There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
[tex]\dfrac{7}{4}[/tex].
To find the groups of fraction,
Simplify the fraction,
[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]
There are two groups in the fraction of [tex]\dfrac{7}{4}[/tex] ,
Integer part which is 1.
And decimal part which is 0.75.
Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].
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Given the function f(x) = −5x2 + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
What do you mean by Polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).
CalculationGiven f(x)=-5x2 + 2x + 9
f(1)=-5(1)2+2(1)+9
∴f(1)=6
f(2)=-5(2)2+2(2)+9
∴f(2)=-7
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
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The diagram below shows a cylinder with diameter 6 cm and height 20 cm. The
Volume, in cm³, of the cylinder is
-6 cm
20 cm
The volume of the cylinder is 180π cm³.
What is volume ?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
As diameter = 6cm
We know that radius is half of diameter
∴ radius = 3 cm
height = 20 cm
Volume = π r² h
= π (3)²×20
= π × 9 × 20
= 180 π cm³
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The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 3 8 13
Tickets 9 24 39
Determine the constant of proportionality.
18
6
5
3
PLS HELP
Answer:
constant of proportionality = 3Step-by-step explanation:
You want to find the number of tickets required per game, given that the relationship is proportional and 9 tickets are required for 3 games.
ProportionThe equation of a proportional relationship can be written as ...
y = kx
where k is the constant of proportionality.
ConstantSolving for k, we have ...
k = y/x
Using a given ordered pair, we find ...
k = 9/3 = 3
The constant of proportionality is 3 (tickets per game).
__
Additional comment
Since the relationship is given as being proportional, we only need one (x, y) pair to find the constant of proportionality.
H(y) models the leading number of home runs for season y of the National League between the years 2000-2010, according to the table.
Season Player # of Home Runs Team
2000 Sammy Sosa 50 Chicago
2001 Barry Bonds 73 San Francisco
2002 Sammy Sosa 49 Chicago
2003 Jim Thome 47 Philadelphia
2004 Adrian Beltre 48 Los Angeles
2005 Andruw Jones 51 Atlanta
2006 Ryan Howard 58 Philadelphia
2007 Prince Fielder 50 Milwaukee
2008 Ryan Howard 48 Philadelphia
2009 Albert Pujols 47 St. Louis
2010 Albert Pujols 42 St. Louis
Which number type is more appropriate for the domain of H?
A number type which is more appropriate for the domain of H include the following: A. Integers.
The appropriate domain include the following: C. 2000 ≤ y ≤ 2010.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1) such as 1, 10, 20, 2000, 2010, etc.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.
Since the variable H(y) represents the leading number of home runs for season y of the National League between the years 2000-2010, an appropriate domain is given by;
Domain = 2000 ≤ y ≤ 2010 or [2000, 2010].
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Complete Question:
Which number type is more appropriate for the domain of H?
A. Integers
B. Real numbers
What's the appropriate domain?
0 ≤ y < 2010
0 < y < 73
2000 ≤ y ≤ 2010
42 ≤ y < 73
2. In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers, 25 have both pensils and pens, 30 have both pencils and rulers while 47 have both pens and rulers, each pupil has at least one of the items. a). write the set notation. b) Draw a Venn diagram to illustrate this information c).How many pupils have pencils only
a) The set notation is shown below.
b) 27 pupil have pencils only.
What is Venn Diagram?A Venn diagram depicts the logical relationships between two or more sets of items by using overlapping circles or other shapes. They frequently serve to graphically organise things, demonstrating how similar and dissimilar the pieces are.
Given:
In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers.
25 have both pencils and pens,
30 have both pencils and rulers while 47 have both pens and rulers.
a) The set notation is
n(p)= 75
n(Pens)= 87
n(R)= 93.
n (p∩ pens) = 25
n (p∩ R) = 30
n (pens ∩ R) = 47
n (p∩ R ∩ pens) = x
c) Number of Pupil that have only pencils
= 75- [(30-7) + 25-7 +7]
=75-(23+18+7)
= 75-48
=27
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a research company is claiming that 75% of college students shop online. jamila takes a sample of 200 college students and finds that 120 college students shop online.
