The parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3
To create a parametric function that models your location on the Ferris wheel at a given time, we need to come up with equations that describe your horizontal and vertical positions as functions of time.
Let's start with the horizontal position. Since the Ferris wheel rotates counter-clockwise, we know that your position on the wheel will increase as time goes on. We can express this as:
x(t) = 80cos(2πt/120)
Here, t represents time in seconds, and the factor of 2π/120 ensures that the function completes one full cycle (i.e. one trip around the wheel) in 120 seconds, or 2 minutes. The cosine function gives us a smooth, periodic curve that oscillates between -80 and 80, corresponding to your position on either side of the wheel's center.
Next, let's consider your vertical position. We know that you start at a height of 3 feet above the ground, and as the wheel rotates, your height will vary sinusoidally over time. We can express this as:
y(t) = 80sin(2πt/120) + 3
Here, the sine function gives us a smooth, periodic curve that oscillates between 77 and 83 feet (i.e. the radius of the wheel plus or minus 3 feet).
So, putting it all together, our parametric function for your location on the Ferris wheel at a given time t is:
(r(t), θ(t)) = (80cos(2πt/120), 80sin(2πt/120) + 3)
Here, r(t) and θ(t) represent your radial distance from the center of the wheel and the angle you've rotated from the starting position, respectively. This parametric function describes a smooth, periodic curve that traces out your path on the Ferris wheel as it rotates counter-clockwise.
Given the information, we know the Ferris wheel has a radius of 80 feet, the bottom is 3 feet above the ground, it rotates counter-clockwise, and has a period of 2 minutes.
To create a parametric function, we need two equations, one for the x-coordinate (horizontal) and one for the y-coordinate (vertical). Let's denote the time variable as t, measured in minutes.
1. X-coordinate (horizontal position):
Since the Ferris wheel rotates counter-clockwise, we can use the following equation for the x-coordinate:
x(t) = 80 * sin(2π * (t/2))
2. Y-coordinate (vertical position):
To account for the bottom of the Ferris wheel being 3 feet above the ground, we need to add 3 to the vertical equation:
y(t) = 80 * cos(2π * (t/2)) + 3
Now, we have the parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3
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Find the volume of the given cone. r=5ft, h=15 ft.
Answer:
392.69908169872 feet3
Step-by-step explanation:
1/3πr^2h
1/3π*5^2*15
125π
392.69908169872 feet3
Butterfly, publisher of children's books, has purchased blue star, another publisher of children's books. both companies' books are sold to the same retail stores and schools. their content is different because butterly produces children's literature, whereas blue star focuses on child-level nonfiction scientific and nature topics. What is probably true about this acquisition?
It is likely that Butterfly acquired Blue Star in order to expand their offerings into the nonfiction scientific and nature topics for children's books, as it was not a focus of their own publications.
This acquisition may allow Butterfly to reach new markets and appeal to a wider range of readers.
The acquisition of Blue Star by Butterfly, both publishers of children's books, likely aims to diversify their offerings and cater to a wider audience. While Butterfly produces children's literature, Blue Star focuses on child-level nonfiction scientific and nature topics. This acquisition allows both companies to expand their reach and provide a more comprehensive range of educational materials to retail stores and schools.
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Another glacier moved a bould that weighed 2 tons.
How many pounds did the boulder weigh?
Answer:
4,000 pounds
Step-by-step explanation:
One ton is equal to 2,000 pounds.
Therefore, a boulder that weighs 2 tons would weigh:
2 tons x 2,000 pounds/ton = 4,000 pounds
So the boulder weighed 4,000 pounds.
Where in the hierarchy does should “Circles” go?
Answer:
Answer with explanation:
→ A circle is a plane figure. It does not have straight sides,so it is not a polygon.
We can say that Circle is a Simple Closed Figure.
In other way, a Circle is a locus of all the points Such that Distance from a fixed point ,called Center is Same.And When you join all these points ,which is infinite in number you , will get a 2 -D Shape called Circle.
In real life, Bangle, Rotation of 3-4 Blade Ceiling Fan forms a Circular Shape.
→→Circle= Simple Closed Figure.
