The difference in the account balances at the end of the loan terms is $313.98.
What is the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Given A homeowner is financing the cost of new windows. Two lenders have approved the homeowner for a $12,000 loan.
principal = $12,000
Offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54-month term
Amount of offer 1 = $14,430
Offer 2: 3.75% annual interest compounded monthly for a 66-month term
the amount is given by,
A = [tex]p(1 + \frac{r}{n} )^{nt}[/tex]
nt = 66 months
n = 12
r = 3.75% = 0.0375
p = $12,000
substitute the values in the formula,
A = 12000(1 + (0.0375/12))⁶⁶
A = 12000(1.228665)
A = $14,743.98
Difference in amounts = $14,743.98 - $14,430
The difference in amounts = $313.98
Hence the difference in amounts is $313.98.
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You and your friend enter a drawing with 3 different prizes. A total of 15 people entered the drawing, and prizes are awarded randomly.
There are 2730 ways to award the prizes.
What is the probability that you win first prize and your friend wins second
prize?
A. 1/2730
B. 15/2730
C. 1/15
D. 13/2730
The probability that you win first prize and your friend wins second
prize is option D: 13/2730.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Total number of prizes awarded = 3
Number of people entering the drawing competition = 15
Number of ways to award the prize = 2730
Out of the 3 prizes the first and the second is needed.
So, the prize for the first and the second positions are fixed and there is no need to consider the remaining 13 people to win the prize.
Hence the remaining number of people who can win the 3rd prize = 13
The number of ways one of them wins the 3rd prize = 13
The total number of ways = 2730
Therefore, the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 13 people is 13/2730.
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Is a triangle 180 or 190?.
Answer:
Step-by-step explanation:
180 degrees in total
PLSSSS I’ll give brainliest!!! Due at 11:59 I’m in 5th grade
Answer:
A -> 3 × 3/4
B -> 4 × 1/4
C -> 2× 2/3
D -> 3 × 1/6
E -> 2 × 2/4
F -> 4 × 5/6
the owner of sports complex wants to carpet a hallway connecting two building the carpet costs $1.50 per square foot. how much does it cost to carpet the hallway?
The cost of the carpet is $526.75
What is the area of any shape?
The area of a shape is a measure of the size of the region occupied by the shape. The formula for finding the area of a shape depends on the specific shape being considered
Based on the information given:
The carpet costs $1.75 per square foot
Get the area of the carpet
Area = 24(7) + 7(15) + 0.5(28) + 0.5(28)
Area of the composite figure = 273 + 28
Area of the composite figure = 301 ft²
Cost of the carpet = 301 * 1.75
Cost of the carpet = $526.75
Hence, the cost of the carpet is $526.75
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Answer: the Coat is $526.75
Ue the entence to anwer the quetion. Mot doctor ay many people who don't get enough leep every night truggle with illne and tre. Which kind of evidence i thi an example of? (1 point)
This kind of evidence is an example of a claim. Hence, the correct answer is option 1.
A claim is a statement or assertion that is made about a particular topic or issue. In this case, the statement is being made by "doctors" and is being presented as evidence of a causal relationship between lack of sleep and negative health outcomes. The statement is not an argument, which would include reasoning or logic to support the claim, nor is it a testimony or excerpt, which would be a statement or quote from a specific person or source.
Option 2, "an argument," is incorrect because it suggests that reasoning or logic is being provided to support the claim. However, in the sentence provided, there is no indication that any reasoning or logic is being presented to support the claim that many people who do not get enough sleep each night suffer from illness and stress. Usually, an argument has a claim and evidence or reasoning to back up that claim.
Option 3, "a testimony or an excerpt," is incorrect because it suggests that a statement or quote is being provided from a specific person or source. However, in the sentence provided, there is no indication of a specific person or source providing the statement. Instead, the statement is being attributed to "doctors" in general rather than any specific individual. A testimony would typically include a statement or quote from a specific person or source, given under oath or affirmation in a formal legal setting.
