a. The probability that a visually impaired student gets less than 6.9 hours of sleep is approximately 0.1562.
b. The probability that a visually impaired student gets between 6.2 and 10.5 hours of sleep is approximately 0.7486.
c. 30% of visually impaired students get less than 7.84 hours of sleep on a typical day.
How to calculate probability of student who gets less than 6.9 hours of sleep?a. To find the probability that a visually impaired student gets less than 6.9 hours of sleep, we need to standardize this value using the z-score formula:
z = (X - μ) / σ
where X is the value we want to find the probability for (6.9 hours), μ is the population mean (8.95 hours), and σ is the population standard deviation (2.11 hours).
z = (6.9 - 8.95) / 2.11 = -1.02
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than -1.02 to be approximately 0.1562. Therefore, the probability that a visually impaired student gets less than 6.9 hours of sleep is approximately 0.1562.
How to calculate probability of student who gets between 6.2 and 10.5 hours of sleep?b. To find the probability that a visually impaired student gets between 6.2 and 10.5 hours of sleep, we need to standardize both values using the z-score formula:
z1 = (6.2 - 8.95) / 2.11 = -1.29
z2 = (10.5 - 8.95) / 2.11 = 0.73
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is between -1.29 and 0.73 to be approximately 0.7486. Therefore, the probability that a visually impaired student gets between 6.2 and 10.5 hours of sleep is approximately 0.7486.
How to number of hours of sleep on a typical day that 30% of student ?c. To find the number of hours of sleep on a typical day that 30% of visually impaired students get less than, we need to find the z-score that corresponds to the 30th percentile of a standard normal distribution. Using a standard normal distribution table or calculator, we can find this value to be approximately -0.52.
Now we can use the z-score formula to solve for X:
-0.52 = (X - 8.95) / 2.11
X = -0.52 * 2.11 + 8.95 = 7.84
Therefore, 30% of visually impaired students get less than 7.84 hours of sleep on a typical day.
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we will eventually see using the theory of taylor series that can be computed using an infinite series: which convergence test shows that the series does in fact converge?
A number of
convergence tests
can be used to examine a Taylor series' convergence, but the Ratio Test is one that is frequently employed. According to the
ratio test, the series converges absolutely if the limit of the
absolute value
of the ratio of the (n+1)th term to the nth term is smaller than 1. In mathematics, this is expressed as:
lim┬(n→∞)〖|a_(n+1)/a_n |<1〗
where a n is the
series' nth term. The series
diverges
if the limit is bigger than 1, and extra tests must be employed if the limit is equal to 1.
Although the
Ratio Test
is a frequently used test for
Taylor series
convergence, it is not always appropriate and other tests can be required based on the unique characteristics of the series.
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five balls are numbered through and placed in a bowl. josh will randomly choose a ball from the bowl, look at its number and then put it back into the bowl. then josh will again randomly choose a ball from the bowl and look at its number. what is the probability that the product of the two numbers will be even and greater than express your answer as a common fraction.
The probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.
What is probability?Probability is a measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event that will not occur, and 1 represents a certain event that will always occur.
According to the given information:
There are 5 balls numbered 1 through 5 in the bowl. The total number of possible outcomes, when Josh chooses a ball, is 5, as there are 5 balls in the bowl.
Now let's consider the probability of choosing a ball with an even number. There are 3 even numbers (2, 4, and 5) out of the 5 possible numbers, so the probability of choosing a ball with an even number is 3/5.
Next, let's consider the probability of choosing a ball with a number greater than 2. There are 3 numbers (3, 4, and 5) greater than 2 out of the 5 possible numbers, so the probability of choosing a ball with a number greater than 2 is also 3/5.
To find the probability that the product of the two chosen numbers will be even and greater than 2, we need to multiply the probabilities of choosing an even number and choosing a number greater than 2.
Probability of choosing an even number: 3/5
Probability of choosing a number greater than 2: 3/5
Multiplying these probabilities, we get:
(3/5) * (3/5) = 9/25
So, the probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.
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An analyst is interested in testing the hypothesis that stock betas are higher in a down market (when the market index returns are negative) than otherwise.
Write the regression equation you would employ to test the analyst’s hypothesis.
