Answer: 167
Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.
Since we want to determine the 76th term, we are going
to substitute 76 in for <em>n</em> in our explicit formula.
Then, will be our first term in our sequence which is 17.
Lastly, <em>d</em> is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.
So we have .
Now we have all the information we need. Just simplify from here.
Make sure to apply order of operations because this is where many
students make mistakes. Inside the parentheses first!
(76 - 1) is going to be 75.
So we have .
Then, we have to make sure we multiply before we add.
So (75)(2) is going to give us 150.
So we have .
Now just add to find that .
So the 76th term is 167.
The markup is $38.80.
What I did:
markup rate=40%
40%=0.4
0.4*97=38.80.
X=120
2/5-(x/300)=0
Simplify= X/300
2/5-X/300=0
Simplify=2/5
2/5-X/300=0
The left denominater is: 5
The right denominater is: 300
Student 1,2, and 3
Student 2,1, and 3
Student 1, 3, and 2
Student 2, 3, and 2
Student 3, 1, and 2
Student 3, 2, and 1
so 6 different orders
The freight train speed = 22 mph
The passenger train speed = 28 mph
Step-by-step explanation:
Assign the speed of the freight train as; <em>x </em>mph
Since the passenger train travels 6 mph faster than the freight train, its speed will be; (<em>x + 6</em>) mph
In 2 hours, the freight and passenger trains will have traveled (distance = speed * time);
2<em>x</em> and 2(<em>x + 6</em>) miles respectively
Both add up to 100 miles. Therefore;
2x + 2(x +6) = 100
4x + 12 = 100
4x = 88
x = 22
x + 6 = 28
The freight train speed = 22 mph
The passenger train speed = 28 mph