We can say that it is true that the function g(x)=(e^x)sinb is an antiderivative of the function f(x)=(e^x)sinb.
How did we arrive at the solution?We can see here that to prove this, we need to show that g'(x) = f(x), where g'(x) is the derivative of g(x).
Using the product rule of differentiation, we have that:
g'(x) = (e^x)(cosb) + (sinb)(e^x).
A further simplification will give us:
g'(x) = (e^x)(cosb + sinb)
Thus, comparing g'(x) with f(x), we have: f(x) = (e^x)(sinb)
Therefore, comparing the two expressions, we can see that:
g'(x) = f(x) if and only if cosb + sinb = sinb.
This is true for all values of b, since:
cosb + sinb = sin(b + pi/4), and sin(b + pi/4) = sinb for all values of b.We can then conclude that g(x) = (e^x)sinb is indeed an antiderivative of f(x) = (e^x)sinb.
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We can say that it is true that the function g(x)=(e^x)sinb is an antiderivative of the function f(x)=(e^x)sinb.
How did we arrive at the solution?We can see here that to prove this, we need to show that g'(x) = f(x), where g'(x) is the derivative of g(x).
Using the product rule of differentiation, we have that:
g'(x) = (e^x)(cosb) + (sinb)(e^x).
A further simplification will give us:
g'(x) = (e^x)(cosb + sinb)
Thus, comparing g'(x) with f(x), we have: f(x) = (e^x)(sinb)
Therefore, comparing the two expressions, we can see that:
g'(x) = f(x) if and only if cosb + sinb = sinb.
This is true for all values of b, since:
cosb + sinb = sin(b + pi/4), and sin(b + pi/4) = sinb for all values of b.We can then conclude that g(x) = (e^x)sinb is indeed an antiderivative of f(x) = (e^x)sinb.
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Help now please math will briain list
According to the given information, the one angle on the straight line inside a circle is 135 then the value of the x = 4 as both angles are supplementary angles.
What are supplementary angles?Supplementary angles are two angles whose sum is 180 degrees. In other words, if we add the measures of two supplementary angles, the result is always 180 degrees.
When two lines intersect, they form four angles at the intersection point. If two of these angles are supplementary, they are called adjacent supplementary angles. In this case, they share a common side and a common vertex, and their non-shared sides form a straight line.
For example, if angle A and angle B are adjacent angles, and angle A measures 120 degrees, then angle B must measure 60 degrees, since 120 + 60 = 180.
According to the given informationIf the two angles are on a straight line, then they are supplementary, meaning their sum is 180 degrees. Therefore, we can set up the equation:
135 + (11x + 1) = 180
Simplifying the left side, we get:
136 + 11x = 180
Subtracting 136 from both sides, we get:
11x = 44
Dividing both sides by 11, we get:
x = 4
Therefore, the value of x is 4.
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Help please -A special safe lets you choose from 5 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there?
Answer:
125
Step-by-step explanation:
the statement " 5 symbols for a 3-symbols- long pass code" in mathematics simply means 5 has a power of 3 or 5^3 = 5×5×5= 125
Let f(x) = x² - 3. Let g(x) = (x + 2)² - 5. Select all statements below that describe the transformation of f(x) to g(x).
The vertex of g(x) is translated left by 2 units and down by 5 units compared to the vertex of f(x).
The shape of the parabola for g(x) is the same as the shape of the parabola for f(x).
The axis of symmetry for g(x) is the same as the axis of symmetry for f(x).
The minimum point of g(x) is lower than the minimum point of f(x).
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
The purchase price of the anitque dresser purchased by Danielle is $120 and the advertised price is $ 300 after which it was sold on profit of $255. Correct answer:optionA
What is profit?
The extra money is left after paying your business expenses is your profit. Gross profit, operating profit, and net profit are the three primary types of profit. The cost foundation for determining profit or loss when selling a product is the price the buyer pays at the time of purchase, known as the purchase price. The price of a product as advertised for marketing purposes is known as the marketed price.
