There are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.
What is least common multiple (LCM)?The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.
Given that, how many distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000,
1000 = 10³ = 2³×5³
Therefore, we get:
x = 2ᵃ×5ᵇ
y = [tex]2^c[/tex]×[tex]5^d[/tex]
where
0 ≤ a, b, c, d ≤ 3
a or c = 3
b or d = 3
To figure out the number of distinct ordered pairs (x, y), we need to find the distinct number of ordered quadruples (a, b, c, d)
there are.
Case 1 : Exactly 2 of a, b, c, d = 3
a = b = 3, c = 0, 1, 2, d = 0,1,2
a = d=3, b = 0, 1, 2, c = 0,1,2
c = b = 3, a = 0, 1, 2, d = 0, 1, 2
c = d = 3, a=0, 1, 2, b = 0, 1, 2
4(1×1×3×3) = 36
Case 2 : Exactly 3 of a, b, c, d = 3
a = b = c = 3, d = 0, 1, 2
a = b = d = 3, c = 0, 1, 2
a = c = d = 3, b = 0, 1, 2
b = c = d = 3, a = 0, 1, 2
4(1×1×1×3) = 12
Case 3 : Exactly 4 of a, b, c, d = 3
a = b = c = d = 3
1(1×1×1×1) = 1
Total =36+12+1=49
Hence. there are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.
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The graph represents the function f(x). Which set of points lie on its inverse f^-1(x)?
Answer:
Third choice: (1, -3); (2, 2); (3, 7)
Step-by-step explanation:
There are two ways to solve this
The easiest way to solve this is to understand that the inverse of a function f(x), denoted by f⁻¹(x) is nothing but a reflection of the function about the line y = x
What that means is that if (x, y) is a specific point on the line, then the inverse point will be (y, x). Basically we are swapping the x, y values
The 3 points on f(x) and the corresponding points on f⁻¹(x) are given below:
f(x) f⁻¹(x)
------ --------
(-3, 1) (1, -3)
(2, 2) (2, 2)
(7, 3) (3, 7)
From the options given we see that the 3rd choice gives the correct values
So answer:
Third choice: (1, -3); (2, 2); (3, 7)
I have not taken the trouble of finding the equation for the line and finding the inverse of that equation since it is not needed in this question
In an isosceles triangle, the length of sides b and c are 8. The length of median B is 7. Find the length of the base of the triangle
The length of the base is 2√15 units. The median of an isosceles triangle divides the triangle into two equal parts.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
A median in a triangle is a line that runs from one corner (or vertice) to the centre of the other side. Triangle congruence makes it easy to demonstrate an isosceles triangle's property that the median to the base is perpendicular to the base.
According to the Pythagorean theorem,
AD² + BD² = AB²
7² + BD² = 8²
BD² = 64 - 49
BD² = 15
BD = √15
The median divides the base into two equal parts.
The length of the base is 2√15.
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Dan is a software salesman. His monthly salary is $1800 plus an additional $60 for every copy of English is Fun he sells.
Let S represent his total salary this month (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating S to N, and then graph your equation using the axes below.
The linear function relating S to N is given as follows:
S(n) = 1800 + 60n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the amount earned for each extra copy.b is the intercept, representing the base monthly salary.The parameter values for this problem are given as follows:
m = 60, b = 1800.
Hence the function is defined as follows:
S(n) = 1800 + 60n.
The function is graphed on the image given at the end of the answer.
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Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h at time t seconds after launch is h(t) = -16(t)^2 +80t. Find the domain of the function.
The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation for this object's height h at time t seconds after launch is,
⇒ h(t) = -16(t)² + 80t
Now, The function is shown a Quadratic equation.
Hence, The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
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A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
The volume of file cabinet is equal to 26 / 3 cubic feet.
