The foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
What is foci of the hyperbola?The two fixed points that are located inside each curve of a hyperbola are known as its foci, and they are important for the formal description of the curve.
Here the given equation of the hyperbola is [tex]4y^2-x^2=16[/tex] .
Now writing the given equation into standard form then,
=> [tex]4y^2-x^2=16[/tex]
=> [tex]-x^2+4y^2=16\\[/tex]
=> [tex]\frac{-x^2}{4}+\frac{4y^2}{4}=\frac{16}{4}[/tex]
=> [tex]\frac{-x^2}{4}+y^2=4[/tex]
=> [tex]\frac{-x^2}{4\times4}+\frac{y^2}{4}=1[/tex]
=> [tex]\frac{-x^2}{16}+\frac{y^2}{4}=1[/tex]
Here we know that [tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex] then a=2 and b=4 , (h , k)=(0,0)
Then c=[tex]\sqrt{a^2+b^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5}[/tex].
Then foci is (0,0+c) and (0,0-c) then,
=> (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex]
Hence the foci of the hyperbola is (0,2[tex]\sqrt5[/tex]) and ([tex]0,-2\sqrt5)[/tex].
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The sum of the numerator and the denominator of a certain fraction is equal to 4140. When the fraction was reduced, the result was 7/13
What was the original fraction?
Answer:
Step-by-step explanation
The answer would be 1449/2691 because of you simply then it would be 7/13
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
i’ll give brainlist
In response to the stated question, we may state that As a result, we can triangle only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
What precisely is a triangle?A triangle is a closed, two-dimensional geometric shape made up of three line segments called sides that intersect at three points called vertices. Triangles may be identified by their sides and angles. Based on their sides, triangles might be equilateral (all sides equal), isosceles, or scalene. Triangles are classed as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles more than 90 degrees) (all angles greater than 90 degrees). The area of a triangle may be calculated using the formula A = (1/2)bh, where A is the area, b is the base of the triangle, and h is the height of the triangle.
To demonstrate the similarity of two triangles, we must demonstrate that their respective angles are congruent and their corresponding sides are proportionate.
∆ABC ~ ∆PQR
We can see from the triangles that angle A is congruent with angle P, angle B is congruent with angle Q, and angle C is congruent with angle R. As a result, we have the angle-angle (AA) similarity:
∆ABC ~ ∆PQR
[tex]AC/PR = 13/16 \\AB/PQ = 5/8 \\BC/QR = 12/16 = 3/4 \\AC/PR = 13/16[/tex]
Because the matching side length ratios are not entirely equal, the triangles are not comparable according to the side-angle-side (SAS) similarity theorem. As a result, we can only state that angle A is congruent to angle P, angle B to angle Q, and angle C to angle R.
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What are the solutions of this quadratic equation
The solution to the given quadratic equation is expressed as:
x = (-1 ± √5)/2
How to find the solution of a quadratic equation?The general form of expression of a quadratic equation is:
y = ax² + bx + c
Where the solution is given by the quadratic formula:
x = [-b ± √(b² - 4ac)]/2a
The given quadratic equation is expressed as:
-3x² + 1 = 3x - 2
Rearranging in standard form is:
3x² + 3x - 3 = 0
Thus, the solution is:
x = [-3 ± √(3² - 4(3 * -3))]/2(3)
x = [-3 ± √(9 + 36)]/6
x = (-1 ± √5)/2
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Fill in this table as you work through the lesson.
The completed text are:
Point of Tangency: A point of contact between a circle and its tangent line.
Secant segment: A segment that intersects a circle twice and has one endpoint on the circle and one endpoint outside of the circle.
Tangent Segment: A segment of a tangent line that has an endpoint at the point of tangency.
Why are the above concept relevant?The concepts of chord, point of tangency, secant segment, and tangent segment are relevant in geometry, particularly in the study of circles.
They provide the foundation for understanding the relationships and properties of circles and their associated segments.
These concepts are essential in various fields such as engineering, physics, and architecture, where circular shapes are commonly used. They are also relevant in solving real-world problems that involve circles, such as determining the area and circumference of a circle.
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Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
PLEASE HELP
Step-by-step explanation:
(a) If the order of the choices is relevant, we can choose the first object in 5 ways, and the second object in 4 ways (since we cannot choose the same object again). Therefore, the total number of ways to choose 2 objects without replacement and with order being relevant is:
5 x 4 = 20 ways
(b) If the order of the choices is not relevant, we need to use the combination formula, which is:
nCk = n! / (k! * (n-k)!)
where n is the total number of objects, and k is the number of objects we want to choose.