Let us consider the purchase price of antique dresser with mirror= p
Given that the advertised price= 250% of her purchase price
=[tex]\frac{250}{100}[/tex] of p
=[tex]\frac{250}{100}[/tex] p
=[tex]\frac{250 p}{100}[/tex]
Also given that the selling price which was 15% less than advertised price= $255
advertised price - 15% of advertised price =$255
[tex]\frac{250 p}{100}[/tex] - 15% of [tex]\frac{250 p}{100}[/tex] =$255
[tex]\frac{250p}{100} - \frac{15}{100} of \frac{250p}{100}[/tex] =$255
[tex]\frac{250p}{100} - \frac{3750p}{10000}[/tex] =$255
[tex]\frac{250p}{100} - \frac{375p}{1000}[/tex] =$255
[tex]\frac{2500p - 375p}{1000}[/tex] =$255
[tex]\frac{2125p}{1000}[/tex] =$255
p = [tex]\frac{255 (1000)}{2125}[/tex]
p = $120
The purchasing price is $120
Advertised price =[tex]\frac{250 p}{100}[/tex]
= [tex]\frac{250(120)}{100}[/tex]
= 25 x 12
= $ 300
The Advertised price is $ 300
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Is 8.005 kilometers or 8.7 kilometers the longest?
8.7 kilometers is longer than 8.005 kilometers.
Answer:
8.7 is longer than 8.005
Step-by-step explanation:
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 5 comma 3, negative 5 comma negative 2, and 7 comma negative 2
The perimeter of the right triangle is 30 units.
What is perimeter?
In geometry, perimeter refers to the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the sum of the lengths of all the sides of the shape.
To find the perimeter of the right triangle, we need to determine the lengths of its sides first.
Using the distance formula, we can find the lengths of the three sides of the triangle:
Side 1: From (-5, 3) to (-5, -2)
[tex]Length = \sqrt{[(3 - (-2))^2 + (-5 - (-5))^2]} = \sqrt{[5^2]} = 5[/tex]
Side 2: From (-5, -2) to (7, -2)
[tex]Length = \sqrt{[(7 - (-5))^2 + (-2 - (-2))^2]} = \sqrt{[12^2]} = 12[/tex]
Side 3: From (7, -2) to (-5, 3)
[tex]Length = \sqrt{[(-5 - 7)^2 + (3 - (-2))^2]} = \sqrt{[144 + 25]} = \sqrt{[169]} = 13[/tex]
We know that the triangle is a right triangle because two of its sides (Side 2 and Side 3) form a straight line along the x-axis, and the third side (Side 1) is perpendicular to this line.
Therefore, Side 1 is the hypotenuse, and Sides 2 and 3 are the legs of the right triangle.
To find the perimeter, we add up the lengths of all three sides:
Perimeter = Side 1 + Side 2 + Side 3 = 5 + 12 + 13 = 30
Therefore, the perimeter of the right triangle is 30 units.
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Myron's family is putting a pool in their backyard. He is so excited that he wants to figure out how
long it will take to fill the pool! He found the blueprints for the pool and recreated the sketches at
right, but he is not quite sure how to use them to find the volume of the pool.
What three-dimensional figures does Myron need to be able to find the volume of before he can
determine the volume of the pool?
To find the volume of an irregular 3D shape like Myron's pool, he needs to determine:
1. The length
2. The width
3. The depth
With those three measurements, he can plug them into the formula for volume of a rectangular prism:
Volume = Length x Width x Depth
So if the pool is:
Length = 20 ft
Width = 10 ft
Depth = 5 ft
Then the volume would be:
20 ft x 10 ft x 5 ft = 1000 cubic feet
Does this make sense? Let me know if Myron has any other questions!
A sample contains 25 cells. The number of cells quadruples every hour. Does this represent an exponential function? Why or why not?