This question should be provided as:
Use the sentence to answer the question. Most doctors say many people who don't get enough sleep every night struggle with illness and stress. Which kind of evidence is this an example of? Responses:
A claim An argument A testimony or an excerptThe correct answer is option 1.
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A line of 20cm ha 4 point ( A,B,C,D ). Line AB=8. 6cm, Line AD=20cm BC=CD
Work out the length of BC
The length of BC is 5.7 cm
A dot is used to symbolise a point, which is a place in any space (.). It does not have any size, shape, length, or height. A line segment has a beginning and an end, but a line is stretched in both directions towards infinity.
It is given that the length of AB is 8.6 cm and length of AD is 20 cm.
Also, BC=CD
As there are 4 points (A, B, C, D) on the line and the length of the lone is 20 cm, we can say
AB+BC+CD= 20 --------------- (1)
Let us consider that BC=CD= x (say)
Substituting the values in equation (1),
8.6+ x+ x=20
Or, 2x =11.4
Or, x=11.4/2
Or, x=5.7 cm
Therefore, we can say that the length of BC is 5.7 cm.
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On March 14 at 1:59, people celebrate Pi Day by eating pie. Why do you
think people celebrate on this day at this time?
Answer:
They celebrated it on March 14 at 1:59 because...
The first few digits of pi are --- 3.14159
The date of March 14 is 3/14. Then you add the 1:59 it makes the first few digits of pi.
Step-by-step explanation:
The tradition to celebrate Pi Day on 14th March started in the late 80's, when the physicist Larry Shaw organized the first Pi Day celebration at the San Francisco Exploratorium. Since then, Pi Day has become a popular way for mathematicians, educators, and students to celebrate and share their interests in mathematics. Many schools, universities, and math clubs around the world host events, such as pi recitation contests, pi-themed games, and pie-eating contests, to celebrate this day.
Eating pie is also a way to join the celebration, as the word "pi" sounds like "pie". People often eat different types of pie on Pi Day, such as pizza pie, sweet pies, and savory pies to celebrate the mathematical constant pi and its connection to the word “pie”.
Write y = -7 + 6x in standard form
Answer: y = -7 + 6x in standard form is 6x - y = 7
Step-by-step explanation: I hope this helps!
Answer: 6x + y= -7
Step-by-step explanation:
y= mx+b
Y-int form
standard form: ax+by=C
So...
6=x
1=y
-7=c
im stuck on this question pls, thank you!
Answer: Area = 28.3cm²
Circumference = 18.9cm
Step-by-step explanation:
Area = πr²
= π × 3²
= 28.27
= 28.3cm² (estimate to 3s.f always)
Circumference = 2πr
= 2 x π x 3
= 18.85
= 18.9cm (estimate to 3s.f always)
The area and the circumferences of the circle are 28.27 square meters and 18.85 meters.
Given is a circle with radius 3m we need to determine the area and the circumferences of the circle,
To determine the area and circumference of a circle with a radius of 3m, we can use the following formulas:
Area of a circle: A = πr²
Circumference of a circle: C = 2πr
Here, "r" represents the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.
Let's calculate the values:
Area:
A = πr²
A = 3.14159 x (3m)²
A = 3.14159 x 9m²
A ≈ 28.27 square meters
Therefore, the area of the circle is approximately 28.27 square meters.
Circumference:
C = 2πr
C = 2 x 3.14159 x 3m
C ≈ 18.85 meters
Therefore, the circumference of the circle is approximately 18.85 meters.
Hence the area and the circumferences of the circle are 28.27 square meters and 18.85 meters.
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express x in terms of y
Answer: (5y+6)/2
Step-by-step explanation:
WILL MARK BRAINLIEST!! 20 POINTS PLEASE HELP ASAP GEOMETRY!
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot
Answer:
124.29ft (approximately 125ft)
Step-by-step explanation:
Refer to the Image
Complete the table to find all the factor pairs of 50.
First factor
5
and
and
and
Factor pairs
Second factor
50
25
The complete table to find all the factor pairs of 50 is. First factor Second factor. 1 and 50. 2 and 25. 5 and 10.