In this case, we want to choose 2 objects out of 5, so n = 5 and k = 2. Therefore, the number of ways to choose 2 objects without replacement and with order not being relevant is:
5C2 = 5! / (2! * (5-2)!) = 10 ways
Therefore, there are 20 ways to choose 2 objects without replacement and with order being relevant, and 10 ways to choose 2 objects without replacement and with order not being relevant.
Which number is prime?
1) 19
2)14
3)10
4)20
Answer: 19
Step-by-step explanation:
number 19 is a prime number
Hello and Greetings YourDeath1.
The prime number is the number 19, since it is only divisible by 1 and itself, while the other numbers (14, 10, and 20) are divisible by other numbers besides 1 and themselves, making them composite numbers.
Option 1 being correct. (19)Step-by-step explanation:We are going to have which of the options in a prime number.
What is a prime number?A prime number is a natural number greater than 1 that has exactly two different divisors, that is, it is only divisible by 1 and itself.
Prime numbers are important in mathematics and cryptography, since they are the basis for the factorization of integers and the security of encryption systems.
We see which of all is a prime number:1. The number 19 is a prime number because it is only divisible by 1 and itself. That is, it has no more exact divisors than these two numbers. There is no other number that can divide 19 without leaving a remainder.
19/1 = 1919/19 = 12. The number 14 is a composite number because it has more than two exact divisors. In this case, 14 is divisible by 1, 2, 7, and 14. Therefore, it is not a prime number.
14/1 = 1414/2 = 714/7 = 214/14 = 13. The number 10 is a composite number because it has more than two exact divisors. In this case, 10 is divisible by 1, 2, 5, and 10. Therefore, it is not a prime number.
10/1 = 1010/2 = 510/5 = 210/10 = 1The number 20 is a composite number because it has more than two exact divisors. In this case, 20 is divisible by 1, 2, 4, 5, 10, and 20. Therefore, it is not a prime number.
20/1 = 2020/2 = 1020/4 = 520/5 = 420/10 = 220/20 = 1The prime number is the number 19, since it is only divisible by 1 and itself, while the other numbers (14, 10, and 20) are divisible by other numbers besides 1 and themselves, making them composite numbers.
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Don’t worry question is easy I’m just not bothered
The completion of the bill showing the total cost for a dishwasher repair is as follows:
Description Number Unit Cost Total
Filter 1 £28.95 £28.95
Basket 8 £1.50 £12.00
Spray arm 2 £10.45 £20.90
Labor charge 1¹/₂ hours at $18 per hour £27.00
Total Cost £88.85
How is the total cost determined?The total cost for the repairs can be computed using multiplication, division, and addition operations.
Multiplication and addition operations are three of the four basic mathematical operations.
Mathematical operations are techniques applied to solve mathematical problems.
Description Number Unit Cost Total
Filter 1 £28.95 £28.95
Basket 8 £1.50 £12.00 (£1.50 x 8)
Spray arm 2 £10.45 (£20.90/2) £20.90
Labor charge 1¹/₂ hours at $18 per hour £27.00
Total Cost £88.85
Thus, the total cost for the dishwasher repair is £88.85.
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If AB= 8x-5 and DC= 5x+4 Find AB+DC
The expression that represents the sum of the segments is:
AB + DC = 13x - 1
How to find the sum of the two segments?
Here we have two segments defined as functions of a variable x, and we can write them as:
AB = 8x - 5
DC = 5x + 4
We want to find an expression that represents AB + DC, we can just replace the two expressions (for each of the segments) in the sum above, then we willget:
AB + DC = 8x - 5 + 5x + 4
Now we can simplify that sum to get:
AB + DC = 8x + 5x - 5 + 4
= 13x - 1
That is the expression we wanted.
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This graph shows the solutions to the inequalities y > 3x + 14 and y < 3x + 2.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
C
This graph in the figure shows the no solutions to the inequalities
Define inequalitiesinequalities can be defined as if two real numbers or the algebraic expressions can be related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called inequalities.
For example, x>3 (x should be greater than 3)
given:system of inequalities y>3x+14 and y<3x+2
the system of inequalities have solutions only when the shaded part satisfies the given inequalities
We are given with the graph of inequalities . The given inequalities have 'and' in between.
so we look at the graph where both inequalities intersects
From the graph we can see that there is no intersection part of both shaded portions
So , we conclude that there is no solution.
