Answers
The equation of the line passing through A and B is y = (4/5)x - (2/5).
What is the line example's equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.
The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:
y - y1 = m(x - x1) (x - x1)
where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.
To calculate the slope, we can use points A (3, 2) and B (8, 6).
m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5
So the equation for the line connecting A and B is:
y - 2 = (4/5)(x - 3) (x - 3)
This equation can be simplified by multiplying both sides by 5:
5y - 10 = 4x - 12
Then we can rearrange it to form the slope-intercept equation, y = mx + b:
5y = 4x - 2
y = (4/5)x - (2/5)
As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).
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Related Questions
if y is given and you need to find third derivative of y (given as y'''), what are the steps: explain what one needs to do and say it in your words.
Answers
The steps for finding out the third derivative of y (given as y''') are explained and given below.
To find the third derivative of y (y'''), you would need to differentiate the function y three times with respect to the independent variable. Here are the steps:
Start by differentiating y once to get the first derivative, y'.
Differentiate y' again to get the second derivative, y''.
Finally, differentiate y'' to get the third derivative, y'''.
You can use the chain rule, product rule, quotient rule, and other differentiation rules as needed to find each derivative.
Here's an example of finding the third derivative of y for the function y = x^4 + 2x^3 - 5x:
y' = 4x^3 + 6x^2 - 5
y'' = 12x^2 + 12x
y''' = 24x + 12
So the third derivative of y is y''' = 24x + 12.
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a system of equations is shown below.
y=3x+5
x + y=-7
Answers
(x, y) = (-3, -4).
Step by step explanation:
To solve the system of equations:
y = 3x + 5 ... (1)
x + y = -7 ... (2)
We can use the substitution method or the elimination method. Here's how to use the substitution method:
From equation (2), we can solve for y in terms of x:
y = -x - 7
We can then substitute this expression for y in equation (1):
x - 7 = 3x + 5
Simplifying this equation, we get:
4x = -12
Dividing both sides by 4, we get:
x = -3
Substituting this value of x in equation (2), we can solve for y:
-3 + y = -7
y = -4
Therefore, the solution to the system of equations is x = -3 and y = -4. We can check that this is the correct solution by verifying that both equations are satisfied when x = -3 and y = -4:
y = 3x + 5 --> -4 = 3(-3) + 5 --> -4 = -4 (true)
x + y = -7 --> (-3) + (-4) = -7 --> -7 = -7 (true)
Therefore, the solution is (x, y) = (-3, -4).
A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors have a mean of $ 170 and a standard deviation of $ 55.
2. You randomly selected 9 LCD compute monitors. What is the probability that their mean cost is less than $ 180? Assume here that the prices are normally distributed
3. You randomly selected 36 LCD compute monitors. What is the probability that their mean cost is less than $ 180?
Answers
The probability that the mean cost of 9 LCD computer monitors is less than $180 is 0.8186 or 81.86% and the probability that the mean cost of 36 LCD computer monitors is less than $180 is 0.9999 or 99.99%.
What is the Central Limit Theorem (CLT)?
The Central Limit Theorem (CLT) is a statistical concept that states that the sample mean of a large number of independent and identically distributed (iid) random variables will be approximately normally distributed, regardless of the underlying distribution of the individual random variables.The significance of the Central Limit Theorem is that it allows us to make inferences about the population mean based on a sample mean, even if the population is not normally distributed. This is because the distribution of the sample mean becomes approximately normal as the sample size increases.
Finding the given probabilities:
To find the probability that the mean cost of 9 LCD computer monitors is less than $180, we can use the formula for the standard error of the mean:
[tex]SE = \sigma / \sqrt{n}[/tex]
where SE is the standard error of the mean, [tex]\sigma[/tex] is the population standard deviation, and n is the sample size. Plugging in the given values, we get:
[tex]SE = 55 / \sqrt(9) = 18.33[/tex]
Next, we can calculate the z-score corresponding to a sample mean of $180:
[tex]z = (180 - 170) / 18.33 = 0.546[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 0.546, which is 0.7079. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 9 LCD computer monitors is less than $180 is:
[tex]P(z < 0.546) = 0.7079[/tex]
Rounding to four decimal places, we get 0.8186 or 81.86%.
To find the probability that the mean cost of 36 LCD computer monitors is less than $180, we can use the same formula for the standard error of the mean:
[tex]SE = \sigma / \sqrt{n}[/tex]
Plugging in the given values, we get:
[tex]SE = 55 / \sqrt{36} = 9.17[/tex]
Next, we can calculate the z-score corresponding to a sample mean of $180:
[tex]z = (180 - 170) / 9.17 = 1.090[/tex]
Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 1.090, which is 0.8621. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 36 LCD computer monitors is less than $180 is:
[tex]P(z < 1.090) = 0.8621[/tex]
Rounding to four decimal places, we get 0.9999 or 99.99%.
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Please help! Need answers as soon as possible!
Answers
1. Time taken to fill one community pool is 2hours 24 minutes.
2. Time taken to audit 30 files is 4 hours 41 minutes.
3. The time taken to erect is 54/7 hours or 7 hours 43 minutes
Define the time and work?Time and work is a branch of mathematics that deals with the calculation of the amount of time required to complete a job or task by a worker or a group of workers working at a certain rate.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool; [tex]\frac{x}{6} + \frac{x}{4} = 1[/tex]
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
[tex]\frac{12x}{5} + \frac{16x}{4} = 1[/tex]
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
[tex]\frac{100x}{8} + \frac{200x}{12} = 1[/tex]
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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1. Time taken to fill one community pool is 2hours 24 minutes. 2. Time taken to audit 30 files is 4 hours 41 minutes. and 3. The time taken to erect is 54/7 hours or 7 hours 43 minutes.
Define the audit?An audit is an independent review of financial statements and related documents in order to confirm their accuracy and compliance with relevant regulations.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool;
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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If the gradient of the equation 2x-ay+2=0 is 1. Then find the value of a.
Answers
Step-by-step explanation:
2x + ay + 2 = 0
the gradient or slope of the line is the factor m of x in the form
y = mx + b
so let's transform the given equation into that form :
ay = -2x - 2
y = (-2/a)x - 2/a
we know that m = 1.
so,
-2/a = 1
-2 = a
Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using
limits.
Y=(1/6) ^-x
Answers
Answer:
The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.
To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.
As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.
As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.
Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.
of the following people, who would be included in the survey conducted by the bureau of labor statistics?
Answers
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
What are the coordinates of the point on the directed line segment from (-6, 6) to
(2, -10) that partitions the segment into a ratio of 1 to 3?
Answers
The coordinates of the point we are looking for are (2, -9).
What are the coordinates of the point ?
The origin is the point at which all lines in a coordinate system intersect. When x and y are both equal to zero, the axes intersect. The origin's coordinates are (0, 0).
To find the coordinates of the point that partitions the line segment from (-6, 6) to (2, -10) into a ratio of 1 to 3, we can use the following formula:
(x, y) = ((32 - 1(-6))/4, (3*(-10) - 1*6)/4)
Here, the ratio of 1 to 3 corresponds to the fact that we are partitioning the line segment into 4 equal parts, with the point we want to find being at the end of the first part (i.e., 1/4 of the way from (-6, 6) to (2, -10)).
Plugging in the values, we get:
(x, y) = ((32 + 6)/4, (3(-10) - 6)/4)
= (2, -9)
Therefore, the coordinates of the point we are looking for are (2, -9).
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Consider the function f (x) = -2/3x + 5.
What is f(-1/2)?
Enter your answer, as a simplified fraction, in the box.
f(-1/2) =
Answers
Answer: f(-1/2) = 16/3
Step-by-step explanation:
Substituting -1/2 for x in the given function:
f(-1/2) = (-2/3)(-1/2) + 5
f(-1/2) = 1/3 + 5
f(-1/2) = 16/3
Therefore, f(-1/2) = 16/3.
FILL IN THE BLANK Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look ______ than it would if it were outside the cloud.
Answers
Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.
Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.
When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.
This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.
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Suppose that the random variable X has the continuous uniform distribution | 1,0
Answers
For the random variable X, the mean of "X-3" is -5/2 and variance of "X-3" is 1/12.
We have to find the mean and variance of the quantity "X-3" , for the random variable X;
⇒ Let y = x-3,
So, Mean of y = E(y),
⇒ E(y) = E(x-3) = E(x) - 3,
⇒ E(x) = [tex]\int\limits^1_0 {x}f(x) \, dx[/tex] = [tex]\int\limits^1_0 {x.1} \, dx[/tex];
⇒ E(x0 = [x²/2]¹₀ = 1/2.
So, E(y) = (1/2) - 3 = -5/2.
⇒ Variance of y is = Var(x-3)
⇒ Variance of y = Var(x) - 0 ...because Var(3) = 0 as the variance of constant is 0.
⇒ We know that, Var(x) = E(x²) - (E(x))²;
⇒ E(x²) = [tex]\int\limits^1_0 {x^{2} f(x)} \, dx[/tex] = [tex]\int\limits^1_0 {x^{2} .1} \, dx[/tex] = [x³/3]¹₀ = 1/3,
So, Var(x) = (1/3) - (1/2)²
⇒ Var(x) = 1/3 - 1/4 = 1/12.
Therefore, the required Mean is -5/2 and the variance is 1/12.
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The given question is incomplete, the complete question is
Suppose that the random variable X has the continuous uniform distribution,
f(x) = {1, 0 ≤ x ≤ 1
{0, otherwise
Suppose that a random sample of n=13 observations is selected from this distribution.
Find the mean and variance of the quantity x-3.
GIven the functions f(x)-x^2+4x and g(x)=x-4 describe of show Bethany how she could find where f(x)=g(x) using a system of equations and name the values for x.
Answers
Answer:
A system of equations is when two equations equal each other. In this case, f(x) and g(x) must equal each other.
f(x) - g(x) = 0
x^2 - x + 4 - (x - 4) = 0
x^2 - 2x - 4 = 0
Using the Quadratic Formula:
x = (2 ± √20)/2
Therefore, the values for x are x = 2 and x = -3.
A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answers
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
Team A scored twice as many points as Team B. If the total number of points scored by both teams was 12, find the number of points scored by each team.
Answers
Answer:
Step-by-step explanation:
Let x be the number of points scored by Team B.
Then, Team A scored twice as many points, or 2x.
The total number of points scored by both teams is 12, so we can set up the equation:
x + 2x = 12
Combining like terms, we get:
3x = 12
Dividing both sides by 3, we get:
x = 4
So Team B scored 4 points, and Team A scored twice as many, or 8 points.
FILL IN THE BLANK.When the group leader uses the skill of _______ he/she is easing the group out of emotional interaction and into cognitive reflection
Answers
When the group leader uses the skill of reframing, he/she is easing the group out of emotional interaction and into cognitive reflection.
Reframing is a technique that involves taking a situation or problem and looking at it from a different perspective. In the context of group dynamics, the group leader can use reframing to help shift the focus of the group from an emotional or reactive response to a more reflective and analytical one.
For example, if a group is discussing a contentious issue and emotions are running high, the group leader might use reframing to help the group reframe the issue in a different way. This could involve asking the group to consider the issue from a different angle, or to think about it in a broader context.
The skill of reframing can be particularly useful in situations where the group is struggling to make progress or where emotions are preventing productive discussion. By using reframing, the group leader can help the group to reorient their thinking and focus on finding solutions rather than getting bogged down in emotional responses.
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Sixth grade >
E.12 GCF and LCM: word problems 288
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Learn with an example
pumpkin seeds
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Franklin wishes to plant pumpkins and sunflowers, so this morning he bought packs of seeds
at a local gardening shop. Pumpkin seeds were sold in packages of 4 seeds, while sunflower
seeds were sold in packs of 8. If Franklin bought the same number of each type of seed, what
is the smallest number of pampkin seeds he must have bought?
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Answers
Therefore, the answer is that Franklin must have bought at least 4 packs of pumpkin seeds to have an equal number of pumpkin and sunflower seeds.
What do you mean by LCM?LCM stands for Least Common Multiple. It's the lowest positive number that's a multiple of two or further given figures. In other words, it's the lowest number that all the given figures divide into unevenly.For illustration, the LCM of 2 and 3 is 6, because 6 is the lowest number that's a multiple of both 2 and 3. Another illustration, the LCM of 4, 6, and 8 is 24, because 24 is the lowest number that's a multiple of all three of those figures.LCM is a useful conception in calculation, especially when dealing with fragments, because it helps us find a common denominatorGiven by the question.
Sure! Then is an explanation of how to break this problem
First, we need to find the least common multiple( LCM) of 4 and 8, because that will tell us the lowest number of seeds that Franklin could have bought. To find the LCM, we can list the multiples of each number until we find one that they've in common
Multiples of 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 8 8, 16, 24, 32, 40, 48, 56, 64.
The first multiple that appears in both lists is 8, so the LCM of 4 and 8 is 8.
Now we know that Franklin bought the same number of pumpkin seeds and sunflower seeds, and that number is a multiple of 8. So, we just need to find the lowest multiple of 8 that's also a multiple of 4. That is 8 itself, because it's formerly a multiple of 4.
So, Franklin must have bought at least 4 pumpkin seed packs, since each pack contains 4 seeds. Any other multiple of 8 that's also a multiple of 4 would also work, but 8 is the lowest similar number.
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Write a quadratic inequality represented by the graph.
Answers
Using the concept of parabola, the quadratic inequality represented by the graph can be written as:
y = x² -2x +2.
Define parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.
The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.
The general equation for a parabola is given as:
y = a(x-h) ² + k
Now here we have:
(x,y) = (2,5)
(h,k) = (1,1)
Putting these values in the equation,
5 = a (2-1) ² + 1
a = 5-1
=4
Substituting the values:
y = (x-1) + 1
y = x² -2x +2
Therefore, the quadratic inequality can be written as: y = x² -2x +2.
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What is the line's slope?
Answers
Answer: y=3x+0
Step-by-step explanation: rise (y) over run (x) would be 3/1, which is 3. The line passes through the origin (0,0) so its 0.
find average speed that was traveled from city a to city p if trip took a half an hour to travel 23 miles
Answers
Step-by-step explanation:
Speed = distance / time
you are given distance = 23 miles and time = .5 hr
distance / time = 23 miles / .5 hr = 46 mph
The absolute value function, shifted to the left 2 units.
Answers
This is the absolute value function shifted to the left 2 units:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
What is function?In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.
Here,
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
To shift the function to the left 2 units, we can replace x with (x+2):
| x+2 | = {
x+2 if x+2 >= 0,
-(x+2) if x+2 < 0
}
Simplifying further, we get:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
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Complete question:
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
Find the function when shifted to the left 2 units.
Suppose you are trying to estimate the average age of the entire CSU student population. You collect a sample of size n-163, and from your data you calculate x =20.1 s 1.8 round your answers to 3 decimal places) 1. The standard error of the mean for this data set is: 2. The approximate 95% margin of error is (Use the approximation method from the notes, in which the critical value is approximately 2.) 3. The approximate 95% CI for lage is
Answers
a) The standard error of mean for this data set is approximately 0.141.
b) The approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.
a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:
SEM = 1.8 / sqrt(163) ≈ 0.141
So the standard error of the mean is approximately 0.141.
b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:
MOE ≈ 2 * 0.141 ≈ 0.282
So the approximate 95% margin of error is approximately 0.282.
c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get
CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376
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PLease help me and answer the questions in the picture below you will make my day!
Answers
Answer:
b the solution is (3,5)
Step-by-step explanation:
look at the points where the lines intersect
Match the definition:HistogramBinDescriptive StaticsMeanMedianModeStandard deviationA. The scatter around a central pointB. is a measure of a data’s variabilityC. is a graph of the frequency distribution of a set of dataD. values calculated from a data set and used to describe some basic characteristics of the data setE. a group in a histogramF. the middle value of a sorted set of dataG. is the most commonly occurring value in a data set
Answers
The matches of Histogram, Bin, Descriptive Statistics, Mean, Median and Standard Deviation are C, E, D, A, F, G and B respectively.
The Match the definition are given.
Histogram - C). is a graph of the frequency distribution of a set of data
Bin - E). a group in a histogram
Descriptive Statistics - D). values calculated from a data set and used to describe some basic characteristics of the data set
Mean - A). The scatter around a central point
Median - F). the middle value of a sorted set of data
Mode - G). is the most commonly occurring value in a data set
Standard Deviation - B). is a measure of a data’s variability
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After y - 4x = 12 is put in slope-intercept form, what is the slope?
-4
-1/4
-3
4
Answers
Add 4x to both sides:
y=4x+12
The function is now in y=mx+b form. The slope is 4.
A random sample of 14
deer mice in a rich forest habitat gives an average body length of ¯=91.1
mm.
Answers
The standard deviation for the given mean length x is found to be: 2.138.
Explain about the standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, the standard deviation enters the picture; it gauges how variable a set of values is, or how dispersed they are from the average. The differential between each value and the group average serves as the basis for the standard deviation.
Given data:
mean μ = 86
standard deviation σ = 8
number of sample n = 14
average body length x = 91.1
The population standard deviation is divided by that of the square root of both the sample size to calculate the standard deviation of the sampled distribution of the sample mean.
So,
σₓ = σ / √n
σₓ = 8 / √14
σₓ = 2.138
Thus, the standard deviation for the given mean length x is found to be: 2.138.
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The complete question is-
Deer mice (Peromyscus manicul.atus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean 86 mm and standard deviation 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of x = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm.
What is the standard deviation of the mean length x?
The circle below has center O, and its radius is 6 yd. Given that m ZAOB-110°, find the area of the shaded region and the length of the arc AB.
Give exact answers in terms of x, and be sure to include the correct units in your answer.
Area of shaded region:
Length of AB:
Answers
The length of arc AB is 7pi/3 yards is the area of the shaded region and the length of the arc AB.
what is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.
To find the area of the shaded region and the length of arc AB, we need to first find the measure of angle ZAB. Let's call this angle x.
Since angle ZAOB measures 110 degrees and angle ZAB and angle BOA are vertical angles, we know that angle BOA also measures 110 degrees. Therefore, angle ZAB + angle BOA = 180 degrees.
So, we can write:
x + 110 = 180
Solving for x, we get:
x = 70
Now, we can use the formula for the area of a sector to find the area of the shaded region. The sector is defined by the central angle ZOB, which measures 360 - 110 - 70 = 180 degrees. So, we have:
Area of shaded region = (180/360) * pi * 6^2 = 18pi
Therefore, the area of the shaded region is 18pi square yards.
To find the length of arc AB, we can use the formula:
Length of arc AB = (x/360) * 2 * pi * 6
Plugging in x = 70, we get:
Length of arc AB = (70/360) * 2 * pi * 6 = 7pi/3
Therefore, the length of arc AB is 7pi/3 yards.
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Find the absolute maximum and minimum values of the function f(x,y) = x^2+y^2-2x
Answers
The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.
The given function is f(x,y)=x²+y²-2x
First find the partial derivative with respect to x and y
f'(x)=2x-2
f'(y)=2y
f'(x)=0=f'(y)
2x-2=0
x=1
and y=0
Now we will cheak maxima and minima at (1,0)
f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)
We know that
rt-s²≥0 and r positive then f is minimum and r negative maximum
r=2 , t=2 and s=0
rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)
f(1,0)=1-2=-1
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A brand new stock is called an initial public offering or IPO. Remember that in this model the period immediately after the stock is issued offers excess returns on the stock(ie it is selling for more than its actually worth). One such model for a class of internet IPOS predicts the percentage overvaluation of a stock as a function of time, as R(t)=2501^2/e^3t where R(t) is the overvaluation in percent and t is the time in months after issue. Use the information provided by the first derivative and second derivate, and asymptotes to prepare advice for clients as to when they should expect a signal to buy or sell (Inflection point), the exact time when they should buy or sell(max/min) and any false signals prior to an as- ymptote. Explain your reasoning. Make a rough sketch of the function.
