The solution is, 5.5% is the interest rate that Andrew's bank provides.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Andrew's bank account started off with a deposit of $750,
and after 4 years he earned $165 in interest.
we know,
formula: I = Prt.
let, the interest rate that Andrew's bank provides = r%
so, solving we get,
r = 5.5%
Hence, The solution is, 5.5% is the interest rate that Andrew's bank provides.
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List the lower class limits for each class
List the upper class limits for each class
List the class boundaries for each class
List the class midpoints for each class
List the class width for each class
Construct a both a relative and cumulative frequency distributions
The following are the information for the grouped data
class upper class lowerclass mid point
1-5 5 1 3
6-10 10 6 8
11-15 15 11 13
16-20 20 16 18
21-25 25 21 23
26-30 30 26 28
The class width is 4
What is grouped data?
Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.
The lower class limit is lowest value of that class interval while upper class limit is highest value of that class interval. So, 60 is the lower limit and 69 is the upper limit.
The midpoint of a class is called its class mark (or midpoint of class interval). It is obtained by adding the two limits and dividing by 2.
Class width is the difference between the Upper class limit and the Lower class limit of a class interval.
Therefore the class width is 5-1 = 4
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What is the height h for the base that is 5/4 units long?
Answer: 16 cm
Step-by-step explanation: i hope it helps
MTH 115 – Principles of Mathematics
Assignment 8.3 – Journal 8
First, complete Technology Assignment 8 before attempting these problems.
You can afford a loan payment of $1200 a month. You have put an offer of $175,000 on a house. You are considering three different loans.
Loan A. P = $175,000 at a rate of 5% with monthly payments for 30 years.
Loan B. P = $175,000 at a rate of 4% with monthly payments for 15 years.
Loan C. P = $175,000 at a rate of 4.5% with monthly payments for 20 years.
Find the payment and total interest for each loan.
Loan A: Payment = Total Interest =
Loan B: Payment = Total Interest =
Loan C: Payment = Total Interest =
Choose the loan you will use and clearly state why you chose that one.
Using the given information, we can use the PMT function in Excel or a financial calculator to find the monthly payment and total interest for each loan.
Loan A:
P = $175,000
r = 5%/12 = 0.004167 (monthly interest rate)
n = 30 years x 12 months/year = 360 months
Payment = $966.45
Total Interest = $153,522.05
Loan B:
P = $175,000
r = 4%/12 = 0.003333 (monthly interest rate)
n = 15 years x 12 months/year = 180 months
Payment = $1,297.53
Total Interest = $33,555.64
Loan C:
P = $175,000
r = 4.5%/12 = 0.00375 (monthly interest rate)
n = 20 years x 12 months/year = 240 months
Payment = $1,095.09
Total Interest = $66,022.37
Based on the information given, I would choose Loan B because it has the lowest total interest and a reasonable monthly payment that fits within my budget of $1200 per month. While Loan A has a lower interest rate, the longer repayment period results in a significantly higher total interest. Loan C has a lower monthly payment, but the longer repayment period also results in a higher total interest.
please answer , im marking brainiest .
The fraction equivalent to the number A = 0.555... is A = 5/9
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the fraction be represented as A
Now , the value of A is
A = 0.555555..
Here , the value of A is 0.555 and the number 5 is repeating
So , the simplified form of the fraction A is given by
A = 5/9
On simplifying the value of A , we get
A = 0.55555...
Hence , the fraction is A = 5/9
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27. A man is climbing down from 225 feet high descending 25 feet per minute. Write an
equation/function that models this situation.
The variables x and y are connected by the equation y=(x-3)(x - 5)(x+2).Some corresponding values of x and y are shown in the table below. X -2 0 1 y 0 30 24 (i) Calculate the value of k -1 24 2 12 3 0 4 -6 5 0 (0) 6 k [1] avis
The value of k is given as follows:
k = 24.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
From the table, we have that when x = 6, y = k, hence the value of k is found replacing each of the three instances of x by 6, as follows:
k = (6 - 3)(6 - 5)(6 + 2)
k = 3 x 1 x 8
k = 24.
