Therefore, the price elasticity of demand by percentage change method is -0.025.
Given the price of a first commodity (p₁) = 6 rs
the price of a second commodity (p₂) = 10 rs
Expenditure on first commodity (s₁) = 120
Expenditure on second commodity (s₂) = 180
We need to find the quantity as
120 = 6 * Q₁. 180 = 10 * Q₂
Q₁ = 120 / 6 Q₂ = 180 / 10
Q₁ = 20 Q₂ = 18
price elasticity of demand by percentage change method as
Eₐ = P / Q * ΔQ /ΔP
ΔQ = Q₂ - Q₁ = 18 -20 = -2
ΔP = p₂ - p₁ = 10 - 6 = 4
Eₐ = 6 / 120 * -2 / 4
Eₐ = - 0.025
Therefore, the price elasticity of demand by percentage change method is -0.025.
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If f(x)=3x-2 determine the value of y for each x value -4, 2, 3
Answer:
Step-by-step explanation:
y = f(x) = 3x -2
When x = -4,
y = 3(-4) -2 = -12-2 = -14
When x = 2,
y = 3(2) -2 = 6-2 = 4
When x = 3,
y = 3(3) -2 = 9-2 = 7
write your answers in Arabic numerals XXXV-VIII
Step-by-step explanation:
٨-٥٢.....................
Solve the following quadratic equation for all values of x in simplest form.
11- x² = -3
Answer:
x = √14
Step-by-step explanation:
11- x² = -3
x² = 14
x = √14
Find the midpoint of points A(-1,-7) and B (3,-4) graphically
(0,0) because that is the center
R6000 is deposited into a savings account. Four years later, R7000 is added to the savings. The interest rate for the first three years is 8% per annum compounded annually. Thereafter, the interest rate changes to 9% per annum compounded annually. Calculate the value of the savings at the end of the seventh year.
Answer:
R 19734.32
Step-by-step explanation:
If an amount P is deposited at R% interest compounded annually for n years, the amount at the end of n years is given by the formula
[tex]P = P(1 + r)^t[/tex]
r = R/100
Note
Interest rate 8% = 8/100 =0.08 for computation
Interest rate 9% = 8/100 =0.09 for computation
Since the interest rate changes after 3 years, the first thing to do is to find out how much the value is after 3 years
[tex]V(3 years) = 6000(1 + 0.08)^3[/tex] = 6000 x1.08³ = 6000 x 1.259712 = 7558.27
After 3rd year interest changes to 9%(0..09) but an additional amount is deposited
Let's find the value after the 4th year at 9% compounded annually using the general formula with r = 0.09 and t =1
V (after 4th year) = 7558.27(1.09)¹ = 7558.27 x 1.09 = 8238.51
We are depositing 7000 at the end of the 4th year so the principal becomes 8238.51 + 7000 = 15,238.51
This new amount accrues interest at 9% for 3 more years (7-4)
So value of savings at end of 7th year is
V = 15238.51(1+0.09)³ = 15238.51 x 1.259712 = 19734.32
Answer:
R19734.32
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Years 1-3Given:
P = R6000r = 8% = 0.08t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000(1+0.08)^3[/tex]
[tex]\implies \sf A=6000(1.08)^3[/tex]
[tex]\implies \sf A=6000(1.259712)[/tex]
[tex]\implies \sf A=7558.272[/tex]
Therefore, the amount in the account after 3 years was R7558.272.
Year 4The interest rate changed to 9%.
Given:
P = R7558.272r = 9% = 0.09t = 1Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=7558.272(1+0.09)^1[/tex]
[tex]\implies \sf A=7558.272(1.09)[/tex]
[tex]\implies \sf A=8238.51648[/tex]
Therefore, the value of savings at the end of the 4th year was R8238.51648.
Years 5-7After four years, R7000 was added to the account.
Given:
P = R8238.21648 + R7000 = R15238.21648r = 9% = 0.09t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=15238.21648(1+0.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.295029)[/tex]
[tex]\implies \sf A=19734.3207...[/tex]
Therefore, the value of the savings at the end of the seventh year is R19734.32.
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What is the MEDIAN of this set of data?
10, 90, 80, 60, 50, 40, 70, 30, 20, 100
Answer:
your answer is 55 as shown by above photo ^^
Answer:
55
Step-by-step explanation:
SOMEONE HELP WITH THIS PROBLEM
Answer:
y < 3x + 2
y> -2x + 2 The symbol should be > with a line under it to show greater than or equal to
Step-by-step explanation:
A ladder leaning against a wall forms a triangle and exterior angles with the wall and the ground. What is the measure of exterior angle formed on the ground? 5 degrees 90 degrees 125 degrees 180 degrees
In linear equation 125 degrees is the measure of exterior angle formed on the ground.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.we know that the sum of all the angles of a triangle is 180
therefore
11x+7x+90=180
18x=90
x=5
exterior angle formed on the ground=180-11x
=180-55
=125
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What is the domain of the function y = 2√x-5?