Answers
The Function of maximum or minimum for t is infinity.
What is first and second subsidiary test?While the principal subordinate can let us know if the capability is expanding or diminishing, the subsequent subsidiary. tells us in the event that the primary subsidiary is expanding or diminishing. On the off chance that the subsequent subsidiary is positive, the first.
To analyze the function R(t) = 2501² / e(3t), we can take the first and second derivatives:
R'(t) = -7503 * 2501² / e(3t)
R''(t) = 22509 * 2501² / e(3t)
To find the inflection point, we can set R''(t) = 0 and solve for t:
22509 * 2501² / e(3t) = 0
t = ln(0) / -3 = undefined
Since there is no real solution to this equation, there is no inflection point for this function.
To find the maximum or minimum, we can set R'(t) = 0 and solve for t:
-7503 * 2501² / e(3t) = 0
t = infinity
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2 2.1 1.1 1.2 1.3 A contractor cofrected to supply water to the Altein ring-road has decided to investigate the fomial impact that the monthly instalents, salaries and the price of fuel bad to his business per month. The contractor will use ONE of his water tanken to conduct an investigation. The contractor was supplying water to the Altein village 5 km ring-road construction site where the road had to be paved using the paving bricks. The paving of the road has started in January 2022 and ran for 10 months. THE MERCEDES BENZ WATER TANKER Adapted from aquatransport.co.za The contractor is still paying for the truck (water tanker) and it is covered for insurance. Monthly Instalment of Truck: R22 301,67 Insurance: RB 500 Loan term: 60 months Write down the Loan term of the truck in years. Determine the monthly repayments that were made towards the water tanker including the insurance cover amount. The contractor had already made half of the monthly instalments towards the truck in June 2022. Determine the total amount of money that was owed to the financer excluding the insurance in June 2022. Give an explanation on the significance of including an insurance cover when a contractor purchases the water tanker. The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4,5 hours). The rate per hour was R92,50 and the rate of pay was doubled on Saturdays. Calculate the amount of money that the tanker driver receive per day during week days. sked in March (2) (2) (2)
Answers
Answer:
Loan term of the truck in years:
The loan term of the truck is 60 months. To convert this to years, we divide by 12 since there are 12 months in a year. Therefore, the loan term of the truck in years is:
60 months ÷ 12 months/year = 5 years
Monthly repayments including insurance:
The monthly instalment of the truck is R22,301.67 and the insurance cover is R500. Therefore, the total monthly repayment including insurance is:
R22,301.67 + R500 = R22,801.67
Total amount owed to the financer excluding insurance in June 2022:
Half of the monthly instalments have been made towards the truck in June 2022, which means that 5 months' worth of payments have been made. Therefore, the total amount owed to the financer excluding insurance in June 2022 is:
(R22,301.67 × 55) - R500 = R1,223,592.35
Significance of including insurance cover:
Including an insurance cover when purchasing the water tanker is important because it provides protection for the contractor against unforeseen events such as accidents, theft, or damage to the vehicle. In the event of an accident or theft, the insurance cover can help cover the costs of repairs or replacement of the vehicle, which can be a significant expense for the contractor. Additionally, having insurance can provide peace of mind for the contractor, knowing that they are covered in case of unexpected events.
Tanker driver's daily pay during weekdays:
The driver works for 5½ days per week and 9 hours per day on weekdays, which amounts to:
5.5 days/week × 9 hours/day = 49.5 hours/week
The rate per hour is R92.50, so the driver's pay per day during weekdays is:
49.5 hours/week × R92.50/hour ÷ 5 days/week = R909.75/day
The difference between a number and -17 is equal to the product of the number and 25
Answers
Answer:
Let's call the unknown number "x".
According to the problem:
x - (-17) = 25x
Simplifying:
x + 17 = 25x
Subtracting x from both sides:
17 = 24x
Dividing by 24:
x = 17/24
Therefore, the unknown number is 17/24.