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Dolores has a block of wax that is 2 1/2 in. long, 2 in. wide, and 4 1/2 in.
high. She melts the wax and pours it into a candle mold. The mold is
a right rectangular prism with a base area of 3 3/4 in.2. What is the
height of the wax in the mold? Show your work.
Answer:
the height of the wax in the mold is 3 inches.
Step-by-step explanation:
The volume of the wax block is:
V = l × w × h
V = (2 1/2) × 2 × (4 1/2)
V = 11 1/4 cubic inches
The base area of the candle mold is 3 3/4 in.2. Let's call the height of the wax in the mold "h2". Then, the volume of the wax in the mold is:
V2 = base area × h2
3 3/4 × h2 = 11 1/4
h2 = 11 1/4 ÷ 3 3/4
h2 = 3
Therefore, the height of the wax in the mold is 3 inches.
Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?
The measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.
A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Christmas trees, carrots, party hats, ice cream cones, and traffic cones are five instances of cones in everyday life (used as road dividers).
Let's look at some actual code examples.
Explanation: A cone is a three-dimensional solid shape with a circular base at one end and one pointy edge serving as a vertex.
So, the formula for the volume of the cone is:
Volume = πr² h/3
Now, insert values and calculate as follows:
Volume = πr² h/3
Volume = π12.5² 2.35/3
Volume = 384.51785
Rounding off: 385 miles³
Therefore, the measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.
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Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?
Answer:
385mi
It is said that 60% of college students have a job outside of school. The college admissions office is investigating on whether this claim is true or not.a) If a test of hypothesis is conducted, describe in in the context of the problem, what would be the type I error:b) If a test of hypothesis is conducted, describe in the context of the problem what would be the type II error:
The type I error, in the context of the problem, would be the incorrect rejection of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is true, when in fact it is not.
The type II error, in the context of the problem, would be the incorrect acceptance of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is false, when in fact it is true.
The college admissions office sets up a hypothesis test with the claim being 60% of college students have a job outside of school.
The null hypothesis would be that the claim is false, or that less than 60% of college students have a job outside of school.
The alternative hypothesis would be that the claim is true, or that at least 60% of college students have a job outside of school.
The type I error would be if the college admissions office incorrectly rejected the null hypothesis, that is, if they concluded that the claim is true and at least 60% of college students have a job outside of school when in fact the claim.
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Write the equation for the perpendicular bisector of a segment that has endpoints (1, –4) and (3, 2).
options:
A)
y = –3x – 1
B)
y = –3x + 5
C)
y = –1∕3x – 1∕3
D)
y = 3x + 5
Answer:
C) y = -1/3x -1/3
Step-by-step explanation:
You want the perpendicular bisector of the segment between the points (1, -4) and (3, 2).
Perpendicular bisectorThe perpendicular bisector is the line perpendicular to the given segment that goes through the midpoint of the given segment. If the midpoint is ...
(h, k) = (x1 +x2, y1 +y2)/2
then the perpendicular bisector equation can be written ...
(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0
ApplicationThe midpoint is ...
(h, k) = (1 +3, -4 +2)/2 = (4, -2)/2 = (2, -1)
The perpendicular line is ...
(3 -1)(x -2) +(2 -(-4))(y -(-1)) = 0
2x -4 +6y +6 = 0
Subtracting 6y and collecting terms, we have ...
2x +2 = -6y
Dividing by -6 puts this in the desired form:
y = -1/3x -1/3
__
Alternate solution
The slope of the segment is ...
m = (y2 -y1)/(x2 -x1) = (2 -(-4))/(3 -1) = 6/2 = 3
The slope of the perpendicular line is the opposite reciprocal of this: -1/3. As above the midpoint is (2, -1), so the point-slope equation is ...
y +1 = -1/3(x -2)
y = -1/3x +2/3 -1 . . . . subtract 1, eliminate parentheses
y = -1/3x -1/3
1853
1854
1850
1851
1852
YEAR
1841
1847
1848
1849
8:59
NUMBER
OF IRISH
IMMIGRANTS
37,772
105,536
112,934
159,398
164,004
221,253
159,548
162,649
101,606
Which of the following statements mos
accurately describes patterns of Irish
immigration in the mid-19th century?
O It remained relatively unchanged.
O
It continually increased between
1847 and 1854.
