The total amount paid for the article is Rs2782
How to determine the amount paid?The given parameters are:
Article = Rs 2750
VAT = Rs 32
The amount paid is calculated using:
Amount = Article + VAT
This gives
Amount = 2750 + 32
Evaluate
Amount = 2782
Hence, the total amount paid for the article is Rs2782
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Triangle ABC = Triangle ADF, AD = 18, BC = 17, DF= [?]
The value of the length DF is 17
How to determine the length DF?The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.
So, we have:
AB = AD
AC = A F
BC = DF
Given that BC = 17;
The equation BC = DF becomes
17 = DF
Rewrite as:
DF = 17
Hence, the value of the length DF is 17
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A company orders 24 boxed lunches from a deli for $177.60. If each boxed lunch
costs the same amount, what is the unit cost of each boxed lunch?
Answer: $7.40
Step-by-step explanation:
You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.
SHOW ALL WORK PLEASE!!!!!!!
The rat population in a major metropolitan city is given by the formula n(t)=89e^0.02t where t is measured in years since 1992 and n(t) is measured in millions
What was the rat population in 1992?
What does the model predict the rat population was in the year 2003?
Answer:
See below ~
Step-by-step explanation:
What was the rat population in 1992?⇒ t represents the years after 1992
⇒ So, in 1992, t = 0
⇒ Apply in the formula
⇒ n(0) = 89e^(0.02 × 0)
⇒ n(0) = 89e⁰
⇒ n(0) = 89,000,000
The rat population in 1992 was 89,000,000.
===========================================================
What does the model predict the rat population was in the year 2003?⇒ Number of years after 1992 : 2003 - 1992 = 11
⇒ Substitute for t in the formula
⇒ n(11) = 89e^(0.02 × 11)
⇒ n(11) = 89e^(0.22)
⇒ n(11) = 89 × 1.24607673
⇒ n(11) = 110,900,829 rats
The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.
Answer:
(a) 89,000,000 rats
(b) 110,900,829 rats
Explanation:
Given equation:
n(t)=89e^0.02tTo find the initial population (1992):
insert t = 0
n(0) = 89e^0.02(0) = 89 million ≈ 89,000,000To find the rat population in 2003 (after 11 years):
insert t = 11
n(11) = 89e^0.02(11) = 89e^0.22 ≈ 110,900,829(2x-2) (x+5) what does x =
Answer:
a
x
2
+
b
x
+
c
=
0
the two roots of the equation take the form
x
1
,
2
=
−
b
±
√
b
2
−
4
a
c
2
a
So, start by adding
−
5
to both sides of the equation to get
2
x
2
+
x
−
5
=
5
−
5
2
x
2
+
x
−
5
=
0
Notice that you have
a
=
2
,
b
=
1
, and
c
=
−
5
. This means that the two solutions will be
x
1
,
2
=
−
1
±
√
1
2
−
4
⋅
2
⋅
(
−
5
)
2
⋅
2
x
1
,
2
=
−
1
±
√
41
4
You can simplify this if you want to get
x
1
=
−
1
+
√
41
4
≅
1.35078
and
x
2
=
−
1
−
√
41
4
≅
−
1.85078
Answer:
(2x-2)=
+2 =+2
(2x)=2
----------
2
x= 1
-----------------------------------------------
(x+5)=
-5=-5
x= -5
Step-by-step explanation:
You just need to separate the variable from the numbers
If p+q = - 2, show that p^3 + q^3 +8 =6pq
Answer:
Step-by-step explanation:
Algebraic Identities:Identity used: (a +b)³ = a³ + b³ + 3ab(a +b)
p + q = -2 ------------------(I)
Both sides take cube,
(p +q)³ = (-2)³
a = p and b =q
p³ + q³ + 3pq(p +q) = -8
p³ + q³ + 3pq*(-2) = - 8 {From (I)}
p³ + q³ - 6pq = -8
p³ + q³ = -8 + 6pq
p³ + q³ + 8 = 6pq
Hence, proved.
I need help I don’t understand please help
A recipe calls for (1 3/8) cups of sugar to make 2 dozens cupcakes. How much sugar is needed to make 60 cupcakes?
Answer:
55/16 cups or 3.4375 cups
Step-by-step explanation:
there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes
simplify (4x^3)^2 (3x^5)
Answer:
16x^6(3x^5)
48x^11
If F(x) = x-3, which of the following is the inverse of F(x)?
O A. F1(x) = x+ 3
B. F¹(x) = 3x
OC. F¹(x) = x-3
OD. F¹(x) = 3-x
Answer:
3-x is the inverse of f(x)=x-3
How do u solve the pythagorean theorem to find out if they right trangles
To solve the theorem, we will take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides
What is Pythagoras theoremPythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides
For instance, let;
c be the longest sidea and b be the other two sidesAccording to the theorem above, mathematically;
c² = a² + b²
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Hi there !
What is a Pythagoras theorem ?
Nonsense = Reported
Thank you
Answer:
Hi! I think you are referring to the Pythagorean Theorem.
Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.
The formula is a squared + b squared = c squared
If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:
3 squared + 4 squared = x squared
(Let x = the longer side)
3 squared = 9
4 squared = 16
9+16 = x squared
25 = x squared
x = 5
So there you go, that's the Pythagorean theorem.
Let me know if this helped!
Answer:
a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Step-by-step explanation:
belle walks 7/10 mile each morning, and 1, 4/10 miles each evening.
how many miles does she walk in 5 days
Answer:
10.5 miles.
Step-by-step explanation:
If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)
We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.
Answer:
10 1/2
Step-by-step explanation:
divide 7/10 which is 0.7 then multiply that by 5 which is 3.5
then divide 4/10 which is 0.4 then multiply that by 5 which is 2, but add 5 which is 7.
then combine all of that together which is 3.5+7= 10.5
then convert that into a fraction which is 10 1/2
What are the zeros of the quadratic function f(x)=8^2-16-15
Answer:
C)
Step-by-step explanation:
f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex] , a=8, b= - 16, c= - 15
[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]
EASY 5TH GRADE QUESTION. WILL GIVE BRAINLIEST
How would you read the number -30?
Answer:
Negative thirty
Step-by-step explanation:
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $3550. How long did each mechanic work?
Firstmechanic:hours
Secondmechanic:hours
Answer:
1st mechanic:20hours
2ndmechanic:15hours
Step-by-step explanation:
1stmechanic:20hours=20x95
=$1900
2nd mechanic:15hours=15x110
=$1650
total=$1900+$1650
=$3550
Worth 30 points! Select the correct answer.
What is the value of x in the triangle? (file is attached below)
Answer:
A
Step-by-step explanation:
tan60=opp/adj
tan60=15/x
15tan60=x
25.98=x (when you calculate 15 root 3 it is the same number)
The graph of which of the following equations has a slope of -and an x-intercept of
(-6,0)?
A y=-x-6
B. y = − ½ x − 3
-
C. y = -x +3
D. y = -x +6
The answer is A
[tex]y = - x - 6 \\ 0 = - x - 6 \\ x = - 6[/tex]
so x intercept : (-6,0)
and slope is negative
Hope it helps
Please give brainliest
The equation of line which a slope is -1 and an x-intercept of (-6,0) will be;
⇒ y = - x - 6
What is Equation of line?The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The slope of the line = - 1
And, The x-intercept = (- 6, 0)
Now,
Let the equation of line;
⇒ y = - x - 6
Slope (m) = dy/dx = - 1
And, The x - intercept is find as;
Put y = 0;
⇒ y = - x - 6
⇒ 0 = - x - 6
⇒ x = - 6
Thus, The correct equation is,
⇒ y = - x - 6
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I want to buy a car for $17,500 and I make 13 an hour roughly how long would it take me to reach my goal? & how many hours would i have to work ?
Answer:
1347 hours
Step-by-step explanation:
Assuming the income is net income (total after taxes etc.):
Cost of car = $17,500Net income = $13 per hourTo calculate the number of hours to be worked to save enough to buy the car, divide the cost of the car by hourly net income:
[tex]\begin{aligned}\implies \textsf{Number of hours to work} & = \dfrac{\textsf{Cost of car}}{\textsf{hourly net income}}\\\\& = \sf \dfrac{17500}{13}\\\\& = \sf 1346.1538...\end{aligned}[/tex]
We have to round the number up to 1347 hours, as only $17,498 will be saved if 1346 hours are worked.
The average working week is approximately 40 hours, therefore to calculate how many weeks it would take to earn enough money to purchase the car, divide the number of hours by 40:
⇒ 1347 ÷ 40 = 33.675
So it would take 34 weeks, working an average of 40 hours a week and not spending any of the money earned, to save enough to purchase the car.
Total hours
Cost/Earnings17500/131346.15Round to the next whole instead of nearest whole to avoid depicit
1347 hours you have to work atleastIn most of the countries the average working hours per week is
45 hoursTotal weeks
1347/4529.930weeks you have to work if you don't spend any money of itSolve for x
(2^2/x) (2^4/x) = 2^12
[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]
Now, since the base on both sides are equal, therefore their exponents are equal as well ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{6}{x} = 12[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{6}{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{1}{2} [/tex]
or
[tex]\qquad \sf \dashrightarrow \:x = 0.5[/tex]
Hope you got the required Answer ~
If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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7,000 dollars is placed in a savings account with an annual interest rate of 3%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answer:
See below
Step-by-step explanation:
Interest 3% in decimal form is .03
interest in ONE year 7000 * .03
interest in SEVEN years 7000 * .07 * 7
this is added to the original deposit of 7000
to become 7000 + 7000 * .03 * 7
or 7000 ( 1 + .03*7 )
or 7000 ( 1.21 ) = $ 8470
IF the interest is compounded
the money in the account will be 7000 ( 1+.03)^7
A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101.
Find the substance's half-life, in days. Round your answer to the nearest tenth.
A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.
What is the formula for half-life?Exponential decay obeys the equation
[tex]m(t) = m_0 e^{-kt}[/tex]
where t = time, days
Given:
Initial mass, m₀ = 8 g
Decay constant, k = 0.101
For half-life, the mass is m = m₀/2.
Therefore,
[tex]m(t) = m_0 e^{-kt}[/tex]
e^{-0.101t} = 1/2
-0.101t = ln 0.5
t = ln 0.5/-0.101
t = 2.98
Therefore, The half-life is 2.98 days.
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A continuous random variable X has cdf F(x)=x² b (a) Determine the constants a and b. for a < 0, for 0 < x < 1, for x > 1.
Any proper CDF [tex]F(x)[/tex] has the properties
• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]
• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]
so we have to have a = 0 and b = 1.
This follows from the definitions of PDFs and CDFs. The PDF must satisfy
[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]
and so
[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]
[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]
Help please i need it
Answer:
4 pints
Step-by-step explanation:
1(2 1/2) + 2(4) + 1(5 1/2) =5/2 + 8 + 11/2 =16/2 + 88 + 816/28/24Therefore each can would contain 8/2 = 4 pints
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Please feel free to comment, ask questions, give feedback, or correct me if I am wrong!
Have a great day!
:)
Find the amount of simple interest on a loan of $2,500 at 4.44% interest for 12.75 months. (Round to the nearest cent)
HELP PLS! A kiddie pool is 9 feet long and 6 feet wide. Surrounding wach side of the kiddie pool is a cement walkway of uniform width. The combined area of the pool and walk way is 108 ft^2. Find the width of the walkway
Answer:
wait I will edit and answer it in a few minutes
The data below represent a demand schedule.
Product Price: $30, $25, $20, $15, $10
Quantity Demanded: 5, 15, 25, 35, 45
Using the midpoint approach, determine the price elasticity of demand between each of the following prices:
A. Between P1 = $30 & P2 = $25, Ed=?
B. Between P1 = $25 & P2 = $20, Ed=?
C. Between P1 = $20 & P2 = $15, Ed=?
D. Between P1 = $15 & P2 = $10, Ed=?
Round your answers to two decimal places. Enter your answers as a positive value (absolute value).
By using the midpoint approach, the price elasticity of demand between each of the given prices are:
5.502.251.170.63What is the price elasticity of demand?The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).
By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:
Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]
Price elasticity of demand = 1/-0.1818
Price elasticity of demand = 5.50.
Part B.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]
Price elasticity of demand = 0.5/-0.2222
Price elasticity of demand = 2.25.
Part C.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]
Price elasticity of demand = 0.33/-0.2857
Price elasticity of demand = 1.17.
Part D.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]
Price elasticity of demand = 0.25/-0.4
Price elasticity of demand = 0.63.
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Solve this system of equations by using the substitution method. y=2x-5 6x+7=y
Answer:
[tex]x = - 3 \: and \: y = - 11[/tex]
Step-by-step explanation:
L
[tex]since \: y = 2x - 5(equation \: 1) \: \\ [/tex]
[tex]substitute \: for \: y \: in \: equation \: 2 \: (6x + 7 = y)[/tex]
[tex]6x + 7 = y \\ 6x + 7 = 2x - 5 \\ collect \: like \: terms \\ 6x - 2x = - 5 - 7 \\ 4x = - 12 \\ x = \frac{ - 12}{4} \\ x = - 3[/tex]
[tex]substitute \: for \: x in \: equation \: 1[/tex]
[tex]y = 2x - 5 \\ y = 2( - 3) - 5 \\ y = - 6 - 5 \\ y = - 11[/tex]
Answer:
[tex]y = 2.x = \frac{1}{11} [/tex]
Step-by-step explanation:[tex] \binom{x - 56x + 7 = y}{y = 2} [/tex]
_______________________
1. Substitute y = 2 :
[tex](x - 56x + 7 = 2)[/tex]
2. Simplify :
[tex]( - 55x + 7 = 2)[/tex]
3. Isolate x for [tex]( - 55x + 7 = 2) : x = \frac{1}{11} [/tex]
4. The solution of the system of equations are :
[tex]y = 2.x = \frac{1}{11} [/tex]
PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day.
Answer:I think it would be 84 + 0.45m + 108.
Which simplified could be 0.45m + 192.
hope this helps!
Step-by-step explanation:
Question 6 of 10 In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? 2x - 4y = 5 6x - 3y=10 A. Multiply the top equation by -2. B. Multiply the top equation by -3 and the bottom equation by 2. C. Multiply the top equation by 3 and the bottom equation by 4. D. Multiply the top equation by -3. SUBMIT
???
Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We are having two equations:-
2x - 4y = 5
6x - 3y=10
When we multiply the first equation by -3 the equation will become as follows:-
-6x + 12y = - 15
6x - 3y = 10
By adding both the equations one variable will be eliminated:-
9y = - 5
Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.
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