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The complete question is:
This graph shows the solutions to the inequalities. does the system of inequalities y>3x+14 and y<3x+2. Does the system of inequalities have solutions? If so, which region contains the solutions?
Jim worked 45 hours this week. He earns time and a half for overtime. He is paid $12.59 per/hour, how much will he earn this week?
Answer: 566.55 US dollars
Step-by-step explanation: i think, please give 5 stars
A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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1 1/2 = 2x
what is the answer?
Answer:
3/4
Step-by-step explanation:
Which is an intercept of the function y = log base of 3 x?
The x-intercept of the function y = log base 3 x is (1, 0)
What is logarithm ?
A logarithm is a mathematical function that is used to solve equations involving exponential expressions. It is the inverse operation of exponentiation.
The logarithm of a number y to a given base b is the power or exponent to which the base must be raised to yield the number y. In other words, if we have the equation [tex]b^x = y[/tex], then the logarithm of y to the base b is x, which we can write as log base b y = x.
For example, if we take the base 2 and the number 8, the logarithm of 8 to base 2 is 3, because [tex]2^3 = 8[/tex]. This is written as log base 2 8 = 3.
According to the question:
The intercept of the function y = log base 3 x is the point where the graph of the function intersects either the x-axis or the y-axis. To find the intercepts, we set one of the variables to zero and solve for the other variable.
To find the y-intercept, we set x = 0 and evaluate the function:
y = log base 3 0
However, it is not possible to take the logarithm of 0 in any base, since 0 is not a positive number. Therefore, the function does not have a y-intercept.
To find the x-intercept, we set y = 0 and solve for x:
0 = log base 3 x
This equation can be rewritten in exponential form as:
[tex]3^0 = x[/tex]
Since any number raised to the 0th power is 1, we have:
1 = x
Therefore, the x-intercept of the function y = log base 3 x is (1, 0).
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Maria and Ming start at the same point and rive in opposite directions. Maria drives 36 mph and Ming drives 32 mph. How far apart will they be in 2 hours
Maria and Ming will be 136 miles apart after 2 hours.
What is Distance?
Distance is the total length of a path an item or person takes to get from one place to another, ignoring the direction of motion. Given that it is a scalar number, it has only a magnitude and no direction. The most common units used to determine distance are meters, kilometers, miles, and feet. (ft).
The distance between Maria and Ming will grow at a rate that is equal to the sum of their speeds because they are traveling in opposite directions:
distance between them = (Maria's speed + Ming's speed) x time
= (36 mph + 32 mph) x 2 hours
= 68 mph x 2 hours
= 136 miles
Therefore, Maria and Ming will be 136 miles apart after 2 hours.
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Above are two different models of the same rectangular hallway. If the length of the model on the top is 6 cm, what is the length of the model on the bottom?
Answer: 15cm
Step-by-step explanation: If the length of the model on the top is 6 cm, then the length of the model on the bottom must be 15 cm
20) Calculate the average rate of change of f(x) = −x² + 3x - 6 on the interval [1, 3].
Answer:
asdf
Step-by-step explanation:
hurry!!!!!!!!!!!!!!!!!!!!!!!
Ruth and Josie will each have collected 117 signatures in one minute.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.The slope and the intercept for this problem are given as follows:
Slope: number of new signatures per minute.Intercept: initial number of signatures.Hence the functions are given as follows:
R(x) = 113 + 4x.J(x) = 116 + x.They will have the same amount when:
R(x) = J(x)
113 + 4x = 116 + x
3x = 3
x = 1 minute.
The amount is of:
J(1) = 116 + 1 = 117 signatures.
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Question:
A student is taking a quiz with one true/false question, one multiple-choice question with four choices, and one question where you must pick option 1 or 2. Each question has a single correct answer. What is the probability of getting all 3 answers correct?
Pls help.
The prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.
What is PrοbabiIity?PrοbabiIity is a measure οf the IikeIihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, with 0 indicating impοssibiIity and 1 indicating certainty. It is used in variοus fieIds such as mathematics, statistics, science, ecοnοmics, and finance.
The prοbabiIity οf getting the true/faIse questiοn cοrrect is 1/2 οr 0.5. The prοbabiIity οf getting the muItipIe-chοice questiοn cοrrect is 1/4 οr 0.25. The prοbabiIity οf getting the Iast questiοn cοrrect is 1/2 οr 0.5.
