Answers
According to the information, we know that the term 125x^5y^4 appears in the expansion when n = 6 and the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.
How to solve this equation and fin the expansion terms?We know that the binomial expansion of (x-y)^n is given by the formula:
(x-y)^n = nC0 x^n y^0 - nC1 x^(n-1) y^1 + nC2 x^(n-2) y^2 - ... + (-1)^n nCn x^0 y^nwhere nCk represents the binomial coefficient "n choose k".
We are given that the term 125x^5y^4 appears in the expansion, so we can set up an equation using the binomial coefficient for that term:
nC5 (x)^5 (-y)^4 = 125x^5y^4Simplifying this equation, we get:
nC5 = 125 / (-1)^4 = 125We can solve for n by finding the smallest value of n for which nC5 is greater than or equal to 125. We can use the formula for binomial coefficients:
nCk = n! / (k! (n-k)!)to calculate the values of nCk for different values of n and k. However, it is easier to use Pascal's triangle to find the binomial coefficients quickly. The fifth row of Pascal's triangle is:
1 5 10 10 5 1We see that the sixth term of this row is 10C5 = 252, which is greater than 125. Therefore, we know that the term 125x^5y^4 appears in the expansion when n = 6.
To find the x^6y^7 term in the expansion, we need to find the coefficient of x^6y^7 in the expansion. We can use the same formula as before, but with k = 7 instead of k = 5:
nC7 (x)^6 (-y)^7We can simplify this expression using the fact that (-1)^7 = -1:
nC7 x^6 y^7We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:
6C7 x^6 y^7We see that 6C7 is zero because we cannot choose 7 items from a set of 6. Therefore, the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.
To find the x^7y^2 term in the expansion, we can use the same formula as before, but with k = 2:
nC2 (x)^7 (-y)^2We can simplify this expression using the fact that (-1)^2 = 1:
nC2 x^7 y^2We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:
6C2 x^7 y^2We can use Pascal's triangle to find that 6C2 = 15. Therefore, the coefficient of x^7y^2 in the expansion is 15, and the x^7y^2 term appears in the expansion as:
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Related Questions
Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answers
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
A researcher is standing in a corner (point c) of a triangler plot. the angle to point a is S76E the angle to point b is N32E The distance between point c and point a is 210 ft and the distance between point c and point b is 150 ft
find the distance between point a and point b
Answers
If a researcher is standing in a corner (point c) of a triangle plot. the angle to point a is S76E . the distance between point A and point B is 210 ft.
How to find the distance between point A and point B?To find the distance between points A and B, we can use the Law of Cosines. Let's first label the angles of the triangle:
Angle ACB = 180 - (76 + 32) = 72 degrees
Angle BAC = 76 degrees
Angle ABC = 32 degrees
Using the Law of Cosines, we have:
AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(ACB)
where;
AB is the distance between points A and B
AC is the distance between points A and C (210 ft
BC is the distance between points B and C (150 ft)
ACB is the angle between AC and BC (72 degrees)
Plugging in the values, we get:
AB^2 = 210^2 + 150^2 - 2(210)(150)cos(72)
AB^2 = 44100
AB = sqrt(44100)
AB = 210 ft
Therefore, the distance between point A and point B is 210 ft.
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) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
Answers
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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A patient takes 110 mg of a drug at the same time every day: Just before each tablet is taken, 5% of the drug present in th
preceeding time step remains in the body. What quantity of the drug remains in the body in the long run?
Hint: First find the quantity of drug present in the body after the second tablet, third tablet, etc to generalize the sequenc
formula for the nth tablet. Then use that sequence to predict the drug remains in the long run.
Answers
The requried quantity of drug that remains in the body, in the long run, is 220 mg.
Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:
[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]
We can see that the formula for [tex]D_n[/tex] is:
[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]
Simplifying this formula, we get:
[tex]D_n = 220 * (1 - 0.95^n)[/tex]
Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex] as n goes to infinity. Using the formula above, we can see that:
[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]
Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.
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Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
Answers
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
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A bag contains 2 gold marbles, 10 silver marbles, and 29 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $4. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answers
Answer:
33 thats with the 1 dollar subtracted for the entry fee
Step-by-step explanation:
first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee
Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
Answers
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
Answers
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
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Rectangle MPAT has vertices M(1,2) , P(1, 3), A(3, 3), and T(3, 2) . Rectangle M’P’A’T . Which coordinates describe the vertices of the image?
Answers
The coordinates of the vertices of the image rectangle M'P'A'T' are:
M'(2,1), P'(3,1), A'(3,3), T'(2,3).
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
To find the coordinates of the vertices of the image rectangle M'P'A'T', we need to apply a transformation to each vertex of the original rectangle MPAT.
We can see that the original rectangle MPAT has sides parallel to the x and y-axes, which suggests that it is aligned with the coordinate axes. We can also see that the length of its sides are equal, which means it is a square.
To transform this square, we can use a combination of translations, rotations, and reflections. However, since we don't have any information about the type of transformation that is being applied, we can assume that the simplest transformation is a reflection across the line y=x.
To reflect a point (x,y) across the line y=x, we swap its x and y coordinates to get the reflected point (y,x). Therefore, the coordinates of the vertices of the image rectangle M'P'A'T' are:
M'(2,1)
P'(3,1)
A'(3,3)
T'(2,3)
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carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
Answers
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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Given f’(x)=4x-3 compute f(5)-f(-1)
Answers
Answer:
To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).
∫f'(x) dx = ∫(4x - 3) dx
f(x) = 2x^2 - 3x + C
where C is the constant of integration.
