Answer:
6.5 %
Step-by-step explanation:
The simple interest formula is
I = Prt
Data:
I = $1755
P = $3000
t = 9 yr
Calculation:
1755 = 3000 × r × 9
1755 = 27 000 r
Divide each side by 27 000
r = 1755/27 000 = 0.065 = 6.5 % APR
The annual percentage rate was 6.5 %.
Answer:
16 cents
Step-by-step explanation:
A = P (1 + r)n
A = $1 (1 + 0.05)3
A = $1 x 1.16
A = $1.16
To find the compound interest only;
Compound Interest = Final Value - Initial Value
Compound Interest = $1.16 - $1
Compound Interest = $0.16
Hence the compound interest John will earn in his savings account will be 16 cents.
Answer:
The answer is 35.5 square units
Step-by-step explanation:
The shape represents a rectangle, a small triangle removed from it at the upper right corner and a bigger triangle is attached to it at the upper left corner.
We get this formula:
A(shape) = A(rectangle) - A(small triangle) + A(big triangle)
SO LET'S FIND EACH!
A(rectangle)= length x width
length= 8 units
width= 4 units
We get:
A(rectangle) =8x4= 32 square unit
A(small triangle)= (base x height)/2
base= 1 unit
height= 1 unit
We get:
A(small triangle) = (1x1)/2 = 1/2 = 0.5 square units
A(big triangle)= (base x height)/2
base= 2 units
height= 4units
We get:
A(big triangle)= (2x4)/2 = 8/2 = 4 square units
For the final result:
A(shape) = 32 - 0.5 + 4 = 35.5 square units
Answer:
Step-by-step explanation:
Given that:
The height of the dock (h) = 6
Let represent d to be the distance between the boat and the dock
Let the length of the rope between the boat and the drum be denoted by (l)
Then, the rate of change for the length of the rope be:
dl/dt = -5 ft/s
Using Pythagoras rule to determine the relationship between these values, we have:
We relate to: 
From the question;
l = 34,
So to find 
, we get;
d = 33.46
So, we have:
Let <em>x</em> be the smallest of the three integers. Then the next two are <em>x</em> + 2 and <em>x</em> + 4.
• "The ratio of the smallest number to 1 less than twice the smallest number..."
This translates to
<em>x</em> / (2<em>x</em> - 1)
• "... the ratio of 3 more than the middle number to twice the largest number."
This translates to
((<em>x</em> + 2) + 3) / (2 (<em>x</em> + 4))
or, simplifying a bit,
(<em>x</em> + 5) / (2<em>x</em> + 8)
The ratioes are said to be equivalent, so
<em>x</em> / (2<em>x</em> - 1) = (<em>x</em> + 5) / (2<em>x</em> + 8)
Solve for <em>x</em> :
<em>x</em> (2<em>x</em> + 8) = (<em>x</em> + 5) (2<em>x</em> - 1)
2<em>x</em>² + 8<em>x</em> = 2<em>x</em>² + 9<em>x</em> - 5
8<em>x</em> = 9<em>x</em> - 5
-<em>x</em> = -5
<em>x</em> = 5
So the three integers are 5, 7, and 9.
