In a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, 0.997 is the probability that at least one of them has been vaccinated.
To compute the probability that at least one of five people selected at random from a large population has been vaccinated if 71% of the population has been vaccinated.
We need to use the Complement Rule.
This rule tells us that the probability of event A not happening is equal to one minus the probability of event A happening.
P (A) + P (A') = 1
where P(A) is the probability of A happening and P(A') is the probability of A not happening.
We need to compute the probability that none of the five people selected at random have been vaccinated.
Then, we will use the Complement Rule to compute the probability that at least one of them has been vaccinated.
The probability that the first person selected has not been vaccinated is:
P(first person not vaccinated) = 1 - 0.71 = 0.29
The probability that the second person selected has not been vaccinated is:
P(second person not vaccinated) = 1 - 0.71 = 0.29
The probability that the third person selected has not been vaccinated is:
P(third person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fourth person selected has not been vaccinated is:
P(fourth person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fifth person selected has not been vaccinated is:
P(fifth person not vaccinated) = 1 - 0.71 = 0.29
We assume that the selections are made randomly and independently of one another.
Thus, we can multiply the probabilities to get the probability that none of the five people selected have been vaccinated:
P(none vaccinated) = 0.29 × 0.29 × 0.29 × 0.29 × 0.29 = 0.0028
We can use the Complement Rule to compute the probability that at least one of the five people selected has been vaccinated:
P(at least one vaccinated) = 1 - P(none vaccinated)P(at least one vaccinated)
= 1 - 0.0028P(at least one vaccinated)
= 0.9972
Thus, the probability that at least one of five people selected at random from a large population has been vaccinated is approximately 0.997 when rounded to three decimal places.
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Julian puts money into two investments on the same day. The first pays out £225 after every 4 years and the second pays out £350 after every 6 years. A) How many years must Julian wait before both of his investments pay out in the same year? b) Give one advantage of each of Julian's investments
Before both of Julian's investments make a profit in the same year, he must wait 12 years.
a) To find the year when both investments pay out in the same year, we need to find the least common multiple (LCM) of the two payout periods: 4 years and 6 years.
The prime factorization of 4 is 2², and the prime factorization of 6 is 2 x 3. The LCM of 4 and 6 is 2² x 3 = 12.
Therefore, Julian must wait 12 years before both of his investments pay out in the same year.
b) One advantage of the investment that pays out £225 after every 4 years is that it provides a steady and predictable income stream. Julian can expect to receive the same amount every 4 years, which can help him plan for future expenses.
One advantage of the investment that pays out £350 after every 6 years is that it offers a higher payout than the other investment. Julian can potentially earn more money from this investment, although it requires a longer waiting period for the payout. Overall, the two investments offer different advantages, and Julian may choose to invest in both to balance steady income with higher potential earnings.
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help please i dont get this
● < P=R " angles opp =sides"
●PQ =QR " Angles opposite = sides"
therefore PQR is an isosceles " 2 opp angles and sides are equal "
If a regular polygon had 360 side, what would each exterior angle measure? What would each interior angle measure?
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
what is angle ?In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.
given
Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:
360 edges / 360 degrees = one degree.
Each interior angle of a regular polygon with n sides can be determined using the following formula:
Inner angle is equal to (n-2) x 180 / n.
When we enter n = 360 into this algorithm, we obtain:
(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.
Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.
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Solve the given equation for z and right the correct answer 4z + 9 = 29
the radius of a circle is changing at .5 cm/sec. find the rate of change of the area when the radius is 4 cm.
The rate of change of the area of a circle when the radius is 4 cm is 4π cm2/sec.
This can be calculated using the formula for the area of a circle (A = πr2) and the chain rule for derivatives. The chain rule states that when the radius (r) changes, the area of a circle (A) is equal to 2πr times the rate of change of the radius (dr/dt).
Therefore, the rate of change of the area of a circle when the radius is 4 cm is equal to 2π(4 cm) × (0.5 cm/sec) = 4π cm2/sec.
