The circumference of the circle with a radius of 16 is 32π using formula for the circumference of a circle is C = 2πr.
The circumference of a circle is the distance around the perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is the constant pi, and r is the radius of the circle.
In this case, the radius of the circle is 16, so we can substitute this value into the formula and simplify:
C = 2πr
C = 2π(16)
C = 32π
This means that if we were to measure the distance around the perimeter of the circle, we would get a value of 32π units, where π is the irrational number approximately equal to 3.14159.
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Find the center of mass of a thin plate of constant density delta covering the given region. The region bounded by the parabola y = 3x - x^2 and the line y = -3x The center of mass is. (Type an ordered pair.)
The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).
To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.
We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .
The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).
We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.
The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.
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mai has a jar of quarters and dimes. she takes at least 10 coins out of the jar and has less than $2.00. write a system of inequalities that represents the number of quarters, `x`, and the number of dimes, `y`, that mai could have.
The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:
x + y ≥ 10 and 0.25x + 0.1y < 2
These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.
Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:
Thus, the first inequality is x + y ≥ 10.
Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+
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For both f(x)= √x and f(x)=1/x, sketch the graph of the parent function, apply the transformations indicated, and state the domain and range. Note: You can sketch the graphs by hand or in digital form.
a) y= f(x+2)-1
b) y= -2f(x)+4
c) y= -2f(-(x-3))+1
Answer: a) Parent function:
f(x) = √x
Domain: x ≥ 0
Range: y ≥ 0
Applying transformations:
shift 2 units left: f(x+2)
shift 1 unit down: f(x+2)-1
Final equation and graph:
y = √(x+2) - 1
Domain: x ≥ -2
Range: y ≥ -1
b) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
multiply by -2: -2f(x)
shift 4 units up: -2f(x)+4
Final equation and graph:
y = -2/x + 4
Domain: x ≠ 0
Range: y ≠ 4
c) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
shift 3 units right: f(-(x-3))
multiply by -2: -2f(-(x-3))
shift 1 unit up: -2f(-(x-3))+1
Final equation and graph:
y = -2/(3-x) + 1
Domain: x ≠ 3
Range: y ≠ 1
Step-by-step explanation:
If a car runs at a constant speed and takes 3 hrs to run a distance of 180 km, what time it
will take to run 100 km?
Answer:
100 minutes
Step-by-step explanation:
We know
It takes 3 hrs to run a distance of 180 km.
180 / 3 = 60 km / h
60 minutes = 60 km
40 minutes = 40 km
What time it will take to run 100 km?
60 + 40 = 100 minutes
So, it takes 100 minutes to run 100 km.
If x=3, solve for y
y=2*3^(3)
Answer:
54
Step-by-step explanation:
Answer:
y=54
as x=3
so y=2*x^3
y= 2*3^3
y=2*27
y=54
22) i) A cuboid has dimensions 60cm x 24cm x 30cm. How many small cubes with side 5cm can be placed in the given cuboid?
Answer:
345.6
Or 345 full cubes
Step-by-step explanation:
To answer this question we first need to find the volume of the cuboid!
To find volume we use the equation...
area of cross-section × heightor l × w × hFor the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...
60 × 24 × 30 = 43200We now need to the the volume of the cube which we can just do by cubing the value given
5³ = 125We now need to divide the two results together to find out how many cubes would fit...
43200 ÷ 125 = 345.6Or 345 full cubesHope this helps, have a lovely day!
y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Answer:
Y=x^2+7x-3
complete the square to re-write the quadratic function in vertex form.
pls help
Step-by-step explanation:
To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.
y = x^2 + 7x - 3
y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)
y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)
y = (x + 7/2)^2 - 49/4 - 3
y = (x + 7/2)^2 - 61/4
So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).
xavier is a teacher and takes home 90 papers to grade over the weekend. he can grade at a rate of 6 papers per hour. how many papers would xavier have remaining to grade after working for 12 hours?
The number of papers xavier have remaining after working for 12 hours is 18
How many papers would xavier have remainingXavier can grade 6 papers per hour, so in 12 hours he can grade:
6 papers/hour x 12 hours = 72 papers
Therefore, after working for 12 hours, Xavier would have
90 - 72 = 18 papers remaining to grade.
