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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12 feet below the surface of the water. What is the pool's depth in feet?
Answer:
Step-by-step explanation:
-12
X 1 3 5 7
у -9 -17 -25 -33
find the equation of the linear function represented by the table in slope intercept form
The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
Given two points (x,y), the slope is the change in y divided by the change in x.
The points are (1,-9) and (3,-17) -
m = (y2-y1)/(x2-x1)
m = [-17-(-9)]/(3-1)
m = -8/2
m = -4
Then the slope equation will be -
y = -4x + b
Taking points (1,-9) and substituting in the equation to get the value of b -
-9 = -4(1) + b
-9 = -4 + b
-9 + 4 = b
b = -5
Therefore, the slope intercept form of equation is y = -4x - 5.
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Find the trigonometric ratios for both acute angles in fraction and decimal form to the nearest ten-thousandths when appropriate.
The trigonometric functions are sin A = 12/13, sin B = 5/13, cos A = 5/13, cos B = 12/13, tan A = 12/5, and tan B = 5/12 as fractions.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric functions are given in the question
Apply the sine ratio on the given right triangle
⇒ sin(θ) = Perpendicular/hypotenuse
sin A = BC/AB
sin A = 12/13
sin B = AC/AB
sin B = 5/13
Apply the cosine ratio on the given right triangle
⇒ cos(θ) = Base/hypotenuse
cos A = AC/AB
cos A = 5/13
cos B = BC/AB
cos B = 12/13
Apply the tangent ratio on the given right triangle
⇒ sin(θ) = Perpendicular/Base
tan A = BC/AC
tan A = 12/5
tan B = AC/BC
tan B = 5/12
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Given:m<1+m<2=90 and m<3+m<4=90,prove m<1=m<4
The proof that the angles m<1 = m<4 is shown below
How to prove the measure of the anglesFrom the question, we have the following parameters that can be used in our computation:
Measure of angles
The angle measurements are then given as
m<1 + m<2 = 90 and m<3 + m<4 = 90
The relationship to prove is also given as
m<1 = m<4
Using the above as a guide, we have the following:
Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90
This gives
m<1 + m<2 = 90
-(m<3 + m<4 = 90)
Evaluate the difference
m<1 + m<2 = m<3 + m<4
When both sides of the angle equations are compared, we have:
m<1 = m<4
m<2 = m<3
Ignoring the second equation, we have
m<1 = m<4
Hence, the measure of the angles has been proved
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Select the best answer for the question.
10. Which one of the following pairs of numbers contains like fractions?
O A.% and 60/70
O B. 12 and 32
O C. 54 and 45
O D. 4 and 12/16
Use the decimals 2.49, 9.19, and 6.7 to write two different addition facts and two different subtraction facts.
The solution to the equations is
Addition : 2.49 + 6.7 = 9.19 ; 6.7 + 2.49 = 9.19
Subtraction : 9.19 - 6.7 = 2.49 ; 9.19 - 2.49 = 6.7
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the three decimals be represented as set x = { 2.49 , 6.7 , 9.19 }
Now , the addition facts are given by equations ,
2.49 + 6.7 = 9.19 be equation (1)
6.7 + 2.49 = 9.19 be equation (2)
And , the subtraction facts are given by the equations ,
9.19 - 6.7 = 2.49 be equation (3)
9.19 - 2.49 = 6.7 be equation (4)
Hence , the equations are solved
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Practice: Determining if a Relation is a Function the Siven is not a funcr...l
since the element in the domain is repeated!
1) {(-1, 8), (0, 15), (1,-4), (2, 0)}2) {(-5,2), (5, 2), (0, -3), (3, -8)} 3) {(-2,7), (6,2), (-2,-3), (0, 9)}
it is a function
because there is not any
Points which have the
X-Coordinate and differe
y-Coordinates.
4) {(7.2), (4,-6), (2,-2). (4,-9)} 5) {(2, 3), (2, 4), (2, 5), (2.6)}
6) {(1,-4), (2,-4), (3, 4), (4-4)}
On solving the provided question, we can say that - here in the function, every element has an unique image
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
every element has an unique image and,
this relation, is not a function, since it is not one-one and onto.
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100 POINTS PLEASE HELP!!! PICTURE IS ATTACHED.
