Answer:
To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:
Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.
Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.
Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.
Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.
Line l has equation y= 5. find the distance between l and the point C (7, 0). Round your answer to the nearest tenth
The distance between the line y = 5 and point C (7, 0) is 5 units.
We have,
To find the distance between a line and a point, we can use the formula for the distance between a point (x1, y1) and a line ax + by + c = 0, which is given by:
Distance = |ax1 + by1 + c| / √(a² + b²)
In this case,
The equation of the line is y = 5, which can be rewritten as 0x + 1y - 5 = 0.
Comparing this to the general form ax + by + c = 0, we have a = 0, b = 1, and c = -5.
The coordinates of point C are (7, 0), so x1 = 7 and y1 = 0.
Let's calculate the distance using the formula:
Distance = |0(7) + 1(0) - 5| / sqrt(0² + 1²)
Distance = |-5| / √(1)
Distance = 5 / 1
Distance = 5
Therefore,
The distance between the line y = 5 and point C (7, 0) is 5 units.
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If 15% of the customers total is $98,880, then the sum total equals what
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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Convert the angle pi/3 radians to degrees.
Answer:
60 degrees
Step-by-step explanation:
To convert radians to degrees, multiply by 180/pi
pi/3 * 180/pi = 180/3 = 60 degrees
Step-by-step explanation:
3 radians =
171.887 degrees
AreaData Transfer RateDigital StorageEnergyFrequencyFuel EconomyLengthMassPlane AnglePressureSpeedTemperatureTimeVolume
ArcsecondDegreeGradianMilliradianMinute of arcRadian
ArcsecondDegreeGradianMilliradianMinute of arcRadian
Formula
3rad × 180/π = 171.887°
Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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Rolling two sixes in a row on a number cube is independent or dependent
Rolling two sixes in a row on a number cube (a fair six-sided die) is an independent event. The outcome of one roll does not affect the outcome of the subsequent roll. Each roll of the number cube is an independent trial, and the probability of rolling a six on each trial is always 1/6, regardless of the previous outcome.
square root 3 radicand x squared 2 multiply square root 4 radicand x squared 3
The simplification of [tex]\sqrt{3x^2} * \sqrt{4x^2} is 2x^2\sqrt{3.[/tex]
The given expression is [tex]\sqrt{3x^2} * \sqrt{4x^2} .[/tex].
To simplify this expression, we can start by simplifying each square root individually and then multiply the simplified expressions.
[tex]\sqrt{3x^2[/tex] can be written as[tex]\sqrt{3} * \sqrt{x^2[/tex]. Since [tex]x^2[/tex] is a perfect square, its square root is x. Therefore, [tex]\sqrt{3x^2[/tex] simplifies to [tex]x\sqrt{3.[/tex]
Similarly,[tex]\sqrt{4x^2[/tex] can be written as[tex]\sqrt{4} * \sqrt{x^2.[/tex]The square root of 4 is 2, and the square root of[tex]x^2[/tex]is x. Thus, [tex]\sqrt{4x^2[/tex] simplifies to 2x.
Now, we can multiply the simplified expressions:
[tex]x\sqrt{3} * 2x.[/tex]
To multiply these terms, we multiply the coefficients (numbers in front) and the variables separately.
The coefficient of [tex]x\sqrt{3[/tex]is x, and the coefficient of 2x is 2.
Multiplying the coefficients gives us x * 2 = 2x.
The variables in x√3[tex]x\sqrt{3[/tex] are x and √3, and the variables in 2x are x and 1.
Multiplying the variables gives us x * x = x^2, and √3 * 1 = √3.
Therefore, the final simplified expression is [tex]2x^2\sqrt{3.[/tex].
In summary,[tex]\sqrt{3x^2 } * \sqrt{4x^2[/tex] simplifies to [tex]2x^2\sqrt{3.[/tex]
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What is the sign of -xy? A:Positive B:Negative or C:Zero
The sign of -xy cannot be determined without knowing the signs of x and y. It can be positive, negative, or zero.
The signs of x and y influence the sign of -xy. A positive result is produced when multiplying two numbers with the same sign (both positive or both negative), while a negative result is produced when multiplying two numbers with opposite signs (one positive and the other negative). Their product is 0 when either one or both of the values are zero.
Therefore, depending on the signs of x and y, the sign of -xy can be positive, negative, or zero.
-xy is negative if x and y are both positive.
-xy is positive if x and y are both negative.
Regardless of the sign of the other number, if either x or y is zero, then -xy is also zero.
