The height of the cylinder is approximately 42/11 inches. The answer is option C.
What is the formula for the volume of the cylinder?
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:
1 and one-third = 4/3
V = π(1/3)²h = 4/3
Simplifying the equation, we get:
h = (4/3) / (π(1/3)²) = (4/3) / (π/9) = (4/3) * (9/π) = 12/π
Approximating π as 22/7, we get:
h ≈ (12/π) ≈ (12/(22/7)) = 42/11 inches
Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.
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Triangular pyramid B is the image of triangular pyramid A after dilation by a scale factor of 1/4. If the volume of triangular pyramid B is 4 cm3, find the volume of triangular pyramid A, the preimage.
Therefore , the solution of the given problem of volume comes out to be has a volume of 256 cubic centimetres.
Describe volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 are two examples of cubic measures. However, the bulk of an item may be employed to estimate its size. Usually, the weight of an item is converted into mass measures like grams and kilos.
Here,
The formula: gives the capacity of a pyramid.
=> V = (1/3)Bh
where B is the base's size and h is the pyramid's height.
The ratio of the volumes of the dilated pyramid to the initial pyramid is (1/4)3 = 1/64 if the scale factor of dilation is 1/4. In other terms, pyramid B's volume is 1/64 that of pyramid A's.
Let V(A) represent the pyramid A's volume. Then:
=> V(B) = (1/64)
=> V(A) = 4
When we multiply both parts by 64, we obtain:
=> V(A) = 256
Pyramid A, the preimage, therefore, has a volume of 256 cubic centimetres.
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Triangle RST was dilated by a scale factor of 5 to create triangle LMN. (Show your work)
If tan R = 5/2.5 find the measure of segments LM and MN.
Therefore , the solution of the given problem of triangle comes out to be segments LM and MN have equal 10x measures.
What exactly is a triangle?A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.
Here,
Given that RS and LM are the respective sides of the two triangles, if we set x as the length of RS, then LM's length is 5x and ST's length is 2x. The duration of MN is five times that of ST, which is ten times longer.
We can now calculate the length of RS using the tangent of angle R:
=> tan R=RS/ST
=> 5/2.5=2
We thus have:
=> RS = 2
=> ST = 2x
We can determine the length of RT using the Pythagorean theorem:
=> RT/ST = sin R
=> RT = ST sin R
=> 2.5 (2/29) = 4.337 sin R = 2.5
We can now determine the lengths of LM and MN using the similarity of the triangles:
=> RM = 5 (2x) LM = 5 = 10
=> MN = 5 ST = 5 (two times) = 10
As a result, segments LM and MN have equal 10x measures.
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The values of LM = 12.5 and MN = 25
Define the term triangle?A triangle is a closed geometric figure consisting of three line segments or sides, connected to each other at three endpoints or vertices. Each side of a triangle intersects with exactly two other sides, and the vertices are the points where the sides meet.
From the given figures, both the triangles are right angle triangle.
[tex]tan R=\frac{5}{2.5} = \frac{ST}{RS}[/tex]
So, ST = 5 and RS = 2.5
Since, ΔRST is 5th to create ΔLMN,
its corresponding sides are 5 times the length LM corresponding sides of RS. So, its length
LM = 5×2.5 = 12.5
LM = 12.5
MN corresponding sides of ST. So, its length
MN = 5×5 = 25
MN = 25
Therefore, The values of LM = 12.5 and MN = 25.
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QUESTION 8 ..... [1.5 marks ] We take a sample of 700 students in Wenatchee Valley College and
observe that 80 are men. Find 90% confidence interval of the true proportion of men in the college.
Please round your answer to the nearest tenth of a percent.
§7.4
Solution. Please write your detailed solution here:
Thus, we can be 90% confident that the true proportion of men in the college is between 8.8% and 14.0%.
What is percent?Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.
by the question.
