Answers
The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0 i.e. {y ∈ R, y ≠ 0} and there is no x-intercept in f(x) = 1/(3x - 4)
The range of the functionThe range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0.
To see this, note that the denominator of [tex]f(x) = \frac{1}{3x+4}[/tex], can take any real value except -4/3, since division by zero is undefined.
Therefore, f(x) can take any value except 0, which means the range of f(x) is {y ∈ R, y ≠ 0}
The reciprocal that is a linear functionThe reciprocal of a is 1/a
From the list of options, we have
f(x) = 1/(x + 3)
The reciprocal is x + 3 and this is a linear function
So, the reciprocal of a function that is linear is f(x) = 1/(x + 3)
The asymptote of the reciprocalThe reciprocal function of the form f(x) = 1/x has a vertical asymptote at x = 0.
Similarly, the reciprocal function of the form f(x) = 1/(ax + b) has a vertical asymptote at x = -b/a.
Comparing the given functions with the above form, we can see that:
f(x) = 1/(x + (5/2)) is of the required form with a = 1 and b = 5/2.
So, it has a vertical asymptote at x = -(5/2)/1 = -5/2.
Therefore, the function with a vertical asymptote at x = -5/2 is option (a), f(x) = 1/(x + (5/2)).
The horizontal asymptote of the functionThe correct answer is (d) All of the above, as all functions a, b and c have a horizontal asymptote at y = 0, when solved by graphs
The true statement about the function f(x)As x approaches (5/3)^+ (from the right-hand side), the function f(x) approaches positive infinity.
So, the true statement is (b) f(x) -> oo
The x-interceptGiven that
f(x) = 1/(3x - 4)
So, we have
1/(3x - 4) = 0
This gives
1 = 0
This means that there is no x-intercept.
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Related Questions
Given this equation what is the value of y at the indicated point?
Answers
Answer:
y = 4
Step-by-step explanation:
given equation of line is
y = - 3x - 2 and (- 2, y ) is a point on the line, then substitute x = - 2 into the equation for y , that is
y = - 3(- 2) - 2 = 6 - 2 = 4
A weather station on the top of a mountain reports that the temperature is currently -10*C and has been falling at a constant rate of 3*C per hour. If it continues to fall at this rate, find each indicated temperature.
What will the temperature be in 5 hours?
What was the temperature 8 hours ago?
PLEASE HELP ME!!!!
Answers
Answer:
The temperature in 5 hours will be -25°C.
The temperature 8 hours ago was 14°C.
Step-by-step explanation:
To find the temperature, y, in degrees Celsius at any given number of hours, x, from the current time, we can create a linear equation in the form y = mx + b, where m is the rate of change and b is the current temperature.
Given the current temperature is -10°C, then b = -10.
Given the temperature falls at a constant rate of 3°C per hour, then m = -3.
Substitute the values of m and b into the formula:
[tex]\boxed{y = -3x - 10}[/tex]
where:
y is the temperature in °C.x is the number of hours.To calculate the temperature in 5 hours time, substitute x = 5 into the equation:
[tex]\begin{aligned}\implies y&=-3(5)-10\\&=-15-10\\&=-25^{\circ}\text{C}\end{aligned}[/tex]
Therefore, the temperature in 5 hours will be -25°C.
To calculate the temperature 8 hours ago, substitute x = -8 into the equation. The value of x is negative since we want to find the temperature 8 hours before the current time.
[tex]\begin{aligned}\implies y&=-3(-8)-10\\&=24-10\\&=14^{\circ}\text{C}\end{aligned}[/tex]
Therefore, the temperature 8 hours ago was 14°C.
[64+{23-(-14+5x12/2-6)}]
Answers
Answer:
77
Step-by-step explanation:
First, let's simplify the expression inside the innermost parentheses:
5x12 = 60
60/2 = 30
-14 + 30 - 6 = 10
Now, we have:
[64 + {23 - 10}] = [64 + 13] = 77
Brandon read the book each day until he finishedit. Explain how you would use the data to label and plot the dotson a dot plot. What is the difference between the longest time andshortest time Brandon spent reading the book?q TEKS 4.9.B ©
1 _ 4 ,1 _ 4 , 1,1 _ 4 ,1 _ 2 ,3 _ 4 ,1 _ 2 ,1 _ 4
Answers
the difference between the longest and shortest time Brandon spent reading the book was 3/4 of a day.