The correct answer is option (d) - one proportion z-test.
The complete question is
A research company is claiming that 75% of college students shop online. Jamila takes a sample of 200 college students and finds that 120 college students shop online. Which type of inference test should Jamila use?
a) Chi-squared test for homogeneity
b) Two-way ANOVA O
c) One-sample t-test
d) One proportion z-test
To determine which type of inference test to use in this situation, Jamila needs to consider the following:
The research question: In this case, the research question is whether the proportion of college students who shop online is significantly different from the proportion claimed by the research company (75%).
The type of data: Jamila has collected data on a sample of college students, rather than the entire population.
The type of variables: The variable of interest is a binary variable (students either do or do not shop online), and the proportion of students who shop online is being compared to a fixed value (75%).
Given this information, the appropriate test to use is a one proportion z-test. The one proportion z-test is a statistical test that is used to determine whether the proportion of a binary variable in a sample is significantly different from a known proportion in the population.
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help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
Because whee your finding the Grange of a fundtlon you Look at the Y value from the smallest Number to the largest Number.
Two marbles are chosen at random, one at a time from a box that contains 7 marbles, 5 red and 2 green, a. Find the probability of drawing 2 red marbles when
The probability of randomly drawing 2 red marbles is P = 0.476
How to find the probability?On the box we have 7 marbles, 5 red ones and 2 green ones. If we assume all the marbles have the same probability of being randomly drawn, then the probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles.
So the probability for the first red marble is:
p = 5/7
For the second one, we will have one red marble less and one marble of the total less, so the probability is:
q = 4/6
The joint probability is the product of these two:
P = (5/7)*(4/6) = 0.476
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please help me with this
Answer:
16 units
Step-by-step explanation:
You want the side length of a square pyramid with height 15 units and slant height 17 units.
Pythagorean theoremThe Pythagorean theorem can be used to find the distance from the midpoint of one side to the center of the square base.
(b/2)² +15² = 17²
(b/2)² = 289 -225 = 64
b/2 = √64 = 8
Then the length of one side of the base is ...
b = 2·8 = 16 . . . . units
Find the product
-20 • (-4) =
Answer:
-20*(-4)=80
Step-by-step explanation:
-20*(-4)=20*4
20*4=80
A researcher wishes to test whether two nominal variables with two and three respective categories are statistically independent. She observes a chi square value from Pearson's chi square test of independence of 10.00430. Consider the following propositions: PROPOSITION ONE: At the 5% significance level the appropriate decision could be a Type II Error; PROPOSITION TWO: At the 1% significance level the appropriate decision could be a Type II Error.
A. Proposition I is true and Proposition II is true
B. Proposition I is true and Proposition II is false
C. Proposition I is false and Proposition II is true
D. Proposition I is false and Proposition II is false
E. None of the above
The correct answer is Option A: Proposition I is true and Proposition II is true.
A researcher can use Pearson's chi square test of independence to determine if two nominal variables are independent or not. In this case, the researcher observed a chi-square value of 10.00430.
To determine whether the null hypothesis should be accepted or rejected, the researcher must compare the chi-square value to a critical value associated with the desired level of significance.
At the 5% significance level, the critical value is usually around 7.815, and at the 1% significance level, the critical value is usually around 10.827. Since the observed chi-square value (10.00430) is higher than the critical values for both the 5% and 1% significance levels, the appropriate decision could be a Type II Error for both levels of significance.
In other words, Proposition I (At the 5% significance level the appropriate decision could be a Type II Error) and Proposition II (At the 1% significance level the appropriate decision could be a Type II Error) are both true.
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a restaurant offers a dinner special for $25 per person plus a $5 per-person tip. Which expressions represent the special?
