The formula for the area of a rhombus is A = a equals StartFraction one-half EndFraction d 1 d 2.d1d2, where d1 and d2 are the l
2 answers:
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Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:
So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:
Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:
So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get:
Answer: <u>Last option</u>
Step-by-step explanation:
The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.
To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.
so
.
Where x is the value of the data, μ is the mean and σ is the standard deviation
In this case :
μ = 12 $/h
= 2 $/h
We need to calculate the Z-scores for and
Then for :
.
Then for :
.
Therefore the answer is:
A cylinder with a circumference of about 50 units is formed.
Step-by-step explanation:
Step 1:
The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.
So the side length of the square is 8 units.
If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.
Step 2:
To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.
The circumference of the cylinder
So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.