Suppose you just won the state lottery, and you have a choice between receiving $4,500,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes
A 1.03% rate of return is built into the annuity.
First optionTo receive a single payment today of $4,500,000Second optionTo receive an annual payment of $250,000.Term is equal to 20 years.Let the rate of return be x%.A series of payments paid at regular intervals is known as an annuity. Regular savings account deposits, mortgage payments, insurance premiums, and pension payments are all examples of annuities. The periodicity of payment dates allows for the classification of annuities.At this rate, the present value of the annuity is $4,500,000.The present value of the first option equals the present value of the second option. $4,500,000 = $250,000[1/x + 1/x² + … + 1/x^20]Upon solving, we get approximately x is 1.03%.To learn more about annuity, visit :
https://brainly.com/question/23554766
#SPJ9
what is the area of the rectangle?
Width;
4x-1 ,
Top length;
2x+17
Bottom Length;
6x+9 .
Please help
==============================================================
Explanation:
Recall that the opposite sides of any rectangle are the same length.
This means the top and bottom sides are the same length
top = bottom
2x+17 = 6x+9
2x-6x = 9-17
-4x = -8
x = -8/(-4)
x = 2
Then we can find each side:
width = 4x-1 = 4*2-1 = 8-1 = 7top = 2x+17 = 2*2+17 = 4+17 = 21bottom = 6x+9 = 6*2+9 = 12+9 = 21We get the same length for top and bottom (21), which confirms the correct x value.
This is a 7 by 21 rectangle with area = length*width = 7*21 = 147 square units.
ming
What is the value of the expression (54+3³) ?
33
Answer:
Submit Answer
OL
C
PLS HELP ASAP
(50 POINTS)
What is the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}?
A) {2,4}
B) {1, 2, 3, 4)
C) {2, 4, 6}
D) {1, 2, 3, 4, 6}
Answer:
a
Step-by-step explanation:
the answer is a
Answer:
C
Step-by-step explanation:
Simplify the expression using order of operations. 14+18÷2×4−7
Answer:
Hi
Your answer is 43.
Solve(Using PEMDAS order of operations):
[tex]18\div \:2\times \:4\\18\div \:2=9\\=9\times \:4\\=36\\=14+36-7\\14+36=50\\=50-7\\=43[/tex]
evaluate the expression 3 to the third power multiplied by 12-2 divided by 2 iready
a survey of 800 households revealed that 400 had only a TV, 100 had only a computer, and 100 had neither a tv nor a computer. how many households have both a tv and a computer?
The number of households which have both TV and computers are 200.
What is defined as the Boolean algebra (logical expressions)?Boolean algebra is a branch of algebra in math and mathematical logic where the value of the variables are indeed the truth values both true and false, typically represented 1 and 0, respectively.Synonyms, such as 'Yes' for 'True' as well as 'No' for 'False,' are sometimes used to represent the statement.Let A be the number of house hold having only TV = 400
Let B be the number of house hold having only computers = 100
Let C be the number of house hold having neither TV nor computer = 100
Let D be the number of house hold having both TV and computer.
Then, the number number of house holds are 800.
A + B + C + D = 800
Put the values;
400 + 100 + 100 + D = 800
D = 800 - 600
D = 200
Therefore, the number of households having both TV and computer are 200.
To know more about the Boolean algebra, here
https://brainly.com/question/2467366
#SPJ9
Use the diagram to find the measures of the lengths of the
sides. The perimeter of the trapezoid on the right is 67
inches.
The length of all four sides of the Isoclesles Trapezium is 67 inches.
What is an area of a Trapezium?Area of a Trapezium is (1/2)(a+b)h.Where and b are the parallel sides of the trapezium and h is the distance between the two parallel side
We know that for a plane 2D figure perimeter is the sum of the lengths of all the sides.
Given an isosceles Trapezium with a perimeter of 67 inches,
As the sides are given in variables we can equate the sum of all the sides with the given perimeter and obtain the value of x.
∴ (x + 1.5x + 2.5x - 5 + x) = 67.
6x = 67 + 5.
6x = 72.
x = 12.
So, the measure of lengths of four sides are [ 12 + 1.5(12) + 2.5(12) - 5 + 12) which is ( 12 + 18 + 30 - 5 + 12 ) = 67 inches.
leran more about trapezium here :
https://brainly.com/question/8208556
SPJ1
What are Conic Sections and how are they formed?