How to determine the volume of the file cabinet
The statement let us infer that file cabinet has the form of right prism with rectangular base, whose formula is shown below:
V = b · h · l
Where:
V - Volume, in cubic feet.b - Base width, in feet.h - Height, in feet.l - Base length, in feet.If we know that b = 2 1 / 6 ft (13 / 6 ft), h = 1 1 / 2 ft (3 / 2 ft) and l = 2 2 / 3 ft (8 / 3 ft), then the volume of the file cabinet is:
V = (13 / 6 ft) · (3 / 2 ft) · (8 / 3 ft)
V = 26 / 3 ft³
RemarkStatement present an anomalous character "2", correct statement is introduced below:
A locker measurement at the bottom as 2 1 / 6 ft wide, 1 1 / 2 ft high and 2 2 / 3 ft long.
Picture is missing but question can be solved by inferential approach.
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Salma is interested in purchasing a portable speaker. The regular price is $118, but the online store is having a 40% off sale. Which expression represents how to calculate the sale price?
The expression represents the :
40% of 118 = Answer - Regular price
The sale price is = $70.8
Now, According to the question:
"Information available from the question"
The regular price is $118,
but the online store is having a 40% off sale.
To find the sale price.
Now, 40% of 118 = 47.2
And the sale price will be:
$118 - $47.2
= 70.8
The expression represents the :
40% of 118 = Answer - Regular price
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A) BCD is a straight line.
Triangle ABC is equilateral.
CE = DE
E
Not drawn
accurately
32
A
X
B
C
D
Work out the size of angle x.
(4)
+
PLEASE HELP ME I AM REALLY STUCK!!!
The size of angle x = 46 degree.
Now, According to the question:
A triangle in which at least two sides are equal is called an isosceles triangle. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal.
"Information available from the question"
Since Δ ABC is equilateral then interior angles = 60°
Since CE = DE then Δ CDE is isosceles and the base angles are congruent,
So,
∠ ECD = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74 degree
BCD is a straight line, then the 3 angles on it sum to 180°, that is
60° + 74° + x = 180°
134° + x = 180° ( subtract 134° from both sides )
Hence, The size of angle x = 46°
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a typical person has an average heart rate of 73.0 beats/min. how many beats does she have in 2.0 years? in 2.00 years? and finally how many beats in 2.000 years?
(a) The number of beats she have in 2.0 years is 7.6 × [tex]10^7[/tex].
(b) The number of beats she have in 2.00 years is 7.57 × [tex]10^7[/tex].
(c) The number of beats she have in 2.000 years is 7.574 × [tex]10^7[/tex].
In the question, a typical person has an average heart rate of 73.0 beats/min.
(a) We have to determine number of beats she have in 2.0 years.
This is a rounding off issue. Pay attention to the fact that 72.0 has three important figures, 2.0 has two, 2.00 has three, and 2.000 has four.
Conversion of 72 beats per minute to beats per year.
72 beats/min = [tex]\left(\frac{1 \text{ min}}{72.0 \text{ beats}}\right)\times\left(\frac{1.00 \text{ hr}}{60.0 \text{ min}}\right)\times\left(\frac{1.00 \text{ day}}{24.0 \text{ hr}}\right)\times\left(\frac{1 \text{ year}}{365.25 \text{ days}}\right)[/tex]
Now simplify
72 beats/min = 3.7869×[tex]10^7[/tex] beats/year
The average person's heart beats in two years are
= 3.7869 × [tex]10^7[/tex] beats/year × 2 years
= 7.5738 × [tex]10^7[/tex] beats
The answer is only two significant digits, or 2.0. The response is 7.6 × [tex]10^7[/tex] beats.
(b) We have to determine number of beats she have in 2.00 years.
The answer is three significant digits, or 2.00. The response is 7.57 × [tex]10^7[/tex] beats.
(c) We have to determine number of beats she have in 2.000 years.
The answer is 4 significant digits, or 2.0. The response is 7.574 × [tex]10^7[/tex] beats.
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jacy arrnanged cans on a store shelf. there are 126 cans in all. jacy makes rows of 6 cans how many rows will she make?
Answer:
126 cans in total / 6 cans per row
126/6 = 21 rows of cans
Find y and x in the following figure
The measure of x is 105° and the measure of y is 45°.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
The given quadrilateral is square.
The diagonals of a square are angle bisectors. Therefore, the diagonals split the right angles of the square into two 45° angles.
Here, y°=45°
Here, a+60° =180°
a=120°
In quadrilateral y°+x°+a°+90°=360°
45°+x°+120°+90°=360°
x°+255°=360°
x°=105°
Therefore, the measure of x is 105° and the measure of y is 45°.
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A circular plot of land has a diameter of 6ft. if the walkway around this piece of land has a width of 2x, what is the total area of the land and walkway combined?
The area of the circle, as a function of x, will be:
A(x) = 3.14*(3ft + 2x)²
What is the total area of the land and walkway combined?We know that for a circle of radius R, the area is:
A = pi*R²
Where pi = 3.14
In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:
R = 6ft/2 = 3ft
And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:
R' = 3ft + 2x
Replacing that in the area equation we will get:
A(x) = 3.14*(3ft + 2x)²
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work out 16^3/2 ??????????????????????
Answer:
2048
Step-by-step explanation:
Find out what [tex]16^{3}[/tex] is:
16x16x16 =
4096.
Now lets divide it by 2:
4096/2 =
2048.
2048 would be your answer to your problem.
In which situation is the distance traveled proportional to time?
Answer:
Step-by-step explanation:
honolululuulu
4hk/20h^2k in simplest form
The simplified form of the expression 4hk/20h²k is 1/5h.
What is the simplified form of the expression?Given the expression in the question;
4hk / 20h²k
To simplify, first cancel out the common factor of 4 and 20.
4hk / 20h²k
4(hk) / 4(5h²k)
hk / 5h²k
Next, cancel out the common factor of h and h²
h(k) / h(5hk)
k / 5hk
Now, cancel out the common factor of k
k(1) / k(5h)
1/5h
Therefore, the simplified form is 1/5h.
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Term to term rule is subtract 2 and multiply 4 the third term is 248 what is the two previous term
The two previous terms of 248 are 64 and 18.
A term-to-term rule is a rule that will describe calculating the following terms of a sequence given by the previous term.
In the given problem, the rule is to subtract 2 and multiply by 4.
Considering that the third term is 248. we can utilize the rule to figure out the subsequent term.
248 = (4 * (x - 2))
248 = 4x - 8
256 = 4x
x = 64
So the subsequent term is 64.
To find the initial term, we can utilize a similar rule once more
64 = (4 * (x - 2))
64 = 4x - 8
72 = 4x
x = 18
So the initial term is 18.
Therefore, the two previous terms of 248 are 64 and 18.
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Can someone please help me on this ASAP?!
A graph is said to represent a function if a vertical line drawn anywhere on the graph of a relation only intersects the graph once by Slope of 3.75b + 5: 3.75
How do you know that a graph represents a function?A graph is said to represent a function if and only if any vertical line intersects it at one precise location. The vertical line only ever crosses the graph D, as seen when looking at the graphs.The graph does not represent a function if a vertical line can cross it at two or more places.In order to represent a function, you often use a function rule, such as y=2.50x, where x is the independent variable and y is the dependent variable. By creating a graph, you may visualize your function. Making a table of inputs and their matching outputs before creating a graph is the simplest way to create a graph.Example:
F(b) = 3.75b + 25
Axis interception points of 3.75b + 25:
X intercepts :(-20/3).
Y intercepts :(0.25)
Slope of 3.75b + 5:
3.75.
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use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class.
(a)The class width = 3
(b) The class midpoint of the first class = 51
(c) The class boundaries of the first class = (49.5, 52.5)
Consider the frequency distribution in the following image.
We know that in frequency distribution the class width is nothing but the distance between the lower limits of consecutive classes.
Whereas the range is the difference between the maximum and minimum data entries.
The smallest number is 50, and the largest is 62.
So the range is 62 - 50 = 12
We know that the formula for the class width:
Class width= upper limit – lower limit +1
So, the class width = 52 - 50 + 1
= 3
The formula for the midpoint of each class:
midpoint = (lower limit of class + upper limit of class)/2
Let us assume that m be the midpoint of the first class.
Using above formula of midpoint:
m = (50 + 52)/2
m = 51
We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.
So, the class boundaries of the first class = (49.5, 52.5)
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Tenisha Gist has a sheet of brass that is 36 inches wide and cuts two pieces that are each 8 3/4 inches wide. What is the width of the leftover brass?
The width of the leftover brass is 18 1/2 inches.
How to determine the width of the leftover brass?From the question, we have the following parameters that can be used in our computation:
Initial length = 36 inches
Length of each piece = 8 3/4 inches
The width of the leftover brass is then calculated as
Width = Initial length - 2 * Length of each piece
substitute the known values in the above equation, so, we have the following representation
Width = 36 - 2 * (8 3/4)
Evaluate
Width = 18 1/2
hence, the width is 18 1/2 inches
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The given point lies on the terminal side of an angle θ in standard position. Find the values of the six trigonometric functions of θ. 3. (−4, −3)
The six trigonometry ratios are:
sinθ = 3/5, cosθ = 4/5, tanθ = 3/4, cotθ = 4/3, secθ = 5/4, cosecθ = 5/3
The point is (4, 3).
Perpendicular = 3
Adjacent Side = 4
Using the Pythagorean Theorem we find the value of Hypotenuse.
h = [tex]\sqrt{4^2 + 3^2}[/tex]
h = √(16 + 9)
h = √25
h = 5
The value of six trigonometric functions are
sinθ = Perpendicular/Hypotenuse
sinθ = 3/5
cosθ = Adjacent Side/Hypotenuse
cosθ = 4/5
tanθ = Perpendicular/Adjacent Side
tanθ = 3/4
cotθ = Adjacent Side/Perpendicular
cotθ = 4/3
secθ = Hypotenuse/Adjacent Side
secθ = 5/4
cosecθ = Hypotenuse/Perpendicular
cosecθ = 5/3
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The complete question is:
The point (4,3) is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?
Part A
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000. Was the change in price a positive or negative change?
Answer:
Positive
V
Part B
What was the percentage of change in the price of the house?
Answer:
%
There was a 125% change in the price of the house.
The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000.
Whatever the case, in order to solve this problem,
you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.
Then 1.25 can be converted to 125%.
So, There was a 125% change in the price of the house.
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What type of equation does the flight of a volleyball make on a serve?
Inverse Variation
Linear
Exponential
Quadratic
Answer:
Step-by-step explanation:
dedede duehdueheuhd it a
What is 3.5 as a fraction in simplest form
Answer:
Mixed Number: [tex]\frac{7}{2}[/tex]
Regular [tex]3\frac{1}{2}[/tex]
Explantion \/ \/
Angle
x
= 076° and angle
y
= 111°.
Find the bearing of point A from point O.
The bearing of point A from point O is 256°.
What are bearings?In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.
Given that, angle x= 076° and angle y = 111°.
Now, the bearing of point A from point O is
180°+ 076°
= 256°
Therefore, the bearing of point A from point O is 256°.
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Solve the system of linear equations by substitution. 4x−2y=14 y=1/2x−1
4x−2y=14
Step-by-step explanation:
Answer:
The solution to the system of linear equations is x = 4, y = 1.
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}[/tex]
To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:
[tex]\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14[/tex]
Solve the equation for x:
[tex]\implies 4x-x+2=14[/tex]
[tex]\implies 3x+2=14[/tex]
[tex]\implies 3x=12[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the second equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)-1[/tex]
[tex]\implies y=2-1[/tex]
[tex]\implies y=1[/tex]
Therefore, the solution to the system of linear equations is:
x = 4, y = 1may u answer this with equation im very confused pls
Answer:
See explanation below.
Step-by-step explanation:
1. (-1, -1) and (2, -2)
m = -2+1 / 2+1
m = -1/3
2. (-1, -4) and (0, -1)
m = -1+4 / 0+1
m = 3/1
m = 3
3. (-4, 0) and (-2, -3)
m = -3-0 / -2+4
m = -3/2
4. (2, 0) and (0, -3)
m = -3-0 / 0-2
m = -3/-2
m = 3/2
5. (-1, 2) and (-4, -3)
m = -3-2 / -4+1
m = -5/-3
m = 5/3
6. (4, 3) and (1, -4)
m = -4-3 / 1-4
m = -7/-3
m = 7/3
If I take a loan of 4500€ at 6.5% and pay it back in 4 years, how much interest will i pay?
The required simple interest would be the amount of 1,170€ on a 4500€ principal deposited for four years at a rate of 6.5%
We have been given data as:
Principal (P) = 4500€
Rate of Interest (R) = 6.5% = 6.5/100 = 0.065
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 4500 × 6.5% × 4
⇒ Simple interest = 4500 × 6.5/100 × 4
⇒ Simple interest = 4500 × 0.065 × 4
Apply the multiplication operation, and we get
⇒ Simple interest = 1,170€
Therefore, the required simple interest would be the amount of 1,170€.
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Part 3: Put It All Together- The table below lists the costs and prices for four businesses involved in
making, distributing, and selling bread. Use the information to answer the questions below.
Cost of Inputs
$0
$0.50
$1.50
$2.25
Price of Output
$0.50
$1.50
Farmer Fred
Baker Bob
Trucker Tom
$2.25
Retail Rob
$3.50
16. Calculate the GDP using value-added approach. Explain how you got your answer.
The GDP using value added approach is $3.50
How to calculate the GDP?GDP using value added approach is calculated by obtaining the sum total of value added by each production unit.
Value added by Farmer Fred = Price of output - Cost of inputs = $0.50 - $0 = $0.50
Value added by Baker Bob = Price of output - Cost of inputs = $1.50 - $0.50 = $1.00
Value added by Trucker Tom = Price of output - Cost of inputs = $2.25 - $1.50 = $0.75
Value added by Retail Rob = Price of output - Cost of inputs = $3.50 - $2.25 = $1.25
GDP = Value added by Farmer Fred + Value added by Baker Bob + Value added by Trucker Tom + Value Added by Retail Rob
GDP = $0.50 + $1.00 + $0.75 + $1.25
GDP = $3.50
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solve these proportion for the variable x. Use the reasoning of scalling to solve
The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is Ratio and Proportion ?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is often read as "x is to y" but may also be written as "x: y" or "x/y." The proportion equation, on the other hand, states that two ratios are equal.
The equality of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio sign (::) is used to express proportions, which aid in solving problems with ambiguous amounts. To put it another way, a percentage is an equation or a claim that shows the equality of two ratios or fractions. If a: b = c: d, then four non-zero values, a, b, c, are said to be in proportion. Let's now compare the two ratios, 3:5 and 15:25. In this case, 3:5 and 15:25 may both be written as 3:5 = 3/5 and 0.6, respectively. We may argue that these two ratios are proportionate because they are both equal.
There are two types of proportions :
Direct ProportionInverse ProportionThe proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is meant by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.An equation that expresses a significant relationship between two or more variables is called a formula.There are two types of proportions :
==>Direct Proportion
==>Inverse Proportion
The proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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Mr.Honkenberg I planning for hi Superbowl party.If he he buy 18 chicken wing for $15 what i the cot of the wing in wing per dollar?
The cost of the wings per dollar is 1.2 wings per dollar ($15 / 18 wings = $0.83 per wing). The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18).
1. Divide the total cost of the wings ($15) by the number of wings (18).
2. The result of this calculation is the cost of each wing ($15 / 18 = $0.83).
3. Divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar).
The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18). This calculation will give the cost of each wing ($15 / 18 = $0.83). To find the number of wings per dollar, divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar). This means that for every dollar spent, 1.2 wings can be purchased.
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Jerry baked 5 apple pies to share equally among 3 of his friends. Jerry thinks each friend will get 3/5 of an apple pie. Do you agree? Support your answer
Yes, 3 apple pies divided among 5 people
Now, According to the question:
"Information available from the question"
Apple shared equally
Portion of each person = 3/5
A possible way that shows how the pies were shared.
7/5 is the ration of the pie to each individual (Jerry and his friends).
Provided that each individual got equal ration....
The ration can be divided into two
The numerator = 3
The denominator = 5.
The numerator shows the number of things that were shared.
Hence, 3 apples were shared.
The denominator shows the number of people involved.
Hence, 5 people were involved.
So, we can conclude that 3 apples were divided among 5 people.
Hence, 3 apple pies divided among 5 people.
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