Yes, this represents an exponential function.
What is exponential function ?
The exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function.
Because the growth rate is inversely correlated with the function's present value, this function is exponential. Regardless of how many cells were present the previous hour the number of cells is multiplied by the same factor of 4 every hour.
Therefore, One can estimate the number of cells for every hour x by evaluating the function at a specific value of x. The function f(x) = 4x implies exponential growth.
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Two friends board an airliner just before departure time. There are only 9 seats left, 2 of which are aisle seats. How many ways:
sits on the aisle?
The 2 people can arrange themselves in
ways.
The 2 people from the 9 people can sit on the aisle in 72 ways
How many ways can the 2 people sit on the aisle?from the question, we have the following parameters that can be used in our computation:
Number of peiple = 9
Number of seats = 2
Using the above as a guide, we have the following:
n = 9 and r = 2
The can arrange themselves in nPr ways.
Where
nPr = n!/(n - r)!
Substitute the known values in the above equation, so, we have the following representation
9P2 = 9!/(9 - 2)!
Evaluate the expression
9P2 = 72
Hence, the number of ways they can arrange themselves is 72
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Suppose the Baseball Hall of Fame in Cooperstown, New York, has approached Hobby−Cardz with a special order. The Hall of Fame wants to purchase 51,000 baseball card packs for a special promotional campaign and offers $0.43 per pack, a total of $21,930.
Hobby−Cardz's total production cost is $0.63 per pack, as follows:
Variable costs:
Direct materials . . . . . . . . . . . . .
$0.14
Direct labor . . . . . . . . . . . . . . . .
0.07
Variable overhead . . . . . . . . . . .
0.12
Fixed overhead . . . . . . . . . . . . . . . . . .
0.30
Total cost . . . . . . . . . . . . . . . . . . . . . . .
$0.63
1.Prepare an incremental analysis to determine whether Hobby−Cardz should accept the special sales order assuming fixed costs would not be affected by the special order.
2.Now assume that the Hall of Fame wants special hologram baseball cards. Hobby−Cardz must spend $5,300 to develop this hologram, which will be useless after the special order is completed. Should Hobby−Cardz accept the special order under these circumstances? Show your analysis.
pop-up content ends
PrintDone
The solution of Unit Problem is Solution of first part is As the contribution margin is positive, accepting the special sales order would be profitable for Hobby-Cardz,and second part is total profit is negative
What is contribution margin ?Contribution margin is the difference between a product's revenue and its variable costs. It represents the amount of money that is available to cover fixed costs and contribute to profit.
According to given information?1)Incremental Analysis without special order:
Revenue from 51,000 packs at $0.43 per pack = $21,930
Total variable costs for 51,000 packs = 51,000 x $0.33 = $16,830
Contribution margin = $21,930 - $16,830 = $5,100
As the contribution margin is positive, accepting the special sales order would be profitable for Hobby-Cardz.
2)Incremental Analysis with special hologram baseball cards:
In addition to the incremental analysis performed in Part 1, we need to consider the additional cost of $5,300 to develop the hologram.
Revenue from 51,000 packs at $0.43 per pack = $21,930
Total variable costs for 51,000 packs = 51,000 x $0.33 = $16,830
Contribution margin = $21,930 - $16,830 = $5,100
Less: Additional cost of hologram development = $5,300
Total profit/loss = $5,100 - $5,300 = ($200)
As the total profit is negative, accepting the special sales order with the hologram development cost would result in a loss of $200. Therefore, Hobby-Cardz should not accept the special order under these circumstances.
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which ones is a function and not a function
Answer:
No,No,No,Yes,No,Yes
Step-by-step explanation:
The distance between Eilat and Jerusalem is 292 kilometers. Give this distance in miles. Round the answer to the nearest tenth.
The distance between Eilat and Jerusalem is 181.4 miles.