This supports the analyst's hypothesis that betas are higher in down markets.
What is the meaning of equations?In algebra, the definition of an equation, in its simplest form, is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the equation.
To test the hypothesis that stock betas are higher in bear markets, we use the following regression equation:
Ri = αi + βi(Rm) + εi
where,
Ri = return on ith stock
Rm = market return
αi = intercept (constant term) of the regression equation of the ith stock.
βi = slope of the market return of the ith stock (regression coefficient).
εi = error period of the ith stock
To test the hypothesis, we include an additional variable in the regression equation that describes the effect of the market return when it is negative. This variable would be a dummy variable that takes the value 1 if the market return is negative and 0 otherwise. Let's call this variable D. So the modified regression equation would be:
Ri = αi + βi(Rm) + γiD + εi
where,
γi = the excess regression coefficient of the ith stock that describes the effect of the market return when it is negative
The coefficient γi measures the difference between the beta value of a stock between a falling market and a non-falling market. If γi is significantly greater than 0, this supports the analyst's hypothesis that betas are higher in down markets.
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help please without guessing ?//
Answer:
D. y ≥ x² - 4x - 5
Step-by-step explanation:
We can observe two characteristics of this graphed inequality:
1. its shading is above it, therefore the inequality sign must be greater than
2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to
From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.
____________
Note:
We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:
[tex]y \ge (x-2)^2 - 9[/tex]
Answer:
The answer is y≥ x²-4x-5
Step-by-step explanation:
x=a,x=b
where a,b are roots of the equation
a= -1 b=5
x= -1,x=5
x+1=0,x-5=0
(x+1)(x-5)=0
x²-5x+x-5=0
x²-4x-5=0
the quality control manager at a computer manufacturing company believes that the mean life of a computer is 80 months, with a variance of 64 . if he is correct, what is the probability that the mean of a sample of 77 computers would be greater than 82.59 months? round your answer to four decimal places.
The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606
The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).
To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula
z = (x - μ) / (σ / √n)
where
x is the sample mean
μ is the population mean (believed to be 80 months)
σ is the population standard deviation (8 months)
n is the sample size (77)
Plugging in the values, we get
z = (82.59 - 80) / (8 / √77) ≈ 1.55
To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.
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Arun has 72 coins. He has 5-cent and 10-cent coins in the ratio 5: 3.
Arun said: I have just over
$5 in total.
Is Arun correct? Explain your answer. Show your working.
Arun is not correct - he has just under $5 in total, not just over.
How to determine how much Arun has in totalLet's start by finding out how many 5-cent and 10-cent coins Arun has.
Let the number of 5-cent coins be 5x and the number of 10-cent coins be 3x (since the coins are in the ratio 5:3).
Then the total value of the 5-cent coins is 5x0.05 = 0.25x dollars, and the total value of the 10-cent coins is 3x0.1 = 0.3x dollars.
So the total value of all the coins is 0.25x + 0.3x = 0.55x dollars.
Since Arun has 72 coins, we know that 5x + 3x = 72, or 8x = 72, or x = 9.
Therefore, Arun has 5x = 59 = 45 5-cent coins and 3x = 39 = 27 10-cent coins.
The total value of these coins is 450.05 + 270.1 = 2.25 + 2.7 = 4.95 dollars.
So Arun is not correct - he has just under $5 in total, not just over.
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write an integral that quantifies the change in the area of the surface of a cube when its side length quadruples from s unit to 4s units.
Answer:
Step-by-step explanation:
Let A be the area of the surface of the cube.
When the side length changes from s to 4s, the new area A' can be calculated as:
A' = 6(4s)^2 = 96s^2
The change in area is then:
ΔA = A' - A = 96s^2 - 6s^2 = 90s^2
To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:
∫(90s^2)ds from s to 4s
= [30s^3] from s to 4s
= 30(4s)^3 - 30s^3
= 1920s^3 - 30s^3
= 1890s^3
Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:
∫(90s^2)ds from s to 4s
= 1890s^3 from s to 4s
= 1890(4s)^3 - 1890s^3
= 477,840s^3 - 1890s^3
Eric's Ford Mustang and Susan's Toyota Prius are insured with the same insurance agent. They have 100/300/50 vehicle insurance coverage. The very week of the windstorm, Susan had an accident. She lost control of her car, hit a parked car, and damaged a storefront. The damage to the parked car was $4,300 and the damage to the store was $50,400. What amount will the insurance company pay for Susan's car accident?