How to solve the problem?
To label and plot the data on a dot plot, we need to first determine the range of values. In this case, we have the following data:
1/4, 1/4, 1, 1/4, 1/2, 3/4, 1/2, 1/4
The range of values is from 1/4 to 1, and we can use a dot plot to represent the data. On the dot plot, we will place a dot above each value on the number line. For example, we will place four dots above the value 1/4 since it appears four times in the data.
The dot plot would look like this:
markdown
Copy code
|
0.2 | x
|
0.4 | x x x x
|
0.6 | x x
|
0.8 | x x x
|
1.0 | x
|
From the dot plot, we can see that Brandon spent the most time reading the book when he read for the full day, which is represented by the dot at 1. The shortest time he spent reading was when he read for 1/4 of a day, which is represented by the dots at 1/4.
To find the difference between the longest and shortest time, we simply subtract the shortest time from the longest time. In this case, the longest time was 1 day, and the shortest time was 1/4 of a day. So the difference is:
1 - 1/4 = 3/4 of a day
Therefore, the difference between the longest and shortest time Brandon spent reading the book was 3/4 of a day.
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Help with this math please if you can !
Answers
Answer:
Step-by-step explanation:
Dilation by 3 means that you increase the length of each of the sides by 3. Since ED was 2 units long, the plotted dilation of ED is 6 units long. By multiplying each of the lengths of the sides by 3 units, you will be able to draw the whole image.
Answer:
see the attached image
Step-by-step explanation:
For a dilation of scale factor 3, we can multiply each side length by 3.
In the diagram shown, ABCD is a square. Suppose AB = 6. Find:
17). AC
18). AO
19). BO
Suppose AO = 4. Find:
20). BO
21). Area of Δ AOB
22). Area of ABCD
Suppose DO = 5. Find:
23). DC
24). Area of Δ DOC
25). Area of ABCD
Answers
ABCD is square, AC = 6, AO = 3√2, BO = 3√2, BO = 4, DC = 6, OC = 2√13 and area is 36 square units.
To solve the problems, we can use the following properties of squares:
The diagonals of a square bisect each other and are equal in length.
The diagonals of a square form two congruent right triangles.
The center of a square is equidistant from all four vertices of the square.
Since ABCD is a square, we have AC = AB = 6.
Since O is the center of the square, AO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:
diagonal² = AB² + BC²
= 6² + 6²
= 72
diagonal = √72 = 6√2
Therefore, AO = (1/2) diagonal = 3√2
Since O is the center of the square, BO is equal in length to AO, which we found in part (18). Therefore, BO = 3√2.
If AO = 4 and BO = AO, then BO = 4.
The area of ΔAOB is half the area of the square ABCD. The area of a square is given by side², so the area of ABCD is 6² = 36. Therefore, the area of ΔAOB is (1/2) × 36 = 18 square units.
The area of a square is given by side², so the area of ABCD is 6² = 36 square units.
Since the diagonals of a square bisect each other, DO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:
diagonal² = AB² + BC²
= 6² + 6²
= 72
diagonal = √72 = 6√2
Therefore, DO = (1/2) diagonal = 3√2
Since ABCD is a square, DC = AB = 6.
The area of ΔDOC is half the area of the square ABCD. Using the Pythagorean theorem, we can find the length of OC:
OC² = AO² + AC²
= 4² + 6²
= 52
OC = √52 = 2√13
Therefore, the area of ΔDOC is (1/2) × 6 × 2√13 = 6√13 square units.
The area of a square is given by side², so the area of ABCD is 6² = 36 square units.
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a skateboard ramp is 11 in high and raises at an angle of 22 in how long is the base of the ramp? Round to the nearest inch.
Answers
Answer: The length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.
Step-by-step explanation:
We can use trigonometry to solve this problem.
Let's call the length of the base of the ramp "x". Then, we can use the tangent function to find x:
tan(22) = 11/x
To solve for x, we can multiply both sides by x and divide by tan(22):
x = 11 / tan(22)
Using a calculator, we can find that:
x ≈ 27 inches
Therefore, the length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.