Step-by-step explanation:
Swiss is a built-in r data frame giving standardized fertility measure and socio-economic indicators for each of 47 french-speaking provinces of switzerland at about 1888.. we are interested in some descriptive statistics related to the agriculture column of swiss. we can access the data directly by using the assignment x <- swiss$agriculture. (in r use ?swiss for info on this dataset.) remember: x <- swiss$agriculture a. Calculate the sample median of x. b. Using the r quantile function, find the .34 quantile of x.(34th percentile) c. Calculate the interquartile range of x using r.
X is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.
a. To calculate the sample median of x, we can use the median function in R. So, the code would be:
median(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the sample median of x.
b. To find the .34 quantile of x, we can use the quantile function in R. The code would be:
quantile(x, 0.34)
where x is the variable that we have assigned the agriculture column of swiss to, and 0.34 represents the desired quantile. Running this code would give us the value of the .34 quantile of x.
c. To calculate the interquartile range of x, we can use the IQR function in R. The code would be:
IQR(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.
The "fertility", "Switzerland", and "x <- swiss $ agriculture" terms.
a. To calculate the sample median of x (the agriculture column in the Swiss dataset), use the following R command:
median_x <- median(swiss$agriculture)
b. To find the 34th percentile (0.34 quantile) of x using the R quantile function, use the following R command:
quantile_x <- quantile(swiss$agriculture, probs = 0.34)
c. To calculate the interquartile range of x (the agriculture column in the Swiss dataset) using R, use the following R commands:
Q1 <- quantile(swiss$agriculture, probs = 0.25)
Q3 <- quantile(swiss$agriculture, probs = 0.75)
IQR_x <- Q3 - Q1
This will give you the interquartile range (IQR) of the agriculture column in the Swiss dataset.
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. . Roulette: In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, 3, 4, .., 36. The odd-numbered slots are Red, and even-numbered slots are black. The numbers are green. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. What is the probability that the metal ball does not land on green? (leave the answer as a simplified fraction like 4/5)
The probability of the ball not landing on green and landing on an even, black slot is:
36/38 * 18/38 = 9/19
To find the probability that the metal ball does not land on green, we first need to determine the total number of non-green slots.
There are 38 slots in total, with 0 and 00 being green. This means there are 36 slots that are not green (18 red odd-numbered and 18 black even-numbered slots).
Now, we can calculate the probability of the metal ball not landing on the green by dividing the number of non-green slots (36) by the total number of slots (38).
Probability = (Number of non-green slots) / (Total number of slots)
Probability = 36/38
Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
Probability = (36/2) / (38/2)
Probability = 18/19
However, we need to take into account that the odd-numbered slots are red and the even-numbered slots are black. Since the question asks for the probability that the ball does not land on the green, we can focus on the even-numbered slots that are black. There are 18 even-numbered slots on the wheel, which means that the probability of the ball landing on an even, black slot is 18/38.
So, the probability that the metal ball does not land on the green is 18/19.
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Under what conditions is our critical point a node? When is this asymptotically stable? Unstable?
The nonlinear systems can exhibit more complicated behavior, and the stability of the critical point can depend on the specific nonlinearities present in the system.
What is the context of a linear autonomous system of differential equations in two dimensions?In the context of a linear autonomous system of differential equations in two dimensions, the critical point is a node if both eigenvalues have the same sign and are nonzero. Specifically, if both eigenvalues are positive, then the node is called a source, and if both eigenvalues are negative, then the node is called a sink.
Whether the node is asymptotically stable or unstable depends on the values of the eigenvalues. If both eigenvalues are negative, then the node is asymptotically stable, meaning that nearby solutions converge to the node as time goes to infinity. If both eigenvalues are positive, then the node is unstable, meaning that nearby solutions move away from the node as time goes to infinity.
If one eigenvalue is positive and the other is negative, then the critical point is a saddle, and the stability of the critical point depends on the direction of the solutions in the vicinity of the saddle.
It is important to note that these conditions for a critical point to be a node and its stability only apply to linear systems. Nonlinear systems can exhibit more complicated behavior, and the stability of the critical point can depend on the specific nonlinearities present in the system.