The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
How simplification of an expression work?The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]
We know that any number raised to the power of 0 is 1.
Therefore,[tex]a^0 = 1[/tex].
Also, any number raised to the power of -1 is its reciprocal.
Therefore, [tex]b^-4 = 1/b^4[/tex]
Simplifying the above expression we get
[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]
Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]
So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]
Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]
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Given K (9,-9), L(2,-2), M(-9,-5), and N (5, y). Find y such that
KL_|_MN.
On solving the provided question, we cans say that - here in coordinates S is given by: [tex](-2,4)[/tex]
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
x-coordinate of [tex]X = -2[/tex]
y-coordinate of[tex]S = 4.[/tex]
S is given by: [tex](-2,4)[/tex]
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On solving the provided question, we cans say that - here in coordinates S is given by: (-2,4)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
x-coordinate of -2
y-coordinate of 4
S is given by: (-2,4)
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on Monday the solar panels on a house produced 37.124 units of energy. On Tuesday, the solar panels produced 2,846 fewer units of energy than on Monday. What is the total number of units of energy in two days.
The total number of units of energy produced in the two days is 71,402.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monday:
Energy = 37,124
Tuesday:
Energy = 37,124 - 2846 = 34278
The total energy produced.
= 37124 + 34278
= 71402
Thus,
The total number of energy in two days is 71,402.
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Simplify in radical form:
-x√28+10√63x²
Radical form is rather simple. It refers to the form of a number or algebraic expression where the number or expression is contained under a radical. The answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].
What does in radical form mean?Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
A radical notation is an expression that makes use of a root, such as the square or cube root.
The fundamentals of radical form are simple. When a numerical or algebraic expression is under a radical, the term refers to that version of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.
[tex]\text { Simplify }-x \sqrt{2} 8+10 \sqrt{6} 3 x^2:-\\\\8 \sqrt{2} x+30 \sqrt{6} x^2 -x \sqrt{2} \cdot 8+10 \sqrt{6} \cdot 3 x^2 \\\\& =-8 \sqrt{2} x+30 \sqrt{6} x^2\end{aligned}$$[/tex]
Therefore, the answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].
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pls help with this question find the slope from 1-6
Answer:
Step-by-step explanation:
1. ( -2, 2), (-1, 5)
(5 - 2)/(-1 + 2)= 3/1= 3
2. (-4, 2), (2, 0)
(0 - 2)/(2 + 4) = -2/6 = -1/3
3. (0, 3), (5, 1)
(1 - 3)/(5 - 0)= -2/5
4. (0, 0), (1, 1)
(1 - 0)/(1 - 0)= 1/1= 1
5. (3, 0), (3, 1)
(1 - 0)/(3 - 3) = 1/0 = undefined
6. (0, -1) (1, -1)
(-1 + 1)/(1 - 0)= 0/1 = 0
-15 POINTS-
Don’t explain.
Y=[?]
Step-by-step explanation:
of course I need to explain it, since you don't know how to get it. that is the purpose of Brainly. not to be a calculator slave to you, but to enable you to solve similar problems on your own in the future.
both shapes are similar.
that means that
1. both have the same angles
2. there is one common scaling factor for all pairs of corresponding sides (and other lengths as heights, ...).
we need 2. here to solve.
AB / EF = f = 3/2
x = AD
x / EH = f = 3/2
x / 2.4 = 3/2
x = 2.4 × 3/2 = 7.2 / 2 = 3.6
Goran wants to build a square picture frame with sides that are
5.25 inches long. Natalie wants to build a square sandbox and needs
11 times the amount of wood that Goran needs to build his frame.
They have 4 pieces of wood that are each 65.5 inches long. How much
wood will they have left over after making the frame and sandbox?
The wood left over after making the frame and the sandbox is 10 inches.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
Thus,
The remaining wood is 10 inches.
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The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1
Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)
What is Midpoint of a LineThe midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.
The x - coordinate is calculated as;
-1 = (4 + x₁) / 2
-2 = 4 + x₁
x₁ = -2 - 4
x₁ = -6
The y - coordinates is calculated as;
8 = (-15 + y₁) / 2
16 = -15 + y₁
y₁ = 16 + 15
y₁ = 31
The coordinates of k is (-6, 31)
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Find the sum of all solutions to the equation $4x(x-3) = 23$.