Greetings! ZenZebra at your service, hope it helps! <33
adding and subtract integrals
Answers
Adding and subtracting integrals is a fundamental technique in calculus that allows you to combine multiple integrals into a single expression. The process involves using the properties of integrals and the rules of algebra to simplify the expression.
How to add integrals?
To add two integrals, you simply add the integrands and integrate over the same limits of integration. For example, if you have two integrals, ∫f(x) dx and ∫g(x) dx
The sum of the two integrals would be
∫[f(x) + g(x)] dx
How to subtract integrals?
To subtract two integrals, you subtract the integrands and integrate over the same limits of integration. For example, if you have two integrals ∫f(x) dx and ∫g(x) dx
The difference of the two integrals would be ∫[f(x) - g(x)] dx
It's important to note that when adding or subtracting integrals, you must ensure that the limits of integration are the same. If they are not the same, you must first adjust one or both integrals to have the same limits of integration.
Another important point to keep in mind is that the properties of integrals allow you to simplify expressions before integrating. For example, if you have an integral of the form:
∫f(x) dx + ∫g(x) dx
You can simplify it as ∫[f(x) + g(x)] dx
before integrating.
In conclusion, adding and subtracting integrals is a straightforward process that involves using the rules of algebra and the properties of integrals. By following these techniques, you can simplify complex expressions and solve integration problems more efficiently.
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Correct question is "How to add and subtract integrals?"
Help please! 100 points!
Sean tossed a coin off a bridge into the stream below.
The path of the coin can be represented by the equation
H= -16t^2 + 72t + 100
t= time in seconds
h=height in feet
Answers
Step-by-step explanation:
The height of the coin, after t seconds, is given by the following equation:
How long will it take the coin to reach the stream?
The stream is the ground level.
So the coin reaches the stream when h(t) = 0.
Multiplying by (-1)
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
This polynomial has roots such that , given by the following formulas
In this question:
So
Time is a positive measure, so we take the positive value.
It will take 5.61 seconds for the coin to reach the stream.The height of the coin, after t seconds, is given by the following equation:
HELP PLSSS. turns out I got the last problem wrong :(
Answers
The amount invested at 4% interest rate that is $3900 and
the amount invested at 3% interest rate is $4300.
Last year Sarah invested money in two accounts. The first account had an interest rate of 3% and the second account had an interest rate of 4%. If she invested $400 more in the first account than the second and her total interest income was $285,
the equations are:
s= f + 400 (1)
0.03s + 0.04f = 285 (2)
modifying (1) and (2) for simpler calculations
3s - 3f = 3 * 400 (3)
3s + 4f = 100 * 285 (4)
by solving eqns (3) and (4) we get
we get f=3900 and s=4300
Here, f is the amount invested at 4% interest rate that is $3900 and
s refers to the amount invested at 3% interest rate is $4300.
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let A=B=R. define R=(x, y)E A×B{x²+y²=1, |x-y|=1}. Find R
Answers
R is the set containing the two points (1, 0) and (-1, 0).
Describe Sets?In mathematics, a set is a collection of distinct objects, called elements or members, that share a common property. The objects in a set can be anything, such as numbers, letters, shapes, or even other sets. Sets are denoted by braces {} and the elements are separated by commas.
Set theory is an important branch of mathematics and is used in various fields such as algebra, geometry, logic, and computer science. Sets provide a foundation for mathematical concepts such as functions, relations, and number systems. They are also used in the study of probability and statistics, and in the design and analysis of algorithms.
To find R, we need to determine the set of all points (x, y) that satisfy the conditions given:
x² + y² = 1 and |x - y| = 1
Let's consider the two cases of |x - y| = 1:
Case 1: x - y = 1
In this case, we can substitute y = x - 1 into the equation x² + y² = 1 to get:
x² + (x - 1)² = 1
2x² - 2x = 0
2x(x - 1) = 0
So x = 0 or x = 1. If x = 0, then y = -1, which does not satisfy the condition x² + y² = 1. If x = 1, then y = 0, which does satisfy the condition. Therefore, we have one point that satisfies the conditions in this case:
R1 = {(1, 0)}
Case 2: x - y = -1
In this case, we can substitute y = x + 1 into the equation x² + y² = 1 to get:
x² + (x + 1)² = 1
2x² + 2x = 0
2x(x + 1) = 0
So x = 0 or x = -1. If x = 0, then y = 1, which does not satisfy the condition x² + y² = 1. If x = -1, then y = 0, which does satisfy the condition. Therefore, we have one more point that satisfies the conditions in this case:
R2 = {(-1, 0)}
Putting both cases together, we have:
R = R1 ∪ R2 = {(1, 0), (-1, 0)}
Therefore, R is the set containing the two points (1, 0) and (-1, 0).