To convert kilometers to miles, we need to multiply the number of kilometers by 0.621371, which is the conversion factor from kilometers to miles. Therefore, to convert the distance between Eilat and Jerusalem from kilometers to miles, we can use the following formula:
distance in miles = distance in kilometers × 0.621371
Substituting the given distance of 292 kilometers into the formula, we get:
distance in miles = 292 km × 0.621371 = 181.417852 miles
Rounding this answer to the nearest tenth, we get:
distance in miles ≈ 181.4 miles
Therefore, the distance between Eilat and Jerusalem is approximately 181.4 miles.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
The correct frequency table is table c.
Find the derivative of y = ((2x - 1) ^ 3)//√(3x + 1)
The derivative of the function y = ((2x - 1)³)/√(3x + 1) is dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
What is the derivative of a function?The derivative of a function is the limit as the change in x tnds to zero of the change in y over the change in x.
To find the derivative of the function y = ((2x - 1)³)/√(3x + 1), we use the quotient rule.
dy/dx = (vdu/dx - udv/dx)/v²
where u = (2x - 1)³ and v = √(3x + 1)
So, du/dx = 3(2x - 1)² and dv/dx = 3/[2√(3x + 1)]
Substituting the values of the variables into the equation, we have that
dy/dx = (vdu/dx - udv/dx)/v²
dy/dx = (√(3x + 1) × 3(2x - 1)² - (2x - 1)³ × 3/[2√(3x + 1)])/[√(3x + 1)]²
dy/dx = (3√(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])/[√(3x + 1)]²
= (3√(3x + 1)√(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])(3x + 1)²
= [3(3x + 1)(2x - 1)² - 3(2x - 1)³/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[3(3x + 1) - 3(2x - 1)/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[9x + 3 - 6x + 3]/[2√(3x + 1)])(3x + 1)²
= (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
So, dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The final counts are:
58 students interested in athletics but not academic clubs, 118 students interested in academic clubs but not athletics, 96 students not interested in academic clubs, 156 students not interested in athletics.How to solveGiven a survey of 240 students, 35% of students were interested in athletics, which is equal to 84 students.
3/5 of students were interested in academic clubs, which is equal to 144 students.
26 students were interested in both athletics and academic clubs.
Using this information, we can fill in the remaining cells of a table to show the number of students in each category.
The final counts are:
58 students interested in athletics but not academic clubs, 118 students interested in academic clubs but not athletics, 96 students not interested in academic clubs, 156 students not interested in athletics.Read more about samples here:
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nangle
In order to justify your general statement above (to give a reason why it is true), construct the angles A, B
and C of triangle 1 around point M as in the diagram below.
H
Are [MN] and [ML] on the same straight line?
Answer:
MN and ML are on the same straight line.
The figure on the right is a scaled copy of the
figure on the left.
V
U
W
T
H
I
G
J
The side GJ in the big one corresponds to the side WT in the small one.
It's not possible to find the scale factor between the two drawings, because there's no numerical information given to show us the relationship between any pair of corresponding sides. (This information is probably there in the book or on the homework sheet you copied the problem from, but for some strange reason, you didn't include it in what you decided to show us.)
Nelly turns 25
today. An investment her grandfather made in her name on the day of her birth is now worth R50 000
. The investment has accumulated interest at 8%
compounded quarterly since the original deposit. How much did her grandfather originally invest?
The principal money her grandfather originally invested is R= 50000/1.08¹²
What is compound interest?
Compound interest is a type of financial phenomenon in which interest you earn in a savings or investment account earns interest of its own over time. It is also said that Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest
the given parameters to help solve the question are
Amount = R50,000
Interest rate = 8%
Time = 25years compounded quarterly
The formula for compound interest compounded quarterly is
A= P × (1 + R/(4 × 100))⁴ⁿ,
where P is the principal and R is the interest rate
50000 = R[1+0.08]⁴*³
50000 = R[1.08)¹²
R= 50000/1.08¹²
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Solve for x.
