Last month, a retailer sold 120 jar candles at $30 per candle. This month the retailer is considering putting the candles on sale. They estimate that for each $2 decrease in price, they will sell 10 additional candles.
a. How much should the retailer charge for each candle in order to maximize its profit?
b. Find the domain and the range in the context of this situation.
A) The amount that the retailer should charge for each candle in order to maximize its profit is; $27
B) The domain of the function is; x ≥ 120
The range of the function is; P(x) ≥ 3645
How to find the domain and range of the problem?
A) Let the total sales be represented by P(x).
Let the number of candles sold be x.
Now, since the retailer 120 jar candles at $30 per candle and estimated that or each $2 decrease in price, they will sell 10 additional candles.. Thus;
P(x) = (30 - 2 * (x - 120)/10)x
P(x) = 30x - x²/5 + 24x
P(x) = - x²/5 + 54x
Using -b/2a, we can get the number of candles that maximizes profit as;
-54/(2 * -1/5) = 135 candles
Plugging 135 for x into the P(x) equation gives;
P(135) = $27
B) The domain of the function is; x ≥ 120
The range of the function is; 135 * 27 = 3645
P(x) ≥ 3645
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In which areas were there many labor shortages during the war?
A. Automotive industry
B. Teachers, nurses, and doctors
C. Farm and military industries
D. Industrial luxury production
The sum of the square of a positive number and the square of 2 more than the number is 20. What is the number?
Answer:
2
Step-by-step explanation:
2^2 is 4 and two more than 2, which is 4, is 16 when squared. 16+4=20
the function f(x) is an unshifted exponential function which goes through the points (2,5) and (3,4).
A. what is the equation for f(x)
B. Find f(10) and f(100)
[tex]f(x) = ae {}^{bx} \\ f(2) = 5 \: \: \: \: \: f(3) = 4[/tex]
[tex]5 = ae {}^{2b} \: \: \: \: \: \: \: 4 = ae {}^{3b} \\ divide \: both \: systems \\ e {}^{b} = \frac{4}{5} \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = \frac{125}{16} [/tex]
[tex]f(x) = \frac{125}{16} e {}^{ln(0.8)x} [/tex]
[tex]f(10) = \frac{125}{16} e {}^{10ln(0.8)} = \frac{65536}{78125} \approx0.838861 \\ f(100) = \frac{125}{16} e {}^{100ln(0.8)} = \frac{4 {}^{98} }{5 {}^{97} } \approx1.59 \times 10 {}^{ - 9} [/tex]
Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 2, negative 2), ( 1, 1), and (2, negative 2). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (negative 1, 1), and (1, 4). A coordinate plane shows 4 points with the following coordinates: (negative 4, 4), (negative 4, 1), (negative 2, 1), and (2, 1). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (1, negative 4), and (1, 1).
The ordered pair that represents a function is:
⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
The given points are;
(-3, -3), (-2, 2), (1, 1), (2, -2)
(-3, 3), (-3, -3), (-1, 1), (1, 4)
(-4, 4), (-4, 1), (-2, 1), (2, 1)
(-3, 3), (-3, -3), (1, -4), (1, 1)
Now, For an ordered pair to be a function, either of the following must be true:
Each x-value have exactly one corresponding y-value.
More than one x-values have the same corresponding y-values.
And, If any of the following conditions is true, then the ordered pair is not a function,
One x-value have multiple corresponding y-values.
More than one x-values have the multiple corresponding y-values.
From the given options, only ordered pair (-3, -3), (-2, 2), (1, 1), (2, -2) satisfies the condition to be a function.
Because none of its x-values have multiple corresponding y-values.
And, Other ordered pairs are either one-to-many or many-to-many.
So, The ordered pair that represents a function is:
⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)
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Someone is 18 1/2 inches long when they are born and their twin is 20 3/4 inches long. What is the difference between how big they are.
Aliyah has $94 in 13 bills in her wallet, including ones, fives, and twenties. If she has one less twenty dollar bill than she has one dollar bills, how many of each denomination does Aliyah have in her wallet?
