After 40 years, the account has a total balance of $49.450.80.
What is an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
here, we have,
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
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A box of Almond Oats contains 15 ounces of cereal made of oat flakes and sliced almonds. Oat flakes
cost 15 cents per ounce, and almonds cost 30 cents per ounce. Write and simplify expressions in
terms of a, the number of ounces of almonds in the box.
a. The number of ounces of oat flakes in the box. o =
b. The cost of the almonds (in cents).c
c. The cost of the oat flakes (in cents). c =
=
d. The total cost of a box of Almond Oats (in cents). c =
Answer:
a. The number of ounces of oat flakes in the box is 15 ounces - a ounces, or 15 - a ounces.
b. The cost of the almonds (in cents) is 30 cents * a ounces, or 30a cents.
c. The cost of the oat flakes (in cents) is 15 cents * (15 - a) ounces, or 15 * (15 - a) cents.
d. The total cost of a box of Almond Oats (in cents) is the cost of the almonds plus the cost of the oat flakes, or 30a + 15 * (15 - a) cents.
A chef buys 15 fresh baguettes daily for sandwiches.if by the end of the day only 11 baguettes were used how many baguettes are left to repurpose into croutons for soup and salads
Answer: 4
Step-by-step explanation: 15-11=4
The table of values shows the height of a Ferris wheel car as it travels in a circular motion. Select each true statement.
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
C:The radius of the Ferris wheel is 35 feet
D:If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel.
The following statements are true:
A:The car makes a complete revolution in 10 seconds
B:The maximum height of the Ferris wheel is 65 feet
What is revolution ?A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.
A. The car makes a complete revolution in 10 seconds:
This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.
B. The maximum height of the Ferris wheel is 65 feet:
This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.
C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.
It is not possible to determine the radius of the Ferris wheel based on the given information alone.
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helpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The correct answer is
d) 4:16
Area and Perimeter of Similar Polygons:
Polygons are said to be similar when their corresponding angles are equal and their corresponding sides are in the same proportion. The perimeters and areas of identical polygons have a unique relationship, just as their corresponding sides do.
Perimeters: The scale factor and the perimeters ratios of perimeters are similar. In reality, the scale factor is identical to any ratio between any two similar forms (diagonals, medians, midsegments, altitudes, etc.).
Areas: If the scale factor of the sides of two similar polygons is [tex]\frac{m}{n}[/tex]
, then the ratio of the areas is [tex](\frac{m}{n} )^{2}[/tex].
(Area of Similar Polygons Theorem). Because area is a two-dimensional quantity, you square the ratio.
It is given that ,
the ratio of perimeters of two similar quadrilateral is 2:4.
now,
to find the ratio of area , we can take two quadrilaterals, say square.
Square ABCD of side 2 units and Square PQRS of side 4 units.
now ratio of areas,
[tex]=\frac{area of square ABCD}{area of square PQRS} \\\\=\frac{2*2}{4*4} \\\\=\frac{4}{16}[/tex]
If the given ratio of perimeters can be further solved as 1:2, then we can see that the ratio of areas can also be further solved as 1:4.
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It is known that g(x) is the inverse function of f (x). This means that the domain of
f (x) is equal to the [Select]
✓of g (x).
The domain of f(x) is equal to the range of inverse function g(x).
What are inverse functions?
A function from a set X to a set Y in mathematics assigns each element of X the exact same number of elements from Y. A function's inverse function reverses the action of a function or f. If and only if the function is bijective, the inverse of f is true.
Given two functions f(x) and g(x).
It is also said that g(x) is the inverse of f(x).
One of the properties of inverse functions is that only one-to-one functions are inverse. If g is equal to f's inverse, then f is equal to g's inverse.
Both f and g are one-to-one functions if they are the inverses of one another.
f and g are inverses of each other if (fog)(x) = x, x ∈ the domain of g.
The range of g equals the domain of f, and the domain of f equals the range of g.
Therefore the domain of f(x) is equal to the range of inverse function g(x).
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World population is about P = 7.68(1.0103)', with Pin billions and t in years since 2020.
(a) What is the yearly percent rate of growth of the world population? % per year
(b) What was the world population in 2020? billion people What does this model predict for the world population in 2026? Round your answer to 3 decimal places. i billion people
(c) Use part (b) to find the projected average rate of change of the world population between 2020 and 2026. Round your answer to the nearest integer. million people per year
To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.