Answer:
In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.
Conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points. 90 ÷ [ 10 + ( 3 2 − 4 ) ]
2.368
Given expression is
90 ÷ [ 10 + ( 3 2 − 4 ) ]
According to BODMAS rule we simplify this expression
The order of operations consist of evaluate the parenthesis, then the exponents, the multiplication, the division, and as last the addition and subtraction.
90 ÷ [ 10 + ( 3 2 − 4 ) ]= 90 ÷ [ 10 + 28 ]
= 90 ÷ [ 38]
= 90 ÷38
= 2.368
To learn more about this visit, https://brainly.com/question/22757001
#SPJ9
Simplify 7+5c+4d-8c+d
Step-by-step explanation:
if there is no typo the expression is :
7 + 5c + 4d - 8c + d
to simplify combine all terms with the same variable and exponent of that variable.
so, this is
7 + (5c - 8c) + (4d + d) = 7 - 3c + 5d
Answer:
-3c+5d+7
Step-by-step explanation:
5.
Audrey gives each of her 6 closest friends a $20 gift card to their favorite store alono
with a small amount of cash during the holiday season. She spends the same amount of
money on each of her friends. If she spends $360 each year on holiday gifts for her
6 closest friends, how much cash does she give each friend?
1.
Define the variable.
3. Solve the equation.
Date
Period,
2. Write an equation that can be used to answer the question.
Explain the meaning of the solution.
Does the solution make sense for the problem? Why or why not?
Answer:
She gives 40 dollars to each friend.
The variable that you are trying to find is the amount of cash she gives to each friend. In the below equation, I call it x.
The equation is x = (360/6) - 20.
Step-by-step explanation:
1. Let the variable be x be the amount of cash Audrey gives to each friend.
2. The equation is 6x + 20 = 360.
3. The solutions is x = 57.
4. Audrey gives each friend $57 in cash along with a $20 gift card to their favorite store during the holiday season.
5. The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
The solution should be rounded to the nearest dollar, making it $57 per friend.
We have,
1.
Let's define the variable "x" as the amount of cash Audrey gives to each of her 6 closest friends.
2.
Since Audrey spends the same amount of money on each friend, the equation can be written as:
6x + 20 = 360
3.
Solve the equation:
Subtract 20 from both sides to isolate the term with "x":
6x = 360 - 20
6x = 340
Now, divide both sides by 6 to solve for "x":
x = 340 / 6
x = 56.67 (rounded to two decimal places)
4.
The solution, x = 56.67, means that Audrey gives each of her 6 closest friends approximately $56.67 in cash along with a $20 gift card to their favorite store during the holiday season.
5.
The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
In real-life situations, the cash given should be a whole dollar amount, not a fractional value like 56.67.
Therefore, the solution should be rounded to the nearest dollar, making it $57 per friend.
Thus,
1. Let the variable be x be the amount of cash Audrey gives to each friend.
2. The equation is 6x + 20 = 360.
3. The solutions is x = 57.
4. Audrey gives each friend $57 in cash along with a $20 gift card to their favorite store during the holiday season.
5. The solution does not entirely make sense for the problem because we cannot give fractional amounts of cash.
The solution should be rounded to the nearest dollar, making it $57 per friend.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ7
what is the HCF of 225 495 and 810
Step-by-step explanation:
Factor of 225
= 3 × 3 × 5 × 5
Factor of 495
= 3 × 3 × 5 × 11
Factor of 810
= 3 × 3 × 3 × 3 × 2 × 5
Now ,
HCF = Common Factor
= 3 × 3 × 5
= 45
[tex]...[/tex]
☘️☘️☘️...
a 3 gallon bottle of bleach costs 15.84. what is the price per cup
Answer: $0.33 per cup
15.84/3 to find the price per 1 gallon.
15.84/3 = 5.28 per gallon
There are 16 cups in a gallon, so divide the price of a single gallon by 16.
5.28/16 = price per cup
5.28/16 = .33
The price for each cup of bleach is $0.33.
learn more of cost prices here
https://brainly.com/question/19091385
#SPJ9
Missing value of principal when rate is 12% and time is 5 years will simple interest is $87
The principal is $145 .
Simple interest is the interest amount for a particular principal amount of money at rate of interest. The interest is calculated by multiplying the principal with the time and rate. The total amount after a certain time is given by the sum of the principal and the interest for that time.