I NEED THIS ASAP
The sum of the solutions of the equation 4x(x - 3) = 23 is 3.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, An equation 4x(x - 3) = 23.
Now, Distributing the terms in the LHS we have,
4x² - 12x = 23.
4x² - 12x - 23 = 0.
By applying Sridhar acharya's formula we have,
[tex]x_{1,\:2}=\frac{-\left(-12\right)\pm \sqrt{\left(-12\right)^2-4\cdot \:4\left(-23\right)}}{2\cdot \:4}[/tex].
[tex]x=\frac{3+4\sqrt{2}}{2},\:x=\frac{3-4\sqrt{2}}{2}[/tex].
Therefore, The sum of the solutions of the equation is,
x + x = (3 + 4√2)/2 + (3 - 4√2)/2.
= (3 + 4√2 + 3 - 4√2)/2.
= 6/2.
= 3.
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Evaluate -3x³-4x for x = -1.
A)-1
B)7
C)1
Answer:
B) 7
Step-by-step explanation:
-3x³-4x =
-3(-1)³-4(-1) =
-3(-1)+4=
3+4 =7
Find the mean, median, and mode for 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7. Round to the nearest tenth if needed.
Answer:
Mean - 6.2 Median - 7 Mode - 9
Step-by-step explanation:
You can find the mean by adding all the given numbers and dividing them by how many numbers you added.
The median is the middle value of the set of numbers, order them from least to greatest and find the middle value.
Mode is the number that occurs the most.
Single payment loan for $1200 repay in 120days interest rate is 7%, what is the maturity value of the loan?
The maturity value of the loan based on the calculation is $1227.72
How to illustrate the interest?From the information, single payment loan for $1200 repay in 120days interest rate is 7% and we want to calculate the maturity value of the loan.
It should be noted that the interest will be calculated as:
= Principal × Rate × Time
= 1200 × 7% × (120/360)
= 1200 × 0.07 × 0.33
= $27.72
Maturity amount = $1200 + $27.72
Maturity amount = $1227.72.
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Find the measure of the missing angles.
Answer:
c = 62 degrees
b = 118 degrees
Step-by-step explanation:
vertical angles are congruent. the 62-degree angle is vertical to angle c
linear pair angles are supplementary. the 62-degree angle is supplementary to angle b. 180 = 62 + b. 118 = b
Use triangles to find the sum of the interior angle measures of the polygon.
SHOW YOUR WORK.
The sum of the interior angle measures of the polygon is 900 degrees
How to determine the sum of interior angles
From the image shown, we can see that the polygon has 7 sides.
A polygon with seven sides is called a heptagon
It is important to note that the number of triangles in a heptagon is 5.
Also, the sum of angles in a triangle is 180 degrees.
Now, the formula for calculating the sum of interior angles of a polygon is expressed as;
= (n - 2) 180
Where; n is the number of sides of the polygon
Substitute the value
= (7-2)180
Subtract the value
= 5(180)
= 900 degrees
Hence, the sum is 900 degrees
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given: p is the midpoint of AN prove: AG=NI (direct proof)
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
what is triangle ?Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the term used to refer 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 because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.
given
p is the midpoint of GI
GP = PI , PN = AP ( as mid point )
∠APG = ∠IPN ( as vertical opp. angle )
∠A = ∠N ( given )
so by ASA congruency ΔAPG = ΔIPN
As a result, AG = NI according to the ASA congruency, where p is the midpoint between AN and AG=NI.
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please help asap
will give brainliest
Answer: 109 it says 109 in the corner of b and d
What are four names for 3.09
Answer: Three and Nine Hundreths
3 9/100
309%
Step-by-step explanation:
i only know 3 sorry :(
Answer:
: Three and Nine Hundredths
: 3 9/100
: 309%
: 3 90/1000
Step-by-step explanation: These are some that I could think of. The last one is an equivalent fraction to the second one. I hope this helped.