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A bag contains 9 red marbles, 6 white marbles, and 6 blue marbles. You draw 3 marbles out at random,
without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
Submit Question
Answers
Step-by-step explanation:
a it be 3/21 to get red which is 0.143
b to get not red if u don't replace red would be 12/18 so it be 0.6666 but if u replace it then it would be 0.517
"complete the table to determine the balance A ror 1900 invested at a rate r for t years and compounred n times per year. round your answers to the nearest cent."
Answers
The balance A for $1900 invested at a rate of 8% for 8 years and compounded n times per year is approximately
$3,538.62, when compounded annually.
$3,601.77 when compounded semi-annually
$3,663.13 when compounded quarterly
$3,710.58 when compounded monthly
$3,748.26 when compounded daily
$3,754.04 when compounded continuously.
We have,
The balance A for $1900 was invested at a rate of 8% for 8 years and compounded n times per year.
A = P(1 + r/n)^(n*t)
where P is the principal amount ($1900 in this case), r is the annual interest rate (8%), t is the number of years (8), and n is the number of times compounded per year.
When compounded annually (n = 1):
A = $1900(1 + 0.08/1)^(1*8) = $1900(1.08)^8 ≈ $3,538.62
When compounded semi-annually (n = 2):
A = $1900(1 + 0.08/2)^(2*8) = $1900(1.04)^16 ≈ $3,601.77
When compounded quarterly (n = 4):
A = $1900(1 + 0.08/4)^(4*8) = $1900(1.02)^32 ≈ $3,663.13
When compounded monthly (n = 12):
A = $1900(1 + 0.08/12)^(12*8) = $1900(1.00666667)^96 ≈ $3,710.58
When compounded daily (n = 365):
A = $1900(1 + 0.08/365)^(365*8) = $1900(1.00021918)^2920 ≈ $3,748.26
When compounded continuously:
A = Pe^(rt) = $1900e^(0.08*8) ≈ $3,754.04
Now,
n 1 2 4 12 365 continuous
A $3,538.6 $3,601.77 $3,663.13 $3,710.55 $3,748.26 $3,754.04
Therefore,
The balance A for $1900 invested at a rate of 8% for 8 years and compounded n times per year is approximately $3,538.62.
When compounded annually, $3,601.77 when compounded semi-annually, $3,663.13 when compounded quarterly, $3,710.58 when compounded monthly, $3,748.26 when compounded daily, and $3,754.04 when compounded continuously.
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Which monomial is a perWhich is the completely factored form of 4x2 + 28x + 49?fect cube?
Answers
The completely factored form of the expression 4x² + 28x + 49 is (x + 7)(4x + 7) (option a).
In this case, we need to factor the expression 4x² + 28x + 49. One way to do this is by using the quadratic formula, which is a formula used to find the roots or solutions of a quadratic equation.
However, since we are only looking for the completely factored form, we can use a simpler method known as "factoring by grouping." This method involves grouping terms with common factors and factoring them separately.
Starting with the given expression:
4x² + 28x + 49
We notice that the first two terms have a common factor of 4x:
4x(x + 7) + 49
Now, we can factor out the common factor of (x + 7) from the first two terms:
4x(x + 7) + 49 = (x + 7)(4x + 49/7)
Simplifying the expression in the second set of parentheses:
4x + 49/7 = 4x + 7
Hence the correct option is (a).
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Complete Question:
Which is the completely factored form of 4x2 + 28x + 49?
a) (x + 7)(4x + 7)
b) 4(x + 7)(x + 7)
c) (2x + 7)(2x + 7)
d) 2(x+7)(x + 7)
What is the surface area of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
10 mm
5 mm
square millimeters
Answers
The surface area of the cylinder is 471 mm².