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[tex]120 divided by 1800[/tex]120 divided by 1800
The requried, 120 divided by 1800 is equal to 0.06666667 or approximately 0.067 when rounded to three decimal places.
To divide 120 by 1800, we can perform the following calculation:
120 ÷ 1800 = 0.06666667
Therefore, 120 divided by 1800 is equal to 0.06666667 or approximately 0.067 when rounded to three decimal places.
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Q5.
WONLY
On the grid draw a triangle with the same area as the shaded rectangle.
Use a ruler.
An example of a triangle with the same area as the shaded rectangle has been attached in the folder below.
What is the area of the rectangle to help us determine the area of the triangle?Looking at the shaded diagram, we can tell that the rectangle has a length of 4cm and a width of 2 cm. The area of a rectangle can be calculated by the formula A = L x W, This amounts to 8 cm.
The area of a triangle can be calculated by multiplying the base by the height and then dividing by two. The formula is: A = 1/2 x base x height.
However, since we know the area of the rectangle is 8cm, we can decide that the height is 4cm and base 4 cm. it becomes 4 x 4 x 1/2 = 8
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Given two points A -3,6 and B -2,9 calculate the slope step by step
Answer:
Step-by-step explanation:
To calculate the slope between two points A (-3, 6) and B (-2, 9), we can use the formula:
slope = (change in y) / (change in x)
where "change in y" is the difference between the y-coordinates of the two points, and "change in x" is the difference between the x-coordinates of the two points.
So, let's plug in the values of the two points into the formula:
slope = (9 - 6) / (-2 - (-3))
slope = 3 / 1
slope = 3
Therefore, the slope between points A (-3, 6) and B (-2, 9) is 3.
[tex]A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-3)}}} \implies \cfrac{3}{-2 +3} \implies \cfrac{ 3 }{ 1 } \implies \text{\LARGE 3}[/tex]
pls help will Mark. brainiest
92 4/5% of ___ = 281.184
Answer:
303
Step-by-step explanation:
92 4/5% = 92.8%
let's call x is the value of 100%
then 92.8% of x = 281.184
or 0.928x = 281.184
x = 281.184/0.928 = 303
i6
ii 30
iii210
What is the next number in this sequence? Why?
Suppose the total income in dollars from a machine is given by the following. I=20e 0.5t
,0≤t≤4,t in hours Find the average income (in dollars) over this 4-hour period. (Round your answer to the nearest cent.) $
approximately $29.54 The average income (in dollars) over this 4-hour period. To find the average income over the 4-hour period, we need to integrate the income function I(t) = 20e^(0.5t) with respect to time (t) over the interval [0, 4] and then divide by the length of the interval (4 hours).
The average income A(t) can be calculated using the formula:
A(t) = (1/4) ∫(20e^(0.5t) dt) from 0 to 4
First, let's find the integral of 20e^(0.5t) with respect to t:
∫(20e^(0.5t) dt) = 40e^(0.5t)
Now, let's apply the definite integral from 0 to 4:
[40e^(0.5(4)) - 40e^(0.5(0))] = 40e^2 - 40
Next, divide by 4 to find the average income:
A(t) = (1/4)(40e^2 - 40) ≈ 29.54 (rounded to the nearest cent)
The average income (in dollars) over this 4-hour period is approximately $29.54.
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use the graph to determine the line of reflection. will mark brainliest if your right
The line of reflection of the given image is: reflection across x = -5
What is the line of reflection of the graph?There are different ways of carrying out transformations and they are:
Reflection
Translation
Dilation
Rotation
Now, a line of reflection is defined as a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).
Looking at the given image, it is very clear that the line of reflection of the image is a reflection across x = -5
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Please provide an explanation of how to solve this.Find the variance for the given data. Round your answer to one more decimal place than the original data. 29) 1, 4, -5, -9, and 6 a. 39.2 b. 31.4 C. 39.4 d. 39.3
The variance for the given data is 11.3.
To find the variance for the given data, follow these steps:
1. Calculate the mean of the data. To do this, add up all the numbers and divide by the total number of values. In this case, the sum is -3 (1+4-5-9+6) and there are 5 values, so the mean is -3/5 = -0.6.