The statement that most accurately describes patterns of Irish immigration in the mid-19th century is: its peaked in approximately 1851. The Option D is correct.
What was pattern of Irish immigration to US in mid 19th century?Irish immigration to the United States in the mid-19th century was characterized by several factors:
Timing: Irish immigration to the United States peaked in the mid-19th century, particularly in the decades following the Great Famine of 1845-1852. During this time, millions of Irish fled to the United States to escape poverty and famine at home.Destination: Irish immigrants tended to settle in cities, particularly in the Northeast, such as Boston, New York, and Philadelphia. These cities offered employment opportunities and a supportive Irish-American community.Employment: Many Irish immigrants in the mid-19th century worked in manual labor jobs, such as construction, manufacturing, and domestic service. They faced significant discrimination and prejudice from the American-born population, who often considered them to be inferior and less capable.Read more about Irish immigration
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What is the physical significance of the slope of a position vs time graph?
Answer:
The slope of a position vs. time graph has a physical significance as it represents the velocity of an object. If the graph is a straight line, then the velocity is constant. If the graph is curved, then the velocity is changing, which means the object is either accelerating or decelerating. The direction of the slope (positive or negative) indicates the direction of the velocity.
What is 16⅐% of 48? Show work
Paying into a retirement savings plan will increase taxable income, true or false
Answer:
true
Step-by-step explanation:
ANSWER ASAP. 50PTS. BRAINLIEST ANSWER.
What is the area of Triangle PQR on the grid?
A triangle PQR is shown on a grid. The vertex P is on ordered pair 1 and 4, vertex Q is on ordered pair 3 and 1, and the vertex R is on ordered pair 5 and 4.
(1 point)
5 square units
6 square units
10 square units
12 square units
The Area of given triangle is 8 square units.
Area of Triangle:Area of triangle is the total area occupied by the triangle or the area enclosed within the three sides of the triangle.
The formula for calculating area of triangle is,
A = 1/2 bh
where b and h represent the base and height of the triangle, respectively.
This formula can be used to calculate triangles of any shape, including scalene, isosceles, and equilateral triangles. Remember that the base and height of a triangle are perpendicular to one another.
Now in the given question,
P(1,4), Q(3,1), R(5,4)
We have PR parallel to the x axis. We'll call that the base,
b = 5 - 1 = 4
The altitude is then the y difference h = 5 - 1 = 4
Then area of given triangle is,
[tex]A=\frac{1}{2}bh\\\\\\A=\frac{1}{2} (4)(4)\\\\A=\frac{1}{2} (16)\\\\A=8[/tex]
Hence, the area of given triangle is 8 square units.
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the student body president of a high school claims to know the names of at least 1000 of the 1800 students who attend the school. to test this claim, the student government advisor randomly selects 100 students and asks the president to identify each by name. the president successfully names only 46 of the students. the advisor then calculates a 99% confidence interval of (0.332, 0.588). interpret this confidence interval in context.
According to the given case, the confidence interval indicates that the probability that the student two-thirds (58.8%) of the students at the school is 99%.
In other words, there is a 99% chance that the president knows the names of between 332 and 558 of the 1800 students at the school. However, this confidence interval doesn't provide us with a definitive answer as to how many students the president actually knows.
The 46 students that the president was able to name are still significantly lower than 1000 he claimed to know. therefore, we cannot be sure that the president knows the names of 1000 students
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Cuantos frascos de perfume de 12 cl se llenan con un bidón de 15 l?
Using the method of unit conversion, the number of bottles that can be filled is obtained as 125.
What is unit conversion?
Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.
We can start by unit converting the volume of the drum from liters to centiliters, as the volume of the perfume bottles is given in centiliters -
15 liters = 1500 centiliters
Now we can find the number of 12 cl perfume bottles that can be filled with the drum by dividing the volume of the drum by the volume of each bottle -
Number of bottles = volume of drum / volume of each bottle
Number of bottles = 1500 cl / 12 cl
Number of bottles = 125
Therefore, 125 12 cl perfume bottles can be filled with a 15 l drum.
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How many 12 cl perfume bottles are filled with a 15 l drum?
calculate and match the relative frequencies for the following situation. sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis
The relative frequencies of sixty adults with gum disease is 8.3%, 16.7%, 33.3%, 25%, 16.7%.