Step-by-step explanation:
Given:
The damage to the parked car was
$4,300and the damage to the store
was
$50,400.
Objective:
The objective is to determine the
amount will the insurance company pay
for Susan's car accident.
Explanation:
Having a 100/300/50 insurance policy
means you have $100,000 in coverage
for bodily injury liability per person,
$300,000 for bodily injury liability per
accident, and $50,000 for property
damage liability.
The anmount insurance company
will pay $4,300 for car damage and
$50,000 for property damage.
So total amount that must be paid is
$50000+$4300=$54300
mark brainly
Graph Y = 1/2x - 4 on the coordinate plane
The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.
Describe Coordinate Plane?Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.
Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.
For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.
The graph is shown below when y=1.
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Graph attached below,
The coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].
Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]
Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]
Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]
Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]
Then coordinates of the plane is
x y
1 -3.5
2 -3
4 -2
6 -1.
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Determine if (-1, 4) is a solution to y < - 3x + 2. If so, graph the inequality.
Answer:
To determine if (-1, 4) is a solution to y < -3x + 2, we need to substitute x = -1 and y = 4 into the inequality and see if the inequality is true:
4 < -3(-1) + 2
4 < 3 + 2
4 < 5
Since 4 is not less than 5, the inequality is false when we substitute x = -1 and y = 4. Therefore, (-1, 4) is not a solution to y < -3x + 2.
To graph the inequality y < -3x + 2, we can first graph the line y = -3x + 2 (which has a y-intercept of 2 and a slope of -3) as a dashed line (since the inequality is "less than" and not "less than or equal to"). Then, we can shade the region below the line to represent all the points that satisfy the inequality.
Here is a graph of y < -3x + 2:
|
|
|
|
| /
| /
| /
| /
| /
-----+----------------
| | | |
-2 0 2 4
The dashed line represents the line y = -3x + 2, and the shaded region represents all the points that satisfy y < -3x + 2.
Write the equation of the line that passes through the point (0, 4) and is parallel to the line with equation y=5x+3
102, 107, 99, 102, 111, 95, 91
Mean
Mode
Median
Range
Answer:
mean: 101 (add all the numbers then divide by 7)
mode: 102 (the most frequent number in the set)
median: 102 (the number in the middle of the set)
range: 20 (the difference between the largest and smallest number)
Mean = 101
Mode = 102
Median = 102
Range = 20
MEAN: Add up all the numbers, then divide by how many numbers there are.
102 + 107 + 99 + 102 + 111 + 95 + 91 = 707
707 ÷ 7 = 101
MODE: Arrange all numbers in order from lowest to highest or highest to lowest and then count how many times each number appears in the set. The one that appears the most is the mode.
91,95,99,102,102,107,111
MEDIAN: Arrange the numbers from smallest to largest. If the amount of numbers is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers in the list.
91,95,99,102,102,107,111
RANGE: Subtract the lowest number from the highest number
111 - 91 = 20
Please fill in all of the blanks
Answer:
The perimeter of this trapezoid is
7 + 5 + 3 + 7 + 4 = 26 cm
rectangle, A = lw, 4 × 7 = 28 square cm
triangle, A = (1/2)bh, (1/2) × 3 × 4 =
6 square cm
(1/2)(4)(7 + 10) = (1/2)(4)(17) = 34 square cm = 28 square cm + 6 square cm
Alfred buys a car for £13960 which depreciates in value at a rate of 0.75% per year.
Work out how much Alfred's car will be worth in 12 years.
Answer:
£12063.57
Step-by-step explanation:
The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.
Given 4 dou of corn and 12 dou of sesame, the total cost is 72 coins. Given 10 dou of sesame and 5 dou of corn, the total cost is 75 coins. Tell: what is the cost of 1 dou of corn and 1 dou of sesame?
The cost of 1 dou of corn is 9 coins and the cost of 1 dou of sesame is 3 coins.
Let x be the cost of 1 dou of corn and y be the cost of 1 dou of sesame.
