a company has issued 8% debentures of rs 10 each at a discount of 10% repayable after 10 years, find out the cost of capital
If a company has issued 8% debentures of INR 10 each at a 10% discount repayable after 10 years. then the cost of capital or pretax cost of debt is 8%.
What is pretax cost of Debt?A bond or other sort of financial instrument that is secured by collateral is referred to as a debenture. Debentures must rely on the issuer's trustworthiness and reputation for support because they lack a collateral backstop. Debentures are commonly issued by both businesses and governments to raise cash or money. The interest paid on these security can be termed as cost of Debt or pretax cost of Debt.
The pretax cost of debt is interest paid on debenture security without giving effect of corporate tax on the rate of interest to be yearly or as per terms and conditions attached to it.
When debt security issued on discount then the loss on issue of these debenture instrument shall also be form part of cost of security or cost of capital.
Thus the year one pretax cost of Debt capital will be Rs. 1 per debenture and 8% cost of debt.
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10. Matt has twice as many stickers as David. If David has d stickers, and Matt gives David 10 stickers, how many stickers does each have in terms of d?
Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
Define term.A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.
What are phrases and statements?A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.
We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.
When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.
So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
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What is this expression in simplified form?
(√22) (5√2)
O A. 10√11
O B.
12√11
O c.
20v/11
OD. 24√/11
Radicals
Simplifying radicalsApplicationStep 1: DefineLet's organize what the problem gives us.
We are given an expression to simplify: [tex]\displaystyle (\sqrt{22})(5 \sqrt{2})[/tex]
Step 2: WorkRecall the specific rules to simplify radicals. We will apply those rules here to help us answer the question:
[tex]\displaystyle\begin{aligned}(\sqrt{22})(5 \sqrt{2}) & = 5 \sqrt{44} \\& = 5 \sqrt{4 \cdot 11} \\& = (5 \sqrt{4})(\sqrt{11}) \\& = (5 \cdot 2)(\sqrt{11}) \\& = \boxed{ 10 \sqrt{11} }\end{aligned}[/tex]
∴ the expression (√22)(5√2) simplifies down to 10√11.
Answer∴ the expression in simplified form is equal to A. 10√11.
___
Topic: Pre-Algebra
Unit: Radicals
Drag each question to the correct location on the table.
Classify the questions as statistical or not statistical.
Each of the questions should be correctly classified as statistical or not statistical as follows:
Not statistical question: "How many hours did I jog yesterday?"Not statistical question: "How many students in my class can swim?"Not statistical question: "How many students in my class watch television?"Statistical question: "How many hours a day do the students in my class watch television?"Statistical question: "How many TV shows did each student in my class watch yesterday?"Statistical question: "How many days a week did each student in my class go swimming in the last month?"What is a statistical question?In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"
What is a non-statistical question?A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"
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Goran invested his savings in two investment funds. The amount he invested in Fund A was 7000 less than the amount he invested in Fund B. Fund A returned a 4% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was 500?
If Goran invested his savings in two investment funds. The amount that Goran invest in Fund B, if the total profit from the two funds together was 500?
How to find the amount invested?Amount Invested in Fund A = x
Amount invested in Fund B = x+7000
Profit from fund A = 0.04x
Profit from fund B = 0.02(x+7000)
0.04x +0.02(x+7000) = 500
0.04 +0.02x + 140 =500
Combine like terms
0.06 x =360
Divide both side by 0.06x
x = 360 /0.06
x = 6,000
Amount Invested in Fund A = x =6,000
Amount invested in Fund B = x+7000
Amount invested in Fund B = 6,000 + 7,000
Amount invested in Fund B = 13,000
Therefore the amount invested in Fund A 6,000 and the Fund B is 13,000.
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how many times does 12 go into 72
Answer:
Step-by-step explanation:
6
write the equation for the hyperbola with foci (-12,6) , (6,6)and vertices (-10,6), (4,6)
The equation for hyperbola with given foci is [tex]\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1[/tex]
What is hyperbola?
In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.
The standard equation of a horizontal hyperbola with center (h,k) is
[tex]\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1[/tex]
The given hyperbola has vertices at (–10, 6) and (4, 6).
The length of its major axis is 2a= 4-(-10)
2a=14
a=7
The center is the midpoint of the vertices (–10, 6) and (4, 6).
The center is [tex](\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)[/tex]
Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.
The c-value is the distance from the center (-3,6) to one of the foci (6,6)
c= 6-(-3)=9
So, 7^2+b^2=9^2
b^2= 9^2-7^2
b^2= 81-49
b^2= 32
Hence, on substituting the obtained values in the standard equation of hyperbola, we get
[tex]\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1[/tex]
[tex]\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1[/tex]
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Which lines are parallel. 1.) The blue and green 2.) blue and red 3.) Red and green 4.) blue,red,green
Answer: 2.) Blue and red
Step-by-step explanation:
The slope of the red and blue ones is - 3 while the green one's slope is -4
Katrina buys a 76-ft roll of fencing to make a rectangular play area for her dogs. Use
2({+w) = 76 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation? Explain.