To calculate the relative frequencies, we first need to count the number of times each flossing frequency was reported. The relative frequency is calculated by dividing the number of adults reporting a certain frequency by the total number of adults (60) and multiplying by 100 to get the percentage.
0 times per week: 5 adults (8.3% relative frequency)
1 time per week: 10 adults (16.7% relative frequency)
2 times per week: 20 adults (33.3% relative frequency)
3 times per week: 15 adults (25% relative frequency)
4 times per week: 10 adults (16.7% relative frequency)
The relative frequency is calculated by dividing the number of adults reporting a certain frequency by the total number of adults (60) and multiplying by 100 to get the percentage.
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The base monthly payment for a car lease is $354.12 per month. If a sales tax of 8.25% is added to the base monthly payment, what is the total monthly lease payment? Round to the nearest cent.
Answer:
the total monthly lease payment is $383.31 rounded to the nearest cent.
Step-by-step explanation:
To calculate the total monthly lease payment, we need to add the sales tax to the base monthly payment.
Sales tax = 8.25% of base monthly payment
Sales tax = 0.0825 x $354.12 = $29.19
Total monthly lease payment = Base monthly payment + Sales tax
Total monthly lease payment = $354.12 + $29.19 = $383.31
Therefore, the total monthly lease payment is $383.31 rounded to the nearest cent.
the following algorithm is intended to take a list of shapes and returns a new list that has no overlapping, blue shapes in it. line 1: procedure removeoverlapping(shapelist) line 2: { line 3: newlist
Here's one possible implementation of the algorithm you described:
Just one possible implementation, and the specific details of the algorithm may vary depending on the specific requirements and characteristics of the shapes being considered.
Define a procedure removeoverlapping(shapelist) that takes a list of shapes as input.
Create an empty list called newlist.
Iterate through each shape in shapelist.
If the shape is blue and does not overlap with any other blue shape in newlist, add it to newlist.
If the shape is not blue, add it to newlist.
Return newlist.
Here's the updated algorithm with code:
python
procedure removeoverlapping(shapelist):
newlist = []
for shape in shapelist:
if shape.color == "blue":
overlap = False
for other_shape in newlist:
if other_shape.color == "blue" and shae.overlaps(other_shape):
overlap = True
break
if not overlap:
newlist.append(shape)
else:
newlist.append(shape)
return newlist
This is only one possible implementation, and the algorithm's precise specifications may change based on the demands and properties of the shapes under consideration.
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Count forward by fives.
56,
Count forward by tens.
270,
Answer:
56,61,67,72,77
Step-by-step explanation:
270,280,290,300,310,320
¿Cuál de las siguientes afirmaciones es verdaderas sobre las funciones?
A) Para cada en el dominio de una función , existe al menos una imagen () en el rango.
B) Un elemento en el rango de no puede ser resultado de más de una en el dominio.
C) Para cada en el dominio de una función , existe exactamente una imagen () en el rango.
D) Si = (), entonces es la variable dependiente de .
In funcion, B) Un elemento en el rango de no puede ser resultado de más de una en el dominio.
¿Qué es una función en matemáticas?En base a las preguntas anteriores, la respuesta más adecuada es B) Un elemento en el rango de no puede ser resultado de más de una en el dominio.
Los términos de una relación se dice que son funciones en matemáticas:
Cada miembro del dominio A está singularmente relacionado con los miembros del codominio B. No hay miembros del dominio A que no estén relacionados únicamente con los miembros del codominio B No hay miembros del dominio A que no estén relacionados con los miembros del codominio BLa función f es una relación que conecta cada miembro de x en un conjunto llamado dominio (Dominio) con un solo valor f(x) de un segundo conjunto llamado región par (Kodominio). El conjunto de valores obtenidos de la relación llamado el área de rendimiento (Rango)
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What Answer of f??
[tex]f = a+ { a }^{ 10.37428 } - \pi[/tex]
f = a + a^10.37428 - 3.14 is an equation that relates two variables, f, and a.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
f = a + [tex]a^{10.37428}[/tex] - π
Now,
f = a + a^10.37428 - 3.14 is an equation that relates two variables, f, and a.