Tο find the prοbabiIity οf getting aII 3 answers cοrrect, we muItipIy the prοbabiIities οf getting each questiοn cοrrect:
0.5 * 0.25 * 0.5 = 0.0625
Sο the prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.
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The bookstore has 27 chapter books, 9 comic books, and 30 picture books. The shop sold
one-third of the books. How many books were sold?
Answer:
22
Step-by-step explanation:
first you would add all books from the book store to get 66
Then you would divide that by 3 to get
66÷3=22
Multiply the expression 23(13m-5)
Answer:
Step-by-step explanation:
294m
The mean hourly salary for a high school graduate is $13.50 per hour with a standard
deviation of $5.75. The mean hourly sdiary for a person with an Associate's degree is
$19.75 with a standard deviation of $9.25. What is the standard deviation of the
difference in the hourly salaries between a high school graduate and a person who
earned an Associate's degree?
The standard deviation of the difference in the hourly salaries between a high school graduate and a person who earned an Associate's degree is approximately $10.89.
To find the standard deviation of the difference in hourly salaries between a high school graduate and a person with an Associate's degree, you need to use the formula for the standard deviation of the difference between two independent variables:
σ_diff = √(σ₁² + σ₂²)
Here, σ_diff represents the standard deviation of the difference, σ₁ represents the standard deviation of the high school graduate's salary ($5.75), and σ₂ represents the standard deviation of the Associate's degree holder's salary ($9.25).
Using the formula:
σ_diff = √(($5.75)² + ($9.25)²)
σ_diff = √(33.0625 + 85.5625)
σ_diff = √(118.625)
σ_diff ≈ 10.89
So, the standard deviation of the difference is approximately $10.89.
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In one town 44% of voters are democrats if two voters are randomly selected for a survey find the probability that they are both Democrats assume events are independent round to the nearest thousand if necessary
the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194
The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".
The AND means we need to MULTIPLY the individual probability of a person being a democrat.
The probability that a voter is democrat is 44% (0.44) -- stated in the problem
Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44
Rounded to the nearest thousandth, 0.194
The last answer choice is correct.
the complete question is-
In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.
0.189
0.880
0.440
0.194
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A store sells chips that are usually $6.00. They are on sale for $5.28. What percentage are they marked down?
Answer:
the chips are marked down by 12%.
Step-by-step explanation:
To calculate the percentage discount, you can use the formula:
percentage discount = (original price - sale price) / original price x 100%
Plugging in the values given in the problem, we get:
percentage discount = (6.00 - 5.28) / 6.00 x 100%
percentage discount = 0.72 / 6.00 x 100%
percentage discount = 0.12 x 100%
percentage discount = 12%
Answer:
The answer is 12%
Step-by-step explanation:
6 - 5.28 = 0.72
0.72/6 = 0.12
0.12 is a decimal, but written as a percent is 12%.
The flag starts at 0 and moves 8 feet right to on the number line. Then the flag moves 12 feet left to on the number line. Then the flag moves 13 feet right to on the number line. Nine is less than 10.
PLEASE HELP
The flag starts at 0 on the number line and moves 8 feet right to 8.
We can calculate this by adding 8 to 0, which gives us 8. Then the flag moves 12 feet left to -4. We can calculate this by subtracting 12 from 8, which gives us -4. Then the flag moves 13 feet right to 9. We can calculate this by adding 13 to -4, which gives us 9. Nine is less than 10, so the flag ends up on the number line at a value less than 10.We can calculate the total distance moved by adding 8 + (-12) + 13, which gives us 9. This means the flag has moved a total of 9 feet. All of these calculations demonstrate that the flag has moved 8 feet right, 12 feet left, and 13 feet right to end up on the number line at 9, which is less than 10.
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PLS HELP FASTTTTTTTTTTTTTTTTTTTTTT
The buying and selling rates of US $ I are NRs 119.25 and NRs 119.85 respectively. Rushbu has 300 USD and goes to a bank to exchange her dollars into Nepali currency. Is it sufficient to her to buy a television costing Rs 35,000 after allowing 10% discount and including 13% VAT from the Nepalese rupees which is exchanged with the dollars? Give reason.
