Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x ---> the number of hours spent on the client’s case each week
f(x) ----> the total charge that week in hundreds of dollars
we have
distribute
This is the equation of the line in slope intercept form
where
The slope or unit rate is
The y-intercept or initial value is
To graph the line we need minimum two points
Find the x-intercept
For f(x)=0
The x-intercept is the point (-2,0)
so
we have
the points (-2,0) and (0,8)
To graph the line, plot the intercepts, connect them and join the points
The graph in the attached figure
Remember that the value of x and the value of f(x) cannot be a negative number
So the given series is "16, 06, 68, 88, __"
Count all the cyclical opening in each of these numbers. For example in 16, there is a one cyclical loop present in it(the one in 6), similarly in 06 it is two(one in zero and one in 6), going ahead, in 68 it is 3(one in 6 and two in 8).
From here on things become simple: hence, the cyclical figures in these equations written down becomes 1,2,3,4,_,3.
Let's now try solving the above sequence, going by the logical reasoning the only number that can fill in the gap should be 4.
Answer:
- The total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
- The total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.
Step-by-step explanation:
a) How much will you have at the middle of the first year?
Using the formula
where
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 0.5 years
To determine:
Total amount = A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
Part b) How much at the end of one year?
Using the formula
where
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 1 years
To determine:
Total amount = A = ?
so using the formula
so substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.
the penny travels at a faster rate by 56.4 kilometers
penny = 153 for 30 min
penny = 306 for 1 hour
rocket = 208 in 50 min
208/5 = 41.6 *6 = 249.6 in 1 hour
penny is faster by 56.4 kilometers
1)volume of the pipeline
The pipeline is a cylinder, therefore;
Volume (cylinder)=πr²h
r=radius
h=height of the cylinder
diameter=6 in*(1 ft / 12 in)=0.5 ft
raius=diameter / 2=0.5 ft / 2=0.25 ft.
height=5280 ft
Volume (pipeline)=π(0.25 ft)²(5280 ft)=330π ft³≈1036.73 ft³.
2) we calculate the number of barrel
1 mile of oil in this pipeline is 330π ft³ of oil.
1 barrel of crude------------------5.61 ft³
x----------------------------------330π ft³
x=(1 barrel*330π ft³) / 5.61 ft³=184.8 barrels
3) we calculate the price.
1 barrel---------------$100
184.8 barrels---------- x
x=(184.8 barrels * $100) / 1 barrel=$18,480
Solution: ≈$18,480