Where a is the independent variable and f is the dependent variable.
It consists of three terms.
= a represents the linear relationship between f and a.
= [tex]a^{10.37428}[/tex] represents a nonlinear relationship between f and a, where 10.37428 is the steepness of the curve.
= -3.14 is a constant that shifts the curve vertically.
Thus,
f = a + a^10.37428 - 3.14 is an equation that relates two variables, f, and a.
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what is the point group for each of the following substituted cyclobutanes? assume that the four-membered ring is flat and that replacing h with x or y changes no other structural parameters.
The point group of a substituted cyclobutene can be determined by examining its symmetry elements.
In group theory, point groups are used to describe the symmetry of a molecule. The point group of a molecule can be determined by examining its symmetry elements, such as rotation axes, reflection planes, and inversion centers.
In the case of substituted cyclobutene, we can assume that the four-membered ring is flat and that replacing hydrogen atoms with other substituents, such as X or Y, does not affect any other structural parameters.
Now, let's consider the point groups for two substituted cyclobutene: 1,1-dimethylcyclobutane and 1,2-dimethylcyclobutane.
1,1-dimethylcyclobutane has two methyl groups attached to the same carbon atom. The symmetry elements of this molecule include a C2 axis that passes through the two methyl groups and perpendicular to the plane of the ring. There are also two perpendicular mirror planes that bisect the ring and pass through the carbon atom with the two methyl groups.
Using the point group flowchart, we can determine that the point group for 1,1-dimethylcyclobutane is C2v.
On the other hand, 1,2-dimethylcyclobutane has two methyl groups attached to adjacent carbon atoms. This molecule has a C2 axis that passes through the two methyl groups and the ring, as well as two perpendicular mirror planes that bisect the ring and pass through the carbon atoms with the methyl groups.
Using the point group flowchart, we can determine that the point group for 1,2-dimethylcyclobutane is Cs.
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What is the meaning of "coefficients"?
A coefficient is a quantity or number that is related to a variable. The variable is frequently followed by an integer that has been multiplied by the variable.
Define Coefficient.In mathematics, a coefficient is a quantity that is multiplied by a variable in a single term or in a polynomial's terms. Any sign that represents a constant value can be used, including numbers. It is often a number, however in other situations it could be a letter. In the formula: ax² + bx + c, for instance, x is the variable and a and b are the coefficients.
Therefore, a coefficient can be actual or hypothetical, expressed as a fraction or decimal, positive or negative, and real or imaginary. According to another definition, a coefficient is "Any number we multiply a variable by." For instance, the coefficient of the variable x in the expression 9.3x is 9.3, whereas the coefficient of the expression -5z is -5.
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Calculating angle of elevation of sun at different times of the day using your height and the length of shadow cast
At noon on a clear day, with a height of 6 feet and a length of the shadow of 6 feet, the angle of elevation of the sun is approximately 45 degrees.
What is the angle of elevation?An angle of elevation is defined as the angle formed between the horizontal plane and the line of sight from the observer's eye to anything above.
Let's assume a height of 6 feet and a length of the shadow of 6 feet.
We'll also assume that we are measuring the angle of elevation at noon on a clear day.
Using the tangent formula, we have:
tan θ = h / s
tan θ = 6/6
θ = tan⁻¹(6 / 6)
θ = tan⁻¹(1)
θ = 45°
Therefore, the angle of elevation of the sun is approximately 45 degrees.
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1
A reforestation drive is conducted in a town. The town had 2,022 trees at the start of the drive. Four months after the start of the
reforestation drive, the town had 4,897 trees.
If n represents the number of months and T represents the number of trees, which of the following equations can be used to model
this situation?
OA. T 718.75 - 2,022
OB. T = 2,022n + 718.75
OC. T 718.75 + 2,022
OD. T = 2875 + 2,022n
Answer: OD. T = 2875 + 2,022n
Step-by-step explanation: What makes the most sense is
OD. T = 2875 + 2,022n
because they added 2875 to the trees already there and 4,897 was the new total after four months, I also want to point out it has nothing to do with decimals or a 700 number.