To find the confidence interval of the true proportion of men in the college, we need to use the formula:
[tex]CI = p ± z\sqrt((p(1-p))/n)[/tex]
where p is the sample proportion (80/700 = 0.114), z is the z-score associated with the confidence level (90% in this case), and n is the sample size (700).
To find the z-score, we can use a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.
Plugging in the values, we get:
[tex]CI = 0.114 ± 1.645\sqrt((0.114(1-0.114))/700)[/tex]
Simplifying, we get:
[tex]CI = 0.114 ± 0.026[/tex]
Therefore, the 90% confidence interval for the true proportion of men in the college is:
[tex]CI = 0.114 ± 0.026[/tex]
Rounding to the nearest tenth of a percent, we get:
CI = (8.8%, 14.0%)
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25 feet equals how many inches
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Please do it in steps
What is the base of a parallelogram with an area of 36 units2 and a height of 9 units?
The base length of the parallelogram found using the area formula is 4 units.
What is a parallelogram?
A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.
A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.
Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.
Given,
The area of the parallelogram A =36 sq. units
The height of the parallelogram h = 9 units
We are asked to find the base length b.
Now the formula for the area of the parallelogram is:
A = b * h
36 = b * 9
b = 36/9 = 4 units.
Therefore the base length of the parallelogram, found using the area formula is 4 units.
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What is the area of the trapezoid? ___ units 2
The area of the trapezoid is 176 square units.
What is a trapezoid?
A trapezoid, which is also referred to as a trapezium, is a flat, closed shape with four straight sides and one set of parallel sides.
A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the length of the parallel sides measured perpendicularly.
The height of the trapezoid is 4 units.
The parallel sides of the trapezoids are 17 units and (5+17+5) = 27 units.
The area of a trapezoid is half of the product of the height and the sum of parallel sides.
The area of the trapezoid is
1/2 × 4 ×(17+27)
= 176 square units
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How does coverage for a business relate to individual insurance? Compare and contrast the different types of individual insurance with business insurance. What are the similarities of individual insurance and business insurance? What are the differences between the two types of insurance? Give an example of each type of insurance.
Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.
Define the term insurance?Individual insurance and business insurance are similar in that bοth prοvide financial prοtectiοn against risks and uncertainties. Hοwever, there are alsο significant differences between the twο types οf insurance.
Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.
Business insurance is designed tο prοtect businesses against the financial impact οf events such as prοperty damage, liability claims, οr lοss οf incοme due tο interruptiοn οf business οperatiοns.
The similarities between individual insurance and business insurance include:
Bοth prοvide financial prοtectiοn against risks and uncertainties.Bοth require payment οf premiums by the pοlicyhοlder tο the insurance cοmpany.Bοth types οf insurance invοlve a cοntractual agreement between the pοlicyhοlder and the insurer.The differences between individual insurance and business insurance include:
The types οf risks cοvered: Individual insurance is designed tο cοver risks that affect individuals and their families, while business insurance cοvers risks that affect a business.The cοst: Business insurance premiums are generally higher than individual insurance premiums due tο the higher value οf assets being cοvered and the higher level οf risk invοlved.The cοmplexity οf pοlicies: Business insurance pοlicies are typically mοre cοmplex than individual insurance pοlicies due tο the variety οf risks being cοvered and the different types οf cοverage required.Example οf individual insurance: A persοn buys a health insurance pοlicy tο cοver the cοst οf medical treatment.Example οf business insurance: A small business οwner purchases liability insurance tο prοtect against claims οf injury οr prοperty damage resulting frοm the business's οperatiοns.To know more about Business Insurance, visit:
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An alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper. A foundry
has 164 pounds of aluminum available. Find the weight of the zinc and copper that will be
needed to make the alloy.
Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:
Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
Cross-multiplying, we get:
164 × 5 = 93.5 × Weight of zinc
Weight of zinc = (164 × 5) / 93.5
Weight of zinc = 8.76 pounds (rounded to two decimal places)
Similarly, cross-multiplying the above ratio gives us:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
164 × 1.5 = 93.5 × Weight of copper
Weight of copper = (164 × 1.5) / 93.5
Weight of copper = 2.63 pounds (rounded to two decimal places)
Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.
