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.
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C * 9/5) + 32
Given:
°C = -19.7
Using the formula, we can plug in the value for °C and solve for °F:
°F = (-19.7 * 9/5) + 32
°F = (-35.46) + 32
°F ≈ -3.5
Therefore, the temperature of -19.7°C is approximately -3.5°F.
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.
Ashley took out a loan for
$4800
and was charged simple interest at an annual rate of
11.5%
.
The total interest she paid on the loan was
$138
.
How long was the loan for, in months?
Do not round any intermediate computations.
To convert Celsius to Fahrenheit, you can use the formula:
°F = (°C * 9/5) + 32
Given:
°C = -19.7
Using the formula, we can plug in the value for °C and solve for °F:
°F = (-19.7 * 9/5) + 32
°F = (-35.46) + 32
°F ≈ -3.5
Therefore, the temperature of -19.7°C is approximately -3.5°F.
---
To calculate the length of the loan in months, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given:
Principal = $4800
Rate = 11.5% or 0.115 (as a decimal)
Interest = $138
Plugging in these values and solving for Time:
$138 = $4800 * 0.115 * Time
Time = $138 / ($4800 * 0.115)
Time ≈ 0.25 years
Since there are 12 months in a year, the loan was for approximately 0.25 * 12 = 3 months.
Therefore, the length of the loan was approximately 3 months.
Evaluate.
5(−5)+ (1-2^3)^2
To evaluate the expression 5(-5) + (1-2^3)^2, we start by simplifying the exponent:
2^3 = 2 x 2 x 2 = 8
Now we can rewrite the expression as:
5(-5) + (1-8)^2
Next, we perform the multiplication and the subtraction inside the parentheses:
5(-5) + (-7)^2
Now, we square the -7:
5(-5) + 49
Next, we perform the multiplication:
-25 + 49
Finally, we perform the addition:
-25 + 49 = 24
Therefore, the value of the expression 5(-5) + (1-2^3)^2 is 24.
A pole that is
3m
tall casts a shadow that is
1.37m
long. At the same time, a nearby building casts a shadow that is
37.5m
long. How tall is the building? Round your answer to the nearest meter.
m
To find the height of the building, we can set up a proportion using the lengths of the shadows and the heights of the objects.
Let x be the height of the building.
Using the given information, we can set up the following proportion:
(height of pole)/(length of pole's shadow) = (height of building)/(length of building's shadow)
3/1.37 = x/37.5
Now, we can cross multiply and solve for x:
1.37x = 3 * 37.5
1.37x = 112.5
x = 112.5 / 1.37
x ≈ 82.12
So, the height of the building is approximately 82.12 meters.
Rounded to the nearest meter, the height of the building is 82 meters.
10/13 as a percentage.
Round your answer to the nearest tenth of a percent.
%
To convert a fraction to a percentage, we can multiply the fraction by 100.
Given:
Fraction = 10/13
To convert 10/13 to a percentage, we multiply it by 100:
Percentage = (10/13) * 100
Calculating the value:
Percentage ≈ 76.9
Therefore, 10/13 as a percentage, rounded to the nearest tenth, is approximately 76.9%.
Find the requested angle.
Complement of 7(1/2)°
Question 1 options:
A)
262(1/2)°
B)
352(1/2)°
C)
82(1/2)°
D)
172(1/2)°
To find the complement of an angle, we subtract the angle from 90 degrees.
Given:
Angle = 7(1/2)°
Complement = 90° - 7(1/2)°
Now we need to convert 7(1/2) to a decimal:
7(1/2) = 7 + 1/2 = 7.5
Complement = 90° - 7.5°
Calculating the value:
Complement = 82.5°
Therefore, the complement of 7(1/2)° is 82(1/2)°.
Answer:
C) 82(1/2)°
Convert the following.
0.085 m^2 to square centimeters
Question 2 options:
A)
8500 cm^2
B)
8.5 cm^2
C)
85 cm^2
D)
850 cm^2
To convert square meters to square centimeters, we multiply the value by the conversion factor (1 m^2 = 10,000 cm^2).
Given:
0.085 m^2
Converting to square centimeters:
0.085 m^2 * 10,000 cm^2/m^2 = 850 cm^2
Therefore, 0.085 m^2 is equal to 850 square centimeters.