Note that if the rate of change of the radius were different, the rate of change of the area would also be different. This formula can be used to calculate the rate of change of the area of a circle at any given radius, as long as the rate of change of the radius is known.
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g in a study, the sample is chosen by separating all cars by size, and selecting 10 of each size grouping what is the sampling method?
The sampling method used in the study where the sample is chosen by separating all cars by size, and selecting 10 of each size grouping is known as stratified random sampling.
Stratified random sampling is a method of sampling that involves dividing the population into smaller sub-groups known as strata. In this method, each stratum is composed of elements that have similar characteristics.
The strata could be based on demographic characteristics such as age, sex, education, and so on. Once the strata have been created, the next step is to select a sample from each of the strata to make up the final sample. The selection is done randomly, and the number of elements selected from each stratum is proportional to the size of the stratum. This ensures that the sample is representative of the entire population in terms of the different characteristics of the population.
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Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap. Name the independent and dependent variables.
Answer:Independent = Her practice time. Dependent= Her lap time.
Step-by-step explanation: The more she practices the faster she can swim.
a bag of elven counters
5 of the counters are white
a counter is taken out of the bag at random and not replaced
a second counter is taken out of the bag
calculate the probality that only one of the counters is white
Step-by-step explanation:
Probabilities
The question describes an event where two counters are taken out of a bag that originally contains 11 counters, 5 of which are white.
Let's call W the event of picking a white counter in any of the two extractions, and N when the counter is not white. The sample space of the random experience is Ω = {WW, W N, NW, N N}
We are required to compute the probability that only one of the counters is white. It means that the favorable options are A = {W N, NW}
Let's calculate both probabilities separately. At first, there are 11 counters, and 5 of them are white. Thus, the probability of picking a white counter is 5/11.
Once a white counter is out, there are only 4 of them and 10 counters in total. The probability to pick a non-white counter is now 6/10.
Thus, the option WN has the probability P(WN) = 5/11 x 6/10 = 30/110 = 3/11
Now for the second option NW. The initial probability to pick a non-white counter is 6/11.
The probability to pick a white counter is 5/10
Thus, the option NW has the probability P(WN) = 6/11 x 5/10 = 30/110 = 3/11
P(A) = 3/11 + 3/11 = 6/11.
SO THE ANSWER IS 6/11!!If this helped you. Could I have a brainliest by any chance? And tell me if I am wrong! :D Bye now! :D And you are welcome.
john conducts emissions inspections on cars. he finds that 6% of cars fail inspection. let the random variable x be the number of cars that john inspects until a car fails an inspection. assume independence. the random variable x is:
The random variable x in this case is a binomial random variable, representing the number of cars that need to be inspected until a car fails an inspection. A binomial random variable is defined as the number of successes, “s”, in “n” independent trials. In this case, “s” would be 1 (the single failure) and “n” would be the number of cars that John inspects until a car fails inspection.
The probability of success, “p”, in this case is 0.06 since 6% of cars fail inspection. The probability of failure is “q”, which would be 0.94 in this case (1 - 0.06). The mean, “μ”, of the random variable x is equal to n * p, or the total number of trials times the probability of success. In this case, the mean would be equal to n * 0.06, or 6%.
The variance, “σ2”, of the random variable x is equal to n * p * q, or the total number of trials times the probability of success times the probability of failure. In this case, the variance would be equal to n * 0.06 * 0.94, or 5.64%.
The binomial random variable x can be used to calculate the expected number of inspections it will take John until a car fails an inspection, as well as the probability of a car failing an inspection. By knowing the probability of success, the number of trials, and the probability of failure, we can calculate the mean, variance, and expected value of the binomial random variable x.
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i need help pleaseeeeee
The equation to represent the function is L(x) = 360 - 15w
What is an equation?Remember that an equation is a mathematical statement that shows that two mathematical expressions are equal, denoted by the equal to sign =
The given parameters that will help to solve the problem are given as follows
Amount = $360
Rate = $15 per week
The problem is to determine the function to represent the scenario
The amount (L) owed in w weeks is represented as:
Amount owed = Amount - Rate* weeks
We used negative because the amount reduces weekly.
So, we have:
L(w) = 360 - 15*w
L(x) = 360 - 15*w
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Doing missing work and I don’t remember how to do these
The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.
What is scale factor?Scale Factοr is used tο scale shapes in different dimensiοns. In geοmetry, we learn abοut different geοmetrical shapes which bοth in twο-dimensiοn and three-dimensiοn. The scale factοr is a measure fοr similar figures, whο lοοk the same but have different scales οr measures. Suppοse, twο circle lοοks similar but they cοuld have varying radii.
The scale factοr states the scale by which a figure is bigger οr smaller than the οriginal figure. It is pοssible tο draw the enlarged shape οr reduced shape οf any οriginal shape with the help οf scale factοr.
4. The scale factor is in the ratio of 2:5
x = QR ≅ VS
x ≅ 30
Now, we have
2/5 = x/30
x = 2/5 × 30
x = 12
Thus, The value of x is 12 when scale factor is 2:5.
5. As ΔABC ≅ ΔAVW
WA = x ≅ CA
x ≅ 28
And in the same way
y ≅ 12
Now, Scale factor is
CB/VW
= 16/10
= 8/5
= 8 : 5
Now,
8/5 = 28/x
x = 28 × 5/8
x = 28 × 5/8
x = 35/2
x = 17.5
And for y
8/5 = y/12
8/5 × 12= y
y = 8/5 × 12
y = 96/5
y = 19.2
Thus, The value of x in ΔPQR is 12 and value of x and y are 17.5 and 19.2 respectively, with the scale factor 8 : 5.
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johnny makes an initial deposit into a bank account that earns compound interest annually. what's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years? please help me and please be specific!! thank youuu
1. The initial deposit is $10,000 since John deposited this amount to open the savings account.
2. The common ratio can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt)
3. After 8 years, the amount will be $13,685.70 in the savings account.
How do we get how much money in account after 8 years?The formula which will be used to calculated the compound interest is A = P(1 + r/n)^(nt). For this problem, the interest is compounded annually, so n = 1.
The annual interest rate is 4%, or 0.04 as a decimal. Plugging these values into the formula, we get:
A = $10,000*(1 + 0.04/1)^(1*8)
A = $10,000*(1.04)^8
A = $10,000*1.36857
A = $13,685.70
Therefore, after 8 years, there will be $13,685.70 in the savings account.
Full question "John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded interest. What's the initial deposit? whats the common ratio? whats the interest rate? how much money is there after 8 years?"
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4
Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The numbe
of incorrect answers given by the students is shown below.
Incorrect Answers Number of Students
What is the relative frequency of students that missed 1 question on the quiz?
Answer: To find the relative frequency of students that missed 1 question on the quiz, we need to first determine the total number of students who missed 1 question. From the table, we see that 9 students missed 1 question.
The relative frequency of students that missed 1 question can be calculated as:
Relative frequency = (Number of students who missed 1 question) / (Total number of students)
Relative frequency = 9 / 25
Relative frequency = 0.36
Therefore, the relative frequency of students that missed 1 question on the quiz is 0.36 or 36%.
Step-by-step explanation:
in an experiment to determine whether or not a person is talking on a cell phone affects the number of driving errors they make, what is the independent variable?
The independent variable is whether or not a person is chatting on a cell phone in an experiment to ascertain whether or not this influences the number of driving errors they commit.
What is a variable?A variable is any aspect that can be changed or changed over time.
For example, in an experiment, a researcher can manipulate the independent variable (such as the amount of light that a plant receives) to see how it affects a dependent variable (like how much the plant grows).
What is an independent variable?An independent variable is a variable that stands on its own and is not affected by the other variables being measured. In the given situation, the independent variable is whether or not the person is talking on a cell phone.
The dependent variable is the variable that changes in response to the independent variable. In the given situation, the dependent variable is the number of driving errors they make.
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true or false (and state why): if a sample from a population is large, a histogram of the values in the sample will be approximately normal, even if the population is not normal.
By the central limit theorem, with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
The complete question is-
true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
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Hint
Use the Pythagorean Theorem to solve for the missing sides
Answer: Shape one: 5, Shape 2: 13
Step-by-step explanation:
shape one
12^2+x^2=13^2
shape two
5^2+12^2=x^2
Answer:
PLEASE MARK ME AS BRAINLLIEST
Step-by-step explanation:
p=12
h=13
b=?
p²+b²=h²
12²+b²=13²
144+b²=169
b²=169-144
= 25
b=root25
b=5m
b=5
p=12
h=?
p²+b²=h²
12²+5²=h²
144+25=h²
h²=169
h=root169
h=13
How many unique triangles are there in the regular hexagon?
Answer:
Step-by-step explanation: There are 6 equilateral triangles in a regular hexagon by connecting the opposite vertices of a regular hexagon.
Exact value of sec 5pi/6
By trigonometric formula, the trigonometric function sec (5π / 6) has the exact value - 2√3 / 3.
How to determine the exact value of a trigonometric function
In this problem we find the case of a trigonometric function, whose exact value can be found by means of trigonometric formula and tables of values:
sec θ = 1 / cos θ
sec (5π / 6) = 1 / cos (5π / 6)
sec (5π / 6) = - 1 / cos (π / 6)
sec (5π / 6) = 1 / (- √3 / 2)
sec (5π / 6) = - 2 / √3
sec (5π / 6) = - 2√3 / 3
The exact value of the trigonometric function sec (5π / 6) is equal to - 2√3 / 3.
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Figure ABCD is reflected across the x-axis.
What are the coordinates of A' , B' , C' , and D'
Answer: A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)
Step-by-step explanation:
We have been given a graph of a quadrilateral and we are asked to find the coordinates of our quadrilateral after reflecting it across the x-axis.We can see that coordinates of quadrilateral ABCD are:A (-1,4),B (-5,8),C (-5,4),D (-4,2).
Since we know that rule for reflecting an image across x-axis is . This means that y-coordinates of our given image will be negative.So after reflecting our given quadrilateral across x-axis, coordinates will be:
A'(-1,-4)B'(-5,-8)C'(-5,-4)D'(-4,-2)
4 cleaner can clean all the rooms in a hotel in 7 1/2 hours. How long will it take 6 cleaners working at the same rate to clean all the rooms in the hotel?
it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
If 4 cleaners can clean all the rooms in a hotel in 7 1/2 hours, we can start by using the concept of work rate. Work rate is a measure of how much work is completed in a certain amount of time. If we assume that the work rate of each cleaner is constant, we can set up a proportion to find how long it will take 6 cleaners to clean the same amount of rooms:
4 cleaners can clean all the rooms in 7 1/2 hours.
Therefore, 1 cleaner can clean all the rooms in (4 x 7 1/2) hours = 30 hours.
So, if 1 cleaner takes 30 hours to clean all the rooms, then 6 cleaners working at the same rate will take:
(time for 1 cleaner) / (number of cleaners) = (30 hours) / (6 cleaners) = 5 hours
Therefore, it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.
It is important to note that this assumes that the work rate of each cleaner is constant and that there are no factors that may affect the cleaning time, such as interruptions or changes in the number of rooms to be cleaned. Additionally, the optimal number of cleaners may vary depending on the size of the hotel and the specific cleaning needs.
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Write an equation for the function g whose graph is the graph f(t) = -100(1.05)^t translated to the right 5 units and up 50 units.
g(t) = -100 * [tex](1.05)^t[/tex] +[tex](1.05)^(-5)[/tex] 50 is equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated to the right 5 units and up 50 units.