2. Calculate the difference between each value and the mean. To do this, subtract the mean from each value. For example, the difference between 1 and -0.6 is 1.6.
3. Square each difference. This is important because we want to give greater weight to values that are further away from the mean. For example, (1.6)^2 = 2.56.
4. Add up all the squared differences. For this data set, the sum of the squared differences is 56.4.
5. Divide the sum of squared differences by the total number of values. In this case, 56.4 divided by 5 is 11.28.
6. Round your answer to one more decimal place than the original data. The answer is 11.3, which matches option d, 39.3, after rounding.
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If the shaded trapezoid has an area of 9 square inches, what is the area, in square inches of this figure below?
(give a possible answer if you can)
Total shaded area is the sum of the areas of the two triangles is 64.5 in²
The area of each of the two triangles can be found from the formula ...
A = (1/2)bh
left triangle
A = (1/2)(9.8 in)(8.6 in) = 42.14 in²
right triangle
A = (1/2)(5.2 in)(8.6 in) = 22.36 in²
Total shaded area is the sum of the areas of the two triangles:
(42.14 +22.36) in² = 64.5 in²
Hence, total shaded area is the sum of the areas of the two triangles is 64.5 in²
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simplify this question its 4 marks
The simplification of the given expression, [tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex], is 7
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
[tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex]
The expression can be simplified as follows:
[tex]\sqrt{\frac{2^{x+2} + 2^{x}}{2^{x-3}} + 9}[/tex]
[tex]\sqrt{\frac{2^{x} \times 2^{2} + 2^{x}}{2^{x} \div 2^{3}} + 9}[/tex]
[tex]\sqrt{\frac{2^{x} (2^{2} + 1)}{2^{x} \times \frac{1}{2^{3}}} + 9}[/tex]
[tex]\sqrt{\frac{(2^{2} + 1)}{ \frac{1}{2^{3}}} + 9}[/tex]
[tex]\sqrt{\frac{(4 + 1)}{ \frac{1}{8}} + 9}[/tex]
[tex]\sqrt{\frac{(5)}{ \frac{1}{8}} + 9}[/tex]
[tex]\sqrt{(5) \div \frac{1}{8} + 9}[/tex]
[tex]\sqrt{(5) \times \frac{8}{1} + 9}[/tex]
[tex]\sqrt{5 \times 8+ 9}[/tex]
[tex]\sqrt{40+ 9}[/tex]
[tex]\sqrt{49}[/tex]
= 7
Hence, the simplified expression is 7
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Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shapest Suppose we assume that the temperatures of healthy humans ara approximately normal with a mean of 98.6 and a standard deviation of 0.8, () 1 healthy person was selected at random, what is the probability that the temperature for this person is 98.5 or lower? (hound your answer to four decimal places.) (1) Would you consider a temperature of to be an unlikely occurrence for a single individual, given that the true average temperature of healthy people s 98.07 Explain No. You expect a reasonable portion of the population to have a temperature this low, so this is not unlikely Yes. The probability is very small (almost 0), so this would be an unlikely occurrence (C) I 135 healthy people are selected at random what is the probability that the average temperature for these people is 3.5 or lower? (Round your answer to four decimal places)
To solve for the probability of a temperature of 98.5 or lower, we need to find the z-score for 98.5 using the formula z = (x - mu) / sigma, where x is the temperature, mu is the mean, and sigma is the standard deviation.
z = (98.5 - 98.6) / 0.8 = -0.125
Using a standard normal distribution table or calculator, we can find the probability of z being less than or equal to -0.125, which is 0.4502. Therefore, the probability of a temperature of 98.5 or lower for a randomly selected healthy person is 0.4502.
No, a temperature of 98.5 is not an unlikely occurrence for a single individual, given that the distribution of human body temperatures is approximately normal with a mean of 98.6 and a standard deviation of 0.8. The probability of a temperature of 98.5 or lower is about 0.45, which means that there is a reasonable chance that a healthy person could have this temperature.
Thus, to solve for the probability of an average temperature of 3.5 or lower for 135 healthy people, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size.