Using the first set of information, we can create the following equation
4x + 12y = 72
Simplifying this equation by dividing by 4, we get
x + 3y = 18
Using the second set of information, we can create another equation
5x + 10y = 75
Simplifying this equation by dividing by 5, we get
x + 2y = 15
Now we have two equations with two variables
x + 3y = 18
x + 2y = 15
Subtracting the second equation from the first, we get
y = 3 coins
Substituting this value of y back into either of the two equations, we get
x + 3(3) = 18
x + 9 = 18
x = 9 coins
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This past semester, a professor had a small business calculus section. The students in the class were William comma Mike comma Allison comma Kristin comma Jim comma Neta comma Pam comma and Jinita. Suppose the professor randomly selects two people to go to the board to work problems. What is the probability that Neta is the first person chosen to go to the board and Jinita is the second?
The probability that Neta is chosen first and Jinita is chosen second is:
1/56(or approximately 0.018.)
There are 8 students in class, so there are 8 choices for first person and 7 choices for second person.
Since we want to calculate probability that Neta is chosen first and Jinita is chosen second, we need to consider the number of ways in which these two students can be chosen in that order.
There is only one way for Neta to be chosen first and Jinita to be chosen second, so the total number of possible outcomes is:
8 x 7 = 56
Therefore, the probability that Neta is chosen first and Jinita is chosen second is: 1/56 or approximately 0.018.
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Solve for X, please write an explanation.
Step-by-step explanation:
2x+20 and 2x-4 are supplementary angles...they form a straight line and thus = 180 degrees when added together
2x+20 + 2x-4 = 180 simplify
4x + 16 = 180 subtract 16 from both sides
4x = 164 divide both sides by 4
x = 41 degrees
what minus 1 1/2 equals 3 3/4
Answer:
5 1/4
Step-by-step explanation:
The radius of a basketball is about 13 centimeters.
What is the volume of the basketball?
Answer:
The answer that you're looking for is approximately 9202.77 and in terms of π it is 2929.33π
Step-by-step explanation:
Using the equation [tex]\frac{4}{3}\pi r^{3}[/tex] you can replace r with 13 to get [tex]\frac{4}{3} \pi 13^{3}[/tex] you then multiply them all to get 9202.77 and divide by π to find the terms of pi which is 2929.33π.
I hope this was helpful!
in order to create two-dimensional geometry such as lines, arcs, and rectangles, what mode should solidworks be in?
To create two-dimensional geometry like lines, arcs, and rectangles in SolidWorks, you should be in the "Sketch" mode. This mode allows you to draw and edit 2D shapes, which can later be used to create 3D models using extrusion or other techniques.
In order to create two-dimensional geometry such as lines, arcs, and rectangles, SolidWorks should be in Sketch mode. This mode allows the user to create 2D sketches that can later be extruded or revolved into 3D objects. Sketch mode can be accessed by clicking on the Sketch icon in the Command Manager or by using the keyboard shortcut "S".
To create two-dimensional geometry like lines, arcs, and rectangles in SolidWorks, you should be in "Sketch" mode. This mode allows you to draw and edit 2D shapes, which can later be used to create 3D models using extrusion or other techniques.
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In order to create two-dimensional geometry such as lines, arcs, and rectangles in SolidWorks, the software should be in the Sketch Mode.
The Sketch mode is used to create 2D profiles that can be used to generate 3D models.
In Sketch mode, users can draw lines, arcs, rectangles, circles, and other shapes using tools such as the Line, Arc, Rectangle, and Circle commands.
Dimension and constrain their sketches to ensure that they are accurate and can be used to generate 3D geometry.
A sketch is complete, it can be used to create 3D geometry using features such as Extrude, Revolve, Sweep, and Loft.
These features allow users to generate complex 3D shapes using the 2D sketches as a basis.
Overall, Sketch mode is a powerful tool in SolidWorks that allows users to create 2D profiles that can be used to generate 3D geometry.
It is an essential part of the software and is used extensively in the design and engineering industries.
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I don’t know what to write for the equation.
fraction wise, a whole is always simplified to 1, so
[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]
so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot, and we also know that 3/4 of that is 12, the guys who chose the bottle of water
[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]
Using the graph, determine the equation of the axis of symmetry.