Starting with the function f(t) = -100[tex](1.05)^t[/tex], to translate it 5 units to the right and 50 units up, we can replace t with (t - 5) to shift it to the right, and add 50 to the whole function to shift it up. This gives us:
g(t) = f(t - 5) + 50
g(t) = -100[tex](1.05)^(t - 5)[/tex]+ 50
Simplifying this equation, we can use the properties of exponents to rewrite [tex](1.05)^(t - 5)[/tex] as [tex](1.05)^t[/tex] * [tex](1.05)^(-5)[/tex]:
g(t) = -100[tex](1.05)^t[/tex] *[tex](1.05)^(-5)[/tex]+ 50
g(t) = -100[tex](1.05)^(-5)[/tex] * [tex](1.05)^t[/tex] + 50
So the equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated 5 units to the right and 50 units up is:
g(t) = -100[tex](1.05)^(-5)[/tex]* [tex](1.05)^t[/tex]+ 50
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Help please it’s urgent
The system of equation with the same solution with 2x + 2y = 16 3x - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, let's solve the system of equation as follows;
2x + 2y = 16
3x - y = 4
multiply equation(ii) by 2
2x + 2y = 16
6x - 2y = 8
add the equations
8x = 24
x = 24 / 8
x = 3
y = 3x - 4
y = 3(3) - 4
y = 9 - 4
y = 5
Therefore,
2x + 2y = 16
6x - 2y = 8
add the equation
8x = 24
x = 24 / 8
x = 3
Therefore,
2(3) + 2y = 16
6 + 2y = 16
2y = 16 - 6
2y = 10
y = 5
Therefore, the equation with the same solution is 2x + 2y = 16
6x - 2y = 8.
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The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate
The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.
The time Jasmine spends biking is indeed a function of the distance she bikes.
The formula to calculate the time Jasmine takes to bike a certain distance is equal to,
time = distance / speed __(1)
Here the speed is the rate at which Jasmine bikes = 18 miles per hour.
Let us consider 'd' be the distance representing the number of miles Jasmine bikes.
This implies,
The function that represents the time Jasmine spends biking in terms of the distance .
Function f(d) representing the time Jasmine spends biking for a distance of d miles
Substitute all the values in the formula (1) we get,
⇒ f(d) = d / 18
Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.
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The above question is incomplete , the complete question is:
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.
Write the function representing the time Jasmine spends biking in terms of the distance?
A 0.2-kilogram softball is thrown toward a catcher’s mitt. The ball is accelerating at a rate of 8 meters per second squared. With what force will the ball hit the catcher’s mitt?
A.7.8N
B.40N
C.1.6N
D.8.2N
please help asap look at the screen shot to help
The mean class size at Mountain View School is 4.4 and at Seaside School is 4.2.
The median class size is 5 for both schools.
The range for Mountain View School is 12 and for Seaside School is 8.
The IQR for Mountain View School is 6 and for Seaside School is 3.
How do we solve this?To find the measures of center, we can calculate the mean and median for both schools.
Mountain View School:
Mean = (2+1+0+5+8+6+9+8+2+0+1+0+6)/15
Mean = 4.4
Median = 5
Seaside School:
Mean = (0+1+2+5+6+8+8+7+6+5+5+4+4+3+1+0)/15
Mean = 4.2
Median = 5
Part B:
To find the measures of variability, we can calculate the range and interquartile range (IQR) for both schools.
Mountain View School:
Range = largest value - smallest value = 12 - 0
Range = 12
IQR = Q3 - Q1 = 8 - 2 = 6
Seaside School:
Range = largest value - smallest value = 8 - 0
Range = 8
IQR = Q3 - Q1 = 7 - 4 = 3
Part C:
If we are interested in a smaller class size, Seaside School would be the better choice. The median class size is the same at both schools, but Seaside School has a smaller mean, which suggests that on average, class sizes are smaller.
Additionally, the range and IQR are both smaller for Seaside School, indicating less variability in class size.
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consider the following table. what is the probability of red? red blue total yes 15 21 36 no 38 13 51 total 53 34 87 g
The probability of red is 0.1724, given the following table.
The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.
The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.
The probability of Red can be calculated using the formula;
P(Red) = (Frequency of Red) / (Total Frequency)
Using the values provided in the table
,P(Red) = 15/87P(Red) = 0.1724
Hence, the probability of red is 0.1724.
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It takes Nancy 12/3 mins to read 1 page in her social studies book. It took her 221/2 mins to complete her reading assignment. How long was the assignment let n represent the number of pages she has read
Step-by-step explanation:
well, we need to see how often 12/3 minutes (for one page) fits into 221/2 minutes (for all pages) :
n = 221/2 / 12/3 = (221×3) / (12×2) = 221 / (4×2) = 221/8
the book had n = 221/8 pages = 27.625 ≈ 27 pages.
as parts of a page do not make sense, we only count full pages.
What is the solution for the system of linear functions represented by y=3x-2 and y=-4x+5
A._ (-3,4)
B._ (-1,-5)
C._ (1,1)
D._ (4,-11)
Answer:
An easy way to finish this problem even if you don't know the correct mathematical approach would be to plug in each ordered pair into both equations and see whether they are true/false. You can even graph both lines and see where the intersect (the solution).
I got (-7,23), which appears to not be one of the available answer choices. Try using the graphing calculator in desmos.
PLEASE HELP, DUE TODAY,
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
The table that represents a linear function is table 2.
How to explain the linear functionA linear function is a function whose graph is a straight line, and the equation of such function has the form y = mx + b, where m is the slope of the line and b is the y-intercept. To determine which table represents a linear function, we can calculate the slope between any two points in the table, and see if the slope is the same for all pairs of points.
Table 1:
The slope between (0,-4) and (1,0) is (0 - (-4)) / (1 - 0) = 4/1 = 4.
The slope between (-1,2) and (0,-4) is (-4 - 2) / (0 - (-1)) = -6/1 = -6.
The slope between (1,0) and (2,2) is (2 - 0) / (2 - 1) = 2/1 = 2.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Table 3:
The slope between (-1, negative sixteen thirds) and (0,-5) is (-5 - (-16/3)) / (0 - (-1)) = -1/3.
The slope between (0,-5) and (2,-13/3) is (-13/3 - (-5)) / (2 - 0) = -8/3.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Table 4:
The slope between (-1,negative two thirds) and (0,-1) is (-1 - (-2/3)) / (0 - (-1)) = -1/3.
The slope between (0,-1) and (2,2/3) is (2/3 - (-1)) / (2 - 0) = 5/6.
The slopes are not the same for all pairs of points, so this table does not represent a linear function.
Therefore, the correct option is table 2.
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Find the surface area of the volume generated when the following curve revolves around the y-axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. (Round your answer to four decimal places.) y = x2 from x = 0 to x = 2 36.7
To find the surface area of the volume generated when the curve y = x^2 revolves around the y-axis from x = 0 to x = 2, we will use the surface area formula for revolution:
Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from x = 0 to x = 2.
First, find the derivative dy/dx:
y = x^2
dy/dx = 2x
Now, plug in the derivative and simplify the expression inside the integral:
sqrt(1 + (2x)^2) = sqrt(1 + 4x^2)
Now, set up the integral with the surface area formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + 4x^2)] dx from x = 0 to x = 2.
Next, we will approximate the integral using a calculator:
Approximate Integral ≈ 9.8433
Finally, multiply by 2 * pi:
Surface Area ≈ 2 * pi * 9.8433 ≈ 61.9362
So, the surface area of the volume generated when the curve revolves around the y-axis is approximately 61.9362 (rounded to four decimal places).