Step-by-step explanation:
Six whole numbers have
a median of 10
a mode of 11
a range of 4
Work out a possibie set of six numbers. Write the numbers in order.
Answer:Answer:
median=10, 6 numbers, so median is between 3rd and 4th
.. 9 11 . .
mode=11
.. 9 11 11 .
range=4
7 8 9 11 11 11
Step-by-step explanation:
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What is the area of trapezoid ABCD?
A) 39 ft2
B) 58 ft2
C) 121 ft2
D) 242 ft2
The area of trapezoid ABCD is 39 ft².
What is trapezoid?A trapezοid is a quadrilateral with twο sides that are parallel. It has fοur sides, fοur angles, and twο pairs οf οppοsite sides that are equal in length. The nοn-parallel sides, οr legs οf the trapezοid, are usually referred tο as the bases οf the trapezοid. The twο parallel sides are referred tο as the bases, the nοn-parallel sides are referred tο as the legs, and the line cοnnecting the twο parallel sides is called the midline. The angles created by the bases and the legs are called the base angles
Area of trapezoid = [tex]\dfrac{a + b}{2} h[/tex]
Here, a = 5ft
b = 21 ft
h = 3ft
Area of trapezoid = [tex]\dfrac{5 + 21}{2} (3)[/tex]
Area of trapezoid = 39 ft²
Thus, The area of trapezoid ABCD is 39 ft².
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Marty has a piece of rope with exactly 7 knots tied at equal intervals as shown. using the rope, he wants to make triangles so that each vertex of the triangle occurs at a knot. how many triangles can Marty make?
(a) 4
(b) 1
(c) 2
(d) 3
Using algebra, Marty can make 4 triangles from a rope with 7 knots.
What do you mean by algebra?Algebra, a branch of mathematics, facilitates the representation of situations or issues as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.
All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, employ algebra. Algebraically, 2x + 4 = 8 is a simple expression.
Now here in the question,
3 knots form the vertices of a triangle.
Remaining 4 knots out of the 7 can be distributed as:
4+0+0 .......(on 3 sides)
3+1+0
2+2+0
2+1+1
Therefore, Marty can make 4 triangles from the rope with 7 knots.
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help with This Math
Answer:
Traingle=180 degrees
U=54
180-54
=126
126/2
=63
R=63
U=54
T=63
Give me some help please
Answer: 56 cm
Step-by-step explanation:
calculate value of x
12cm, 7cm, 121 degrees
trigonometry
The side x = 16.72 approximately to two decimal places using the cosine rule.
What is the cosine rule?In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Considering the given triangle, we shall calculate for the side x is using the cosine rule as follows;
a² = b² + c² - 2(b)(c)cosA
x² = 7² + 12² - 2(7)(12)cos121°
x² = 49 + 144 - 168(-0.5150)
x² = 193 + 86.52
x² = 279.52
x = 16.7189 {take square root of both sides}
Therefore, using the cosine rule, we can conclude the value of the side x of the triangle is 16.7189.
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Write the prime factorization of 30. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answer:
2 * 3 * 5
Step-by-step explanation:
The factors of 30 are 1,2,3,5,6,10,15, and 30. Lets just pick out the prime numbers from this and see if they multiply to 30.
[tex]2\times 3\times 5=30[/tex]
The density of iron is 7.87 g/cm³. What is the volume of a 2.9 kg block of iron in cubic centimeters? Round to the nearest hundredth.
Answer:
368.49 cm3
Step-by-step explanation:
[tex]2.9kg=(2.9)(1000)=2900g[/tex]
[tex]V=2900/7.87[/tex]
[tex]368.49 cm^{3}[/tex]
nearest hundredth
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Step by step would be preferred thank youuu!!