(a) The yearly percent rate of growth of the world population is 1.0103%.
(b) The world population in 2020 was 7.68 billion people. The model predicts that the world population in 2026 will be 8.336 billion people.
(c) The projected average rate of change of the world population between 2020 and 2026 is 0.556 million people per year.
(a) The yearly percent rate of growth of the world population can be found by taking the exponential rate of change of the equation. The rate of change is 1.0103%.
(b) To find the world population in 2020, we can plug in t=0 into the equation. This gives us P=7.68 billion people. To find the world population in 2026, we can plug in t=6 into the equation. This gives us P=8.336 billion people.
(c) To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.
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estimate the percent of 18% of 48
Answer:8.64
Step-by-step explanation:
Answer:
8,64
Step-by-step explanation:
[tex]\frac{18}{100}[/tex]*48=8,64
help omg….
please help
Answer:
Step-by-step explanation:
Straight line= 180 degrees
|_= 90 degrees
180-90=90
3s-2=52
2s+2=38
52+38=90
s=18
solve the equations to find where they intersect
y = 6x - 8
y=-3x+10
Answer:
(2,4)
Step-by-step explanation:
This is a sketch of y = sin x.
The vertex A is at (90°, 1).
Write down the coordinates of the vertex A of the curve with equation
a) y = sin x + 2
b) y=-sin x
Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.
EquationsThe vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:
A = (90°, 1 + 2) = (90°, 3)
Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).
b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:
A = (90°, -1)
Therefore, the coordinates of the vertex A of the curve y = -sin x are
(90°, -1).
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help i need it
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Answer:
Step-by-step explanation:
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The pto is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 200 tickets sold. The winter gets a prize worth $76.
Answer:
Step-by-step explanation:
The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.
Let's first calculate the total revenue:
Number of tickets sold = 200
Price per ticket = $4
Total revenue = 200 * $4 = $800
Next, let's calculate the cost of the tickets:
Number of tickets sold = 200
Price per ticket = $4
Total cost = 200 * $4 = $800
Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:
Profit = Total revenue - Total cost
Profit = $800 - $800 = $0
So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.
An ant can travel at a constant speed of 980 inches every 5 minutes.
How far does the ant travel in 1 minute?
At this rate, how far can the ant travel in 7 minutes?
The ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
What is cross multiplication?To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
Given that the ant can travel at a constant speed of 980 inches every 5 minutes.
Thus,
5 minutes = 980 inches
1 minute = x inches
Using cross multiplication method or Butterfly method of multiplication we have:
x = 980/5
x = 196 inches.
In 7 minutes the ant can travel:
(7)(196) = 1372 inches.
Hence, the ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
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2. Rence and Sunil each shot 4 arrows at the target shown. Renee shot 3 arrows into A and I into B. Her score was 19. Sunil shot 2 into A and 2 into B. His score was 22. How many points were given for an arrow in B?
Using a system of equations, the number of points given for an arrow in target B is 7.
What is a system of equations?A system of equations means two or more equations solved at the same time or concurrently.
A system of equations is also described as simultaneous equations since they are solved simultaneously.
Target A Target B Total Score
Rence shots 3 1 19
Sunil shots 2 2 22
Let the points for an arrow into target A = x
Let the points for an arrow into target B = y
Equations:3x + y = 19 ... Equation 1
2x + 2y = 22 ... Equation 2
Multiply Equation 1 by 2:
6x + 2y = 38 ... Equation 3
Subtract Equation 2 from Equation 3:
6x + 2y = 38
-
2x + 2y = 22
4x = 16
x = 4
From Equation 1, substitute x = 4:
3x + y = 19
3(4) + y = 19
12 + y = 19
y = 19 -12
y = 7
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The circumferrence of the circle at the center of a basketball court is 37.68 feet. Find the area of the circle at center court. Use 3.14 for pi. Please answer.
113.097 is the area (i used 3.14) pls comment for explanation :)
Geometry question! Please help
The values 6, 4 and 12 are the measures of PR, PQ and RI respectively.
