If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 508 Americans would differ from the population proportion by greater than 3%
Answers
Answer:
The probability that the sample proportion would differ from the population proportion by greater than 3% is 0.008.
Step-by-step explanation:
The complete question is:
A statistician calculates that 7% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 508 Americans would differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Solution:
Let the random variable X represent the number of Americans owning a Rolls Royce.
The proportion of Americans who own a Rolls Royce is, p = 0.07.
A random sample of n = 508 Americans were selected.
As the sample size is quite large, i.e. n = 508 > 30, according to the central limit theorem the sampling distribution of sample proportion would follow a normal distribution approximately.
The mean and standard deviation are as follows:
\(\mu_{\hat p}=p=0.07\)
\(\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.07(1-0.07)}{508}}=0.01132\)
Compute the probability that the sample proportion would differ from the population proportion by greater than 3% as follows:
\(P(|\hat p-p|>0.03)=P(\hat p<-0.03\ \cup\ \hat p>0.03)\)
\(=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}}<\frac{-0.03}{0.01132}\ \cup\ \frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}}>\frac{0.03}{0.01132})\\\\=P(Z<-2.65\ \cup\ Z>2.65)\\\\=P(Z<-2.65)+P(Z>2.65)\\\\=P(Z<-2.65)+1-P(Z<2.65)\\\\=0.00402+1-0.99598\\\\=0.00804\\\\\approx 0.008\)
*Use the z-table.
Thus, the probability that the sample proportion would differ from the population proportion by greater than 3% is 0.008.
Related Questions
in the fruit bowl there are 12 bananas 8 apples and 4 oranges. do for every one orange there are ___ bananas
Answers
For every 1 orange in the fruit bowl there are three bananas.
According to the question,
We have the following information:
In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.
Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:
4 oranges = 12 bananas
Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.
So, we have the following expression:
1 orange = 12/4 bananas
1 orange = 3 bananas
Hence, for every 1 orange in the fruit bowl there are three bananas.
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Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
Answers
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.
Please help it’s due in 3 minutes
Answers
The medians are about the same.
Option C is the correct answer.
How to solveThe median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.
We have,
Movie theater 1.
From the box plot given,
The median is 995.
Movie theater 2.
From the box plot given,
The median is 995.
Thus,
The median in both the box plot is the same.
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Which of the following is the correct equation for this function?
A. Y=-x²+3x - 4
B. Y= (x+1)(x-3)
c. Y= (x + 1)(x − 3)
D. Y + 1 = -(x − 3)²
Answers
Standard form of a parabola: y = a(x – h)^2 + k.
Since the parabola opens downwards, the leading coefficient, a, will be negative. This means option B can be ruled out as incorrect.
The vertex is at (1,4) and is also the maximum. As this is (h,k) in vertex form, you can start substituting values to find the equation. Start with y = -(x – 1)^2 + 4 and simplify by squaring the terms in parentheses and distributing the negative in front of the parentheses.
y = - (x-1)(x-1) + 4
= -(x^2 - x - x + 1) + 4
y = -x^2 + 2x + 3.
Also written as y = -(x + 1)(x - 3)
The graphed function is shown to cross the x-axis at -1 and 3.
I hope this helps a little!
Suppose that 1% of the employees of a certain company use illegal drugs. This company performs random drug tests that return positive results 99% of the time if the person is a drug user. However, it also has a 2% false positive rate. The results of the drug test are known to be independent from test to test for a given person.
a) Steve, an employee at the company, has a positive test. What is the probability that he is a drug user?
b) Knowing he failed his first test, what is the probability that Steve will fail his next drug test?
c) Steve just failed his second drug test. Now, what is the probability that he is a drug user?
Answers
Answer:
a) Pr(drug user| positive test) = 0.3333
b) The probability that he will failed his first test = 0.9703
c) the probability that he is a drug user since failed his second drug test
= 0.961165
Step-by-step explanation:
From the given information:
Suppose that 1% of the employees of a certain company use illegal drugs.
Probability of illegal drug user = 0.01
Probability of user that do not use drug = 1 - 0.01 = 0.99
From the person that is a illegal drug user, the company performs random drug tests that return positive results = 0.99
Therefore, the negative result for illegal drug user = 1 - 0.99 = 0.01
However, it also has a 2% false positive rate.
i.e the probability of the user that do not use drug has a positive result of 2% = 0.02
Thus, the probability of the user that do not use drug has a negative result of = 1 - 0.02
= 0.98
We are tasked to answer the following questions.
a) Steve, an employee at the company, has a positive test. What is the probability that he is a drug user?
i.e This employee we are taking about is a drug user and he has a positive test.
Thus;
Pr(drug user| positive test) = \(\dfrac{0.99 \times 0.01}{0.99 \times 0.01+ 0.02 \times 0.99}\)
Pr(drug user| positive test) = \(\dfrac{0.0099}{0.0099+0.0198}\)
Pr(drug user| positive test) = \(\dfrac{0.0099}{0.0297}\)
Pr(drug user| positive test) = 0.3333
b) Knowing he failed his first test, what is the probability that Steve will fail his next drug test?
The probability that he will failed his first test = ((0.01 × 0.01) + (0.99×0.98))
The probability that he will failed his first test = ( 1 × 10⁻⁴ + 0.9702)
The probability that he will failed his first test = 0.9703
c) Steve just failed his second drug test. Now, what is the probability that he is a drug user?
the probability that he is a drug user since he failed his second drug test using Bayes theorem can be expressed as:
= \(\dfrac{0.01 \times(0.99\times 0.99)}{0.01 \times (0.99 \times0.99)+ 0.99(0.02 \times0.02)}\)
the probability that he is a drug user since failed his second drug test
= \(\dfrac{0.01 \times(0.9801)}{0.01 \times (0.9801)+ 0.99(4 \times 10^{-4})}\)
the probability that he is a drug user since failed his second drug test
= \(\dfrac{0.009801}{0.009801+ 3.96 \times 10^{-4}}\)
the probability that he is a drug user since failed his second drug test
= 0.961165
Fill in the blank with the correct answer choice. A ___________ has exactly one pair of parallel lines. a. square c. trapezoid b. parallelogram d. rectangle Please select the best answer from the choices provided A B C D
Answers
Answer: C
Step-by-step explanation:
The rest of the quadrilaterals provided have 2 pairs of parallel lines.
The choice is:
CExplanation:
The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.
Here's what a trapezoid looks like :
\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)
Hence, this makes C the correct choice.Whats the correct answer answer asap for brainlist
Answers
The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.
Definition of the word "obstinancy", its uses and example:Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.
We often use the word "obstinancy" for the followings:
to describe someone's persistence in pursuing a particular course of action despite obstacles or challenges.to describe someone's reluctance to change their opinion or attitude in light of new evidence.to describe someone's refusal to give in to the demands or requests of others.Read more about Obstinancy
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Please help I’ll upvote your work
Answers
Functions, f[g(1)] = 0.5 and g(g(1)) = g(-7) by using the details of question.
What are the Functions?
Given that the graphs of y = f(x) and y = g(x) intersect at (-2.5, 0.5), we know that f(-2.5) = g(-2.5) = 0.5.
To find g(1), we can use the equation of the line passing through the points (-3, 3) and (-2.5, 0.5). The slope of this line is:
m = (0.5 - 3) / (-2.5 + 3) = -2.5
So the equation of the line is:
y - 3 = -2.5(x + 3)
Simplifying this equation, we get:
y = -2.5x - 4.5
Therefore, g(1) = -2.5(1) - 4.5 = -7.
To find f[g(1)], we need to evaluate f(x) at x = g(1). Since we don't have an equation for f(x), we need to use the fact that the graphs of f(x) and g(x) intersect at (-2.5, 0.5). This means that:
f(g(1)) = f(-7) = 0.5
Therefore, f[g(1)] = 0.5.
Finally, to find g[g(1)], we need to evaluate g(x) at x = g(1). Since we know that g(1) = -7, we can write:
g(g(1)) = g(-7)
We don't know the equation of the function g(x), so we can't determine g(-7) without additional information.
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Complete question is: f[g(1)] = 0.5 and g(g(1)) = g(-7)
Joesph and molly each have coin collections. Joesph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins to each month. If Joseph and molly continue to collect this way, how many coins will each person have after 10 months?
Answers
Answer:
Joseph- 265 coins
molly- 275 coins
Over the summer, Paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. He works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?
Answers
Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand B. Of all these soft drink consumers, 20% prefer Brand A and are female, and 40% prefer Brand B and are female. What is the probability that a randomly selected consumer is female, given that the person prefers Brand A? A. 0.18 B. 0.21 C. 0.34 D. 0.67
Answers
Answer:
The answer to this question should be D. 0.67
Hope this helped.
What number added to four and five-tenths, is twelve?
Answers
Answer:
7.5
Step-by-step explanation:
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seven and five-tenths
Step-by-step explanation:
help me please in this problem
Answers
The half-life of caffeine in a person's bloodstream is about 6 hours. If a person's bloodstream contains 70 milligrams of caffeine,how much of that caffeine will remain after 15 hours ?
Answers
Answer:
12.4 mg
Step-by-step explanation:
a = p(1/2)^(t/h)
p is the initial quantity = 70
t is the time = 15
h is the half life = 6
plug in the givens
a = 70(1/2)^(15/6)
a = 12.3743686708
12.4 mg
The woods behind Wendy’s house were 8 miles wide and have an area of 24 mi.² what is the length of the woods 
Answers
Answer:
48 miles
Step-by-step explanation:
i think thats it.
Answer: 4.
Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.
Hope this helps!
Find the Value of X.
Answers
The value of x is 33.2
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.
Also the ratio of corresponding sides of similar triangles are equal.
Therefore;
Triangle EHG and EFG are similar
39/36 = 36/x
36 × 36 = 39x
39x = 1296
divide both sides by 39
x = 1296/39
x = 33.2
Therefore the value of x is 33.2
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increase 1352 by the sum of 897.23 and 39.89
Answers
Answer:
2289.12
Step-by-step explanation:
Answer:
2289.12
Step-by-step explanation:
the sum of 897.23 and 39.89 is 937.12
937.12+1352=2289.12
Rewrite the parametric equations in Cartesian form: x(t)=4+t, y(t)=2sqrt(t).
y=?
Answers
Answer:
Both of these curves are equal to each other.
Step-by-step explanation:
We have
\(x(t) = 4 + t\)
and
\(y(t) = 2 \sqrt{t} \)
Solve for t in the x function
\(x = 4 + t \)
Subsitue this in for t.
\(y = 2 \sqrt{x - 4} \)
We get
a square root function shifted to right 4 units and stretched vertically by a factor of 2.
We can also prove this by graphing.
Exac
Two
If BD = 2.8, what is CP? Round
your answer to the nearest tenth. Write NA if
there is not enough information given.
RN=
Con
Diac
Answers
The shape represents an isosceles trapezoid
The value of CP is 1.1 units
How to calculate the length of CPThe given parameters are:
Length BD =2.8Length AP = 1.7Angle ADB = 37 degreesAngle BDC = 34 degreesThe shape is an isosceles trapezoidThe diagonals of an isosceles trapezoid are congruent.
This means that:
\(CA = BD = 2.8\)
Also, we have:
\(CA = CP + AP\)
Substitute values for CA and AP
\(CP + 1.7 = 2.8\)
Subtract 1.7 from both sides
\(CP = 1.1\)
Hence, the value of CP is 1.1 units
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A research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years. When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years
a) What is the population of interest in this situation?
b) How many samples were described?
c) Is the average age of 37 years a parameter or a statistic?
d) Tell whether this information represents a quantitative or qualitative variable? - age of the visitor - whether the visitor has a season pass
e) What possible explanation is there for the large difference in age between the two samples?
Answers
Answer:
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic.
(d) The above information represents a quantitative variable.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
Step-by-step explanation:
We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.
When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. \(\bar X_1\) = 37 years.
(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)*(F - 32), where F is the Fahrenheit temperature and C is the Celsius temperature.
If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer?
Our input is 77.
C = (5/9)*(77 - 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person's shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.
Answers
The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.
Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.
Weekly salary = Hourly pay rate * Number of hours worked
Weekly salary = $12/hour * 20 hours
Weekly salary = $240
So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.
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What is the area of this parallelogram?
Answers
Answer:
30.6 if im wrong someone correct me in comments and explain why
Step-by-step explanation:
I multiplied 2.3 by 4.5 and got 10.35 then divided it by 2 and got 5.175 and multiplied it by 2 and got 10.35 then I multiplied 4.5 by 4.5 and got 20.25 and added it to 10.35 and got 30.6
Easier way just add the two lengths and multiply it by height
x/4 - 1/2 (6-x)=7x+3 (6-2x)-1
Answers
Hope this helps! Have a great day! :)
does anyone know where y=x-8 is on a graph lol
Answers
Please help me to answer the question
Answers
The range of the function for one day of work is 75 ≤ y ≤ 425. So, correct option is B.
Describe Function?In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.
Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.
The linear function that models the daily cost of hiring an electrician can be written as:
y = 50x + 75
where x is the number of hours worked by the electrician and y is the cost in dollars.
Since the electrician works a maximum of 7 hours per day, the domain of the function is 0 ≤ x ≤ 7.
To find the range of the function, we can substitute the maximum and minimum values of x into the function and see what values of y we get:
When x = 0 (no hours worked), y = 50(0) + 75 = 75.
When x = 7 (maximum hours worked), y = 50(7) + 75 = 425.
Therefore, the range of the function for one day of work is:
75 ≤ y ≤ 425
So the answer is (B) 75 ≤ y ≤ 425.
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What's the solution to the following linear system?
y = 4x + 1
y = 4x
Question 4 options:
(−2, 3)
(4, 0)
Infinitely many solutions
No solution
Answers
Answer:
No solution
Step-by-step explanation:
4x = 4x + 1
0 unequal to 1
Answer: D. No solution
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A cylinder has a height of 12 inches. A similar cylinder has a height of 15 inches. What is the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder?
Answers
The ratio is 15+\(r_2\) : \(12+r_1\).
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here surface area of the cylinder = \(2\pi rh+2\pi r^2\) square unit
=> A = \(2\pi r(h+r)\) square unit.
Now Height = 12 in , radius = r1 then,
=> \(A_1 = 2\pi r_1(12+r_1)\) -----> 1
Now Height = 15 in , radius = r2 then,
=>\(A_2=2\pi r_2(15+r_2)\)-------> 2
Now the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder then,
=>\(2\pi r_2(15+r_2) : 2\pi r_1(12+r_1)\)
=>\(15+r_2:12+r_1\)
Hence the ratio is \(15+r_2:12+r_1\).
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Answer:
25:16
Step-by-step explanation:
I took the
Please awnser asap I will brainlist
Answers
Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.
How many tickets of each kind has been sold?Let's solve the problem step by step.
Let:
x = number of $10 tickets sold
y = number of $20 tickets sold
z = number of $30 tickets sold
From the given information, we can form the following equations:
Equation 1: x + y + z = 3318 (Total number of tickets sold)
Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)
Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)
We can use these three equations to solve for the values of x, y, and z.
First, let's substitute Equation 2 into Equation 1:
x + (x + 109) + z = 3318
2x + 109 + z = 3318
2x + z = 3209 (Equation 4)
Now, let's substitute the value of y from Equation 2 into Equation 3:
10x + 20(x + 109) + 30z = 61760
10x + 20x + 2180 + 30z = 61760
30x + 30z = 59580
x + z = 1986 (Equation 5)
We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.
Multiplying Equation 4 by 30, and Equation 5 by 2, we get:
60x + 30z = 96270 (Equation 6)
2x + 2z = 3972 (Equation 7)
Now, subtract Equation 7 from Equation 6:
(60x + 30z) - (2x + 2z) = 96270 - 3972
58x + 28z = 92298
Simplifying, we have:
29x + 14z = 46149 (Equation 8)
Now, we can solve Equations 5 and 8 simultaneously:
x + z = 1986 (Equation 5)
29x + 14z = 46149 (Equation 8)
Multiplying Equation 5 by 14, and Equation 8 by 1, we get:
14x + 14z = 27804 (Equation 9)
29x + 14z = 46149 (Equation 8)
Now, subtract Equation 9 from Equation 8:
(29x + 14z) - (14x + 14z) = 46149 - 27804
15x = 18345
Divide both sides of the equation by 15:
x = 18345 / 15
x = 1223
Substituting the value of x into Equation 5, we can find z:
1223 + z = 1986
z = 1986 - 1223
z = 763
Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:
1223 + y + 763 = 3318
y + 1986 = 3318
y = 3318 - 1986
y = 1332
Therefore, the solution to the problem is:
x = 1223 (number of $10 tickets sold)
y = 1332 (number of $20 tickets sold)
z = 763 (number of $30 tickets sold)
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The line plot shows the distance Lena walks each day for 10days. Each X represents Iday
Distances Walked
How many miles does Lena walk in 10days?
OA 23 miles
OB 11 miles
OC. 10 miles
OD. 19 miles
XX
X X
X.
Xx
X
X X
X
X
1 1 1 1 2 2 2 2 3
Distance (miles
Answers
Answer: Lena walks 63 miles in 10 days.
Step-by-step explanation:
To find out how many miles Lena walks in 10 days, you need to add up all the distances she walks each day.
From the information provided, it seems that the distances walked each day are:
23 miles, 11 miles, 10 miles, 19 miles and the remaining days is not given.
So, to find the total miles Lena walks in 10 days, you would add up the distances walked each day:
23 + 11 + 10 + 19 = 63 miles
So, Lena walks 63 miles in 10 days.
The total miles in 10 days will bed 14 miles. The closest option is OD, which is 19 miles.
How to calculate the distance covered?To find the total distance Lena walks in 10 days, we need to add up all the distances on the line plot:
Starting from day 1, we can count the distances and add them up:
On day 1, Lena walks 1 mile
On day 2, Lena walks 2 miles
On day 3, Lena walks 1 mile
On day 4, Lena walks 1 mile
On day 5, Lena walks 2 miles
On day 6, Lena walks 1 mile
On day 7, Lena walks 2 miles
On day 8, Lena walks 1 mile
On day 9, Lena walks 1 mile
On day 10, Lena walks 2 miles
Adding up all these distances, we get:
1 + 2 + 1 + 1 + 2 + 1 + 2 + 1 + 1 + 2 = 14
Therefore, Lena walks a total of 14 miles in 10 days.
Thus, the closest option is OD, which is 19 miles.
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please help i’m struggling
Answers
The vertices of the image of triangle ABC under the transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 are A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).
What is transformation?Transformation in maths is the process of changing the position, size, orientation or shape of a figure or shape. It involves various techniques such as translation, rotation, reflection and scaling.
The transformation (x, y)-- (x-3,y+1) followed by a dilation centered at the origin with scale factor 2 is a combination of a translation and a dilation. A translation is a transformation that moves the shape without changing its size or orientation. In this case, the translation moves the triangle 3 units to the left and 1 unit up. A dilation is a transformation that enlarges or reduces a shape. In this case, the dilation uses a scale factor of 2, so the triangle will be twice as big as it was before.
The vertices of the original triangle ABC are (A(x1,y1), B(x2,y2), C(x3,y3)). After the translation, the vertices will be (A(x1-3,y1+1), B(x2-3,y2+1), C(x3-3,y3+1)). After the dilation, the vertices will be (A(2(x1-3),2(y1+1)), B(2(x2-3),2(y2+1)), C(2(x3-3),2(y3+1)).
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