A) 6
B) 9
9)
D)
15
4
3
5
The value of x in the given chords is determined as 9.
What is the measure of x?
The measure of length x is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
3 (3 + x ) = 4 ( 4 + 5 )
9 + 3x = 36
collect similar terms ang solve for x;
3x = 36 - 9
3x = 27
divide both sides of the equation by 3;
3x/3 = 27/3
x = 9
Thus, the value of x in the given chords is determined by applying chord theorem.
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A pole that is 3.2 m tall casts a shadow that is 1.3 m long. At the same time, a nearby tower casts a shadow that is 46.75 m long. How tall is the tower? Round your answer to the nearest meter. Please help /:
Answer:
115 meters
Step-by-step explanation:
Think of this like a ratio [tex]\frac{3.2}{1.3} =\frac{x}{46.75}[/tex]
Then solve for x [tex](\frac{3.2}{1.3} )*46.75 = 115.08[/tex]
A plane moving at 450 miles per hour is flying in your direction. At one moment the angle formed between the ground and your line of sight to the plane is 45 degrees. One minute later the angle is 60 degrees. Find the altitude of the plane. Make sure to draw a complete diagram, show all calculations and explain your process.
The altitude of the plane is approximately 21.65 miles.
What is altitude means ?An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
We have an observer on the ground (you) and a plane flying towards you. Let's call the distance between the observer and the point directly below the plane "x", and let's call the altitude of the plane "h".
At the first moment, the angle between the ground and your line of sight to the plane is 45 degrees. This means that the angle between the plane's altitude and the ground is also 45 degrees (since the plane is flying horizontally towards you). We can use trigonometry to find the value of "x" in terms of "h".
In the right triangle formed by the observer, the point directly below the plane, and the plane's altitude, we have:
tan(45) = h/x
Since tan(45) = 1, we can simplify this to:
h/x = 1
h = x
So the distance between the observer and the point directly below the plane is equal to the altitude of the plane.
One minute later, the angle between the ground and your line of sight to the plane is 60 degrees. We can use the same approach to find the new value of "x" in terms of "h".
In the right triangle formed by the observer, the point directly below the plane, and the plane's altitude, we have:
tan(60) = h/(x + 450/60)
Simplifying this, we get:
h = (x + 7.5h) * sqrt(3)
Solving for "x", we get:
x = (h / sqrt(3)) - 7.5h
Now we can substitute the value of "x" from the first moment (which is equal to the altitude of the plane) into this equation to find the altitude of the plane:
h = (h / sqrt(3)) - 7.5h
h = h(1 / sqrt(3) - 7.5)
h = 21.65 miles (rounded to two decimal places)
Therefore, the altitude of the plane is approximately 21.65 miles.
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New center 13 has just released tomorrow’s weather forecast high temperature is 74° and the low temperature is have that of the high temperature. What is the low temperature
If the high temperature is 74° and the low temperature is have that of the high temperature then low temperature is 37°
Given that New center 13 has just released tomorrow’s weather forecast high temperature is 74°
High temperature = 74°
The low temperature is have that of the high temperature
Low temperature =1/2× High temperature
=1/2×74
=37
Hence, If the high temperature is 74° and the low temperature is have that of the high temperature then low temperature is 37°
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victoria has another account at the bank that pays 2 1/2% simple interest. how much inter will she earn in 8 years on an initial deposit of 250$ assuming she neither adds to nor withdraws from the account
rest, Using the simple interest formula, P x R x T, the total interest that Victoria will earn in 8 years on an initial deposit of $250 at 2¹/₂% simple interest is $50.
What is simple interest?Simple interest is a system of interest that charges interest only on the principal at the end of each period.
Unlike compound interest, the simple interest system does not accumulated interest in order to charge interest on accumulated interest.
The initial deposit = $250
Simple interest rate = 2¹/₂%
Investment period = 8 years.