THE ANSWER IS IN THE PHOTO
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2)?
At (4.472 , 4.236) in the first quadrant , the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2) .
The equation of circle with center (h,k) and radius r can be written as
(x-h)²+(y-k)²=r²
In the given question
the center of the circle is (0,2) and the radius of the circle is 5 .
So the equation of circle become
(x-0)²+(y-2)²=5²
x²+(y-2)²=25 ...(i)
It is given that y=0.5x+2 intersects the circle
y = 0.5x+2
Rewriting the equation we get
y-2=0.5x
(y-2)=0.5x
x=(y-2)/0.5
x = 2(y-2) ...(as 0.5=1/2) ....(ii)
Squaring both sides
x² = (2(y-2))²
x² = 2²(y-2)²
x² = 4(y-2)² ...(iii)
Substituting the value of equation (iii) in equation (i) we get ,
4(y-2)²+(y-2)²=25
5(y-2)²=25
(y-2)²=25/5
(y-2)²=5
Taking Square root both the sides , we get
√(y-2)²=√5
y-2 = √5
y=(√5)+2
y=2.236+2
y=4.236
Substituting the value of y in (ii) we get
x=2(4.236-2)
x=2*2.236
x=4.472
Therefore , the circle with radius 5 and center (0, 2) will intersect the line with equation y = 0.5 x + 2 in the first quadrant at (4.472 , 4.236).
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d•r=r•d
O Commutative Property of Multiplication
O Identity Property of Multiplication.
O Zero Property of Multiplication
O Commutative Property of Addition
Answer:
Commutative property of multiplication
3x+18+4x+15=180 what is x
Answer:
x = 21
Step-by-step explanation:
Adding numbers:
3x+ 18 + 4x + 15 = 180
3x + 33 + 4x = 180
Combine Like terms:
3x + 33 + 4x = 180
7x + 33 = 180
Subtract:
7x + 33 - 33 = 180-33
7x = 147
Divide:
[tex] \frac{7x}{7} = \frac{147}{7} [/tex] x = 21I need help asap please!
Answer:
5x+10
Step-by-step explanation:
[tex](f \circ g)(x)=f(g(x)) \\ \\ =f(-5x-6) \\ \\ =-(-5x-6)+4 \\ \\ =5x+6+4 \\ \\ =5x+10[/tex]
A transportation company charges a fee of $125 plus $50 per hour to rent a limousine. If John paid $425 for a limousine, for how many hours did he rent the limousine?
A. 7
B. 6
C. 5
D. 4
John rented the limousine for 6 hours.
The minimum fee charged by the transportation company to rent a limousine is $125.The hourly fee charged by the transportation company to rent a limousine is $50.The amount of money paid by John to rent a limousine is $425.Let the number of hours for which John paid for the rent of the limousine be "x".A formula that represents the equality of two expressions by linking them with the equals sign is known as an equation.The above-given data helps us to form the linear equation given below :425 = 125 + 50x300 = 50xx = 6Thus, John rented the limousine for 6 hours.To learn more about equations, visit :
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f(x) = cube root 2x
g(x) = 2x + 1
Find (f/g) (X) Include any restrictions on the domain
Divide 6/13 by 6/12 .
A. 12/13
B. 9/16
C. 1/12
D. 13/12
You need a 25% alcohol solution. On hand, you have a 325 mL of a 20% alcohol mixture.
You also have 50%
alcohol mixture. How much of the 50% mixture will you need to add to obtain the desired solution?
You will need
mL of the 50% solution
We need 65 ml of 50% mixture to obtain the desired solution.
Here, we need to make a 25% alcohol solution by mixing some amount of 50% alcohol mixture with 325 mL of a 20% alcohol mixture.
Let the amount of 50% alcohol solution be x
The the quantity of alcohol in 50% alcohol solution = 50% of x
= 0.5x
Similarly the the quantity of alcohol in 20% alcohol solution = 20% of 325
= 65ml
The total quantity of 25% alcohol solution = (325 + x) ml
Thus, the the quantity of alcohol in 25% alcohol solution = 25% of (325 + x)
= 0.25 (325 + x)
= 81.25 + 0.25x
Thus, we can form the following equation-
0.5x + 65 = 81.25 + 0.25x
0.5x - 0.25x = 81.25 - 65
0.25x = 16.25
x = 16.25/ 0.25
x = 65
Thus, we need 65 ml of 50% mixture to obtain the desired solution.
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Which of the following properties is demonstrated by the equation below?
9(x+3)=9x+27
distributive property
inverse property of addition
associative property of addition
communitive property of addition
Answer: Distributive Property
Step-by-step explanation:
This is an example of the distributive property because the 9 is being distributed into each term, yielding the 9x and the 27.
A bag contains 10 marbles: 5 are green, 3 are red, and 2 are blue. Deandre chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is red and the second is blue? Write your answer as a fraction in simplest form.