A. 25m+5
B. 30m
C. 25m+5m
D. 25m+5m
E. 25+5m
Answer:
The expression is B. 30m
How did the Three-Fifths Compromise affect the 1790 census results? *
Use the following information to answer the questions.
A. Citizens in each state were counted as three-fifths of a person.
B. Enslaved persons in each state were counted as three-fifths of a person.
C. Only three-fifths of the citizens in each state were eligible to vote in elections.
D. Only three-fifths of enslaved peoples in each state were eligible to vote in elections.
The way that the Three-Fifths Compromise affected the 1790 census results was B. Enslaved persons in each state were counted as three-fifths of a person.
What was the Three - Fifths Compromise ?A settlement known as the "three-fifths compromise" was reached at the 1787 Constitutional Convention and permitted Southern states to count some of their enslaved population as three-fifths of a person for taxes and representational purposes. This first happened in the 1790 census results.
Many of the Founding Fathers recognized that slavery went against the ideal of liberty that was at the heart of the American Revolution, but they were unable to act decisively to end it because they were dedicated to the sanctity of private property rights, the ideas of limited government, and the pursuit of intersectional harmony.
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Use point-slope form to write the equation of a line that passes through the point
(12, 10) with slope 1/3.
Answer:
y - 1/3x - 10 + 4 = 0
Step-by-step explanation:
What we know:
x = 12
y = 10
slope (m) = 1/3
y - y1 = m(x - x1) Point-slope form
Substitute in the values we have
y - 10 = 1/3(x - 12)
Bring all the values to one side
y - 10 - 1/3(x - 12) = 0
y - 1/3x - 10 + 4 = 0
The edge of a cube has length 10 inches with a possible error of 1%. The possible error, in cubic inches, in the volume of the cube is: a) 3 b) 1 c) 10 d) 30 e) all of these
Answer:
d) 30
Step-by-step explanation:
1% of 10 inch is 0.1 inch
10 inch + 0.1 inch = 10.1 inch
10 inch - 0.1 inch = 9.9 inch
V = s³
For s = 9.9 in., V = (9.9 in.)³ = 970.299 in.³
For s = 10.1 in., V = (10.1 in.)³ = 1030.301 in.³
For 10 in., V = (10 in.)³ = 1000 in.³
|1000 in.³ - 970.299 in.³| = 29.701 in.³
|1000 in.³ - 1030.301 in.³| = 30.301 in.³
The error is 30 in.³.
11 12 13 14 15 16 17 18 19 20 Given: AB = BC Prove: B is the midpoint of AC. A line contains point A, B, C. A flow chart has 3 boxes that go from top to bottom. The first box is labeled given and contains A B = B C. The second box is labeled definition of congruent segments and contains Line segment A B is-congruent-to Line segment B C. The third box is labeled definition of a midpoint and contains B is the midpoint of Line segment A C. What is the format of this proof? two-column proof one-paragraph proof flowchart proof two-paragraph proof Mark this and return
A list of assertions and the justifications for each assertion are included in a two-column geometric proof.
What is The Structure of a Proof?Either two columns or a paragraph can be used to write a geometric proof. A two-column proof stated in sentences is all that a paragraph proof is. But since it's simpler to omit stages when writing a paragraph proof, we'll study the two-column technique.A list of assertions and the justifications for each assertion are included in a two-column geometric proof. The reasons why the claims are true are mentioned in the right column, while the statements themselves are listed in the left column. A row in the two-column proof represents each phase of the proof, or each conclusion reached.Make the illustration of the proof-in-use in a figure. Either the figure will be drawn for you already, or you will need to draw it yourself.List the assertions that are made, and then the assertions that must be proven. At this point, the proof has a start and a finish.Based on what you can infer about the figure from the provided details, mark it accordingly. You actually learn how to make the proof at this stage of the proof process, as well as whether or not you can support the assertion that has been stated.Mark any congruent sides, angles, etc. so you can see for yourself what has to be said in the evidence to persuade the reader that you are correct in your conclusion.Without omitting even the simplest, carefully note down each step. The stated statements are frequently among the initial steps (though not always), and the conclusion you want to prove is the last step.To Learn more About geometric proof refer To:
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A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 39 miles per hour is passed by a second shuttle that left 30 minutes later traveling at a rate of 42 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle?