Given is a cylinder of height 5 mm and radius 10 mm, we need to find the surface area of the cylinder,
So, the surface area of the cylinder is = 2π × r (h+r)
= 2 × 3.14 × 5 (5+10)
= 2 × 3.14 × 75
= 471 mm²
Hence, the surface area of the cylinder is 471 mm².
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PLEASE HELP I NEED IT RIGHT NOW, WILL GIVE BRAINLIST Which represents the number of square centimeters covered by the figure?
Answers
Answer:
B- 24cm^2
Step-by-step explanation:
for the square part of the shape the length is 7-2=5, 5*4=20
For the triangle, the base is 2, the height is 4, 2*4 is 8, since it’s a triangle the area is divided by 2 so 8/2 is 4.
Adding the areas of the shapes together you get 20+4=24cm^2
Alex earns $18 per hour at his job as a store clerk and is paid monthly. He worked 140 hours this month. His most recent paycheck includes the following deductions: FICA $180.00 Federal income tax $215.00 State income tax $62.00 Health insurance $72.89 Retirement savings $50.00 Considering his deductions, what percentage of his gross pay did Alex take home?
Answers
Answer:
Alex's gross pay for the month is $18/hour x 140 hours = $2520.
The total deductions from his paycheck are:
$180.00 (FICA) + $215.00 (Federal income tax) + $62.00 (State income tax) + $72.89 (Health insurance) + $50.00 (Retirement savings) = $579.89
So Alex's net pay (take-home pay) is:
$2520 (gross pay) - $579.89 (deductions) = $1940.11
To find the percentage of his gross pay that he took home, we can divide his net pay by his gross pay and multiply by 100:
($1940.11 / $2520) x 100 = 77.06%
Therefore, Alex took home 77.06% of his gross pay after deductions.
Your new computer cost $1500 but it depreciates in value by about 18% each year, how long will it take before your computer is worth $50?
Answers
1. What is 18%? 1500 * .18 = 270
2. Write the equation. 1500 - 270(x) = 50
3. Single out your X by subtracting 1500 from both sides. -250x = -1450
4. X still isn't singled out. Divide by -250. x = 1450/270 (two negatives produce a positive).
5. Simplify. x = 145/27 (fraction), 5.370370 (decimal)
Assuming 18% each year is constant through the months (say, 1.5% decrease each month), your computer will be worth $50 around 5.4 (rounded) years.
Which statements are true about circle Q? Select three options.
The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
Answers
Answer:
Step-by-step explanation:
The three true statements about circle Q are:
1. The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
2. The area of the shaded sector is 4 units 2.
3. The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the circumference of the circle.
The True statements are:
The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
What is Circumference?The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
First, The measure of the central angle is 45°.
So, ratio of the central angle to the entire circle
= 45/360
= 9/72
= 1/8
Now, area of shaded sector
A = πr² = π(6²) = 36π
or, 1/8(36π)
= 36π/8
= 18π/4
= 9π/2
= 4.5π square units.
Since, we use the circle's radius to determine area, the shaded sector's area is dependent on the circle's radius.
Given that the sector is a portion of the circle, its size is also influenced by the size of the circle.
and, The ratio of the shaded sector's area to the circle's area wouldn't be the same as the ratio of the arc's length to the circle's area.
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Callie spent 1 1/2 hours outside with her sister. They spent half of that time jumping on the trampoline. How long did they jump on the trampoline?
Answers
Answer:
45 Minutes
Step-by-step explanation:
1.5 Hours = 90 Minutes (1.5*60)
90/2 = 45
45 Minutes on the trampoline.
mathematics
please click the image, and answer. show your solution please.
thank you po!!
Answers
Answer:
1) 35%
2) 73%
3) 23%
4) 57%
5) 13%
6) 37%
Step-by-step explanation:
The general solution is to grab the total, which is 100%, and subtract the percentage of the given problems to find the solution. In some problems you have to add some percentages togheder to finish the problem.
So, in the first problem you subtract the percentage of girls to the whole class percentage: 100%-65%=35%.
In the second, whole package minus the red ones: 100%-27%= 73%
In the third, group of children minus swimmers: 100%-78%=22%
In the fourth, 100%-43%= 57%.
In the fifth, there is won percentage, loss percentage, and the remaining percentage you need to add to make 100% is the tie percentage.
