Find the reciprocals of the numbers below.
The reciprocal of 19 is :
The reciprocal of 3/4 is :
The reciprocal of 19 is 1/19.
The reciprocal of 3/4 is 4/3.
The Bryants are saving up to go on a family vacation in
3
years. They invest
$2300
into an account with an annual interest rate of
1.27%
compounded quarterly.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent.
(a) Assuming no withdrawals are made, how much money is in the Bryants' account after
3
years?
$
(b) How much interest is earned on the Bryants' investment after
3
years?
$
(a) To find the amount of money in the Bryants' account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = amount of money in the account after t years
P = initial investment
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the values given:
P = $2300
r = 1.27% or 0.0127 (as a decimal)
n = 4 (quarterly compounding)
t = 3 years
A = 2300(1 + 0.0127/4)^(4*3)
A ≈ $2443.37
Therefore, there is approximately $2443.37 in the Bryants' account after 3 years.
(b) To find the interest earned on the Bryants' investment after 3 years, we can subtract the initial investment from the final amount:
Interest earned = A - P
Interest earned = $2443.37 - $2300
Interest earned ≈ $143.37
Therefore, the interest earned on the Bryants' investment after 3 years is approximately $143.37.
Suppose Deon places
$4000
in an account that pays
14%
interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
$
(b) Find the amount in the account at the end of 2 years.
(a) To find the amount in the account at the end of 1 year, we can use the formula for compound interest:
A = P(1 + r)^t
where:
A = amount of money in the account after t years
P = initial investment
r = annual interest rate (as a decimal)
t = number of years
Plugging in the values given:
P = $4000
r = 14% or 0.14 (as a decimal)
t = 1 year
A = 4000(1 + 0.14)^1
A ≈ $4560
Therefore, the amount in the account at the end of 1 year is approximately $4560.
(b) To find the amount in the account at the end of 2 years, we can use the same formula:
A = P(1 + r)^t
Plugging in the values:
P = $4000
r = 14% or 0.14 (as a decimal)
t = 2 years
A = 4000(1 + 0.14)^2
A ≈ $5195.20
Therefore, the amount in the account at the end of 2 years is approximately $5195.20.
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass
4 kg
, the acceleration of the object is
19 /ms2
. If the same force acts upon another object whose mass is
38 kg
, what is this object's acceleration?
We can use the inverse variation formula to solve this problem. The formula states that if the acceleration of an object varies inversely with its mass, then the product of the mass and acceleration is constant.
Let a be the acceleration and m be the mass.
For the first object, we have a = 19 m/s^2 and m = 4 kg.
Using the formula, we get: a * m = k, where k is a constant.
So, 19 * 4 = k, which means k = 76.
For the second object, we have m = 38 kg.
Using the formula again, we get: a * 38 = 76.
Dividing both sides of the equation by 38, we get: a = 76 / 38 = 2 m/s^2.
Therefore, the second object's acceleration is 2 m/s^2.
Answer the questions below.
(a)The perimeter of a rectangular parking lot is
356m
.
If the width of the parking lot is
82m
, what is its length?
Length of the parking lot :
(b)The area of a rectangular pool is
4466 m^2
.
If the length of the pool is
77m
, what is its width?
Width of the pool :
(a) To find the length of the rectangular parking lot, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Given:
Perimeter = 356 m
Width = 82 m
Plugging in these values and solving for the length:
356 = 2(length + 82)
178 = length + 82
length = 178 - 82
length = 96
Therefore, the length of the parking lot is 96 m.
(b) To find the width of the rectangular pool, we can use the formula for the area of a rectangle:
Area = length * width
Given:
Area = 4466 m^2
Length = 77 m
Plugging in these values and solving for the width:
4466 = 77 * width
width = 4466 / 77
width ≈ 57.96
Therefore, the width of the pool is approximately 57.96 m.
Susan is planning on visiting Toronto next week on business. Checking her WorldTemp app, she notices that on the day she arrives, the high temperature is forecast to be
−19.7°C
. What is this temperature in degrees Fahrenheit (
°F
)?
Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.