The complete table to find all the factor pairs of 50 is
First factor Second factor
1 and 50
2 and 25
5 and 10
What are factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
How to find all the factor pairs of 50
From the question, we have the following parameters that can be used in our computation:
Factor pairs
The number is then given as
Number = 50
The given table of values is incomplete
So, we fill them one after the other
The number 50 can be expressed as
50 = 1 * 50
So, the factor pairs are 1 and 50
The number 50 can also be expressed as
50 = 2 * 25
So, the factor pairs are 2 and 25
Lastly, the number 50 can also be expressed as
50 = 5 * 10
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associative property commutative property distributive property
Different properties, significance of those properties and their applications in mathematics.
Associative property : Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but it doesn’t hold for subtraction and division. This can be observed from the following examples.
Addition:
a+ (b+c) = (a+b) + c
Subtraction:
a-(b-c) ≠ (a-b) – c.
Multiplication:
a x (b x c) = (axb) x c
Division:
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Distributive property : This property is used to eliminate the brackets in an expression. The distributive property states that each term inside the bracket should be multiplied with the term outside. This property is very useful while simplifying the expressions and solving the complicated equations.
Addition:
a(b+c) = ab + ac
Subtraction :
a(b-c) = ab – ac
Commutative property : This property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.
Addition:
a+b = b+a.
Subtraction:
a-b ≠ b-a.
Multiplication:
a x b = b x a
Division:
a ÷ b ≠ b ÷ a.
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Van has 45 new baseball cards. He puts them in a binder that holds 9 cards on each page. How many pages dose he fill?
To find out how many pages Van fills with his new baseball cards, we need to divide the total number of cards by the number of cards that fit on each page.
He has 45 baseball cards and each page holds 9 cards.
So, we can divide 45 by 9.
45 / 9 = 5
Therefore, Van fills 5 pages with his new baseball cards.
It's worth noting that this method gives the number of full pages that are filled and if there are any remaining cards, we have to add one more page for the remaining cards.
What is a 45 degree angle called?.
A 45 degree angle is called an acute angle
There are 5 types of angles according to their measure:
1) Acute angle: it is the one that measures more than 0° and less than 90°.
2) Right angle: an angle that measures 90°.
3) Obtuse angle: an angle measuring more than 90° and less than 180°.
4) Extended angle: an angle measuring 180°.
5) Complete angle: an angle that measures 360°.
What is an angle?An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.
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4. Mariela purchases a used microwave for $50. She marks the price up 60%. If a 5.8% sales tax is also added, what is the final price of the microwave?
Mariela spends $50 on a used microwave. By 60%, she raises the price. When a 5.8% sales tax is additionally included, the ultimate cost is 20 in 60% and 47.1 in 5.8%.
How do you mark up 60%?Cost plus markup % multiplied by cost is the formula used to increase a product's markup percentage. Let's say you're utilising a markup of 60% and the item costs $75. multiplying by 60 percent $75. Now you have $45. For instance, the markup percentage would be 50% if the cost to produce your product was $50 and the selling price was $75: ($75 - $50) / $50 =.50 × 100=50%.
0.6 is 60 hundredths of a unit, thus write it as 0.60. 60% is equal to 60 hundredths. The decimal point can alternatively be shifted two places to the right to find the % equivalent. As a result, the markup equation is now: markup = 100 × (revenue - cost) / cost. Last but not least, use revenue = cost + cost × markup / 100 to determine the selling price.
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inequality of x is -11
The required solution to the given inequality is x > - 5.5 which means x is greater than -5.5.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The statement is given as "twice x is greater than -11"
This can be in the algebraic form written as :
2x > - 11
Divided both sides of the above inequality, we get
x > - 11/2
x > - 5.5
Thus, the required solution to the given inequality is x > - 5.5.
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The question seems incomplete, the complete question would be as:
What is the solution to the inequality that represents twice x is greater than -11?
The steps taken to correctly solve an equation are
shown below, but one step is missing.
-2(x-3)=-6(x+4)
-2x+6=-6x-24
?