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Natalya designed a patio for her backyard. The two brick
sections will be the same size and concrete fills the rest of
the patio. Her design and the scale she will use to build
the patio are both shown below.
The concrete portion of the patio will cost $3 per square
foot to construct and the brick portion of the patio will
cost $6 per square foot to construct.
How much will Natalya spend constructing the patio with
concrete and brick?
Scale
1 cm = 4 ft.
A
B
6 cm
$432
$648
Brick
Concrete
6 cm
3 cm
Brick
3 cm
OPTIONS
A
$432
B
$648
C
$2,160
D
$3,024
The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.
We are given that;
The concrete portion of the patio cost=$3 per square
To construct and the brick portion of the patio cost= $6 per square
Now,
The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:
6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft
Therefore, the area of the concrete portion is:
24 ft x 12 ft = 288 ft^2
The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:
3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft
Therefore, the area of one brick rectangle is:
12 ft x 24 ft = 288 ft^2
Since there are two brick rectangles, the total area of the brick portion is:
2 x 288 ft^2 = 576 ft^2
Now we can multiply the areas by their costs per square foot to get the costs of each portion:
Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456
The total cost of constructing the patio is the sum of the costs of each portion:
Total cost = $864 + $3456 = $4320
Therefore, by area the answer will be $4320.
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The express that is equivalent is?
Step-by-step explanation:
Multiply the L side of the equation by d/d ( this is just multiplying by 'one' )
2/d * d/d = 2d / d^2
7+(2x4)-8÷(12-6)x(6÷2)
Answer:
11
Step-by-step explanation:
Remember PEMDAS
7+(2x4)-8÷(12-6)x(6÷2)
7 + 8 - 8 : 6 × 3 =
7 + 8 - 8/6 × 3 =
7 + 8 - 4 =
11
which two transformations are applied to pentagon ABCDE to create A''B''C''D''E''
The two transformations applied to pentagon ABCDE to create A''B''C''D''E'' are rotation and reflection.
To determine the two transformations applied to pentagon ABCDE to create A''B''C''D''E'', we need more specific information about the transformations or the corresponding points.
Transformations can include translations, rotations, reflections, dilations, or combinations of these.
Without knowing the specific transformations applied or having additional information, it is challenging to provide an accurate answer.
However, I can briefly explain some common transformations that could potentially be applied to a pentagon:
Translation: A translation involves moving the entire figure in a specific direction without changing its shape or orientation.
This transformation can be described by shifting the points of the pentagon horizontally or vertically.
Rotation: A rotation involves rotating the pentagon about a fixed point. The point of rotation could be inside or outside the pentagon, and the angle of rotation would determine the final position of the points.
Reflection: A reflection involves flipping the pentagon across a line, called the line of reflection.
Each point of the pentagon would be reflected across the line, resulting in a mirrored image.
Dilation: A dilation involves scaling the size of the pentagon by a certain factor.
This transformation can result in an enlarged or reduced version of the original pentagon.
Without specific details or information about the corresponding points in A''B''C''D''E'', it is not possible to determine the exact transformations applied.
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Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
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ery Test
What is the solution of this equation?
1
-3+
4
z = 1
Enter the correct answer.
The solution of this equation is z = 3.
We are given that;
1-3+4z = 1
Now,
To solve for z, we need to isolate it on one side of the equation. We can do this by following these steps:
Subtract −31
from both sides to eliminate it from the left side.
Multiply both sides by z to eliminate the fraction on the left side.
Divide both sides by 4 to isolate z on the left side.
Let’s see how this works:
−31+z4=1
−31+z4=1
z4=1+31
z4=34
4=4/3 z
z=3*4/4
z=4/4×3
z=3
Therefore, by the equation answer will be z = 3.