The formula for calculating the Interest on a Principal(P) , time(t) and rate(R).
Interest=P×R×t
Now let us consider the principal to be P.
Time(t)=5 years
Simple Interest(I)=$87
Rate(R)=12%=0.12
Now let us find the principle for the this interest using the above formula.
I=P×R×t
Substituting the given values we calculate the Principal(P).
[tex]87=P\times0.012\times5\\or,P=87\div(0.012\times5)\\or,P=87\div0.6\\or,P=145[/tex]
Therefore the Principal for the simple interest of $87 for 5 years at rate of 12% is $145.
To learn more about principal and simple interest:
https://brainly.com/question/25845758
#SPJ9
Divide:
35x³-25x4y³/5x²y²
Answer:
35x³-25x4y³/5x²y² = −5x6y5+35x3
what is the net decimal equivalent if all discounts were applied in the series?
40% 15% 30%
The net decimal equivalent of the series 40/15/30 is 0.357;
Here we assume let X be retail price.
So,
X - 0.40 × X = Y ⇒ first discounted price.
Y - 0.15 × Y = Z ⇒ second discounted price.
Z - 0.30 × Z = T ⇒ total discounted price.
Now
X - 0.40 × X = (1 - 0.40) × X = 0.60 × X = Y
Y - 0.15 × Y = (1 - 0.15) × Y = 0.85 × Y = Z
Z - 0.30 × Z = (1 - 0.30) × Z = 0.70 × Z = T
Also, Z = 0.85 × Y, then 0.70 × Z = 0.70 × 0.85 × Y
And, Y = 0.60 × X, then 0.70 × Z = 0.70 × 0.85 × 0.60 × X
So,
= 0.70 × 0.85 × 0.60 × X
= 0.357X;
To learn more about this; visit: https://brainly.com/question/10495085
#SPJ9
A bank charged $10 to open an account. Shelly opened an account then deposited
$125 into the account. She then wrote checks for $15 and $35, made a deposit of
$50, then got $40 quick cash from an ATM which charged her a fee of $2.50. What is
her balance?
Answer:
$72.50
Step-by-step explanation:
-$10
+$125
-$50
+$50
-$42.50
find the distance between the two points in simplest radical form. (8,-1) and (2,-9)
What is the value of the underlined digit: 498,217 *
Answer:
B.) 90.000
Step-by-step explanation:
Your pre-selected answer choice is correct. The 9 is in the Ten Thousands place.
▶ Use the part of the nutrition label on the right. If protein contains approximately 4 calories per gram, find the percent of calories from protein from one serving of this food. (Round to the nearest tenth of a percent.) ww. The percent of calories from protein from one serving of this food is %. Nutritional information per serving Calories 277 Protein Carbohydrate Fat 11g 45g 6g
The percent of calories from protein from one serving of the food is found as 15.88%.
What is defined as the term percentage?A relative value representing the hundredth part of any quantity One percent (denoted 1%) is one hundredth part; thereby the, 100 percent describes the entire amount and 200 % identifies twice the given amount.
For the given information;
The total calories is 277.
Nutrients information in food.
Protein - 11g
Carbohydrate - 45g
Fat - 6g
The protein contains 4 calories per gram.
Thus, 11 grams of protein contains 4×11 = 44 calories per grams.
Find the % content of protein out of 277 calories;
p% of 277 = 44
p% = (44×100)/277
p% = 15.88%.
Therefore, the percentage of protein contained in the serving food is 15.88%.
To know more about the percentage, here
https://brainly.com/question/24877689
#SPJ9
I dont understand the problem i think it's 4.5 but i dont know
Answer:
probably 4.5
"Step-by-step explanation:
To break even, we need the total profit to be equal to 0. If we make x dollars in 2012, then we need to solve
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
This gives us x = 0.45 in thousands.
Since the question asks us to give the answer in hundreds, we multiply by 10 and get 4.5. Thus the profit in 2012 must be 4.5 (in hundreds) to break even."