To find the distance that the first shuttle traveled before it was passed by the second shuttle, we need to use the formula d = rt, where d is the distance traveled, r is the speed at which the shuttle is traveling, and t is the time elapsed. We can use this formula to find the distance traveled by each shuttle and then subtract the distance traveled by the first shuttle from the distance traveled by the second shuttle to find the distance the first shuttle traveled before it was passed.
For the first shuttle, the speed is 39 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the first shuttle is 39 miles/hour * 0.5 hours = 19.5 miles.
For the second shuttle, the speed is 42 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the second shuttle is 42 miles/hour * 0.5 hours = 21 miles.
Therefore, the distance that the first shuttle traveled before it was passed by the second shuttle is 21 miles - 19.5 miles = 1.5 miles.
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A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
The number of new members that are women will be 25 women.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A games group has 65 men and 35 ladies as individuals. Another movement has quite recently started and a few new individuals have joined. Considering that the quantity of men is currently 60% of the absolute number of individuals.
The number of new members is 50.
Let the number of new men be 'x'. Then the equation is given below.
(65 + x) / (100 + 50) = 60%
(65 + x) / 150 = 0.60
65 + x = 90
x = 25
The number of new members were women will be given as,
⇒ 50 - 25
⇒ 25
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In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
OA. m/1=m/7
OB.
O C.
O D.
m23=m26
m25+ m28 = 90°
m26+ m27 = 180°
Answer:
A. ∠1 = ∠7
B. ∠2 = ∠6
D. ∠6 + ∠7 = 180°
Step-by-step explanation:
⭐ Why A is correct
∠1 = ∠7 because when two parallel lines are cut by a transversal, alternate exterior angles are formed. Alternate exterior angles are congruent.∠1 and ∠7 are alternate exterior angles.Therefore, ∠1 = ∠7.⭐ Why B is correct
∠2 = ∠6 because when two parallel lines are cut by a transversal, corresponding angles are formed. Corresponding angles are congruent.∠2 and ∠6 are corresponding angles.Therefore, ∠2 = ∠6.❌ Why C is incorrect
∠5 + ∠8 is not equal to 90° because ∠5 and ∠8 are adjacent angles.Adjacent angles sum to 180°.Therefore, ∠5 + ∠8 is not equal to 90°.⭐ Why D is correct
∠6 + ∠7 = 180° because ∠6 and ∠7 are adjacent angles.Adjacent angles sum to 180°.Therefore, ∠6 + ∠7 = 180°.
People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
250
7
2
+6
2
(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
100
7
2
+
150
6
2
(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
250
7
2
+6
2
(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
100
7
2
+
150
6
2
The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Level A:
S.D. = 7
Level B: Mean = 20
S.D. = 6
So, [tex]\nu_1[/tex] = 22
[tex]\nu_2[/tex] = 20
Then, [tex]\nu_1[/tex] - [tex]\nu_2[/tex] = 22-20=2
and, [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex]
= (7)² ÷100+ 6² /150
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DUE SOON PLEASE HELP! QUESTION DOWN BELOW PLEASE EXAPLIN HOW IT IS THAT ANSWER SO I KNOW FOR NEXT TIME!
The sum of two even integers and one odd integer will be an odd integer. Then the correct option is D.
What is the Odd and Even?If the number is divisible by 2 then the number will be an even number. Similarly, if the number is not divisible by 2 then the number will be an odd number.
Some of the properties of the even and odd number are given below.
The sum of two odd numbers is an even number.The sum of two even numbers is an even number.The sum of odd and even numbers is an odd number.The sum of even and odd numbers is an odd number.The sum of two even numbers will be even and the sum of two even numbers and odd numbers will be odd numbers.
The amount of two even whole numbers and one odd whole number will be an odd whole number. Then, at that point, the right choice is D.
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What is the location of Point F, which partitions the directed line segment from D to E into a 5:6 ratio?
Answer:
Step-by-step explanation:
write a quadratic equation with -6 and 3/4 as its roots. write the equation in the form ax^2 + bx + c = 0, where a,b, and c are integers.
The quadratic equation whose roots are -6 and 3/4 is 14x²+21x-18=0
How to find quadratic equations?We should know that a quadratic equation is that whose highest power of the variable is 2
The given roots are
x=-6 and x=3/4
Let (x+6)(x-3/4)=0
Multiplying the brackets we have
[tex]X^{2}-\frac{3x}{4} +6x-\frac{18}{4}[/tex] =0
Find the LCM of the denominators
[tex]\frac{4X^{2}+21x-18 }{4} =0[/tex]
Cross and multiplying we have
[tex]4x^{2} +21x-18=0[/tex]
Therefore, the equation is expressed in the form ax²+bx+v=0 Where a=4, b=21 and c=-18
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Could someone help me with this trig question?
k= 5.
Step-by-step explanation:1. Write the expression.[tex]ksin^{2} (x)+kcos^{2} (x)=5[/tex]
2. Factorize k.[tex]k(sin^{2} (x)+cos^{2} (x))=5[/tex]
3. Simplify using pythagorean identities.Check attached image 1.
[tex]k(1)=5\\ \\k=5[/tex]
4. Verify.Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.
Check attached image 2.
As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.
Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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[tex]5^{2} -2^{2} =[/tex]
the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Maribelle uses x yards of material yo make a quilt. A customer requests 5 quilts that are 20% larger than the normal pattern. Write an expression to represent the total yards of material needed for the requested quilts in two different ways.
The expression to represent the total yards of material needed for the requested quilts is 5(1.2x) or 6x.
What is the expression to represent the total yards of material needed for the requested quilts?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, Maribelle uses x yards of material to make a quilt and a customer requests 5 quilts that are 20% larger than the normal pattern.
The expression for this will be:
= 5[x + (20% × x)]
= 5[x + 0.2x]
= 5(1.2x]
= 6x
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TASK 4
Managing multiple items
Manage a number of items in an ordered structure
For this task you are required to use your knowledge of lists from the Coding Preparation section to manage a number of items in an ordered structure.
You are going to be creating a program that represents the movements of the line for the lady's bathroom. To begin, create a list that represents the line, it must contain the five names of the women initially waiting (you can make these up).
The following events occur, and you must represent them in the list and print the list out after each action.
A woman named Jenny arrives who only wanted to check her lipstick, she asks to join the front of the line, and all the women let her.
The woman third in line’s phone started ringing, and she left the line to answer.
A new woman named Alice joined the line.
This program uses a list to represent the line and the built-in Python list methods insert(), pop(), and append() to manage the line according to the specified events.
What is a program?This program represents the line with a list and manages the line using the built-in Python list methods insert(), pop(), and append().
Here is one way you could implement this program using a Python list:
# Initialize the list of women waiting in line
line = ["Samantha", "Emily", "Rebecca", "Karen", "Linda"]
# Jenny arrives and joins the front-of-the-line
line.insert(0, "Jenny")
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Rebecca', 'Karen', 'Linda']
# The woman third in line leaves the line
line.pop(2)
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda']
# Alice joins the line
line.append("Alice")
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda', 'Alice']
The final list after all events have occurred is ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda', 'Alice'].
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Circles P and Q are externally tangent to each other and have radii 18 meters
and 32 meters, respectively. As shown, circles P and Q are externally tangent
to a line segment at points X and Y, respectively. What is XY?
Answer:
48 m
Step-by-step explanation:
You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.
Pythagorean theoremAs shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.
a² +b² = c²
14² +b² = 50²
b² = 50² -14² = 2304
b = √2304 = 48
The length of XY is 48 meters.
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Additional comment
In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.