Solving similar trianglesThe given diagram is a triangle and the expression to be used based on the theorem is expressed as:
TP/TQ = PR+3/15
3/5 = PR+3/15
5(PR +3)= 3(15)
5(PR + 3) = 45
PR + 3 = 9
PR = 9 - 3
PR = 6
For the measure of PQ
PQ^2 = 5^2 - 3^2
PQ^2 = 25 - 9
PQ = 4
Determine the measure of RI
3/PQ = TR/RI
3/4 = 9/RI
1/4 = 3/RI
RI = 12
Hence the measure of PR, PQ and RI are 6, 4, and 12 respectively
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help me with this please i need help because i dont get it <33
Answer:B
Step-by-step explanation:
Answer:
Step-by-step explanation
D
because V = 1/3Hxr
^
pie
so 1/3(5)pie(1.75)
1.75 is from the diameter 1/2 which makes 1.75 the radius
4x=3x+10 transversal
Answer:
x=10.
Step-by-step explanation:
4x = 3x + 10
4x - 3x = 10
x = 10
the table below shows the number of hours students spend playing video games at home.which is a valid inference about the data
A valid inference about the data of Video Games Play Time among students is A). 50% of students spend 2- or 3 hours playing video games.
What is an inference?An inference is an evidence-based conclusion.
Inferences are reached when the necessary facts are available, and the researcher has done some calculations and reasoning using the facts.
Video Games Play Time
Hours Played Number of Students
0 2
1 4
2 6
3 8
4 5
5 or more hours 3
Total number of students 28
2 or 3 hours:Number of students = 14 (6 + 8)
14/28 - 50%
50% = 50%
4 or more hours:Number of students = 8 (5 + 3)
8/28 = 28.6%
28.6% > 10%
1 or 2 hours:Number of students = 10 (4 + 6)
10/28 = 35.7%
35.7% > 10%
3 or 4 hours:Number of students = 13 (8 + 5)
13/28 = 46.3%
46.3% ≠ 50%
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Question Completion with Answer Options:Video Games Play Time
Hours Played Number of Students
0 2
1 4
2 6
3 8
4 5
5 or more hours 3
Total number of students 28
A). 50% of students spend 2- or 3 hours playing video games.
B). Less than 10% of the students spend 4 or more hours playing video games.
C). Less than 10% of the students spend 1- or 2 hours playing video games.
D). More than 50% of the students spend 3- or 4 hours playing video games.
Two angles form a linear pair. If one angle is
9 times the measure of the other angle, what are
the measures of each angle?
Answer:
18°, 162°
Step-by-step explanation:
Angles that form a linear pair are supplementary, so their measures add to 180°.
Let the measure of the smaller angle = x.
The larger angle measures 9x.
9x + x = 180
10x = 180
x = 18
9x = 9(18) = 162
Answer: 18°, 162°
I need help answering this
Answer: god
Step-by-step explanation: god god god god god god god god
Use the data display to answer 11 and 12.
11. Analyze and Persevere What does the mean
describe in the data set?
12. Analyze and Persevere What does the range
describe in the data set?
Answer:
563
Step-by-step explanation:
Select the correct answer from each drop-down menu. Stacy rolls a pair of six-sided fair dice. The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is , and the two events are exclusive.
The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3
The two events are mutually exclusive
"Information available from the question"
Stacy rolls a pair of six-sided fair dice.
Now, According to the question:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favorable outcomes of either a multiple of 3 or an even number are:-
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
Probability = Number of fav. outcomes/ Total no. of outcomes
The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.
In our case this will be;
24/36 = 2/3
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f(x) = x4 - 7x3 + 2x2 + 40x ; x-5
The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5
We need to find the value of f(5)
Plug x=5 in the above function
f(x) = x⁴ - 7x³ + 2x² + 40x
f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)
=625-875+50+200
=0
Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x
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Complete question is below
f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)
Every day, Austin packs his favorite sandwich in a plastic sandwich box. Austin's sandwich box is 13 centimeters long and 12 centimeters wide, but only 3 centimeters tall. What is the volume of Austin's sandwich box?