So if we do the reverse (subtracting both win and loss percentage to have the tie percentage): 100%-45%-42%=13%.
In the sixth, it's the same thing as the fifth problem: subtracting the basketball and hockey from the whole children percentage that chose the sport: 100%-35%-28%=37%.
I hope this helped
Find the surface area of a sphere with the circumference of 13mm
Answers
well, we know the sphere's "great circle" has a circumference of 13mm, so
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=13 \end{cases}\implies 13=2\pi r\implies \cfrac{13}{2\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{13}{2\pi } \end{cases}\implies SA=4\pi \left( \cfrac{13}{2\pi } \right)^2 \\\\\\ SA=\cfrac{169}{\pi } \implies SA\approx 53.79~mm^2[/tex]
Kenny, Marcus, and Sean each ate 1/5 gallon of ice cream from a
I-gallon tub. When they were done, how much ice cream was left?
If they wanted to eat 3/5gallon each, how much ice cream would
they need?
Answers
if they each wanted 3/5 of a gallon they would need 1 4/5 gallons of ice cream.
explanation: 1/5 X 3 = 3/5. 5/5 - 3/5 = 2/5
3/5 x 3 = 9/5 = 1 4/5
The tractor will cost £64,950 the compound interest rate is 4% per annum. You will pay back the loan in 36 equal monthly payments. What will you pay each month?
Answers
Answer: You will pay £1,912.54 each month.
Step-by-step explanation:
We can use the formula for the monthly payment of a loan with compound interest:
monthly payment = (principal * monthly interest rate) / (1 - (1 + monthly interest rate)^(-n))
where principal is the amount borrowed, monthly interest rate is the annual interest rate divided by 12, and n is the total number of monthly payments.
In this case, the principal is £64,950, the annual interest rate is 4%, so the monthly interest rate is 4%/12 = 0.00333, and the number of monthly payments is 36.
Plugging in these values, we get:
monthly payment = (64950 * 0.00333) / (1 - (1 + 0.00333)^(-36)) = £1,912.54
Therefore, you will pay £1,912.54 each month.
Factor the polynomial
40w^11 + 16w^6
Answers
This polynomial cannot be factored any further using integer coefficients, so our final factored form is: 40w²11 + 16w²6 = 8w²6(5w²5 + 2)
How to solve?
To factor the polynomial 40w²11 + 16w²6, we need to look for common factors in the two terms. We notice that both terms have a factor of 8w²6, so we can factor that out:
40w²11 + 16w²6 = 8w²6(5w²5 + 2)
Now, we have factored out the greatest common factor of the two terms, leaving us with the remaining factor of 5w²5 + 2. This polynomial cannot be factored any further using integer coefficients, so our final factored form is:
40w²11 + 16w²6 = 8w²6(5w²5 + 2)
This form of the polynomial is useful for simplifying expressions, finding roots, and solving equations.
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A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of a crate filled with g oranges is 24.5 pounds. Write an equation that represents the relationship between the weight of the crate and the number of oranges it contains.
Empty crate:15 ib
Orange:0.38 ib
24.5=___+___×___
Answers
The weight of the empty crate is 15 pounds.
Therefore, the total weight of the crate filled with g oranges is 15 + 0.38g pounds.
We can write this relationship as:
Weight of crate = 15 + 0.38g
And we can substitute the given value of 24.5 pounds to get:
24.5 = 15 + 0.38g
Simplifying this equation, we get:
0.38g = 9.5
g = 25
Therefore, the crate contains 25 oranges.
SHOW WORKINGS PLEASE.
The MNC must pay a 25% tax on remitted funds, and the stable exchange rate is C$1.02 per US$ over the next two years and a rate of C$1.025 per US$ in year 3.
All cash flows are remitted to the parent and there is no tax on salvage.
Required:
i) Calculate the after-tax operating cash flows that will be remitted to the parent
company each year.
ii) Calculate the Net Present Value of the project.
iii) Explain whether or not the MNC should accept the project?
iv) Flagstaff Corp. is a U.S.-based firm with a subsidiary in Mexico. It plans to reinvest its earnings in Mexican government securities for the next 10 years since the interest rate earned on these securities is so high. Then, after 10 years, it will remit all accu- mulated earnings to the United States. What is a drawback of using this ap- proach? (Assume the securities have no default or interest rate risk.).