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Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
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I will give brainliest out please help me answer the unsolved ones
For the given triangles:
(1) x = 5.4
(2) x = √23
(3) θ = 25.84 degree
(4) x = 9.5
(5) n = 41
(1) In the given triangle,
One angle = 16 degree
Perpendicular = x
Hypotenuse = 20
Since we know that
Sinθ = opposite side of θ/hypotenuse
Therefore,
⇒ sin 16 = x/20
⇒ 0.27 = x/20
⇒ x = 5.4
(2) In the given triangle,
Hypotenuse = 12 km
Base = 11 km
perpendicular = x
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (12)²= (x)² + (11)²
⇒ 144 = (x)² + 121
⇒ x² = 23
Taking square root both sides we get,
Hence,
⇒ x = √23
(3) In the given,
Base = 20
Perpendicular = 42
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ (Hypotenuse)² = (42)² + (20)²
⇒ (Hypotenuse)² = 2164
Taking square root both sides,
⇒ (Hypotenuse) = 46.51
⇒ cosθ = Adjacent/hypotenuse
= 42/46.51
= 0.90
Taking inverse of cosθ,
⇒ θ = 25.84 degree
(4) In the given triangle,
One angle = 30 degree
Base = x
Hypotenuse = 11
Since we know that
cosθ = Adjacent/hypotenuse
Therefore,
⇒ cos 30 = x/11
⇒ √3/2 = x/11
⇒ x = 9.5
(4) In the given triangle,
Base = 40
Perpendicular = 9
Hypotenuse = n
We know that the Pythagoras theorem for a right angled triangle:
⇒ (Hypotenuse)²= (Perpendicular)² + (Base)²
⇒ n² = 9² + 40²
⇒ n² = 81 + 1600
⇒ n² = 1681
⇒ n = 41
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The expression that is equivalent to 6/q is
The expression that is equivalent to 6/q is 6q/q²
How to determine what the expression is equivalent toFrom the question, we have the following parameters that can be used in our computation:
6/q = ?/q²
Multiply both sides of the equation by q²
So, we have
q² * 6/q = ?/q² * q²
Evaluate the products on both sides of the equation
? = 6q
Hence, the expression that is equivalent to 6/q is 6q/q²
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Jim is participating in a 6-day cross-country biking challenge. He biked for 59, 52, 66, 45, and 68 miles on the first five days. How many
miles does he need to bike on the last day so that his average (mean) is 59 miles per day?
miles
I Don't Know
Submit
X
G
©2023 McGraw H LLC Al Rights Reserved. Terms of the 1 Privacy Center
DOU
Answer:295
Step-by-step explanati: 59 5 .
What is the meaning of "only under the assumption that at least one set X exists"?
The phrase "only under the assumption that at least one set X exists" means that a certain statement or conclusion holds true or can be deduced only if there is a set X that exists.
Answer to the questionIn other words, the validity or applicability of the statement is conditional upon the existence of at least one set X.
This phrase indicates that the argument or reasoning being presented depends on the existence of a specific set or group. Without the existence of such a set, the statement or conclusion being made may not hold true or may not be applicable.
It's important to note that without further context, the meaning and implications of this phrase may vary depending on the specific subject or context in which it is used.
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How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the the square tiles has an edge of 3/4 ft.
A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.
Given:
Length of the rectangular floor = 14 ft
Width of the rectangular floor = 6 ft
Edge length of square tile = 3/4 ft
First, let's calculate the number of tiles that can fit horizontally:
Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft
Since we want a whole number of tiles, we need to round down or take the floor value:
Number of tiles horizontally = floor(56/3) = 18 tiles
Next, let's calculate the number of tiles that can fit vertically:
Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft
Again, we round down or take the floor value:
Number of tiles vertically = floor(24/3) = 8 tiles
To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:
Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles
Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.
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a tip of $10 is typically suitable for which kind of service?
a mover delivering furniture
a valet who parks your car
a waiter at a fast food restaurant
In English classmates teacher gifts for horses each worth five points after three quizzes. She has the score for three and four. What does she need to get on the last quiz to have a mean score for
Answer:
5
She must therefore earn 5 points on the last test to achieve a mean score of 4.
Step-by-step explanation:
The sum of the data divided by the total number of data represents the mean, which is the average of a set of data.
The population of a small country is 2.457 million and its national debt is $5.99 billion. What is the amount of debt per person? Round to the nearest whole number.
The amount of debt per person in the small country is approximately $2,439. This means that, on average, each person in the country would be responsible for around $2,439 of the national debt.
To calculate the amount of debt per person in the small country, we divide the total national debt by the population and round the result to the nearest whole number. Let's perform the calculation.
The population of the small country is 2.457 million, which is equivalent to 2,457,000 people. The national debt is $5.99 billion.
To find the debt per person, we divide the national debt by the population:
$5.99 billion / 2,457,000 = $2,439.05 (rounded to two decimal places)
Since we want the answer in whole numbers, we round the result to the nearest whole number:
Debt per person = $2,439 (rounded to the nearest whole number)
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-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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Please and this question ASAP. Multiply 31.5 percent times 600
Answer:
189
Step-by-step explanation:
To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.