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Masons backyard deck is rectangular. The width is 12 feet less than the length. The perimeter is 64 feet. What is the length?
As Masons backyard deck is rectangular, the length of the deck is 22 feet.
Let's start by using algebra to solve for the length of the rectangular deck.
Let L be the length of the deck.
Then, the width of the deck is L - 12.
The perimeter is the sum of all four sides, so we have:
Perimeter = 2L + 2(L - 12) = 64
Simplifying the equation, we get:
2L + 2L - 24 = 64
Combining like terms, we get:
4L - 24 = 64
Adding 24 to both sides, we get:
4L = 88
Dividing both sides by 4, we get:
L = 22
Therefore, the length of the deck is 22 feet.
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An amount of $5000 is invested at 6% per year until it triples in value. When will that be?
Answer:
50 years
Step-by-step explanation:
Assuming it doesn't compound, 5,000*3 = 15,000.
5,000 * 6% = 5,000 * 0.06 = 300.
15,000 / 300 = 50 years.
Calculate Suppose that on each of the
4,500 dives Alvin has made, a new pilot and two new scientists were on board.
How many scientists have seen the
deep ocean through Alvin's windows? How
many people, in total, traveled in Alvin?
The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and
a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.
What is the explanation for the above calculation?1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:
4,500 dives x 2 scientists per dive = 9,000 scientists
Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.
2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:
4,500 dives x (1 pilot + 2 scientists)
= 4,500 x 3
= 13,500 people
Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.
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how to integrate directly using substitution given the same initial condition does this match your taylor series
The integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.
Step 1: Find the Taylor series of the given function f(x).
f(x) = e^(x^2)cos(x)
Therefore, we can say that the Taylor series of the given function is: f(x) = 1 + x^2 + (1/2)x^4 + (1/6)x^6 + (1/24)x^8 + ...
Step 2: Substitute the required value of x into the Taylor series. Let us substitute x = 1 into the Taylor series we got above.
f(1) = 1 + 1^2 + (1/2)1^4 + (1/6)1^6 + (1/24)1^8 + ...
f(1) = 1 + 1 + (1/2) + (1/6) + (1/24) + ...
Step 3: Simplify the expression to get the answer. We can simplify the above expression by using the formula for the sum of an infinite geometric series. The formula is given as follows:
Sum of infinite geometric series = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 1/4. Sum of the series = a / (1 - r) = 1 / (1 - 1/4) = 4/3.
Therefore, we can say that the integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Jose's account has gone into overdraft. His balance is $-27.14. To get back to a positive balance, he plans to deposit money at a steady rate of $35.03 per week. How much will be in his account after 7 weeks?
Answer:
yo your dûmb asl
Step-by-step explanation:
plsss help theorical probability
calculate the theoretical probability of a 1 eyed, 1 horned, flying, purple, people eater
The theoretical probability for the 1 horned, 1 eyed, flying, people eater purple is found to be 1/120.
Explain about the theoretical probability?Experimental Probability: Based on actual results rather than mathematical calculations, the experimental probability of an occurrence is the likelihood that the event will actually occur.
Theoretical Probability: Considering that the event is ideal, the theoretical chance that it will occur is the theoretically ideal probability of a specific result. The flaws in the system are not taken into consideration by theoretical probability.
Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.
The given probability are;
1 eyed - 3/41 horned - 1/5flying - 2/3 purple -3/8 people eater - 1/2Let P(E) be the theoretical probability 1 horned, 1 eyed, flying, people eater purple.
Then,
P(E) = 3/4 * 1/5* 2/3* 3/8* 1/2
P(E) = 1/120
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Select the correct answer. Which graph represents this equation? A. The graph shows an upward parabola with vertex (minus 3, minus 4.5) and passes through (minus 7, 3.5), (minus 6, 0), (0, 0), and (1, 3.5) B. The graph shows an upward parabola with vertex (3, minus 4.5) and passes through (minus 1, 3.5), (0, 0), (6, 0), and (7, 3.5) C. The graph shows an upward parabola with vertex (minus 2, minus 6) and passes through (minus 5, 7), (minus 4, 0), (0, 0), and (1, 7) D. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7)
Answer:
A
Step-by-step explanation:
Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)
Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.
Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.