Answers
i) The after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, 110.30 and USD 146.34.
ii) The Net Present Value of the project are USD 66.85, USD 91.90 and USD 107.50.
iii) The MNC may want to consider other investment opportunities or reassess the assumptions used in this analysis.
iv) As per the subsidiary, the firm may be better off remitting earnings on a regular basis to minimize exchange rate risk and invest in a diversified portfolio of assets to mitigate other types of risks.
i) To calculate the after-tax operating cash flows that will be remitted to the parent company each year, we need to first calculate the operating cash flows in CAD and then convert them to USD while taking into account the tax on remitted funds. Let's assume the operating cash flows for each year are CAD 100, CAD 150, and CAD 200, respectively.
In year 1, the CAD 100 operating cash flow is remitted to the parent company in USD. Using the exchange rate of C$1.02 per US$, this is equal to USD 98.04. However, the MNC must pay a 25% tax on this amount, so the after-tax cash flow is USD 73.53.
In year 2, the CAD 150 operating cash flow is remitted to the parent company in USD. Using the same exchange rate of C$1.02 per US$, this is equal to USD 147.06. After the 25% tax on remitted funds, the after-tax cash flow is USD 110.30.
In year 3, the CAD 200 operating cash flow is remitted to the parent company in USD. However, the exchange rate has changed to C$1.025 per US$, so the CAD 200 is now equal to USD 195.12. After the 25% tax on remitted funds, the after-tax cash flow is USD 146.34.
Therefore, the after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, USD 110.30, and USD 146.34, respectively.
ii) To calculate the Net Present Value (NPV) of the project, we need to discount the after-tax operating cash flows back to their present value using a discount rate that reflects the riskiness of the project. Let's assume a discount rate of 10%. Using this rate, we can calculate the present value of each year's after-tax cash flow as follows:
Year 1: USD 73.53 / (1 + 0.10)¹ = USD 66.85
Year 2: USD 110.30 / (1 + 0.10)² = USD 91.90
Year 3: USD 146.34 / (1 + 0.10)³ = USD 107.50
iii) Based on the calculated NPV, the MNC should not accept the project. The negative NPV indicates that the project is not expected to create value for the MNC's investors. Additionally, the after-tax operating cash flows that will be remitted to the parent company each year are not sufficient to compensate for the investment's costs and the 25% tax on remitted funds.
iv) The drawback of Flagstaff Corp.'s approach of reinvesting earnings in Mexican government securities for 10 years before remitting accumulated earnings to the United States is that it exposes the firm to exchange rate risk. Over the course of 10 years, exchange rates between the Mexican peso and the U.S. dollar could fluctuate significantly, potentially eroding the value of the accumulated earnings when they are finally remitted. Additionally, there is no guarantee that the Mexican government securities will continue to provide a high interest rate over the entire 10-year period.
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What is the inverse of the function, f(x)=2x−1‾‾‾‾‾‾√3−3?
Responses
f−1(x)=(x+3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x plus 3 close parentheses cubed minus 1 over denominator 2 end fraction
f−1(x)=(x−3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed minus 1 over denominator 2 end fraction
f−1(x)=(x−3)3+12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed plus 1 over denominator 2 end fraction
f−1(x)=(x+3)3+12
Answers
Answer:
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Melissa deposited $5000 into an account with a 4.8% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $5960?
Answers
Assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.
How to find how long will it take for the investment to grow to $5960To answer this problem, use the compound interest formula:
A = (1 + r/n)(n*t).
We're looking for t so we can rearrange the formula to find it:
n = (log(A/P) / log(1 + r/n))
When we substitute the provided values, we get:
12.63 t = (log(5960/5000) / log(1 + 0.048/12))
Hence, assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Match the description with the correct answer
Answers
Answer:
Y-intercept: (0,4)
Slope: 2
Domain: input values
Range: output values
Increasing graph
x-intercept: (-2,0)
Step-by-step explanation:
According to the graph, the y-intercept is (0,4)
the rate of change every x-unit is 2
the x-intercept is (-2,0) as shown in the graph. The rest are just input and output values. Since the slope is positive, the graph is increasing
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