The volume of the rectangular sandwich box of Austin is given by the equation V = 468 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular box be represented as V
Now , the equation will be
The length of the sandwich box = 13 cm
The width of the sandwich box = 12 cm
The height of the sandwich box = 3 cm
And , volume of the rectangular box V = Length x Width x Height
Substituting the values in the equation , we get
Volume of the rectangular box V = 13 x 12 x 3
On simplifying the equation , we get
Volume of the rectangular box V = 468 cm³
Hence , the volume of rectangular box is 468 cm³
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Given: AABC, CD 1 AB, AC = BC Area of AABC = 32 cm?. • M
The value of CD is 9.92 cm
How to find this value?Given:
∆ABC,CD ⊥ AB,AC = BC,Area of ABC = 32 cm2,m∠A = 72°Find: CD
Triangle ABC is an isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,
m<A = <mB = 72°
The sum of the measures of all interior angles is 180°, thus
m<C = 180° -72° - 72° = 36°
The area of the triangle ABC is
AABC= 1/2AC.BC.sin<C
If we expand,
AC = 10.43cm
Consider right triangle ACD. In this triangle,
sin <A = CD/AC
sin 72° = CD/10.43
therefore,
CD = 9.92 cm.
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Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°
Find: CD
Find all complex zeros of a polynomial function. Give the exact values. List multiple zeros as necessary. f(x)=2x5+11x4+17x3+21x2+45x
The zeros of the polynomial function f(x) are:
x = -1, -3/2, -2 + i/2, -2 - i/2
To find the complex zeros of the given polynomial function f(x), we can use the fact that every polynomial with complex coefficients has at least one complex zero.
First, we can use the Rational Zeros Theorem to find any rational zeros. The possible rational zeros are of the form p/q, where p is a factor of the constant term 45 and q is a factor of the leading coefficient 2. Therefore, the possible rational zeros are ±1, ±3/2, ±5, ±9/2, ±15, and ±45/2. We can test each of these values using synthetic division or long division to see if they are actually zeros of the polynomial.
Using long division, we find that x=−1 and x=−3/2 are zeros of the polynomial. Therefore, we can factor out (x+1) and (x+3/2) from the polynomial to get:
f(x) = (x+1)(x+3/2)(2x^3+8x^2+14x+30)
Next, we can use the quadratic formula to find the zeros of the cubic factor 2x^3+8x^2+14x+30. The quadratic formula gives:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 8, and c = 15. Plugging in these values, we get:
x = (-8 ± sqrt(8^2 - 4(2)(15))) / 4
= (-8 ± 2i) / 4
= -2 ± i/2
These are the exact values of the complex zeros of the polynomial function.
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PLEASE HELP ASAP
Circular pizza pies at Pat's Pizza's come in 10-inch and 16-inch diameters.
Which is closest to the difference in the areas of the pizza pies?
A
129.12 inches
B
183.46 inches
C
122.46inches
D
142.96 inches
Answer:
C
Step-by-step explanation:
The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and pi times (16/2)^2=201.06. 201.06-78.54 = about 122.52, which is closest to 122.46, or C.
In 2015, there were about 22 million teenagers (aged 13–17) in the United States. They each sent an average of 800 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation.
The number of text messages all of the teenagers in the United States send each month is 17600 million.
What are integers?In mathematics, an integer is a grouping comprising both positive and negative numbers. Integers are similar to whole numbers in that they do not include the fractional portion. Integers are thus numbers that can be positive, negative, or zero but not fractions. All mathematical operations, including addition, subtraction, multiplication, and division, can be carried out on integers.
Given that,
Number of teenagers = 22 million
Text sent on average = 800
Total messages sent = (22)(800) = 17600 million
Hence, the number of text messages all of the teenagers in the United States send each month is 17600 million.
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A certain car gets 23 miles to the galloon open highway. How far can it travel on 12 gallons of gas on open highway?
a. What is the rate in this problem?
b. What unit fraction is associated with this rate?
c. Answer the question (how far it can travel on 12 gallons) using the rate.
a) The rate in this problem is 23 miles.
b) The unit fraction is associated with this rate is 23/1.
c) In 12 gallons the car will travel 276 miles.
What is Unit rate?Unit rate is the ratio of two different units, with denominator as 1.
Given:
A certain car gets 23 miles to the galloon open highway.
a) The rate in this problem is 23 miles
b) The unit fraction is associated with this rate is 23/1.
c) In 12 gallons the car will travel
23/ 1 = x/ 12
x= 23 . 12
x= 276 miles
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