4x=-30
x=-7.5
Which set of statements shows the equation that is
most likely the missing step and the property that
justifies the missing step?
4x-6=24
This step is justified by the additive property of equality
4x-6=24
This step is justified by the multiplicative property of equality
4x+6=-24
This step is justified by the multiplicative property of equality.
4x+6=-24
This step is justified by the additive property of equality.
Answer:
Step-by-step explanation:
-2(x-3)=-6(x+4) [Original Equation]
-2x+6=-6x-24 [remove the parentheses]
? -2x+6x+6 =-24 [add 6x to both sides]
4x + 6 = -24 [combine like terms]
-2x+6x+6=-6x-24+6x [Add 6x to both sides]
4x+6x+6=-6x-24+6x
-2x+6x+6=-24 [Add 6x and subtract 6 from both sides]
4x + 6 = -24 [This step is justified by the additive property of equality.]
x=-7.5
Which set of statements shows the equation that is
most likely the missing step and the property that
justifies the missing step?
4x-6=24
This step is justified by the additive property of equality
4x-6=24
This step is justified by the multiplicative property of equality
4x+6=-24
This step is justified by the multiplicative property of equality.
The correct answer is:
4x+6=-24
This step is justified by the additive property of equality.
Why is addition commutative and subtraction is not?.
Addition is commutative because the order in which two numbers are added does not affect the result.
Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.
Addition is commutative because the order in which two numbers are added does not affect the result. For example, 1 + 2 = 2 + 1 = 3. In contrast, subtraction is not commutative because the order in which two numbers are subtracted does affect the result. For example, 1 - 2 = -1, but 2 - 1 = 1. The operation is different when the order of the numbers are changed.
so, addition is commutative because the order in which two numbers are added does not affect the result.
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help plsssssssssssss
Answer:
-28
Step-by-step explanation:
f(-4) = 5(-4) - 2³ = -20 - 8 = -28
What system is Y =- 2x 3?.
The equation Y = -2x + 3 is a linear equation in slope-intercept form.
This equation represents a straight line with a slope of -2 and a y-intercept of 3.
The slope -2 tells us that for every unit increase in x, the value of y will decrease by 2. The y-intercept 3 tells us that the line passes through the point (0,3) on the coordinate plane.
It's a line that goes down as the slope is negative and the line can be represented by a graph, that can be easily plotted using the slope and the y-intercept. This equation can be used to model real-world situations like linear regression and many other fields.
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How many solutions does the nonlinear system of equations graphed below
have?
It depends on the specific nonlinear system of equations. Generally speaking, there could be one or multiple solutions, or there could be no solutions.
What is nonlinear system?A nonlinear system is a system of equations or functions which does not yield a linear relationship or linear solution when solved. A nonlinear system is often difficult to solve due to its inherently complex nature. Nonlinear systems can be found in multiple areas, such as engineering, economics, and mathematics.
If the equations are linear, then there will be exactly one solution. If the equations are nonlinear, then there could be no solutions, one solution, or multiple solutions (including infinitely many solutions). To find the exact number of solutions, you would need to solve the system of equations.
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The price of a TV i £260
In a ale the price i decreaed by 20%
Work out the price of the TV in the ale
The price of the TV is £208.
given the initial price of the TV as £260
now the Percentage rebate on TV is 20%
so the rebate is given by
=> 20 /100 * 260
=> 2 *26
=> 52
so total off on the TV is £52
Actual price of the TV is £260 - £52 = £208
Describe percentage rebate:An initial product or service price reduction that is expressed as a percentage of the original price is known as a percentage rebate. It is a technique for providing a discount or incentive to clients, and it is typically provided for a brief period of time or on particular goods or services. For instance, a 10% rebate on a product would entitle the buyer to a 10% discount off the list price.
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1/6.= Please I need
Answer:
≈ 0.17
Step-by-step explanation:
1/6 ≈ 0.17
A job hotline service charges $25 plus a 4% commission, c, on the first month of earnings if it finds work for a client. Write an equation that represents the total cost, T, to find a job through the hotline. What is the cost if a client earns $1500 the first month? Please someone help!!!!