Answer:
D) 850 cm^2
Find the area.
43 yd 47 yd 36 yd
Question 3 options:
A)
1548 yd^2
B)
1010.5 yd^2
C)
774 yd^2
D)
924.5 yd^2
To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height
Given:
Base = 43 yd
Height = 47 yd
Plugging in these values into the formula:
Area = (1/2) * 43 yd * 47 yd
Area = 0.5 * 43 yd * 47 yd
Area = 1010.5 yd^2
Therefore, the area of the triangle is 1010.5 square yards.
Answer:
B) 1010.5 yd^2
Find the exact values of the indicated trigonometric functions.
Write fractions in lowest terms.
55 33 44
Find sin A and cos A.
Question 4 options:
A)
sin A = (4/3); cos A = (3/4)
B)
sin A = (4/5); cos A = (3/5)
C)
sin A = (3/5); cos A = (4/5)
D)
sin A = (5/4); cos A = (5/3)
To find the values of sin A and cos A, we need to use the given triangle.
Given:
Opposite side = 55
Adjacent side = 33
Hypotenuse = 44
Using the definitions of sin and cos, we can calculate the values:
sin A = Opposite/Hypotenuse = 55/44 (which can be simplified to 5/4)
cos A = Adjacent/Hypotenuse = 33/44 (which can be simplified to 3/4)
Therefore, the correct values are:
sin A = 5/4
cos A = 3/4
Answer:
D) sin A = 5/4; cos A = 3/4
Solve the problem.
To convert a Fahrenheit temperature to Celsius, one formula to use is F = (9/5)C + 32, where F is the Fahrenheit temperature (in degrees) and C is the Celsius temperature.
What is the Celsius temperature (to the nearest degree) when Fahrenheit temperature is 77°?
Question 5 options:
A)
145°C
B)
171°C
C)
25°C
D)
39°C
To convert a Fahrenheit temperature to Celsius using the given formula:
F = (9/5)C + 32
We can rearrange the formula to solve for C:
C = (F - 32) * (5/9)
Given:
Fahrenheit temperature = 77°
Plugging in the value for F and calculating:
C = (77 - 32) * (5/9)
C = 45 * (5/9)
C ≈ 25
Therefore, the Celsius temperature when the Fahrenheit temperature is 77°, rounded to the nearest degree, is approximately 25°C.
Answer:
C) 25°C
Solve the problem.
Alonso can't decide which size pizza to order.
The 10-inch cheese and sausage pizza is $5.99, while the 12-inch deluxe is $6.99.
If he gets the 10-inch pizza, the total price will be divided among 3 people.
If he chooses the 12-inch pizza, then the total price will be divided among 4 people.
Which is the better buy?
How much will each person pay? (Use 3.14 for π.)
To determine which pizza is the better buy, we need to compare the price per square inch.
For the 10-inch pizza:
Area = π * (radius)^2 = 3.14 * (5)^2 = 78.5 square inches
Price per square inch = 5.99 / 78.5 ≈ 0.0763 dollars per square inch
For the 12-inch pizza:
Area = π * (radius)^2 = 3.14 * (6)^2 = 113.04 square inches
Price per square inch = 6.99 / 113.04 ≈ 0.0619 dollars per square inch
The 12-inch pizza has a lower price per square inch, making it the better buy.
Next, let's calculate how much each person will pay.
For the 10-inch pizza divided among 3 people:
Total price = 5.99
Amount each person pays = Total price / Number of people = 5.99 / 3 ≈ 1.9967 dollars per person
For the 12-inch pizza divided among 4 people:
Total price = 6.99
Amount each person pays = Total price / Number of people = 6.99 / 4 ≈ 1.7475 dollars per person
Therefore, each person will pay approximately $1.9967 if they choose the 10-inch pizza, and approximately $1.7475 if they choose the 12-inch pizza.
A)
10-inch pizza; $1.75
B)
12-inch pizza; $2.00
C)
12-inch pizza; $1.75
D)
10-inch pizza; $2.00
Apologies for the confusion in the previous response. Let's correct the answer.
To determine which pizza is the better buy, we will compare the price per square inch.
For the 10-inch pizza:
Area = π * (radius)^2 = 3.14 * (5)^2 =