Answer:
1/15
Step-by-step explanation:
3/10 x 2/9 = /90 Dived the top and bottom by 6 and you will get 1/15.
The first time there were 10 marbles and she wanted red. There were only 3 red so the chances of getting a red is 3/10. Now she only has 9 marbles left. She was a blue so her chances are 2/9.
the difference of twice
a number and seven is nine
Answer:
16!
Step-by-step explanation:
Just 17 and 18 please!
[16] f(-3) = -5
#17 is asking us to find what the function equals when x is equal to -3. We will find x = -3 on the graph, then find what y equals.
[17] f(4) = 0
#17 is quite similar, it is asking us to find what the function equals when x is equal to 4. We will find x = 4 on the graph, then find what y equals.
You asked in the comments for #16 and #17, I hope this helps.
Jack walks around the his schools track field and completes 1 lap in 30seconds.How long does it take Jack to complete 1 mile? How far will he run after 30 min?What is my speed in minutes per hour
Read this excerpt from “The All American Slurp”
In china we never ate celery raw or any other kind of vegetable raw. We always had to disinfect the vegetables in boiling water first. When we were presented with our first relish tray, the raw celery caught us unprepared
What story element does the author develop in this excerpt?
Conflict between family members.
Character traits of the Lin family.
Plot details about the Gleason party.
Setting details about the Lins hometown.
From the excerpt that we have here the story element that the Character traits of the Lin family.
What does the character trait mean?This is the term that is used to refer to the words that are used in order to offer the characterization of a person. These are the terms that would help to show the personalities and the qualities that a person has. It tells us who these persons are and the way they would be described if we are to talk about them to other people.
Based on the description that I have given here, the way that we would be able to talk about this family would be that they are known to prepare their food in a different way that the Americans made theirs.
From what they said, they would always have to put their vegetables first in boiling water. This would make it less raw. But from what they were offered in America, they had to eat the vegetables that had been left raw.
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work
Question 2, 2.3.5
Part 1 of 2
Select the correct choice below and, if necessary, fill in the answer box within your choice
OA. The slope is (Simplify your answer.)
OB. The slope is undefined.
←
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical
(7.1) and (2.1)
The slope of the line passing through the pair of points is
Given points are:
A (7,1) = (x₁ , y₁)
B (2,1) = (x₂ , y₂)
slope of a line is : y₂ ₋ y₁/x₂ ₋ x₁
Slope equals a height change /Change in width. You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y.
Assume that the line's slope is'm'.
m = y₂ ₋ y₁/x₂ ₋ x₁
m= 1 ₋ 1/2 ₋ 7
m = 0/₋5
m = 0
hence, when the slope is 0 then the line is horizontal .
Therefore, the slope is 0 which indicates that the line is horizontal.
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Right angle ABC is taken by a dilation with center P and scale factor 1/2 to angle A'B'C'. What is the measure of angle A'B'C'?
Answer: 90 degrees
Step-by-step explanation:
Dilations preserve angle measure.
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
j2 + 20j +
Please explain in detail.
Answer:
the quadratic equations is 22+×3÷78=36-54The set of real numbers is composed of rational and irrational numbers.
A. true
B.false
Answer:
true..... ............
Stanley can purchas a 15.4-ounce bottle of
olive oil for $5.39 or a 23.6-ounce bottle of olive oil for $7.08.
Which bottle is the better buy? Explain.
Answer: They are the same deal
Step-by-step explanation:
15.4/5.39=3.33333...
23.6/7.08=3.333333...
11. Convert the number to scientific notation.
0.000001019
1.02 x 10-⁹
1.02 x 10-6
10.19 x 10-7
1.02 x 106
Solve the system by back substitution.
-4x - 8y - 2z - 6w = 5
3y + 18z + 6w = 24
z + w =2
-2w = -6
Solution should be set like {( _ , _ , _ , _ )}
The values of all the variables are:
w = -3z = 5y = -16x = 33 approxWhat are equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.Given equations:
-4x - 8y - 2z - 6w = 53y + 18z + 6w = 24z + w =2-2w = -6To find the values of x, y, w, and z:
-2w = -6w = -6/2w = -3Substitute (w = -3) in z + w = 2:
z + w = 2z -3 = 2z = 2 + 3z = 5Substitute (w = -3) and (z = 5) in 3y + 18z + 6w = 24:
3y + 18z + 6w = 243y + 18(5) + 6(-3) = 243y + 90 - 18 = 243y + 72 = 243y = 24 - 723y = - 48y = - 16Substitute (y = - 16), (w = -3) and (z = 5) in -4x - 8y - 2z - 6w = 5
-4x - 8y - 2z - 6w = 5-4x - 8(-16) - 2(5) - 6(-3) = 5-4x + 128 - 10 + 18 = 5-4x + 118 + 18 = 5-4x + 136 = 5-4x = 5 - 136-4x = - 131x = 131/4x = 32.75Rounding off: x = 33Therefore, the values of all the variables are:
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