Find the area of this circle 7cm and 3 for pi
Answer:
far t more far t
Step-by-step explanation:
how to find the lcd and subtract the following fractions what is the answer of 5 over 6 minus 1 over 4 pls
Answer:
[tex]\displaystyle \frac{7}{12}[/tex]
Step-by-step explanation:
When we are subtracting fractions with different denominators, we find the least common denominator of each one. In the case of 6 and 4, they both share 12 as the least common denominator, so we can rewrite each fraction as equivalents with denominators of 12:
[tex]\displaystyle \frac{5}{6}-\frac{1}{4}=\frac{5*2}{6*2}-\frac{1*3}{4*3}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12}[/tex]
Step-by-step explanation:
This calculator subtracts two fractions. First, convert all fractions to a common denominator when fractions have different denominators
Please help
Match the items.
a. Multiplicative Inverse
b. Additive Inverse
c. Commutative Property of Multiplication
d. Distributive Property
e. Additive Identity Property
f. Associative Property of Addition
1. 5.6=6-5
2. -8+0= -8
3. (3+5) +9=3+ (5+9)
4. 5.1=1
5. 7+(-7)=0
6. 5(x−4)=5x−20
The matching of the items as follows ,a - 4 , b - 5, c - 1 , d - 6 , e - 2 , f - 3
What is a number ?
number is used to represent the quantity of number and it is even used for calculations.
a) Multiplicative inverse
if the product the given number and reciprocal of the given number is 1.
so,
5 * 1/5 = 1
as LHS = 5 * 1/5 = 1
RHS = 1
Hence , a - 4
b ) Additive inverse
if the summation of the given number and opposite sign of given number results 0 .
7 + (-7) = 0
LHS = 7+ (-7) = 0
RHS = 0
hence , b - 5
c ) Commutative Property of Multiplication
if a.b = b.a hence it is in Commutative Property of Multiplication .
so, 5.6 = 6.5
hence , c - 1
d) Distributive property
if a ( b + c ) = a*b + a*c than it is in distributive property .
hence , d - 6
e) Additive Identity Property
if a+ 0 = a hence it is Additive Identity Property
so , b - 2
f ) Associative Property of Addition
if (a+b) + c = a + (b+c ) hence it is in Associative Property of Addition
so , f - 3.
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What is the equation of the line that passes through the points (-2, 3) and (2, 7)? (5 points)
O x-y=-1
Ox-y=-2
Ox-y=-5
O x-y=-6
The equation of the line that passes through the points (-2,3) and (2,7) is:
x-y=-5
Therefore, option(C) x-y= -5 is correct answer.
Step-by-step solution:
The algebraic representation of a line's equation is the collection of points that make up the line in a coordinate system.
Given the line passes through the points (-2,3) and (2,7)
So, the equation of the line passing through the two points is given by:
[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{y-3 }{7-3} } =\frac{x-(-2) }{2-(-2) }[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]
[tex]y-3 = x+2[/tex]
Now rearranging the above equation:
x - y + 3 + 2 = 0
x - y + 5 =0
Therefore, the equation of the line passing through the points (-2,3) and (2,7) is: x-y=-5
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What is the solution to the system of equations?
{x+y=4
{x=y=1
O (3, 1)
O (2, 2)
O (1/2, 3/2)
Answer:
hat are the solution(s) to the system of equations shown below? x2 + y2 = 5 y = 2x. 1) x = 1 and x = −1. 2) x = 1. 3) (1,2)
Step-by-step explanation:
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
=> y+ x = 3
=> y= 3-x
=> x= y = 1
=>3-x =1
=> x = 2
=> y = 2
(2,2)
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
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the chef mixes 12 tablespoons of flour to 8 tablespoons of sugar what fraction of the mixture is sugar.
Answer:
2/5
Step-by-step explanation:
To find the fraction that is sugar,
part sugar/ total
The total is sugar + flour = 8+12 = 20
8/20
We can simplify
Divide the top and bottom by 4
8/4 =2
20/4 = 5
The fraction is 2/5
Answer:
[tex]\sf\frac{8}{20}[/tex]
Step-by-step explanation:
First let us find the total.
Total = Flour + Sugar
Total = 12 + 8
Total = 20
Now we know that, there are 8 tablespoons of sugar in the whole mixture.
So, write it as a fraction, you have to divide the number of tablespoons of sugar by the total.
Sugar = 8/20