Graph the following figure in the coordinate plane. Find the perimeter. X(0,1), Y(4, -2), Z(-5, -2)
The perimeter of the figure is 8 + √14 units
How to graph the figure in the coordinate plane and find the perimeter?The coordinates are given as
X(0,1), Y(4, -2), Z(-5, -2)
Next, we plot the above coordinates on a coordinate plane
See attachment for the plot of the coordinates on a coordinate plane
Next, we calculate the distance between the points using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have
XY = √(0 - 4)^2 + (1 + 2)^2 = 5
XZ = √(0 + 5)^2 + (1 + 2)^2 = √14
YZ = √(4 + 5)^2 + (-2 + 2)^2 = 3
The perimeter is calculated as
P = XY + XZ + YZ
So, we have
P = 5 + √14 + 3
Evaluate
P = 8 + √14
Hence, the perimeter of the figure is 8 + √14 units
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
A motorboat can maintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 33 minutes; the return trip takes 19 minutes. What is the speed of the current?
Answer:
7 mph
Step-by-step explanation:
A boat whose speed in still water is 26 mph makes a trip upstream in 33 minutes and returns in 19 minutes. You want to know the speed of the current.
SetupThe travel time is inversely proportional to the speed, so we can write the proportion (using c for the current speed in mph) ...
time upstream / time downstream = speed downstream / speed upstream
33/19 = (26 +c)/(26 -c)
SolutionMultiplying by 19(26 -c) gives ...
33(26 -c) = 19(26 +c)
(33 -19)(26) = (33 +19)c . . . . add 33c -19(26)
14(26)/(52) = c = 7
The speed of the current is 7 miles per hour.
I just need that one answer please
Answer:50.5
Step-by-step explanation:
because if you put the numbers from the smallest to largest in a line and take the middle numbers and divide by 2 you get 50.5.
what is the answer for this question using long divison with decimal remainders
4÷717
Answer:
179 R1
Step-by-step explanation:
Which value c makes the expression x2 + 2x + c a perfect square trinomial?
The value of the c is 1 which makes the perfect square trinomial.
According to the statement
We have to find that the value of the c.
So, For this purpose, we know that the
An expression obtained from the square of the binomial equation is a perfect square trinomial.
From the given information:
The Given statement is:
x² - 2x + c
is a perfect square of the form
(x - a)² = x² - 2ax + a²
Now,compare with x² - 2x + c, then
- 2a = - 2 ⇒ a = 1,
thus
a² = 1² = 1 = c
(x - 1)² = x² - 2x + 1 ← perfect square trinomial
It means the value of c is 1.
So, The value of the c is 1 which makes the perfect square trinomial.
Learn more about perfect square trinomial here
https://brainly.com/question/1538726
#SPJ9
Measure the length and width of a rectangular room in your house/apartment in feet. Determine the area of the room in square feet. Convert the area to both square inches and square yards. Explain how you made these conversions. When would you want to have the area in square feet? Square inches? Square yards?
Then measure the height of the room in feet. Calculate the volume of the room in cubic feet. Convert the volume to both cubic inches and cubic yards. Explain how you made these conversions. When would you want to have the area in cubic feet? Cubic inches? Cubic yards?
1) The area of the room in square feet, square inches, and square yards is as follows:
Area = 120 ft²
Area = 1,440 in²
Area = 40 yards²
2) The volume of the room in cubic feet, cubic inches, and cubic yards is as follows:
Volume = 1,440 ft³
Voluem = 17,280 in²
Volume = 480 yards²
What are the conversion rates?The conversion rates are:
1 foot equals 12 inches 3 feet are equivalent to 1 yard.The mathematical operations of multiplication and division are used.
Data and Calculations:Let the length = 12 feet
Let the width = 10 feet
Let the height = 12 feet
1 foot = 12 inches
3 feet = 1 yard
Area = 120 ft² (12 x 10)
Area = 1,440 in² (120 x 12)
Area = 40 yards² (120/3)
Volume = 1,440 ft³ (12 x 10 x 12)
Voluem = 17,280 in² (1,440 x 12)
Volume = 480 yards² (1,440/3)
Learn more about unit conversion rates at https://brainly.com/question/675275
#SPJ1
7x + 3x + x⁴ divided by x-2
Answer:
10x + x^4/x-2
Step-by-step explanation:
Combine like terms
(10x + x^4)/(x-2)
A bowl weighs 11/40 pound express this weight as a decimal
Answer:
0.275 lb
Step-by-step explanation:
Use a calculator to divide 11 by 40.
11/40 = 0.275
Answer:
0.275 pounds
Step-by-step explanation:
divide 11 (numerator) by 40 (denominator).