In AIJK, IJ || LM. Given that KI = 18, KL=8, and LM = 20, find IJ.
K
W
IJ =
Answer:
the length of IJ is 7.2 units.
Step-by-step explanation:
Since IJ is parallel to LM, we can use the property of similar triangles to solve for IJ.
Triangles KIJ and KLM are similar, so we have:
IJ/KL = KI/LM
Substituting the given values, we get:
IJ/8 = 18/20
IJ/8 = 9/10
Multiplying both sides by 8, we get:
IJ = (8)(9/10)
IJ = 7.2
Therefore, the length of IJ is 7.2 units.
the distance between (-7, 3) and (5, 3)
Answer:
12
Step-by-step explanation:
7+5
Answer:
.
Step-by-step explanation:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) = (-7, 3) and (x2, y2) = (5, 3).
Substituting these values, we get:
d = sqrt((5 - (-7))^2 + (3 - 3)^2)
= sqrt((12)^2 + (0)^2)
= sqrt(144)
= 12
Therefore, the distance between (-7, 3) and (5, 3) is 12 units.
The value of x in the equation 14(12x−36)=5x+18 is?
Answer:
x=522/163
Step-by-step explanation:
14(12x−36)=5x+18
168x-504=5x+18
168x-504+504=5x+18+504
163x=522
163x/163=522/163
x=522/163
x=3.20
Answer:
I got 3.2 in decimal form or 522/163 in a fraction
Four components of 55
Answer: 1, 5, 11, 55
Step-by-step explanation:
A central angle has a measure of 2.3 radians and the subtended arc length is 12 cm.
What is the radius of the circle to the nearest 10th
Therefore , the solution of the given problem of circle comes out to be the circle's radius is about 5.2 centimetres.
What is circle?A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry. Additionally, it rotates evenly in all directions around the centre.
Here,
The following equation determines the extent of a circle's arc:
=> arc length = radius * central angle
We can determine the radius by solving for the centre angle,
which is known to be 2.3 radians, and the arc length, which is 12 cm:
=> radius = arc length / central angle
=> 12 cm / 2.3 radians
=> 5.22 cm
We calculate the radius to be 5.2 cm by rounding to the closest tenth. As a result, the circle's radius is about 5.2 centimetres.
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If the length and breadth of a rectangle are 12 cm and 5 cm respectively, what will be the length of its diagonal?
Find the total number of outcomes.
There are 3 true-false questions on a quiz.
The total number of outcomes in the quiz is 8
How to determine the total number of outcomesFrom the question, we have the following parameters that can be used in our computation:-
Options = True or FalseQuestions = 3Using the above as a guide, we have the following:
For each question, there are two possible outcomes: true or false.
So, the total number of outcomes for all three questions is:
Total = 2 x 2 x 2
Evaluate
Total = 8
Hence, there are 8 possible outcomes in total.
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Complete question
Find the total number of outcomes of the following experiment
There are 3 true-false questions on a quiz.
Find f(x) + g (x). f(x) = 8-4x-x``3 g(x) = x`2 + 7x - 9
After answering the presented question, we can conclude that equation Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex]
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
To find f(x) + g(x),
[tex]f(x) = 8 - 4x - x^3\\g(x) = x^2 + 7x - 9\\f(x) + g(x) = (8 - 4x - x^3) + (x^2 + 7x - 9)\\f(x) + g(x) = -x^3 + x^2 + 3x - 1\\[/tex]
Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex][tex]-x^3 + x^2 + 3x - 1.[/tex]
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Solve for ps pleaseee
Answer:
PS=21.3
Step-by-step explanation:
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Igbo bought five (5) books at N40.00 each and sold them What is the for N150.00. loss?
In response to the given question, we can state that As a result, Igbo expressions experienced a N50.00 loss.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.
Igbo spent N40.00 on 5 books, for a total of N40.00.
