In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
Answer:
95% of monthly food expenditures are between $110 and $190.
Step-by-step explanation:
Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.
To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?
Solution :
At 95% of the data is between two standard deviation to left and right of the mean is given by,
To the left side, 
To the right side, 
We have given,
The sample mean 
The standard deviation 
Substitute in the formula,








Therefore, 95% of monthly food expenditures are between $110 and $190.
The answer is :150 square inches because: a cube have equal lengths like a square so therefore 5x5 = 25. There are 6 sides of a cube so: 25x 6= 150
Answer:
Let X be the number of weeks.
2x - 16 = 14
we add 16 on both sides.
2x = 30
now we divide 2 on both sides to get rid of the 2 to the x, we want to get x on its own.
X = 15
For this case we have that by definition, the standard way to write the equation of a line, is given by:

Where a, b and c are integers.
Given 
We can write it in the standard way:

and by the previous definition, the numbers a, b and c must be integers.
Thus, we multiply the equation by 2, on both sides so as not to alter the equality.


Thus, the equation of
, in its standard form is given by:

Answer:
Option B