Step-by-step explanation:
x = -4 ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)
What is the range of the function shown in the graph below
Step-by-step explanation:
'Range' is the 'y' values a graph can have....
this one goes from a high of -8 down through - inf
-8 <= y < -inf
(-inf, -8]
April is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her balloon payment at the end
of 7 years?
OA. $173,819.97
OB. $170,118.49
OC. $225,368.29
OD. $170,245.98
SUBMIT
The balloon payment at the end of 7 years would be $173,819.97, which is option A.
How to find the balloon payment at the end of 7 yearsA 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.
To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:
n = 23 * 12 = 276 (total number of payments)
r = 4.15% / 12 = 0.003458 (monthly interest rate)
P = (r * PV) / (1 - (1 + r)^(-n))
where
PV is the present value of the loan (the loan amount)n is the total number of paymentsr is the monthly interest ratePV = $197,000
P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)
Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.
Using the formula for the remaining balance of a loan after t payments:
B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)
Where
B is the remaining balancePV is the initial loan amount r is the monthly interest rateP is the monthly payment t is the number of payments madet = 84 (number of payments made)
B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)
B = $173,819.97
Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.
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A world cup soccer ball that costs $38.50 is on sale for 20%
How much money are you saving?
Answer: 7.7
Step-by-step explanation: is how much you save because when you intact 20% from 38.5 you get 30.8 and if you add 7.7 you get 38.5
Please please help me!!
see the attached item for more information
Answer:
Set your calculator to degree mode.
[tex] \tan(39) = \frac{12}{x} [/tex]
[tex]x \tan(39) = 12[/tex]
[tex]x = \frac{12}{ \tan(39) } = 14.818766[/tex]
So the area of this triangle is
(1/2)(14.818766)(12) = 88.91 (B)
in a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a halloween costume to the office at least once. what is the margin of error, using a 95% confidence level, for estimating the true population proportion of adult office workers who have worn a halloween costume to the office at least once?
The margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .
What is known by random variable?A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiment's outcomes.
What is meant by proportion?A proportion is an equation in which two ratios are set equal to each other.
The margin of error for estimating the true population proportion can be calculated using the formula:
Margin of Error = Critical Value * Standard Deviation
where the Critical Value is determined based on the desired confidence level and the Standard Deviation is an estimate of the variability of the population proportion.
Given that the sample size is large (n = 1200) and we are using a 95% confidence level, we can use the standard normal distribution (Z-distribution) for the Critical Value. The critical value for a 95% confidence level in a standard normal distribution is approximately 1.96.
The Standard Deviation can be estimated using the sample proportion, which is given as 32% or 0.32 in this case. The sample proportion is a point estimate of the population proportion.
Using these values, we can calculate the margin of error as follows:
Margin of Error = 1.96 * √( (0.32 * (1 - 0.32)) / 1200 )
= 1.96 * √( 0.2176 / 1200 )
= 1.96 * √( 0.00018133333 )
= 1.96 * 0.01345451543
= 0.02633 (rounded to 5 decimal places)
So, the margin of error for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once, using a 95% confidence level, is approximately 0.02633 .
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When x is 2, what is the value of the expression 124+3(8−x)12
12
4
+
3
(
8
−
x
)
12
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When x is 2, the value of the expression is 9.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.
Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.
Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.
When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:
12/4 + 3(8 - 2) - 12
= 3 + 3(6) - 12
= 3 + 18 - 12
= 9
Therefore, when x is 2, the value of the expression is 9.
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The complete question is :
When x is 2, what is the value of the expression 12/4+3(8−x)-12?
If you watch from ground level, a child riding on a merry-go-round will seem to be undergoing simple harmonic motion from side to side. Assume the merry-go-round is 10.6 feet across and the child completes 8 rotations in 120 seconds. Write a sine function that describes d, the child's apparent distance from the center of the merry-go-round, as a function of time t.
The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)
How to write a sine function that describes the child's apparent distance?To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.
Amplitude:
The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.
Period:
The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.
From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.
Phase shift:
The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).
In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.
With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:
d(t) = 5.3 sin(2π/15 * t)
where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.
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Answer:
r = 2
center: ( -7,0 )
Step-by-step explanation: