The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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Write the symbolic statement in words. Use p, q, r, s, t, and u as defined below.
p: The tour goes to Italy.
q: The tour goes to Spain.
r: We go to Venice.
s: We go to Florence.
t: The hotel fees are included.
u: The meals are not included.
r → ~s
We go to Florence and we do not go to Venice.
We go to Venice if and only if we do not go to Florence.
We go to Venice and we do not go to Florence.
If we do not go to Florence, then we will go to Venice.
If we go to Venice, then we will not go to Florence.
The definition of the symbolic statement r → ~s is:
If we go to Venice, then we will not go to Florence.
What is the definition of the given symbolic statement?First, we have to look at the definition of the events.
Event r means that the person goes to Venice.Event s means that the person goes to Florence, hence event ~s means that the person does not go to Florence.The operation → is a implication operation, hence a → b is: if a then b.In this problem, the statement is:
If r then not s.
Considering events r and s, the correct option is:
If we go to Venice, then we will not go to Florence.
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why do you multiply 10 by the repeating decimal to make a fraction.
Solution :
Repeating or recurring decimals :
Repeating or recurring decimals are those decimal expansions that do not terminate or end after a specific number of digits. Such numbers have an infinite number of digits after the decimal point. And there is a repetitive pattern in those digits.
Decimal numbers can be converted to fractions by dividing the number with a power of 10 which is equal to the number of decimal places. For example, 1.5 = 15/10 = 3/2. But with repeating decimals, it is impossible to count the number of decimal places as it is infinite. So, there are some specific steps to be followed to convert repeating decimals to fractions.
The repeating decimal to fraction steps of conversion are given below:
Step 1: Identify the repeating digits in the given decimal number.
Step 2: Equate the decimal number with x or any other variable.
Step 3: Place the repeating digits to the left of the decimal point by multiplying the equation obtained in step 2 by a power of 10 equal to the number of repeating digits. This way you will get another equation.
Step 4: Subtract the equation obtained in step 2 from the equation obtained in step 3.
Step 5: Simplify to get the answer.
Let us take an example to understand the conversion of repeating decimals to fractions in a better way. Convert 0.77777... to a fraction.
Step 1: We can observe that 7 is repetitive in the given decimal number.
Step 2: Let x = 0.7777...
Step 3: There is only 1 repetitive digit, so multiply this equation by 10. We get, 10x = 7.7777...
Step 4: Subtract x = 0.7777... from 10x = 7.7777... We will get 9x = 7.
Step 5: x = 7/9. Therefore, 0.7777... = 7/9.
Hence,
you multiply 10 by the repeating decimal to make a fraction
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Line A and Line B are parallel. Line P is a transversal. If the measure of angle 8 is 140°, find the measures of the rest of the angles in the diagram. Then tell what the angle relationship is to angle 8.
The angle measures are;
Angle 7 is 40° = Angles 8 : supplementary
Angle 3 is 40° = Angles 8: supplementary angles
Angle 5 = 140° = Angle 8; corresponding angles
Angle 1 = 140° = Angle 8; corresponding angles
Angle 6 = 40° = Angle 8; supplementary angles
Angle 2 = 140° = Angle 8; corresponding angles
Angle 4 = 140° Angle 8; corresponding angles
How to determine the anglesGiven that angle 8 measures 140 degrees
It is important to note that angles on a straight line equals 180 degrees
Then,
angle 7 + angle 8 = 180°
Substitute the values of angle 8
Angle 7 + 140 = 180
Angle 7 = 180 - 140
Angle 7 = 40°
Thus, If angle 7 is 40° then angle 3 is 40°, corresponding angles
Angle 5 = Angle 8; corresponding angles
Angle 1 = Angle 8; corresponding angles
Angle 6 = Angle 7; corresponding angles
Angle 2 = Angle 8; corresponding angles
Angle 4 = Angle 8; corresponding angles
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f(x) = 4x³ + 5x² 3x6
g(x) = 4x - 5
Find (f - g)(x).
The value of (f-g)(x) is 4x3+5x2-7x-1.
Real- or complex-valued functions defined on the set Z+ of positive integers are arithmetic functions. They explain arithmetic characteristics of numbers and are frequently applied in number theory. For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")Mathematical branch known as arithmetic deals with the study and use of numbers, relationships between numbers, and observations on numbers.
f(x)=4x3+5x2-3x-6
g(x)=4x-5
Therefore,
(f-g)(x)=f(x)-g(x)
=(4x3+5x2-3x-6) – (4x-5)
= 4x3+5x2-3x-6-4x+5
=4x3+5x2-(4+3)x-(6-5)
=4x3+5x2-7x-1
Hence, the value of (f-g)(x) is 4x3+5x2-7x-1
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Completely stumped. If anyone can help, that would be greatly appreciated! Picture below.
Using translation concepts, we have that the table of values for the function p(x) = x - 7 is given by:
x = -2, p(x) = -9.x = -1, p(x) = -8.x = 0, p(x) = -7.x = 1, p(x) = -6.x = 2, p(x) = -5.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
y = f(x).
A translation down 7 units is represented by a subtraction by 7 in the range, that is:
p(x) = f(x) - 7 = x - 7.
The numeric values to be inserted in the table are given by:
x = -2, p(x) = -9.x = -1, p(x) = -8.x = 0, p(x) = -7.x = 1, p(x) = -6.x = 2, p(x) = -5.In the graph at the end of the exercise, both functions are shown.
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How do I find the next three numbers in the sequence -2,-1,-1,0,-1,1,-2?
Solve for x.
-4≤16-4x
0 x <-5
Ο x <5
0 x > -5
Ο χ>5
The solution to the given inequality (-4 < 16 - 4x) is x < 5.
Hence, option B) x < 5 is the correct answer.
What is the solution to the given inequality?Given the in equality in the question;
-4 < 16 - 4x
First, rewrite the inequality such that x is on the left side.
-4x + 16 > -4
Subtract 16 from both sides
-4x + 16 - 16 > -4 - 16
-4x > -20
Divide both sides by -4
Note that when dividing both sides of an inequality by a negative value, the inequality sign flips direction.
-4x/-4 < -20/4
x < -20/-4
x < 5
The solution to the given inequality (-4 < 16 - 4x) is x < 5.
Hence, option B) x < 5 is the correct answer.
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Three men went into a second-hand shop to buy a
television.
It was priced in the window at £30.
Each of them handed over £10 to the shop assistant.
As the assistant opened the till, the manager had a quiet
word with him, "that TV is in the sale and is only £25
now, you will have to give them £5 back."
The assistant was very lazy and couldn't be bothered to
count out the right change for each man.
Instead, he took 5 £1 coins out of the till.
He put two of them in his own pocket and gave each
man £1 back.
Here's the problem:
The men have now paid £9 each for the TV.
The assistant has kept £2 for himself.
3 x £9 = £27.
£27 + £2 = £29.
But £30 was handed over in the first place.
WHERE IS THE MISSING £1?
Step-by-step explanation:
The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25). This is instead a sum of a smaller amount the people could have paid ($9 × 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). Another way to say this is, the $27 already includes the bellhop's tip. To add the $2 to the $27 would be to double-count it. So, the three guests' cost of the room, including the bellhop's tip, is $27. Each of the 3 guests has $1 in his pocket, totaling $3. When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30.
To obtain a sum that totals to the original $30, every dollar must be accounted for, regardless of its location.
Thus, the sensible sum can be expressed in this manner:
fx(7)(87x+7y)(5)⁴is equal to the root of?
If anyone can help me to solve this!!
73 term for the arithmetic sequence 18,30,42
The 73rd term of the arithmetic sequence 18,30,42 = 882.
What is arithmetic sequence ?An arithmetic sequence seems to be a series of numbers that are ordered and share a common difference amongst each succeeding term. There are arithmetic sequences 3, 9, 15, 21, and 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.
What does not constitute an arithmetic sequence?The sequence is not arithmetic if the difference between subsequent terms is not constant. Subtracting two consecutive elements from the sequence yields a common difference.
According to the given data:Let us now look for the explicit rule for with this arithmetic sequence. We have the following:
aₙ = a₁ + (n - 1) * d
= 18 + 12 * (n - 1)
= 12n + 6.
The 73rd term is 12 (73) + 6 = 882.
The 73rd term of the arithmetic sequence 18,30,42 = 882.
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Knowledge Check
Question 10
The circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for Media and Engineering combined is
$30,000,000, what is the total annual budget?
Answer: 150,000,000
Step-by-step explanation:
Total percentage of editorial + engineering = 20%
Total budget of editorial + engineering = 30,000,000
So, Total budget*20/100 = 30,000,000
Total budget = 5*30,000,000
Total budget = 150,000,000
A triangle has side lengths of (26 +5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
The perimeter of the triangle will be 26 + 2c + 20b + 11d.
How to calculate the value?It should be noted that the perimeter of the triangle will be the addition of all the sides.
This will be:
26 + 5c + 10b + 7d + 4d - 3c
Collect like terms
26 + 5c - 3c + 10b + 11d
= 26 + 2c + 20b + 11d
Therefore, the perimeter of the triangle will be 26 + 2c + 20b + 11d.
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A triangle has side lengths of (26 +5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
4c + 26d
b + d + 26
26 + 2c + 20b + 11d.
PLEASE HELP ALGEBRA 2
just do the first 2 or 3
6:12 12:
Missing equivalent ratio
Answer:
24
Step-by-step explanation:
you multiplied 6 by 2 so you have to multiply 12 times 2 and you will get 24
What’s 1,234,320 rounded to the nearest thousand
Answer:
4,000
Step-by-step explanation:
Rounding rule:
"4 or less, round down / keep the same."
"5 or more, round up."
Since the hundreds place has a 3, that means we round the thousands place to 4,000, because the hundreds place is lower than 5.
Carry out these operations as if they were calculations of experimental results, and express each answer in the correct units and with the correct number of significant figures:
(2 × 103 g + 6.317 g) / (0.063 cm3 − 0.029 cm3) = g/cm3
Answer:
2
Step-by-step explanation:
B3jrnr2j3uiedbwbwbbw3kejr
Michael is arranging 14 cans of food in a row on a shelf. He has 5 cans of carrots, 1 can of beets, and 8 cans of corn. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
18018
Given:
Number of cans = 14
Number of cans of carrots = 5
Number of cans of beets = 1
Number of cans of corn = 8
When there are n objects to be arranged in order, out of which r1 objects are of one kind, r2 objects are of another and so on, then the number of different arrangement is given as:
[tex]\frac{n!}{r_{1!*rx_{2 }! }.......r_{n} ! }[/tex]
n=14, r1= 5 ,r2=8
therefore 14!/(5!*8!)
=18,018
Therefore, the distinct orders in which the cans can be arranged is 18018
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The total cost of an annual pass for admission to a national
park plus camping for x days can be modeled by the function
f(x) = 20x + 80. A senior citizen pays $20 less than half of
this price for x days. What is the total cost for a senior citizen to
go camping for three days in the park?
The total cost paid by the senior citizen for 3 days = $50
Function word problemsThe function representing the total cost of the annual pass is:
f(x) = 20x + 80
A senior citizen pays $20 less than half of this price for x days
The total cost paid by the senior citizen = [tex]\frac{f(x)}{2} -20[/tex]
The total cost paid by the senior citizen =[tex]\frac{20x+80}{2} -20[/tex]
Simplify the resulting expression:
The total cost paid by the senior citizen =10x + 40 - 20
The total cost paid by the senior citizen = 10x + 20
x represents the number of days
Substitute x = 3 into the resulting equation
The total cost paid by the senior citizen for 3 days =10(3)+20
The total cost paid by the senior citizen for 3 days = $50
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When the chef turned the new freezer on, the temperature on the internal thermometer was 2 °C.
After breakfast had been served, the temperature had gone down by 15 °C.
What was the new temperature?
Answer: -13 °C.
Step-by-step explanation:
Compare the square root of one hundred forty and one hundred five ninths using <, >, or =.
square root of one hundred forty is greater than one hundred five ninths
square root of one hundred forty is equal to one hundred five ninths
one hundred five ninths is greater than square root of one hundred forty
square root of one hundred forty is less than one hundred five ninths
The square root of one hundred forty is less than one hundred five ninths. So, option D is correct.
According to this question we have to compare the square roots of both numbers One Hundred Forty and One Hundred Five Ninths. So, we have to calculate their square roots.
The square root of One hundred Forty: √140
The square root of One hundred Forty: 11.832
The square root of One Hundred Five Ninths: √159
The square root of One Hundred Five Ninths: 12.609
Comparing both of their square roots we can clearly see that :
(11.832) < (12.609)
The square root of 140 < Square root of 159
Hence, option D is correct. The square root of 140 is less than 159.
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What transformation carries the parallelogram below onto itself?
M(-2,3),
H(-4,-3)
A(4,3)
T(2,-3)
The transformation that carries the parallelogram below onto itself is a rotation by 180 degrees
How to determine the transformation?The coordinates are given as:
M(-2,3),
H(-4,-3)
A(4,3)
T(2,-3)
The rule of rotation by 180 degrees is
(x, y) = (-x, -y)
When the above rule is applied, we have
M(-2,3), = T(2,-3)
H(-4,-3) = A(4,3)
A(4,3) = H(-4,-3)
T(2,-3) = M(-2,3)
Hence, the transformation that carries the parallelogram below onto itself is a rotation by 180 degrees
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Find the difference.
8518- 2259 =
the correct answer is 6259
Find the value of the x in the triangle shown below. Please help!
Answer:
B x=√28 using Pythagorean theorem
By the Empirical Rule, how many students in a class of 200 would score within the range μ ± 2σ ?
The number of students that score within the range μ ± 2σ is; 190 students
How to use the empirical rule of statistics?
The empirical rule is a tool for finding the ranges that are 1 standard deviation, 2 standard deviations, and 3 standard deviations from the mean, in which you'll find 68, 95, and 99.7% of the normally distributed data respectively.
This means that 2 standard deviations from the mean would indicate that 95% of the students would score within the given range.
Thus, number of students that score within the range μ ± 2σ is;
95% * 200 = 190 students
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1 Without graphing, determine the characteristics of the graph.
(a) y = |x-3) -1
What is the vertex?
Answer: (3, -1)
Step-by-step explanation:
y = |x-3|-1
When y=|x|, vertex is (0, 0).
Now, let's translate the graph so it becomes y = |x-3|-1.
|x| ==> |x-3| Translate the graph 3 units to the right
Vertex: (0+3, 0) ==> (3, 0)
|x-3| ==> |x-3|-1 Translate the graph 1 unit down
Vertex: (3, 0-1) ==> (3, -1)
Vertex: (3, -1)
if √64 = a , then a is equal to ____.
32
16
8
irrational
Answer:
8
Step-by-step explanation:
The
[tex] \sqrt{64} [/tex]
is 8. Because when you divide 64 by 8 you get 8 which makes it a perfect square.
David and John own 37-1/2 acres of land. David owns 3/5 and John owns 2/5 of the land. They decide to section it off into ¾ acre lots to rent out as garden space for people who do not have garden space at their homes. The price for the entire summer for the rent of each lot is $50. Since there is no water supply to water the gardens, David and John have asked their renters if they would like a 100-gallon water tank or a 70-gallon water tank. 60% of the renters chose 100 gallons and 40% chose 70 gallons. David calculated that they would need to fill each tank 2 times and the cost of a gallon of water is $.05.
The total spent amount on water is $220
The total area is 37.5=75/2
The number of lots is 75/2/3/4=50 nos
Total rent is 50×50=2500
So 3/5 will go to david 2500×3/5=1500
2/5 will go to john 2500×2/5=1000
So 60% Renters choose 100 gallons
Total renters is 50
60% renters is 50×60%=30 nos
40% renters choose 70 gallons
40% of 50 is 20 nos
The tank fills twice
100×30+70×20=4400 to be filled
Per gallon cost is $0.05
So the total cost is 4400×0.5=$220
So they spent $220 on water
A fraction shows part of a whole. This entire may refer to a place or a group of places.A fraction can be a portion or section of any quantity out of a whole, where the whole can be number of any value.To learn more about fraction visit:
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Acasa Insurance Company offers several plans for home insurance.
Plan A has a $700 yearly premium with a $3,000 deductible.
Plan B has a $1,200 yearly premium with a $1,000 deductible.
The average payout by the insurance company for a fire claim is $27,000. Suppose 5% of the claims were for fire damage. What would Acasa's expected value (loss or gain) be per customer who chooses plan A
Acasa's expected value loss be per customer who chooses plan A
Assumption
Fill customers choose plan A
The average payout is the same for plans A & B
Expected value = net payment in -Net payment out
⇒ 1000% × 700$ - 5% ×[27000$ - 3000$]
⇒ 700$ - 1200$
⇒ -500$
What are a profit and loss?
A profit and loss statement is a record of revenue and expenses incurred by a business in a given period of time. A profit and loss statement is also called a P&L, an income statement, a statement of profit and loss, and income and expense statement, or a statement of financial results.
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A chemist is using 357 milliliters of a solution of acid and water. If 18.1% of the solution is acid, how many milliliters of acid are there? Round your
answer to the nearest tenth.
milliliters
If 18.1 percent of the solution is acid, 64.07 milliliters of acid are there.
What is a percentage?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.Multiplying this fraction by 100 and adding a percent sign will get the percentage. Percentage Equals 100 * numerator / denominator.As per the question,
18.1 Percent of 357 ml of solution used is acid, therefore,
=(18.1/100)*357
= 64.07 ml of acid
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