Answer:
$1 x 4
$20 x 3
$5 x 6
Step-by-step explanation:
$94
at least 4 $1 bills
$90
at least 3 $20 ($60)
$30
the remaining $30 can be made up of 6 $5 bills
4 + 3 + 6 = 13 bills total
17. TRAFFIC SIGNS The diagram shows a sign used to warndrivers of a school
zone or crossing. Measure and classifyeach numbered angle.
each numbered angle is
1. right angle
2. obtuse angle
Road signs, often known as traffic signs, are posted along the side of roadways or above them to inform and direct drivers. Simple wooden or stone milestones were the oldest types of signs. Later, directional signs with arms were developed, such as the fingerposts used in the United Kingdom and their wooden equivalents in Saxony. Since the 1930s, as traffic volumes have increased, many nations have adopted pictorial signs or have similarly standardized and simplified their signs in an effort to overcome linguistic barriers and improve traffic safety. Such pictorial signals are typically based on international norms and use symbols (often silhouettes) in place of words. These signs were initially created in Europe and have since been adopted in varied degrees by the majority of nations.
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The complete question is attached below
After a 25%increase, the price is 300€.how many euros was the increase?
Step-by-step explanation:
the €300 as current price is 125% relative to the original price. in other words : 1.25 times the original price.
to get the amount of the increase we need to get the original price first and then subtract the original price from the current price.
to get the original price we need now to divide the actual price by 1.25 to undo the increase.
the original price
OP = 300/1.25 = €240
the price increase (of 25%) was then
300 - 240 = €60
set of even numbers less than 15
Step-by-step explanation:
for positive numbet (2, 4, 6, 8, 10, 12, 14)
2, 4, 6, 8, 10, 12, and 14.
Step-by-step explanation:
even number is 2,4,6,8.....
odd number is 1,3,5,7.......
wish you have a great day
Find the value of |-8| + 4(-5 + 9) ÷ 2.
0
24
12
16
The value of the given expression is 16. The correct option is the fourth option 16
Evaluating an ExpressionFrom the question, we are to find the value of the given expression
The given expression is
|-8| + 4(-5 + 9) ÷ 2
Simplifying by applying PEMDAS
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Simplifying
|-8| + 4(-5 + 9) ÷ 2
8 + 4(4) ÷ 2
8 + 16 ÷ 2
8 + 8
= 16
Hence, the evaluation of the expression is 16
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The half life of the isotope dubnium-263 is 29 seconds. A sample of dubnium-263 was first measured to have 1024 atoms. After t seconds, there were only 32 atoms of the isotope remaining.
Write an equation in terms of t that models the situations
Question based on Khan Academy
The radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}
What is radioactive decay?Radioactive decay is the spontaneous disintegration of atoms with the emission of radiation.
What is half life of a radioactive isotope?The half life of a radioactive isotope is the time it takes for half the number of atoms in a given sample to disintegrate.
How to Write an equation in terms of t that models the situations?To model the situation, we use the equation for radioactive decay which is given below
[tex]N = N_{0}e^{-{\lambda}t}[/tex] where
N = Number of atoms remaining after t seconds, N₀ = initial number of atoms, λ = decay constant = 0.693/T where T = half life of isotope and t = time of decayGiven that the half life of the isotope dubnium-263 is 29 seconds and sample of dubnium-263 was first measured to have 1024 atoms. Then, after t seconds, there were only 32 atoms of the isotope remaining. we have that
N = 1024 atoms, N₀ = 32 atoms, T = 29 sSo, λ = 0.693/29 s = 0.0239 /s
So, susbtituting the values of the variables into the equation, we have
[tex]N = N_{0}e^{-{\lambda}t}[/tex]
[tex]32 = 1024e^{-(0.0239/s)t}[/tex]
So, the radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}
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Every rhombus is a parallelogram
Answer: A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.
Step-by-step explanation:
Graph the image of rectangle ABCD after a dilation with a scale factor of 1/2 
Answer:
I took the time to graph the image onto the image that you had used, I hope this helps! <3
Step-by-step explanation:
Dilating by 1/2, is a contraction, it makes the pre-image smaller than the image.
Is this relation a function? Justify your answer.
A. Yes, because every x-and y-value is positive.
• B. Yes, because the number of x values is the same as the number of
y-values.
• C. No, because two points with the same x-value have different y
values.
• D. No, because two points with the same y-value have different x-
values.
Answer:
C.
Step-by-step explanation:
• C. No, because two points with the same x-value have different y
values. Points with coordinates (7;4) and (7;6).
is 4 33/100 a repeating decimal
Answer:
no
Step-by-step explanation:
4 33/100 is equal to 4.33, it is 4.33, not 4.33 with the dot on it, it means recurring decimal. It is jot a recurring decimal. :)
Ten grams is what percent of 1 ounce? Round your answer to the nearest tenth percent.
Answer:
0.4oz
Step-by-step explanation:
conversion factor 1oz = 28.35g
(10g/1)(1oz/28.35g) cross out grams
10/28.35oz = 0.3|527 = 0.4oz
8.
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
The measure of the central angle m∠VWU is 69 degrees
How to find central angles?Central angle is the angle formed by two arms and having the vertex at the centre of a circle.
The diameter of a circle runs from the centre of a circle.
The diameter SU and RT intersect each other at point Q.
Therefore,
m∠VWS = m∠TWU (Vertically opposite angles)
m∠VWU = m∠SWT (Vertically opposite angles)
Hence,
m∠TWU = 111 degrees.
Therefore,
m∠VWU = 360 - 111 - 111 /2
m∠VWU = 360 - 222 / 2
m∠VWU = 138 / 2
m∠VWU = 69 degrees
Therefore, the measure of the central angle m∠VWU is 69 degrees
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Which of the following shows 16 more than a number, written as an algebraic expression?
16n
16 − n
n − 16
16 + n
Answer:
16 + n
Step-by-step explanation:
Whenever something says "more" it typically includes addition.
It says 16 more than a number, meaning that you add 16 to an number (n)
*Please mark brainliest
Answer:
16 + n
Step-by-step explanation:
I got 100% on the test
The basketball team has developed a carnival game at
homecoming to raise money for new uniforms. They are
charging $3 per ticket to play. The expected pay out for each
play is $1.75. What can you conclude from this situation?
C
Answer:
Step-by-step explanation:kfn
What is the solution to 12x+31 = 15?
OA. X = 6
O
O
B. X = 6 or X=-6
C. X = 6 or x = -9
D. No solutions exist.
The solution of the equation 12x + 31 = 15 is x = -4/3
In this question we have been given an equation.
12x + 31 = 15
We need to find the solution of the given equation.
12x + 31 = 15
12x + 31 - 31 = 15 - 31 ..............(Subtract 31 from each side)
12x = -16
x = -16/12 .............(Divide each side by 12)
x = -4/3
Therefore, the solution of the equation 12x + 31 = 15 is x = -4/3
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A car's fuel consumption is 7.0 litres per 100km. What is
this in miles per gallon? (A gallon is about 4.5 litres, and
a mile is about 1.6km)
Please help.
The car's fuel consumption is 1.6 gallons per 62.50 miles
What is the car's fuel consumption is miles per gallon ?The mathematical operation that would be used to solve this question is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
The first step is to convert litres to gallons. To convert to gallons, divide 7.0 liters by the unit of conversion.
7 / 4.5 = 1.6 gallons
The second step is to convert kilometer to mile. To do this, divide 100 by the unit of conversion
100 / 1.6 = 62.50 miles
The car's fuel consumption is 1.6 gallons per 62.50 miles
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Write the ratio of frogs to flies in simplest form.
*
Captionless Image
The ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form is 2:4.
What is a ratio and how can it be calculated?A ratio can be described as the ordered pair of numbers in mathematics which do comes in form of a and b, and this can be written as a / b as well as a:b which is the ratio of two terms where both of them is not equal to zero.
In the case above, 4 frogs and 8 flies =4:8 =2:4
Therefore, the ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form is 2:4.
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Complete question:
Write the ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form.
How do i solve 5+2(6+3 ÷ 3)
Answer:
19
Step-by-step explanation:
Arrange into parentheses and start at the innermost parentheses
[tex]5 + (2 \times (6 + (3 \div 3)))[/tex]
Start with 3 ÷ 3
[tex]3 \div 3 = 1[/tex]
Continue with the other parts of the equation in order
[tex]1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19[/tex]
Hope this helped you understand better, have a great day!
If KL = 3x, LM = 2, and KM = x + 4, what is KM?
The value of KM is equal to 5.
A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within.
Consider a point L on a line segment KM such that:
We have the values,
KL = 3x ;
LM = 2
Now, we know,
KL + LM = KM
KM = 3x + 2 ---------(1)
Now, KM = x + 4 ---------(2)
Equating the equations (1) and (2),
We get,
3x + 2 = x + 4
Now, subtract 2 from each side of the equation.
3x + 2 - 2 = x + 4 - 2
3x = x + 2
Subtracting x from each side of the equation.
3x - x = x + 2 - x
2x = 2
Dividing each side of the equation by 2.
( 2x / 2 ) = ( 2 / 2)
x = 1
Therefore,
KM = x + 4
KM = 1 + 4
KM = 5
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ANSWR ASAP ILL GIVE BRAINLYEST AND 5 STAR
The missing steps of the expression are as follows;
[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷452 - 10.4 ÷ 4How to solve an expression?The expression can be solved as follows:
step 1
[tex](\frac{3^{2} + 4 }{|-0.25|} ) - 10.4[/tex] ÷ 4
Step 2
The absolute value will remove the minus sign of the denominator.
[tex](\frac{3^{2} + 4 }{0.25} ) - 10.4[/tex] ÷ 4
Step 3
We have to find the square of the 3 in the numerator. Therefore, the step 3 will be as follows:
[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷ 4
Step 4
We have simplify the numerator.
[tex](\frac{13 }{0.25} ) - 10.4[/tex] ÷ 4
Step 5
52 - 10.4 ÷ 4
Step 6
Using PEMDAS rule, we have to solve the division sign. Therefore, the step 6 is as follows;
52 - 2.6
Step 7
49.4
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A prism has a volume of 528 cubic feet, a length of 6 feet, and a height of 11 feet. What is the width of the prism rounded to the nearest foot?
Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.
What is the width of the given rectangular prism?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length.
Given the data in the question;
Volume of the rectangular prism V = 528 ft³Length l = 6ftHeight h = 11ftWidth w = ?To determine the with of the rectangular prism, plug the given values into the formula above and solve for w.
V = w × h × l
528 ft³ = w × 11ft × 6ft
528 ft³ = w × 66ft²
Reorder the equation and divide both sides by 66ft²
w × 66ft = 528 ft³
( w × 66ft )/66ft² = 528 ft³ / 66ft²
w = 528 ft³ / 66ft²
w = 8ft
Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.
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Simplify 5¹⁰ ^ 5²
...........................................
It should be noted that simplifying 5¹⁰ × 5² will be 5^12.
How to calculate the value?It should be noted that these values have to do with powers. In this case, since that have same base and we want to multiply, we will add their powers.
Therefore, 5¹⁰ × 5² will be:
= 5¹⁰ × 5²
= 5^12
In conclusion, the value will be 5 raise to power 12
Therefore, based on the information, it should be noted that the value of 5¹⁰ × 5² will be 5^12.
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Simplify 5¹⁰ × 5²
Lisa wants to take a trip during her vacation. She has 8 months to save towards a trip that she
expects will cost her $4,775 including airfare, hotels, and food. Her monthly income is $3,742
with monthly costs of: $304 for taxes, $750 for housing, $631 for transportation, $521 for
food, and $803 for miscellaneous expenses, such as phone and loan payments. How much
will she be able to save in 8 months?
Answer:
$5,864
Step-by-step explanation:
If you subtract all of the monthly costs from her monthly income, it will drop down to $733 and multiply that by 8.
can someone please help?
Approximately 7.4 is 1.9 times larger than 3.9.
[tex]10^{-8}[/tex] is 3 times smaller than [tex]10^{-5}[/tex] .
7.4 x [tex]10^{-8}[/tex] is 1.9 x x [tex]10^{-3}[/tex] smaller than 3.9 x [tex]10^{-5}[/tex].
What is the scientific notation?Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, when 100 is written in scientific notation it becomes 1 x 10².
For negative numbers, the sign in front of the power would be negative. For example, 0.0012 becomes 1.2 x [tex]10^{-3}[/tex] in scientific notation.
0.000039 becomes 3.9 x [tex]10^{-5}[/tex]
Difference between 7.4 and 3.9 : 7.4 / 3.9 = 1.9
Difference between [tex]10^{-8}[/tex] and x [tex]10^{-5}[/tex]
= [tex]10^{-8 - (-5)}[/tex]
= [tex]10^{-8 + 5}[/tex]
= [tex]10^{-3}[/tex]
[tex]10^{-8}[/tex] is three times smaller than [tex]10^{-5}[/tex]
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