The function g(x) repreent M(x) = 9 co (x - #) 3 after tranlating
I unit left and 4 unit up
Which equation repreent g(x)?
The equation for g(x) would be g(x) = 9cos(x-1) ^3 + 4.
This is because the function M(x) = 9cos(x)^3 represents a cosine function cubed, which results in a three-dimensional graph that oscillates and has multiple local maxima and minima. By translating the function one unit left, represented by the subtraction of 1 from the x value inside the cosine function, the entire graph is shifted one unit to the left.
The translation of 4 units up is represented by the addition of 4 to the overall function. This means that the entire graph of g(x) is now 4 units higher than the original function M(x).
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What is the solution to the system of equations y 3x 2 5x 2y 15 40 19?.
The solution to the system of equations y 3x 2 5x 2y 15 40 19 is ( -19,55)
A solution of the system is any collection of x 1, x 2, x 2,... x n values that simultaneously satisfies the system of linear equations presented above. The equations are referred to as consistent if the system of equations has one or more solutions.
It can be written as-
y= -3x-2
=> 3x+y= -2...................(1)
5x+2y = 15.....................(2)
multiplying Eqn (1) by 2 and
removing from equation (2)
x= -19
replacing x with -19 in equation (1)
3×(-19) +y= -2
y = 55
Consequently, the lines indicated by the
Equations given intersect at (-19, 55).
The resolution of an equation system
= ( -19,55)
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Jasmine started a new job in 2010 with an annual salary of $38,000. If her salary increases by 5.4% each year, how much did she make in 2019?
Type your answer as a decimal rounded to the nearest cent.
Jasmine will make $61000 annually in 2019.
What is percentage increase?A percent increase refers to how much a percentage has gone up over time.
Given that, Jasmine started a new job in 2010 with an annual salary of $38,000, her salary increases by 5.4% each year,
We know that, percentage of increase =
A = P(1+r)ⁿ
A = Final amount
P = Initial amount
r = rate
n = time
Here, A = ?
P = 38000
Time = 2019 - 2010 = 9
r = 5.4% = 0.054
A = 38000(1+0.054)⁹
A = 38000(1.054)⁹
A = 61002.7053
A ≈ 61000
Hence, Jasmine will make $61000 annually in 2019.
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find the length of the arc on a circle of radius r intercepted by a central angle θ
The length of the arc on a circle of radius r intercepted by a central angle θ is about 67.02 inches.
What is length of arc?
The distance between two places in a curve's section is known as the arc length. Any portion of a circle's circumference is an arc. An arc's angle at any given location is the angle created by the two line segments connecting that point to the arc's endpoints.
A circle has circumference 2πr.
240° is 240/360 of a circle or
24/36 = 6/9
= 2/3 of the circle
The arc is 2/3 of 2πr
= 2/3 x 2pi x 16 inches
General formula for the length of an arc is -
Arc Length = θ × r, with θ in radians 240 degrees
= 4π/3 radians
Arc = 4pi/3 x 16
= 64pi/3
= about 67.02 inches
Therefore, the length of arc is about 67.02 inches.
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Li is proving that TriangleLMN and TrianglePMQ are
similar. As part of her proof, she wants to
show that AngleMPQ is congruent to AngleMLN.
Which additional piece of information does
Li need to prove that AngleMPQ is congruent to
AngleMLN?
In order to prove that ∠MPQ is congruent to ∠MLN, she requires that PQ and LN should be parallel.
What are parallel lines?
When two lines in a plane do not cross at any point, they are said to be parallel. Lines that never cross paths with one another and do not have a common junction point are said to be parallel. They are equally spaced apart and have the same incline.
We know that corresponding angles of parallel lines are equal.
As shown in the figure, ∠MPQ and ∠MLN are corresponding angles.
So, if she is provided that PQ and LN are parallel, then, she can prove that ∠MPQ is congruent to ∠MLN and thus, the triangles are similar.
Hence, she requires that PQ and LN should be parallel.
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