Answer:
Rushbu exchanges 300 USD at the buying rate of NRs 119.25, so she will receive:
300 x 119.25 = NRs 35775
After allowing a 10% discount, Rushbu will need to pay:
35000 - (10/100 x 35000) = NRs 31500
Including 13% VAT, Rushbu will need to pay:
31500 + (13/100 x 31500) = NRs 35655
Since Rushbu received NRs 35,775 after exchanging her 300 USD, she will have enough Nepali currency to buy the television, even after accounting for the discount and VAT.
Therefore, Rushbu will have enough money to buy the television, and she will have NRs 120 less than she received from exchanging her 300 USD, but that does not affect her buying capacity in this case.
Which expressions are equivalent to 3x + 3(x+y)? Choose all answers that apply: A 6x + 3y CO U 3(x + x + y) 3xy Stuck? Review related articles/videos or use a hint. Report
Two equivalent expressions to 3x + 3(x+y) are:
3*(x + x + y) 6x + 3yWhich expression is equivalent to the given one?Two expressions are equivalent if we can rewrite one into the other, in such a way that we only use algebra to do so.
Here we start with the expression:
3x + 3(x + y)
If we take 3 as a common factor, then we can write:
3x + 3(x + y) = 3*(x + (x + y)) = 3*(x + x + y)
That is an equivalent expression, now if we simplify this:
3*(x + x + y) = 3*(2x + y)
Distribute that product.
3*(2x + y) = 6x + 3y
These is other equivalent expression.
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Which two points would a line of fit go through to best fit the data? (6, 4) and (9, 1) (3, 5) and (10, 1) (1, 8) and (10, 1) (1, 5) and (7, 3)
Answer: Therefore, the set of points that have the smallest SSE is (1, 5) and (7, 3), and the line of fit would go through these two points to best fit the data.
Step-by-step explanation:
To determine the line of best fit, we need to find the equation of the line that passes through the given points. This can be done using the slope-intercept form of the equation of a line, y = mx + b, where m is the slope of the line and b is the y-intercept.
For each set of points, we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
and then use one of the points to solve for b.
(6, 4) and (9, 1):
m = (1 - 4) / (9 - 6) = -3/3 = -1
Using point (6, 4):
4 = -1(6) + b
b = 10
So the equation of the line is y = -x + 10.
(3, 5) and (10, 1):
m = (1 - 5) / (10 - 3) = -4/7
Using point (3, 5):
5 = (-4/7)(3) + b
b = 41/7
So the equation of the line is y = (-4/7)x + 41/7.
(1, 8) and (10, 1):
m = (1 - 8) / (10 - 1) = -7/9
Using point (1, 8):
8 = (-7/9)(1) + b
b = 71/9
So the equation of the line is y = (-7/9)x + 71/9.
(1, 5) and (7, 3):
m = (3 - 5) / (7 - 1) = -1/3
Using point (1, 5):
5 = (-1/3)(1) + b
b = 16/3
So the equation of the line is y = (-1/3)x + 16/3.
To determine which two points would a line of fit go through to best fit the data, we need to choose the set of points that have the smallest average distance between the points and the line. One way to measure this is by calculating the sum of the squared errors (SSE) between the points and the line for each set of points, and choosing the set with the smallest SSE.
Using the equations we found for each set of points, we can calculate the SSE:
(6, 4) and (9, 1):
SSE = (4 - (-1(6) + 10))^2 + (1 - (-1(9) + 10))^2 = 29
(3, 5) and (10, 1):
SSE = (5 - (-4/7)(3) + 41/7)^2 + (1 - (-4/7)(10) + 41/7)^2 = 16.9
(1, 8) and (10, 1):
SSE = (8 - (-7/9)(1) + 71/9)^2 + (1 - (-7/9)(10) + 71/9)^2 = 28.7
(1, 5) and (7, 3):
SSE = (5 - (-1/3)(1) + 16/3)^2 + (3 - (-1/3)(7) + 16/3)^2 = 7.6
luke wants to buy an ipod. determine the equivalent cash price if luke makes 18 monthly payments of $31.48 at an interest rate of 15.2% compounded monthly
Answer:
We can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.
Substituting the given values, we have:
PV = $31.48 x [(1 - (1 + 0.152/12)^(-18)) / (0.152/12)]
PV = $31.48 x [(1 - 0.5159) / 0.0127]
PV = $1,007.97
Therefore, the equivalent cash price of the iPod is $1,007.97.
Solve for x. Round to the nearest tenth.
x =
(40 points)