Use Algorithm, to find the transitive closures of these relations on {1, 2, 3, 4). a) {(1, 2), (2,1), (2,3), (3,4), (4,1)) b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3)} c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)} d) {(1, 1), (1,4), (2,1),(2,3), (3,1), (3, 2), (3,4), (4,2))
Transitive closures are: a) {(1,2),(2,1),(2,3),(3,4),(4,1)}; b) {(2,1),(2,3),(3,1),(3,4),(4,1),(4,3)}; c) {(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}; d) {(1,1),(1,4),(2,1),(2,3),(3,1),(3,2),(3,4),(4,2)}.
Transitive conclusion is a central idea in chart hypothesis and alludes to the most common way of finding every one of the hubs in a coordinated diagram that are reachable from a given hub. All in all, it is the most common way of deciding every one of the potential ways from a given hub to any remaining hubs in the chart. This can be significant in different settings, like in deciding the connections between objects in a data set, or in dissecting the design of PC programs. Transitive conclusion can be tracked down utilizing different calculations, including the Floyd-Warshall calculation and the Warshall calculation.
To find the transitive conclusion of a connection utilizing the calculation, we follow these means:
Begin with the first connection R.
Process the piece of R with itself (R∘R).
Take the association of R and R∘R.
Assuming the association has changed, rehash stages 2 and 3 until there is no change.
a) {(1, 2), (2,1), (2,3), (3,4), (4,1))
R^2: {(1,1), (1,3), (1,4), (2,2), (2,1), (2,4), (3,1), (3,4), (4,2), (4,1)}
R^3: {(1,1), (1,4), (2,1), (2,4), (3,4), (4,1)}
Transitive conclusion: {(1, 2), (1,4), (2,1), (2,4), (3,4), (4,1)}
b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3)}
R^2: {(2,1), (2,4), (3,1), (3,3), (3,4), (4,1)}
Transitive conclusion: {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3), (3,1), (3,3), (2,4)}
c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)}
R^2: {(1,3), (1,4), (2,4), (3,4)}
Transitive conclusion: {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)}
d) {(1, 1), (1,4), (2,1),(2,3), (3,1), (3, 2), (3,4), (4,2)}
R^2: {(1,1), (1,3), (1,4), (2,1), (2,2), (2,4), (3,1), (3,2), (3,4), (4,2)}
R^3: {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2)}
Transitive conclusion: {(1, 1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2)}.
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We choose a number from the set {1, 2, 3, . . . , 100} uniformly at random and denote this number by X.
For each of the following choices decide whether the two events in question are independent or not
(a) A = {X is even}, B = {X is divisible by 5}.
(b) C = {X has two digits}, D = {X is divisible by 3}.
(c) E = {X is a prime}, F = {X has a digit 5}. Note that 1 is not a prime number.
(a) Not independent, as the occurrence of X being even affects the probability of X being divisible by 5 and vice versa.
(b) Not independent, as the occurrence of X having two digits affects the probability of X being divisible by 3 and vice versa.
(c) Independent, as the occurrence of X being a prime does not affect the probability of X having a digit 5, and vice versa.
Two occurrences are often considered independent if their occurrence has no impact on the likelihood of their occurrence. The occurrences in (a) and (b) are not independent since one event's occurrence affects how likely the other is. Because the chance of one event in (c) is unaffected by the likelihood of the other, the occurrences are independent in (c).
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2. By using a truthtable determine whether the following argument is valid or not If 10,836 is divisible by 12 then 10836 is divisible by 3. If 10,836 is divisible by 3 then the sum of the digits of 10836 is divisible by 3. Therefore, if 10,836 is divisible by 12 then the sum of the digits of 10836 is divisible by 3. (10 marks)
Based on the truth table constructed, the premises and conclusions are true, hence, the argument is valid.
What is the validity of the argument?The validity of the argument is determined as follows:
First statement, S1:
10836/12 = 903
10836/3 = 3612
Second statement, S2:
10836/3 = 3612
1 + 0 + 8 + 3 + 6 = 18
18/3 = 6
Statement 3, S3:
10836/12 = 903
1 + 0 + 8 + 3 + 6 = 18
18/3 = 6
The truth table is given below
Premise 1 Premise 2 Conclusion
S1. T T T
S2. T T T
S3. T T T
Since all the premises and conclusions are true, the argument is valid.
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