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
Here,
We have the following for the rectangle's perimeter:
2 ( l + w ) = 64
Here,
W = width, and L = length.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
Now,
2 ( l + w ) = 64
l + w = 32
Thus, the sum of the length and breadth measurements must equal 32.
The possible widths are 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We think about
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
Values for width and length are used as the x- and y-axes, respectively.
Below is a graph of the data.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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7sur 15 plus 6sur25 FRACTION
Answer:
53/75
Step-by-step explanation:
15 = 3 × 5
25 = 5²
PPCM = 3 × 5² = 75
75/15 = 5
75/25 = 3
7/15 + 6/25 =
= (7 × 5)/(15 × 5) + (6 × 3)/(5 × 3)
= 35/75 + 18/75
= 53/75
The value of z varies inversely with the value of w. The constant of variation is 2. Which are possible values for z
3
and w? Check all that apply.
Oz=.
z = 1+₁ w = 2/1/201
O z = 2, w = 3
O z=
z = -1/₁w=2
O z
4,
= 1/5, w = 2/1/201
z = 1/2/3₁, w = 2/1/201
Answer:A,C,D
As a result of the inverse relationship between z and w, their product is constant.
What does "inverse connection" actually mean?There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.
According to the information:z * W is equal to 1.
The statement indicates that the constant's value is 2/3, so:
z * w = 2/3
The result of solving for any of the variables is:
either w = (2/3) / z or z = (2/3) / w
The following values fit that relation:
z w = (2/3) / z
-8/9 (2/3) / (-8/9)
= - (2/3) * (9/8) = -3/4
- 4/9 (2/3) / (-4/9)
= - (2/3) * (9/4) = - 3/2
- 2/9 (2/3) / (-2/9)
= - (2/3) * (9/2) = - 3
2/9 (2/3) / ( 2/9)
= (2/3) * (9/2) = 3
4/9 (2/3) / (4/9)
= (2/3) * (9/4) = 3/2
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Write three to five sentences explaining which levels of production provide Alonzo’s Cycling with the maximum profit
The data provided in the table implies that Alonzo's Cycling should produce five or six bikes if it wants to maximize its profits.
What is profit maximization?Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.
This is because the sixth bike is the point at which the marginal revenue matches the marginal cost. The company will make $90 in profit with the sale of its fifth or sixth bike each day. After that, the profit begins to fall with each sale.
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Show that 113 +112 = 225, using at least three daily life examples.
Answer:hope this helps!
1. Step-by-step explanation:
there is a blanket costing 112
and a chair costing 113
after going to the register you find that the total is
225
2. Step-by-step explanation:
there is a printer costing 112
and a laptop costing 113
after going to the register you find that the total is
225
3. Step-by-step explanation:
there is a pillow costing 112
and some makeup costing 113
after going to the register you find that the total is
225
hope this helps i was in a rush so sorry if it was bad
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Step-by-step explanation:
hope this is right hehe.....
Help me please!!! 20 points
Answer:
x=4, y =5
Step-by-step explanation:
there's no factorization involved, just elimination and substitution. First subtract equation 1 and 2. The x's cancel out and you get y by itself and can solve for it. Then plug the value of y into equation 2 and solve for x and you get it. (In my picture I put value of y in equation 1 but your question asks for putting it in equation 2 so do that instead)
find the nth term of the following sequence :
5, 20, 45, 80, 125
The nth term of the following sequence is: 5n²
What is arithmetic sequence?Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
We are given the sequence are;
5, 20, 45, 80, 125
The quadratic sequence formula : an²+bn+c
2nd difference 2a = 10
a = 5
1st difference 3a+b = 15
Then substitute 5
3(5)+b = 15
b = 0
The nth term rule : a + b + c = 5
Now substitute a and b values into equation
5 + 0 + c = 5
c = 0
The nth term is: 5n²
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PLEASE HELP FIND THE SOLUTION IN SLOPE INTERCEPT FORM
Answer: y= -3/4x+8
Step-by-step explanation:
an altitude is drawn from the vertex of an isosceles triangle forming a right angle and two congruent triangles. as a result, the altitude cuts the base into two equal segments. the length of the altitude is 30 inches, and the length of the base is 10 inches. find the triangles perimeter. round to the nearest tenth of an inch.
The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches
How to find the perimeter of the isosceles trianglePerimeter of a triangle refers to the surface dimensions, this is calculated by the formula
Perimeter, P = a + b + c
where
a, b, c are sides of the triangle
The third side of the triangle will be calculated using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches
plugging the values as in the problem
let x be the required distance
x² = 30² + 5²
x² = 900 + 25
x² = 925
x = √925
x = 30.41 inches
Perimeter of the isosceles triangle
= 30.41 + 30.41 + 10
= 70.82 inches
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(30 points easy) write the equation of side B seat inside AC to determine if the three points could form a right triangle
write the equation of the line for side B C, and side AC, If the points were connected, could this be a right triangle explain why
(use the graph in the photo)
Answer:
Side BC: y = -2x + 10
Side AC: y = 2x + 4
Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.
x−2y=3
Determine the missing coordinate in the ordered pair (−4,?) so that it will satisfy the given equation.
