<u>Answer:</u>
Option D is the correct answer.
D. This is a linear function because there is a common difference of 2.
<u>Step-by-step explanation:</u>
Linear function--
A function is said to be linear if the rate of change is constant.
i.e. the function is increasing by a fixed constant.
Here the table is given by:
Hour (x) Number of Customers f(x)
1 2
2 4
3 6
From the table of values we observe that as the value of increasing by 1 the value of y is increasing by 2.
i.e. the rate of change is constant i.e. 2.
Also, the common difference is 2.
Since,
4 - 2 = 2
and
6 - 4 = 2
Hence, the table represents a linear function.
Alright, lets get started.
If Matthew wants to complete packages at an average rate of at least 39 packages per hour.
And they worked 4 hrs only due to picnic, yesterday, it means they have to make
packages.
But they made only 112 packages means they are short of
packages.
Suppose they are working today t hrs, and his department will complete 43 packages per hour today.
It means they are going to make 43 t packages today.
This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.
So, average will be
(39 average given in question)
Cross multiplying

Adding 44 in both sides


Subtracting 39 t in both sides


Dividing 4 in both sides
t = 11 hrs
Hence they have to woth 11 hrs today : Answer
Hope it will help :)
Solution:
The square of the given equation can be completed as below:
Here we will make the terms on left hand side such that it gets the form of 

Hence the correct option is isolating the constant , -3.
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: he will be able to play 32.6 games at the arcade
Step-by-step explanation: