Answers
The expression for the area under the graph of f(x) = √x as a limit of Riemann sums is A = lim [n -> ∞ ] Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
For a continuous function f(x), the area A of the region S that lies under the graph of the function can be expressed as the limit of the sum of the areas of approximating rectangles. Each rectangle has a width of Ax, where A is the interval over which we want to find the area and x is a point within that interval. The height of each rectangle is f(x).
Using this definition, we can find an expression for the area under the graph of f(x) = √x, where 1 ≤ x ≤ 13. We start by dividing the interval [1, 13] into n subintervals, each of width Ax = (13-1)/n = 12/n. We can label the endpoints of the subintervals as x₁, x₂, ..., xₙ+1, where x₁ = 1 and xₙ+1 = 13.
Next, we approximate the area under the curve using n rectangles. The height of the ith rectangle is f(xi), where xi is any point in the ith subinterval. The width of each rectangle is Ax, so the area of the ith rectangle is f(xi) Ax. The total area of the rectangles is then the sum of the areas of each rectangle:
f(x₁) Ax + f(x₂) Ax + ... + f(xₙ) Ax
We can simplify this expression by factoring out the common factor of Ax:
Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
Taking the limit as n approaches infinity, we obtain:
A = lim [n -> ∞] Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
To evaluate the limit, we need to find a formula for the sum of f(xi) for i = 1 to n.
This is a sum of square roots, which can be approximated using numerical methods or evaluated exactly using calculus techniques such as the definite integral.
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Answer:
[tex]\displaystyle \lim_{n \to \infty}\sum^n_{i=1}\left(\dfrac{12}{n}\right)\sqrt[7]{1+\dfrac{12i}{n}}[/tex]
Step-by-step explanation:
The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.
Definite Integral Notation (Reimann Sum)The area under the curve of f(x) on the interval [a, b] is represented by:
[tex]\boxed{\begin{minipage}{6cm}$\displaystyle \int^b_af(x)\; \text{d}x=\lim_{n \to \infty}\sum^n_{i=1}f(x_i) \cdot \Delta x$\\\\\\where $\Delta x=\dfrac{b-a}{n}$ and $x_i=a+\Delta x \cdot i&\\\end{minipage}}[/tex]
Δx is the width of each rectangle.
[tex]f(x_i)[/tex] is the height of each rectangle.
[tex]x_i[/tex] is the right endpoint of each rectangle.
Therefore:
[tex]\begin{aligned}\displaystyle \int^b_af(x)\; \text{d}x&=\lim_{n \to \infty}\sum^n_{i=1}f(x_i) \cdot \Delta x\\\\&=\lim_{n \to \infty}\sum^n_{i=1}f\left(a+\left(\dfrac{b-a}{n}\right)i\right) \cdot \left(\dfrac{b-a}{n}\right)\end{aligned}[/tex]
The given interval is [1, 13]. Therefore, a = 1 and b = 13:
[tex]\implies \Delta x=\dfrac{13-1}{n}=\dfrac{12}{n}[/tex]
As f(x) = ⁷√x then:
[tex]\implies f(x_i)=f(a+i \Delta x)=\sqrt[7]{a+\Delta x \cdot i}=\sqrt[7]{1+\dfrac{12i}{n}}[/tex]
Substituting into the summation formula:
[tex]\begin{aligned}\displaystyle \int^{13}_1 \sqrt[7]{x}\; \text{d}x&=\lim_{n \to \infty}\sum^n_{i=1}\sqrt[7]{1+\left(\dfrac{13-1}{n}\right)i} \cdot \left(\dfrac{13-1}{n}\right)\\\\&=\lim_{n \to \infty}\sum^n_{i=1}\left(\dfrac{12}{n}\right)\sqrt[7]{1+\dfrac{12i}{n}}\\\\\end{aligned}[/tex]
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Related Questions
Mrs hanger is painting the following picture of a h to hang in the entryway of her home she has made the following scale as her model the scale is used on the drawing is 1:6 on the scale drawing h is centered on the page and 5/6 inches from the top bottom and sides of the drawing as you can see the h is to be painted red in the center of a rectangular beige background what is the actual width of the painting what is the actual height of the painting what is the actual height of the h actual width of the h through the center actual distance from the left edge of the painting to the left edge of the h
Answers
Actual height = (5/6) x 6 = 5 inches
To find the actual width of the h through the center, we can use the same scale. The width of the h on the scale drawing is 1/3 inches (since the h is symmetric). Therefore, the actual width of the h through the center is:
Actual width = (1/3) x 6 = 2 inches
The actual width of the painting is equal to the actual width of the h plus twice the distance from the left edge of the painting to the left edge of the h. On the scale drawing, the distance from the left edge of the h to the left edge of the drawing is (1/6) inches. Therefore, the actual width of the painting is:
Actual width = 2 + 2 x (1/6) = 2 1/3 inches
To find the actual height of the painting, we need to add twice the distance from the top of the h to the top of the painting, and twice the distance from the bottom of the h to the bottom of the painting. On the scale drawing, the distance from the top of the h to the top of the drawing is (5/6) inches, and the distance from the bottom of the h to the bottom of the drawing is also (5/6) inches. Therefore, the actual height of the painting is:
Actual height = 5 + 2 x (5/6) = 6 2/3 inches
A restaurant serves a 20 ounce steak. How much does the steak weigh in ponds and ounces?
Answers
Pls help
The shape below contains a rectangle and four semi-circles.
Round your responses to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
Answers
Answer:
perimeter: 47.12 unitsarea: 151.60 square unitsStep-by-step explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
PerimeterIf you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
AreaThe area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
TotalThe area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
__
Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.
(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Horizontal translation
Vertical translation
Reflection across the x-axis
90° clockwise rotation
Answers
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
Option A is the correct answer.
We have,
A horizontal translation moves every point of a figure the same distance in the same direction.
In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.
A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.
A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.
A 90° clockwise rotation would rotate the figure 90 degrees to the right.
Thus,
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
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Select the correct answer.
Which graph represents the solution to this system of inequalities?
x+y<4
2x-3y²12
O A.
-10
y 10
-5
10
Answers
The two inequalities that the graph represents are:
y < -x + 4
y ≤ ²/₃x - 4
How to interpret the Inequality Graph?An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The first inequality is the one with the dashed line and a y-intercept of 4 and so since shaded below line, we will use the symbol <.
The slope from two coordinates on the line (0, 4) and (4, 0) is:
(0 - 4)/(4 - 0) = -1
Thus, inequality is:
y < -x + 4
The first inequality is the one with the solid line and a y-intercept of -4 and so since shaded below line, we will use the symbol ≤.
The slope from two coordinates on the line (0, -4) and (6, 0) is:
(0 + 4)/(6 - 0) = 2/3
Thus, inequality is:
y ≤ ²/₃x - 4
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LINES AND ANGLES
Circle the correct answer to each of the following questions. Show your work, if necessary.
1 Which of the following objects is two-dimensional?
a. a pair of dice
b. a basketball
C
tree
d. a circle
Answers
What is two ten thousandths in decimal form
Answers
Two ten thousandths are 0.0002.
The number 2 will be in ten thousand place
TENS ONES . TENTHS HUNDREDTHS THOUSANDTHS
. 0 0 0
TEN THOUSANDTHS
2
Please help me PLEASE ANYEONE?!!!?!!
Answers
Step-by-step explanation:
1/3 ÷ 3
= 1/3 ÷ 3/1
= 1/3 X 1/3 = 1/9
Similarly
1/4 ÷ 5 = 1/4 X 1/5 = 1/20
Answer: 1/9
Picture a pie and and having 1 slice out of the total 3 pieces, which would be 1/3 of the pie. Now, we want to divide the the pie into 3 more equal-piece groups. This means every original piece of the pie would now have 3 slices in each piece, so the pie would have a total of 9 pieces now. We want to keep our original 1 slice of pie, but now we have taken 1/9 of the pie, a much smaller slice.
What we have done is simply multiplied the denominator (bottom number of the fraction) by 3. In other words, the number of total pieces of pie is tripled from 3 to 9, meaning more slices would have to be cut, but the amount of pie stays the same. We are just taking a smaller slice. This is why the rule for dividing fractions is Keep Change Flip, because we really just want to the denominator to multiply.
Question 10: 1/4÷5
Answer: 1/20
The same logic applies.
what is the mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure? the density of copper is 8 850 kg/m³.
Answers
The mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure when the density of copper is 8 850 kg/m³ is 3.
How to calculate the valueMass per running meter = density x area x length
Substituting the values for density, area, and length, you get:
Mass per running meter = 8,850 x [(b x h) / 2] x length
Simplifying the equation, you get:
Mass per running meter = 4,425 x b x h x length
Mass = 8850 / 4425
Mass = 2
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Find the volume of the sphere. Give the answer in terms of Pi and rounded to the nearest cubic foot. the radius is 5 ft.
Answers
The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.
Given a sphere.
Radius of the sphere = 5 feet
The formula to find the volume of the sphere is,
Volume of the sphere = 4/3 πr³,
where r is the radius of the sphere.
Substituting the given radius,
Volume of the sphere = 4/3 × π × (5)³
= 4/3 × π × 125
= 166.67π
Hence the volume of the sphere is 166.67π feet³.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answers
The position of an object is determined as (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j.
None of above is the correct answer.
What is the particle's position?The position of an object is defined as the product of velocity of the object and the time of motion of the object.
So to obtain the position of the particle, we will integrate the velocity of the particle as follows;
The velocity is given as;
v(t) = t²i/(1 + t³) + sin 2t j
Integrate i component as;
Let u = 1 + t³
du/dt = 3t².
dt = du / (3t²)
∫ t²/(1 + t³) dt =∫ (1/u) x (t²/3t²) du
= (1/3) ∫ (1/u) du
= (1/3) ln |u| + C
= (1/3) ln|1 + t³| + C
Integrate j component as follows;
∫ sin(2t) dt = - ¹/₂cos(2t) + C
∫ v(t) dt = (1/3) ln|1 + t³|)i - ¹/₂cos(2t)j
So finally, we add the initial position of 2i + 3j, as follows;
x = (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j
So none of the options matches this solution, the closet is B.
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Solve the following for θ, in radians, where 0≤θ<2π.
−6sin2(θ)−5sin(θ)+3=0
Answers
Answer:correct answers 0.42
2.73
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
-6u^2 - 5u + 3 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -6, b = -5, and c = 3. Substituting these values, we get:
u = (5 ± sqrt(5^2 - 4(-6)(3))) / 2(-6)
u = (5 ± sqrt(109)) / (-12)
Therefore, either:
sin(θ) = (5 + sqrt(109)) / (-12)
or:
sin(θ) = (5 - sqrt(109)) / (-12)
27 divided by 187 ( so the work please
Answers
Answer:
Answer:
= 6 R 25
= 6 25/27
187 divided by 27 equals
6 with a remainder of 25
Step-by-step explanation:
what’s the answer? To solve the law of cosine I don’t understand this math I rly need help.
Answers
The length of u to the nearest centimeter is about 30 cm.
We are given that;'
s = 730 cm, t = 270 cm and U=125°.
Now,
The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:
c2=a2+b2−2abcosC
To find c = u. Plugging in the values, we get:
u2=7302+2702−2×730×270×cos125°
Using a calculator, we get:
u2≈912.9
Taking the square root of both sides, we get:
u≈30.21
Rounding to the nearest centimeter, we get:
u≈30cm
Therefore, by the law of cosine the answer will be 30 cm.
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Amelia gathered data about the heights of students at her school. Based on the displays, what inferences can you make about each sample?
Answers
Amelia can make inferences by using
The range of heightsThe shape/mean of the distributionThe presence of outliers, etc.What is the inferences about?Inferences from data on student heights include range determination based on minimum and maximum values, indicating greater variability with a larger range.
The average height of students can be determined using measures like mean, median, and mode. The distribution's shape can be determined by the histogram or box plot, indicating how the heights are distributed. inferences can be made by the use of height samples to gain insight into school population.
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Select the correct answer.
A glass case is in the shape of a rectangular prism. The volume of the case is cubic foot. How many cubic blocks with a side length of foot would
be required to find the volume of the glass case?
OA 2
OB 3
OC. 4
D. 5
Reset
Answers
From the question that we have, the solution that we have gotten is that 4 cubic blocks with a side length of foot would be required to find the volume of the glass case
How to solve the problemWe have been given that a glass case is in shape of a rectangular prism.
The volume of a single cubic block is:
We have
Volume of block
= (1/5) * (1/5) * (1/5)
= 1/125 cubic feet
Next we will now have to divide the volume of the glass case by the volume of a single cubic block:
V olume of case / Volume of the block =
(4/125) / (1/125)
= 4
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A glass case is in the shape of a rectangular prism. The volume of the case is cubic 4/125 foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case?
1. Joe has a chocolate box whose shape resembles a rectangular prism. Its length is 6 in, height is 2 in and width is 4 in. Find the volume of the box.
length= 5 in , width= 4 in, height= 3 in
Answers
Answer:
48 square inches
Step-by-step explanation:
lxwxh
6x4x2
Which relation is a function?
Answers
The only graph that represents a function is: Graph D
How to identify a function?A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
From the graphs, we can see that:
Graph A has 2 outputs at x = -2
Graph B has 2 outputs at x = 0
Graph C has two outputs at x = -1
Graph D has a unique output for every input and as such it is a function
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I need help with this pre calculus question , i understand how to find the period i just don’t understand this graph
Answers
The period of the function in the graph is 2π
What is period of a function?Period represents the distance across horizontally located between successive duplicates of an equivalent outline within a graphed function.
In other words, we can say that period is the distance to complete an oscillation where this distance is counted in time. Hence period is measured is seconds
In the graph, the period can be calculated using the points
2π and 0 OR -π and πThese points shows a complete oscillation.
Using from 2π to 0
= 2π - 0
= 2π
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The exchange rate for 15 American Dollars is 17.1 Euro. And 7 Euro are worth 435.2 Dominican Pesos. How
much is 12 American dollars worth in Dominican Pesos?
Answers
Answer:
First, we need to convert 15 American dollars to Euro:
15 USD * 17.1 Euro/USD = 256.5 Euro
Then, we can use the exchange rate between Euro and Dominican Pesos to convert Euro to Dominican Pesos:
1 Euro = 435.2 Dominican Pesos/7 Euro
Therefore, 256.5 Euro = (256.5/7) * 435.2 Dominican Pesos = 9,475.2 Dominican Pesos
Finally, we can use the proportion:
12 USD / 15 USD = x Dominican Pesos / 9,475.2 Dominican Pesos
Solving for x, we get:
x = (12/15) * 9,475.2 = 7,580.16 Dominican Pesos
Therefore, 12 American dollars is worth 7,580.16 Dominican Pesos.
Question 10(Multiple Choice Worth 10 points) (04.05 MC) Davenport University claims to accept 63% of applicants. In a random sample of 1,000 Davenport University applicants, 602 were accepted. Calculate the 95% confidence interval and evaluate whether Davenport's claim seems accurate.
Answers
The confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
How to solve for the confidence levelSolve for the sample proportion
= 602/1000 = 0.602
z* is the critical value from the standard normal distribution at the 95% confidence level = (1.96)
n = sample size (1000)
CI = 0.602 ± 1.96√((0.602(1-0.602))/1000)
CI = 0.602 ± 0.032
0.602 - 0.032 , 0.602 + 0.032
CI = (0.57, 0.63)
Hence the confidence interval using the 95 percent level of significance is given as CI = (0.57, 0.63)
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Hurry pls (Time limit)
Give me the domain and range
Tell me if the graph is a function or not.
The answer choices are below
Answers
The graph is a function: yes.
The domain of this function is: all real numbers.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.
Range = {-∞, ∞}, y|y ∈ R, or all real numbers.
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Write a polynomial function with the given zeros and their correspond possible answers. f(x) = Zeros 0 -6 -7 Mult. 1 3 1
[tex] - 13(t - 7) {6(t + 1) {8(t - 2)}^{?} }^{?} [/tex]
Answers
The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions have zeroes 0, - 6, - 7 with multiplicity 1, 3, 1
Hence, We can formulate;
The value of a polynomial function with the given zeros would be,
⇒ f (x) = (x - 0)¹ (x - (- 6))³ (x - (- 7))¹
⇒ f (x) = x (x + 6)³ (x + 7)
⇒ f (x) = x (x + 7) (x + 6)³
Thus, The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
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Celia bought 40 lbs of clay for her art projects. She used 17.4 lbs to make a sculpture, and 1.01 lbs for each mug. How many mugs did Celia make if she had 7.45 lbs of clay left over?
Answers
The requried, Celia made 15 mugs if she had 7.45 lbs of clay left over.
To determine the number of mugs that Celia made, we need to first subtract the weight of the sculpture and the leftover clay from the initial weight of the clay. This will give us the total weight of clay that Celia used for the mugs:
Total weight of clay used for mugs = 40 lbs - 17.4 lbs - 7.45 lbs = 15.29 lbs
Next, we can divide the total weight of clay used for the mugs by the amount of clay used per mug:
Number of mugs = Total weight of clay used for mugs / Amount of clay used per mug
Amount of clay used per mug = 1.01 lbs/mug
A number of mugs = 15.29 lbs / 1.01 lbs/mug = 15.13
Therefore, Celia made 15 mugs.
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Determine if the two expressions are equivalent and explain your reasoning. 8m+4-3m and 3+ m+2m+1+2m
Answers
The two expressions "8m+4-3m" and "3+ m+2m+1+2m" are equivalent because they simplify to the same-value.
To determine if the two expressions are equivalent, we can simplify each expression and then compare them.
Simplifying the first -expression,
We have,
⇒ 8m + 4 - 3m can be simplified by combining like terms;
⇒ 8m - 3m + 4 = 5m + 4
Next, Simplifying the second-expression,
we have,
⇒ 3 + m + 2m + 1 + 2m can also be simplified by combining like-terms:
⇒ (1 + 3) + (m + 2m + 2m) = 4 + 5m
So we have:
(i) 8m + 4 - 3m = 5m + 4
(ii) 3 + m + 2m + 1 + 2m = 4 + 5m
Since both simplified expressions are equal to "5m + 4", we can conclude that the two original expressions are equivalent.
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Three cakes are sliced into 20 pieces each. Each cake contains 1 gold ring What is the
probability one person who eats one piece of cake from each of the 3 cakes will find 3 gold
rings?
Answers
Answer:
1/60
Step-by-step explanation:
For each cake, there is a 1/20 chance to find the gold ring since it is in one of the 20 slices. The probability for each cake is independent of each other, so we multiply
1/20 x 1/20 x 1/20
=1/60
I need help
Given the function f(t) = 2t + 1 and its domain is described by the set (1, 2, 3, 5) what is the range? (Enter the values of the range from least to greatest
Answers
The range of the given linear function; f(t) = 2t + 1 given its domain (1, 2, 3, 5) is; (3, 5, 7, 11).
What is the range of the given function?It follows from the task content that the range of the given function is to be determined given its domain as defined by the set; (1, 2, 3, 5).
Therefore;
At t = 1; f(1) = 2(1) + 1 = 3.
At t = 2; f(2) = 2(2) + 1 = 5.
At t = 2; f(3) = 2(3) + 1 = 7.
At t = 5; f(5) = 2(5) + 1 = 11.
Ultimately, the range of the given function as required is given by the set; (3, 5, 7, 11).
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The functions s and t are defined as follows. s (x) ニーx+5 t(x) =2x+2 Find the value of t (s (2)).
Answers
The value of the composite function t(s (2)) is 8
Finding the value of the composite function t(s (2))From the question, we have the following parameters that can be used in our computation:
s(x) = -x + 5
t(x) = 2x + 2
The composite function t(s(x)) is calculated as
t(s(x)) = 2s(x) + 2
Substitute the known values in the above equation, so, we have the following representation
t(s(x)) = 2(-x + 5) + 2
Again, substitute the known values in the above equation, so, we have the following representation
t(s(2)) = 2(-2 + 5) + 2
Evaluate
t(s(2)) = 8
Hence, the value of t(s(2)) is 8
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List at least five combinations of nickels and dimes such that the number of nickels is double the number of dimes.
Answers
2 nickels and 1 dime
4 nickels and 2 dimes
6 nickels and 3 dimes
8 nickels and 4 dimes
10 nickels and 5 dimes
b) The Median and Mode of the following wage distribution are known to be $33.5 and $34 respectively. Three frequency values from the table are, however, missing. Find the missing values. Wages (in $) 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50-60 60-70 Frequencies (f) 10 10 ? ? ? 6 230 repsectively
Answers
The missing values are 60, 100 and 40 if the Median and Mode of the wage distribution are known to be $33.5 and $34 respectively
Wages (in Rs)_freq____ CF
0-10________4___________4
10-20_______16________20
20-30_______x________20+x
30-40______y_________20+x+y
40-50______z________20+x+y+z
50-60______6_______26+x+y+z
60-70______4______30+x+y+z
Since total 230
So, 30+x+y+z=230
x+y+z=200
Mode =34
Median = 33.5
By solving the equations we get x=60, y=100 and z=40
Hence, the missing values are 60, 100 and 40
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