Answer:
y=-3.5
Step-by-step explanation:
substitute -4 for x
add 4 on both sides to get rid of the -4
divide -2 on both sides to isolate y
and you get 3.5 for y
The value of y that will satisfy the equation given is -3.5.
What is an equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,
To find the same, just replace the value of x by -4,
-4-2y = 3
-2y = 7
y = -3.5
Hence, the value of y that will satisfy the equation given is -3.5.
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Write an expression with 5 terms where one of the terms is a constant of 3
Answer:
Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.
how are algebraic expressions used to represent and solve problems
Answer:
How are algebraic expressions used to represent and solve problems?
The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation, and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.
Step-by-step explanation:
How can you use algebraic expressions to solve problems?
To solve an algebraic word problem:
1. Define a variable.
2.Write an equation using the variable.
3.Solve the equation.
4.If the variable is not the answer to the word problem, use the variable
to calculate the answer.
How are algebraic expressions applied in real life situations?
utilizing linear algebra, and this uniqueness starts to expose a lot of applications. Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.
What is algebraic expression why it is used in mathematics?
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3×2 − 2xy + c is an algebraic expression.
There are 13 muffins in each box. Which shows the tota
number of muffins in 4 boxes?
(4 × 10) + (4 x 3) = 52
(4 x 10) + 3 = 43
A
B
4+ (10 x 3) = 34
5 (4+10)+(4+ 3) = 21
The total number of muffins in 4 boxes by the arithmetic equation is (4 × 10) + (4 x 3) = 52.
What is arithmetic equation?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence.
Every term in an arithmetic sequence is created by adding a specified number (either positive, negative, or zero) to the term before it.
the number of boxes of muffins is 4
The muffins in each box is 13
so the total number of muffins in 4 boxes is 4 x 13
⇒ 4 x (10 + 3)
⇒ (4 x 10) + (4 x 3) = 52
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What is the equation of a line with a slope of 3 and a point (3. 1) on the line? Express the equation in the form of y Enter your answer in the box mz+ b where m is the slope and b is the y-intercept
A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.
What do you meant by y-intercept ?If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.
In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).
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Clare has $150 in her bank account. she buys a bike for $200. what is Clare's account balancenow?
Answer:
-50
Step-by-step explanation:
Answer:
Step-by-step explanation:
if she had $150 in he bank account and buys a bike that costs 200 she possibly can't afford it since she is $50 dollars short so even if she borrows $50 dollars she has to repay the person 50 dollars before she starts earning another money so i think it is -50. if it doesn't help am sorry I hope you got this answer correct. goodluck
A project requires you to figure out the area of a triangular lot. You take measurements and find that the lot has a base of 32 ft., while the altitude of the triangle, or height is 24 ft. What's the area of this lot?
f(x)=-2x+3 find f(3)
answer: -3 lmk if you want an explanation!
PQ || NM. What equation can you use to find the length of OQ?
On solving the provided question, we can say that - As a result, Orthocenter triangle is the answer to the given triangle issue (0, - 5 ).
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
determine LN's slope.
[tex]m = (y2 - y1)/ (x2- x1) = 1-5/8-0 = 2[/tex]
formula for altitude
[tex]y - 1 = 2(x - 3) (x - 3)\\y - 1 = 2x - 6\\[/tex]
y = 2x - 5
Altitude of N and LM
[tex]m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4\\y - 1 = (x - 8) (x - 8)\\y - 1 = x - 6\\[/tex]
y = x - 5
[tex]8x - 20 = 3x - 20\\5x - 20 = - 20 \\5x = 0 = > x = 0\\[/tex]
y =0 - 5 = - 5
It is the orthocenter (0, - 5 )
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[tex] \: \: \: \: \: \rm \: 25x {}^{2} = - 25 + 50x[/tex]
Find possible values of x
Answer:
[tex]\boxed{\boxed{\sf x=1}}[/tex]
Step-by-step explanation:
[tex]\sf 25x^2=-25+50x[/tex]
Simplify both sides of the equation:-
[tex]\sf 25x^2-50x=-25[/tex]
Subtract 50x-25 from both sides:-
[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]
[tex]\sf 25x^2-50x+25=0[/tex]
Factor left side of equation:-
[tex]\sf 25(x-1)(x-1)=0[/tex]
Set factors equal to 0:-
[tex]\sf x-1=0\: or\: x-1=0[/tex]
[tex]\sf x=1[/tex]
___________________
Hope this helps!
Have a great day!
whats the second step of calculating the present value of an ordinary annuity by table lookup
The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.
What is the present value of an ordinary annuity?The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.
The present value is higher when the discount rate is lower, and vice versa.
The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.
In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).
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