To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:
f(0) = 2(0)^2 - 3(0) + C = C
Therefore, C = 5.
Hence, the function f(x) is:
f(x) = 2x^2 - 3x + 5
Now, we can find f(5) and f(-1) and compute their difference:
f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)
f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)
f(5) - f(-1) = 35 - 10
f(5) - f(-1) = 25
Therefore, f(5) - f(-1) = 25.
Write an absolute value equation that has the following solution set.
-8 and -2
Thank you!
Answers
The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3
What is an absolute value equation?
An absolute value equation can be written as |expression| = value
To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.
We can write,
|x + 5| = 3
To solve for x, we have two cases,
Case 1: x + 5 is positive
If x + 5 is positive, then the equation becomes x + 5 = 3
Solving for x,
x = -2
This matches one of the solutions we want.
Case 2: x + 5 is negative
If x + 5 is negative, then the equation becomes -(x + 5) = 3
Solving for x,
x = -8
This also matches the other solution we want.
Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.
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Here are two complex numbers being multiplied: (4 + 2)(6-3) = ?
Without calculating the exact result of the multiplication, how can
you tell that the result will be a real number?
Answers
Answer: 18
Step-by-step explanation:
ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answers
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
Becky ate 7.5 x 10^5 milligrams of rice. Carter ate 3.1 x 10^6 milligrams of rice. who ate more?
Answers
Answer:
The Correct answer is Carter
3) Given the formula F=ma where * F represents force, *m represents mass and has units of kilograms (kg), and • a represents acceleration and has units of meters per second squared (). Select an appropriate measurement unit for force.
Answers
The appropriate measurement unit for force is kg.m/s²
What is the appropriate measurement unit for force?A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.
From Newton's Second Law, force is expressed as;
F = m × a
Where is mass of object and a is the acceleration
One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
Since F = m × a
Plug in m = kg and a = m/s²
F = kg × m/s²
F = kg.m/s²
Therefore, the unit of measurement is kg.m/s².
Option B is the correct answer.
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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answers
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
Help corrections due in 3 hours! giving 25 points and brainlist
Answers
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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As seen in the diagram below, Austin is building a walkway with a width of x feet to go around a swimming pool that measures 8 feet by 10 feet. If the total area of the pool and the walkway will be 360 square feet, how wide should the walkway be?
Answers
Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles.
A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.
A rectangle with four equal-length sides is a square.
Squares are not always rectangles, but rectangles are always squares.
So, the pool and walkway together have a 360 square foot total space.
Assume that the walkway is w feet in width.
Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).
Thus, we can construct the following equation:
(8 + 2w) x (10 + 2w) = 360
By enlarging and condensing the left side, we obtain:
4w² + 36w - 80 = 0
Using the quadratic formula, we can find w:
w = (-b ± √(b² - 4ac)) / 2a
Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:
w = (-36 ± √(36² - 4(4)(-80))) / 8
w = (-36 ± √(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.
Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
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Mohal plans to repaint some classroom bookcases. He has 1 1 /8 gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?
Answers
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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Solve for x.
A. 7
B. 4
C. 3
D. 5
Answers
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT
what is √29 Place a dot on the number line at the BEST approximation
Answers
Answer:
5.4
Step-by-step explanation:
square of 29 = 5.385164807
5.385164807 estimated is 5.4
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
Answers
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
Write 80cm to 2km as rate
Answers
One per 2,500 can be used to represent the rate of 80cm to 2km.
Writing measures as a rate.To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):
80 cm/100,000 = 0.0008 km
Now we can express the rate as:
0.0008 km per 2 km
Or we can simplify it by dividing both the numerator and denominator by 0.0008:
1 per 2,500
Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.
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Help please i dont know
Answers
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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complete the equatiotin 3 over 4 x 6 =
PLEASE HELP
Answers
Answer:
1/8
Step-by-step explanation:
If "over" refers to (4 * 6) as a whole,
[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]
If "over" refers to division,
[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]
I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.
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Which expresion has the greatest value when n is equal to 4
Answers
The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.
How do we calculate?To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.
A. 5n = 5(4) = 20
B. n + 30 = 4 + 30 = 34
C. 50 - n = 50 - 4 = 46
D. 80 ÷ n = 80 ÷ 4 = 20
The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Answers
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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find the factors to this polynomials i need help SHOW YOUR WORK.
Answers
Answer:
hope this will help you...
HELP ME PLEASE!!! HELPPP!!! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and an area of 500 ft2. Which of the following could be the pool's length and width? 15 feet and 30 feet, 10 feet and 35 feet ,50 feet and 10 feet, 25 feet and 20 feet
Answers
Answer:
(d) 25 feet and 20 feet
Step-by-step explanation:
You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.
AreaThe area is the product of the length and width. The area of the pools offered in the answer choices are ...
(a) 15·30 = 450 . . . square feet
(b) 10·35 = 350 . . . square feet
(c) 50·10 = 500 . . . square feet
(d) 25·20 = 500 . . . square feet
The area requirement eliminates answer choices A and B.
PerimeterThe perimeter is twice the sum of length and width. The perimeters of the possible pools are ...
(c) 2(50 +10) = 120 . . . feet
(d) 2(25 +20) = 90 . . . feet
The perimeter requirement eliminates answer choice C.
The pool's possible length and width are 25 feet and 20 feet, choice D.
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Additional comment
You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.
If x is the width, then 45-x is the length, and the area is ...
x(45 -x) = 500
x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square
x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension
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