N200.00 = 5 books x N40.00 each
Igbo lost money since he sold the books for N150.00. To find the amount of the loss, subtract the selling price from the cost price:
Cost Price - Selling Price = Loss
N200.00 - N150.00 = Loss
Loss = N50.00
As a result, Igbo experienced a N50.00 loss.
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The mean for the math component of the New Century Achievement Test is reported as 100, with a standard deviation (σ) of 15. A sample of 400 students throughout a particular school district reveals a mean (Symbol) score of 110. Estimate the mean score for all the students in the district, using a 99% confidence interval.
Answer: To estimate the mean score for all the students in the district, we can use a confidence interval. We are given that the sample size is 400, the sample mean is 110, the population means is 100, and the population standard deviation is 15. We are asked to find a 99% confidence interval for the population mean.
The formula for a confidence interval for the population mean with known population standard deviation is:
Confidence interval = sample mean ± z*(σ/√n)
where:
sample mean = 110 (given)
σ = 15 (given)
n = 400 (given)
z = the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.
Substituting the values, we get:
Confidence interval = 110 ± 2.576*(15/√400)
Confidence interval = 110 ± 1.92
Therefore, the 99% confidence interval for the population mean score is (110 - 1.92, 110 + 1.92), or (108.08, 111.92). We can be 99% confident that the true population mean score for all the students in the district falls between 108.08 and 111.92.
Step-by-step explanation:
A recipe for bread calls for 4 cups of flour for every 1/2 cup of water. Using the same recipe, how much
water will you need for 5 cups of flour?
Answer:
According to the recipe, the ratio of flour to water is 4:0.5 or 8:1 (since 1/2 can be simplified to 0.5).
To determine how much water is needed for 5 cups of flour, we can use this ratio:
8:1 = 5:x
where x represents the amount of water needed.
To solve for x, we can cross-multiply:
8x = 5 * 1
8x = 5
x = 5/8
Therefore, you will need 5/8 cup of water for 5 cups of flour, using the given recipe.
Step-by-step explanation:
Khrysteen is paid semimonthly with $1,978.50 per pay. What is her annual
pay?
Answer:
Since Khrysteen is paid semimonthly, she receives 24 paychecks in a year (12 months x 2 pay periods per month).
To calculate her annual pay, we can multiply her semi-monthly pay by the number of paychecks she receives in a year:
Annual pay = Semi-monthly pay x Number of paychecks in a year
Annual pay = $1,978.50 x 24
Annual pay = $47,484
Therefore, Khrysteen's annual pay is $47,484.
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Use appropriate method to solve the following. 1. If twice the age of a son is added to age of a father, then the sum is 56. If twice the age of the father is added to the age of son, then the sum is 82. Find the ages of father and son. 2. In a two-digit number, the sum of the digits is 13. Twice the tens digit exceeds the units digit by one. Find the numbers. 3. I am thinking of a two-digit number. If I write 3 to the left of my number, and double this three digit number, the result is 27 times my original number What is my original number?
Answer:
Step-by-step explanation:
Let the age of the son be $s$ and the age of the father be $f$. From the first equation, we have $2s + f = 56$, and from the second equation, we have $f + 2s = 82$. Solving this system of equations, we get $s = 12$ and $f = 32$, so the son is 12 years old and the father is 32 years old.
Let the two-digit number be $10t+u$, where $t$ is the tens digit and $u$ is the units digit. We are given that $t+u=13$ and $2t-u=1$. Solving this system of equations, we get $t=7$ and $u=6$, so the two-digit number is $76$.
Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit. We are given that $2(10+x+y) = 27(10x+y)$, or $20+2x+2y = 270x+27y$. Simplifying this equation, we get $268x-25y = 10$. Since $y$ is a digit, we know that $0 \leq y \leq 9$. We can check that $x=1$ is too small, so we try $x=2$. Plugging in $x=2$, we get $536-25y=10$, which gives $y=21/5$, which is not a digit. Thus, there is no solution for a two-digit number.