Simple interest = $50 ($250 x 2¹/₂% x 8)
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Simplify the expression.
2e + tr + 4y + e - y + tr
Answer:
3e + 3y + 2tr
Step-by-step explanation:
2e + tr + 4y + e - y + tr
=> (2e + e) + (tr + tr) + (4y - y)
=> 3e + 2tr + 3y
=> 3e + 3y + 2tr
Answer: The answer is 3e + 3y - 2tr
Step-by-step explanation:
2e + tr + 4y + e - y + tr
=(2e + e) + (tr + tr) + (4y- y)
=3e + 2tr + 3y
=3e + 3y +2tr
Find the value of x, y, and z in the rhombus below.
(-y-5)
(-27+8)
(-10x-8)
989
Help me please, I need help! Thanks
Answer:
5w² + 4
Step-by-step explanation:
there's no like terms, so just write the expression again
6th grade math help ty
The surface area of this cylinder is about 45,413.59 square yards.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.From the circumference of the outside of the cylinder, the radius can be calculated as follows;
Circumference = 2πr
512.49 = 2(3.14)r
Radius, r = 512.49/6.28 = 81.61 yards.
By substituting the given parameters into the surface area of a cylinder formula, we have;
Surface area (SA) of cylinder = (2 × 3.14 × 81.61 × 7) + 2 × 3.14 × 81.61²
Surface area (SA) of cylinder = 3,587.58 + 41,826.01
Surface area (SA) of cylinder = 45,413.59 square yards.
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i start with y, add 5 and then, double the result
Answer:
2y + 10Step-by-step explanation:
i start with y, add 5 and then, double the result
y add 5
y + 5 double the result
(y + 5) × 2 solve
2y + 10
or
(y + 5) × 2 =
2y + 10
QUESTION 10
The following headline refers to change. Identify the change as absolute or relative.
"Enrollments at Northeastern University are expected to increase by 1,700 students"
The change referred to in the headline is an absolute change. An absolute change is a difference or increase in a quantity that is measured without reference to the original or initial value.
In this case, the headline states that enrollments at Northeastern University are expected to increase by 1,700 students. This means that the actual number of students is expected to increase by 1,700 from its current or previous level, without any reference to the original number of students enrolled at Northeastern University.
An absolute change is usually expressed in units of the quantity being measured, such as students, dollars, or meters. In contrast, a relative change is expressed as a percentage or ratio of the original or initial value. A relative change indicates how much a quantity has changed in proportion to its initial value.
For example, if enrollments at Northeastern University were expected to increase by 10%, this would be a relative change because it represents a percentage of the current or previous level of enrollment. However, the headline specifies an absolute increase of 1,700 students, which does not depend on the current or previous level of enrollment.
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In a recent year, women spent $2 million on swimwear and purchased 92,000 swimsuits. During the same year, men spent $500,000 on swimwear and purchased 37,000 swimsuits.
a. Find the ratio of the amount men spent on swimwear to the amount women spent on swimwear.
b. Find the ratio of the amount men spent on swimwear to the total amount men and women spent on swimwear. Write the ratios as fractions in simplest form.
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It is also the comparison of two like or similar quantities.
How to determine this,
The ratio of the amount men spent on swimwear to the amount women spent on swimwear
When the amount men spent on swimwear = $500,000
Amount women spent on swimwear = $2,000,000
Ratio = 500,000 : 2,000,000
Ratio = 500,000/2,000,000
Ratio = 1/4
Ratio = 1 : 4
The ratio as a fraction = 1/4
b. To find the ratio of the amount men spent on swimwear to the total amount men and women spent on swimwear.
Amount men spent on swimwear = $500,000
Total amount men and women spent on swimwear
= $2,000,000 + $500,000
= $2,500,000
Ratio = $500,000 : $2,500,000
Ratio = 500,000/2,500,000
Ratio = 1/5
Ratio = 1 : 5
Ratio expressed as a fraction = 1/5
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