15p+15p+25p=30p+25p=55p
Answer:
168 girls.
Step-by-step explanation:
There are a total of 6 + 7 = 13 'parts'.
So one part = 364 / 13 = 28.
So the number of girls = 6 * 28
= 168.
Radius = r = 1 foot
Angular velocity = w = 1 revolutions in 4 seconds
So,
w = 0.25 revolutions per second
Since,
1 revolution = 2π radians
We can write the above equation as:
w = 0.25 x 2π radians per second = 0.5π radians per second
Linear Velocity = v = r w
Using the values, we can write:
v = 1 x 0.5π
= 0.5 π
= π/2 feet per second
Therefore, the correct answer is option B
Answer:
The population will reach 34,200 in February of 2146.
Step-by-step explanation:
Population in t years after 2012 is given by:

In what month and year will the population reach 34,200?
We have to find t for which P(t) = 34200. So



Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:



In this question:

So 
Then



We only take the positive value.
134 years after 2012.
.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.
So the population will reach 34,200 in February of 2146.
Answer:
The minimum sample size needed is 125.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
The margin of error is:

For this problem, we have that:

99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?
This minimum sample size is n.
n is found when 
So






Rounding up
The minimum sample size needed is 125.