior angles theorem
- m∠LFG = m∠DEH ---> Alternate exterior angles theorem
- m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem
- m∠DEJ = m∠EFL ---> Corresponding interior angles theorem
- m∠LFG + m∠GFK = 180 ---> linear pair
The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:
∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are equal based on the vertical angles theorem.
- m∠HED = m∠FEJ ---> Vertical angles theorem
∠KFE and ∠FEJ are alternate interior angles, therefore, they are equal based on the alternate interior angles theorem.
- m∠KFE = m∠DEH ---> Alternate interior angles theorem
∠LFG and ∠FEJ are alternate exterior angles, therefore, they are equal based on the alternate exterior angles theorem.
- m∠LFG = m∠DEH ---> Alternate exterior angles theorem
∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.
- m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem
∠DEJ and ∠EFL are corresponding angles, therefore, they are equal based on the corresponding angles theorem.
- m∠DEJ = m∠EFL ---> Corresponding interior angles theorem
∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.
- m∠LFG + m∠GFK = 180 ---> linear pair
Learn more about angle relationship on:
brainly.com/question/12591450
Answer:
Draw an open circle on 2 and continue the arrow left.
Step-by-step explanation:
The answer is = (x + 5y) (x + 7y)
Break the expression into two groups.
x^2 + 12xy + 35y^2
(x^2 + 5xy) (7xy + 35^2)
Factor out x from x^2 + 5xy: x(x + 5y)
Factor out 7y from 7xy + 35y^2: 7y(x + 5y)
=x(x + 5y) + 7y(x + 5y)
Next, factor out the common term (x+ 5y).
Answer = (x + 5y) (x + 7y)
I believe it would be 68 miles per hour! To find the unit rate here you would divide miles by hours, or 340 by 5, which would give you 68.
