First distribute the 2/3.
(2/3)n + (2/3)*6 = 10
(2/3)n + 4 = 10
Subtract 4 from both sides
(2/3)n = 6
Multiply both sides by (3/2) to clear the fraction
n = 9
Circumference of a circle= πd = 10π
Divide by 2 and then add 10
Final answer= 25.7
Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.
Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.
Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).
You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.
The slope of the line joining two points is the rise divided by the run. That means
m = (y2 - y1) / (x2 - x1)
So we put in the values of (30, 180) and (50, 220):
m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.
The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:
y = 2x + b.
This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:
220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.
Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:
y = 2x + 120.
For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.
Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:
y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.
Now you try it with your question.
Answer: Hope this helps
Step-by-step explanation:
6.39 = 639
100
= 639
100
as a fraction
To convert the decimal 6.39 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
6.39 = 6.39
1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,
6.39
1
= (6.39 × 100)
(1 × 100)
= 639
100
.
(This fraction is alread reduced, We can't reduce it any further).
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 639
100
is also equal to 639
100
when expressed as a mixed number
Answer:
No, the clay will not pour out easily. I know this because the angle of the truck bed is less than 50°, which is the minimum angle for easy pouring.
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
If α represents the angle of the truck bed, this means ...
sin(α) = 9/15
We can find α using the inverse sine function:
α = arcsin(9/15) ≈ 36.87°
We note this angle is less than 50° so we expect the clay will not pour out easily.