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5. Find x and h.
x =
h =
Using pythagoras' theorem in the right-angled triangle
x = 3 andh = 3√3What is a right-angled triangle?A right-angled triangle is a polygon with 3 sides in which one angle is a right angle
Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have
h² + (12 - x)² = 12² - 6² (1)
Also, h² + x² = 6² (2)
So, h² + (12 - x)² = 12² - 6²
h² + (12 - x)² = 144 - 36
h² + (12 - x)² = 108 (3)
From equation (2), h² = 36 - x²
Substituting this into equation (3), we have that
h² + (12 - x)² = 108 (3)
36 - x² + (12 - x)² = 108 (3)
Expanding the brackets, we have that
36 - x² + 144 - 24x + x² = 108
36 + 144 - 24x = 108
180 - 24x = 108
-24x = 108 - 180
-24x = -72
x = -72/-24
x = 3
Since h² = 36 - x²
h = √(36 - x²)
So, substituting the value of x = 3 into the equation, we have that
h = √(36 - x²)
h = √(36 - 3²)
h = √(36 - 9)
h = √27
h = 3√3
So,
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on saturday a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers.the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold?
Answer: Let x be the number of hamburgers sold.
Then, the number of cheeseburgers sold is 3x.
The total number of burgers sold is x + 3x = 4x.
Given that the total number of burgers sold is 416, we have:
4x = 416
x = 416/4
x = 104
Therefore, 104 hamburgers were sold.
Step-by-step explanation:
Can somebody help me, please
Answer:
uh I don't even know what this is
Answer: x = 500
Step-by-step explanation:
Use the Pythagorean Theorem
a²+b²=c²
300² + 400² = x²
90000 + 160000 = x²
250000 = x²
√250000 = √x²
500 = x
hope i explained it :)
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = - " x+1' PA approximate f(0.2)
To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.
For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.
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(I NEED HELP, QUICK)
[50 PTS]
Answer:
In the picture.
34 ft.
a chef at a restaurant uses 12 pound of butler each day
Answer:
Every day, the chef consumes 5443.20 grams of butter, which is calculated using the conversion coefficients 16 oz/1 pound and 28.35 grams/1oz.
A restaurant chef uses 12 pounds of butter every day, as specified in the question.
We need to figure out how much butter the chef uses each day in grams.
Applying the conversion parameters provided, 16 oz/1 lb and 28.35 grams/1oz
According to the data provided, the needed solution is as follows: 12 lb 16 oz/1 lb 28.35 g/1 ounce 5443.20 grams
As a result, the chef consumes 5443.20 grams of butter every day.
Step-by-step explanation:
Brainliest pls
Find the area under the curve y = 2 x^-3 from x = 6 to x = t and evaluate it for t = 10 , t = 100 . Then find the total area under this curve for x ≥ 6 .
(a) t = 10
(b) t = 100
(c) Total area
The total area under the curve for x ≥ 6 is 449/4500.
The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:
We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]
Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.
Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6
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Aubrey used
4
7
liter
7
4
literstart fraction, 4, divided by, 7, end fraction, start text, space, l, i, t, e, r, end text of paint for a mural in her room and
2
10
liter
10
2
literstart fraction, 2, divided by, 10, end fraction, start text, space, l, i, t, e, r, end text for a wall in her bathroom.
The total amount of paint Aubrey used is more than 1/2 liter but less than 1 liter
Estimating the total amount of paint Aubrey usedTo estimate the total amount of paint that Aubrey used for both the mural and the wall, we can add the fractions of paint used
So, we have
Total = 4/7 + 2/10
Evaluate the sum in decimals
This gives
Total = 0.77 (approximated)
This value is between 0.5 liters and 1 liter
Hence, the estimate is between 0.5 liters and 1 liter
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Complete question
Aubrey used 4/7 liter of paint for a mural in her room and 2/10 for a wall in her bathroom.
Determine a reasonable estimate for the total amount of paint Aubrey used
Answer: B or the one that is more than 1/2 but it is less than 1
Step-by-step explanation: Took quiz on khan
Simplify to an expression involving a single trigonometric function with no fractions.
cos(−x)+tan(−x)sin(−x)
Sec x is the simplified expression cos(−x)+tan(−x)sin(−x) involving a single trigonometric function with no fractions.
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
The Given expression is
cos(−x)+tan(−x)sin(−x)
Now,
cos(−x) + tan(−x)sin(−x)
= cos x + (- tan x) (- sin x)
= cos x + tan x * sin x
= cos x + (sin x / cos x) * sin x
= (cos²x + sin²x) / cos x ( As sin²x + cos²x = 1)
= 1/ cos x
= sec x (As sec x = 1/cos x)
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sam made fruit punch for a party. he mixed 3 gallons of orange juice, 2 quarts of pineapple juice, 4 pints of cranberry juice, and 6 cups of apple juice. how many quarts did he make in all? (2 points) a 14 b fifteen and one half c seventeen and one half d 20
The answer is c): 17 and one-half quarts
To answer the question, we need to find the total amount of juice Sam made by adding the given quantities. However, the given quantities are in different units, which makes the addition difficult. Therefore, we need to convert all quantities to the same unit before adding them.
1 gallon = 4 quarts (since 1 gallon is equal to 128 ounces, and 1 quart is equal to 32 ounces,
thus 1 gallon = 128/32 = 4 quarts)
1 quart = 2 pints
1 pint = 2 cups
Therefore, 3 gallons = 3 x 4 = 12 quarts
2 quarts = 2 x 1 = 2 quarts
4 pints = 4 / 2 = 2 quarts
6 cups = 6 / 4 = 1.5 quarts
Now, we can add all the quantities in quarts to get the total amount of juice that Sam made:
12 + 2 + 2 + 1.5 = 17.5 quarts
Therefore, Sam made 17 and one-half quarts in all. Thus, the correct option is (c) seventeen and one half.
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Lesson: 3.03
Buffy and Addy launch their rockets at the same time. The height of Buffy's rocket, in
meters, is given by the function f x=-4.9x²+25x. where x is the number of seconds
after the launch. The height of Addy's rocket, in meters, is given by the function
g x=-4.9x² +16x+15 where x is the number of seconds after the launch. Algebraically
find the moment when the rockets are at the same height, and then use that to
calculate the height. Round to the nearest hundredth.
Answer:
21.93 meters.
Step-by-step explanation:
To find when the rockets are at the same height, we need to set the two functions equal to each other and solve for x:
-4.9x² + 25x = -4.9x² + 16x + 15
Simplifying this equation, we get:
9x = 15
x = 15/9
x ≈ 1.67
Therefore, the rockets are at the same height after approximately 1.67 seconds.
To find the height at which the rockets are at the same height, we can plug this value of x into either of the two functions. Let's use Buffy's function:
f(1.67) = -4.9(1.67)² + 25(1.67)
f(1.67) ≈ 21.93
Therefore, the height at which the rockets are at the same height is approximately 21.93 meters. Rounded to the nearest hundredth, this is 21.93 meters.
MR. Swanson wants to buy some mugs as gifts on his trip to California.There are three gifts shops, and each is offering a different deal. Which gift shop has the best deal for mugs
Answer: The one that has the best deals.
Step-by-step explanation:
Given ΔABC with measure of angle B equals 78 degrees, measure of angle C equals 52 degrees, and a = 16 inches, what is the length of b?
To find the length of side b in triangle ABC, we can use the Law of Sines. The length of side b is approximately 20.058 inches.
To find the length of side b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Using the Law of Sines, we have:
sin(A)/a = sin(B)/b
We are given the measure of angle B as 78 degrees and side a as 16 inches. We can substitute these values into the equation:
sin(A)/16 = sin(78)/b
To find sin(A), we can use the fact that the sum of the angles in a triangle is 180 degrees:
A + B + C = 180
A + 78 + 52 = 180
A = 180 - 78 - 52
A = 50 degrees
Now we can substitute the values into the equation again:
sin(50)/16 = sin(78)/b
To solve for b, we can cross-multiply and isolate b:
b = (16 * sin(78))/sin(50)
We can calculate the length of side b by evaluating this expression using a calculator. The measurement will be roughly 20.058 inches.
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andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
the sale price of the cell phone after the 35% discount is $315.25.
How to solve and what is sale?
To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:
Sale price = Regular price - Discount amount
Sale price = $485 - (0.35 x $485)
Sale price = $485 - $169.75
Sale price = $315.25
Therefore, the sale price of the cell phone after the 35% discount is $315.25.
A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.
In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.
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