31.5 percent = 31.5/100 = 0.315
Multiplying 0.315 by 600 gives us:
0.315 * 600 = 189
Therefore, 31.5 percent of 600 is equal to 189.
you are dealt one card from a 52-card deck. find the probability that you are not dealt a two
Answer:
Step-by-step explanation:
48 out 52 cards are not a 2:
[tex]P(not 2)=\frac{48}{52} =\frac{12}{13}[/tex]
Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £80 per night, how much will Tara pay for 5 nights?
Tara will pay £360 for 5 nights if she chooses a hotel with a regular room price of £80 per night that has a 25% off sale on its prices, and the VAT charge of 20% must be added at the end of the transaction.
Tara looked up hotel room prices for her holiday. A hotel had a 25% off sale on its prices. A VAT charge of 20% must be added at the end of the transaction, after any discount. If the regular price of a room is £80 per night, then we have to determine how much Tara will pay for 5 nights.
A 25% discount on £80 is: 25/100 * 80 = £20. So the discounted price of a hotel room is: £80 - £20 = £60.Next, we add VAT of 20% to the discounted price: 20/100 * £60 = £12.
Hence, the final price for one night is: £60 + £12 = £72.Since Tara needs to stay in the hotel for 5 nights, she will pay: £72 * 5 = £360.
Therefore, Tara will pay £360 for 5 nights if she chooses a hotel with a regular room price of £80 per night that has a 25% off sale on its prices, and the VAT charge of 20% must be added at the end of the transaction.
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
To find out how many months it takes to pay off the credit card and the total amount paid including interest, we can use the following steps:
Step 1: Calculate the monthly interest rate
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate.
Monthly interest rate = 14.5% / 12 = 0.145 / 12 = 0.01208 (rounded to 5 decimal places)
Step 2: Set up the equation for the number of months
Let's denote the number of months it takes to pay off the card as 'n'. The monthly payment is $1,200.00, and the initial balance is $3,287.90. The monthly interest rate is 0.01208. The equation for the number of months can be written as:
(1) $3,287.90 ×[tex](1 + 0.01208)^n[/tex] - $1,200.00 ×[tex][(1 + 0.01208)^n[/tex] - 1] = 0
Step 3: Solve the equation
To find the value of 'n', we need to solve equation (1). However, solving it algebraically can be complex. Instead, we can use numerical methods like trial and error, or we can use a spreadsheet or a calculator to find the solution.
Using a spreadsheet or a calculator, we can input the values and increment 'n' until we find the point where the equation equals zero.
After performing the calculations, it is determined that it takes approximately 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
Therefore, the answer to the original question is that it takes 4 months to pay off the card, and the total amount paid, including interest, is $4,871.78.
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Need help with those 3 questions
The general form of the solutions of the recurrence relation is
[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
We are given that;
Series=1, 1, 1, 1, -2, -2, -2, 3, 3, -4
Now,
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
If the characteristic equation has repeated roots, then the general solution is modified by multiplying each term by a polynomial in n whose degree is equal to the multiplicity of the root minus one. For example, if r is a root of multiplicity m, then the corresponding term in the general solution is
[tex]a_n = (A + B n + C n^2 + … + Z n^(m-1)) r^n,[/tex]
where A, B, C, …, Z are arbitrary constants.
In this question, the characteristic equation has roots 1, 1, 1, 1, -2, -2, -2, 3, 3, -4. The root 1 has multiplicity 4, the root -2 has multiplicity 3, and the roots 3 and -4 have multiplicity 2 each.
[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
where A, B, C, D, E, F, G, H, I, J and K are arbitrary constants.
Therefore, by the equation answer will be [tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]
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I need help with this homework It's 3 AM right now. I'm so tired
I will mark the first person to help me brainliest, they will also get 50 points
The missing parts of the hierarchy of the quadrilaterals is listed below
KiteRectangleSquareRhombusParallelogramQuadrilateralTrapezoidSquareWhat are the quadrilateralsA four-sided polygon is called a quadrilateral. A polygon having four sides is referred to as a four-sided polygon in general.
A geometric figure with two pairs of parallel sides. The quadrilateral shape known as a trapezoid (or trapezium in certain areas) can be restated in different words.
A quadrilateral having four angles measuring 90 degrees each and having opposite sides parallel is called a parallelogram.
Rhombus shape: This particular four-sided shape is distinguished by having every angle measuring 90 degrees.
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See text below
Hierarchy of a Quadrilateral Assignment
Fill in each of the missing parts of the hierarchy of the
quadrilaterals. Include the properties of each of the figures