The standard error of the mean (SEM) is calculated as SEM = sigma/sqrt (n), where sigma is the population standard deviation and n is the sample size.
SEM = 0.8 / sqrt(135) = 0.068
The z-score for an average temperature of 3.5 is calculated as z = (3.5 - 98.6) / 0.068 = -1375.74
Using a standard normal distribution table or calculator, we can find the probability of z being less than or equal to -1375.74, which is essentially 0. Therefore, the probability of an average temperature of 3.5 or lower for 135 healthy people is almost 0.
To answer your questions, we will use the normal distribution properties of human body temperatures.
(1) To find the probability that the temperature for a randomly selected healthy person is 98.5 or lower, we need to calculate the z-score:
z = (X - μ) / σ
z = (98.5 - 98.6) / 0.8
z = -0.1 / 0.8
z = -0.125
Now, we can look up the probability in a standard normal distribution table or use a calculator to find the area to the left of z = -0.125. The probability is approximately 0.4505 (rounded to four decimal places).
(2) A temperature of 98.5 is not an unlikely occurrence for a single individual, given that the true average temperature of healthy people is 98.6. The probability of having a temperature of 98.5 or lower is 0.4505, which is not very small, so this is not an unlikely event.
(3) To find the probability that the average temperature for a sample of 135 healthy people is 98.5 or lower, we first need to find the standard error (SE) of the sample mean:
SE = σ / √n
SE = 0.8 / √135
SE ≈ 0.0688
Next, we calculate the z-score for the sample mean:
z = (X - μ) / SE
z = (98.5 - 98.6) / 0.0688
z ≈ -1.451
Now, we look up the probability in a standard normal distribution table or use a calculator to find the area to the left of z = -1.451. The probability is approximately 0.0735 (rounded to four decimal places).
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Consider a normal distribution with mean 31 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 31?
The probability that a value selected at random from this distribution is greater than 31 is essentially 1.
Since the mean of the normal distribution is 31 and the standard deviation is 3, we know that the distribution is centered around 31 and the values are spread out within a range of approximately 3 units on either side of the mean. To find the probability that a value selected at random from this distribution is greater than 31, we need to look at the area under the curve to the right of 31.
Using a z-score table or a calculator, we can find that the z-score for 31 in this distribution is 0. This means that 31 is exactly at the mean of the distribution. To find the area under the curve to the right of 31, we need to find the area between 31 and positive infinity in terms of standard deviations from the mean.
Since the standard deviation is 3, we can find the distance between 31 and positive infinity in terms of standard deviations by dividing by 3:
(infinity - 31) / 3 = infinity/3 - 31/3 = infinity - 10.33
This tells us that the area under the curve to the right of 31 is the same as the area to the right of 10.33 standard deviations above the mean. However, since the normal distribution is continuous and extends infinitely in both directions, the area to the right of any finite value is essentially 1 (i.e. the probability of selecting a value greater than any specific value is essentially 100%).
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the average cost of a family home in 1997 was $156,100. by 2010, the average cost was $254,400. write an equation to represent the price (p) of a house as a function of the year, t. let t=0 correspond to 1997. how much would the average price of a home be today?
The equation that represent the average price of a house as a function of the year can be presented as follows;
p = (7561 7/3)·t + 156,100The average price of a house today is; $352,700What is an average of a value?The average of a value, such as the average price of a houses is the ratio between the sum of the prices of the houses to the number of houses.
The average cost of a family house in 1997 = $156,100
The average cost of the family house in 2010 = $254,400
The equation for the price (p) of a house as a function of the year, t where t = 0 corresponds to 1997, can be found as follows;
The slope of the equation is; (254,400 - 156,100)/(2010 - 1997) = 98300/13
98300/13 = 7561 7/13
The linear equation is therefore;
p - 156100 = (98300/13) × (t - 0)
p = (98300/13) × t + 156100
p = (7561 7/13) × t + 156100
The average price of a house today, 2023 can be found by plugging in the value, t = 2023 - 1997 = 26 in the above equation as follows;
p = (98300/13) × 26 + 156100 = 352,700
The price of a house today is $352,700
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a triangle drawn on a map has sides of lengths 7.0 cm, 10 cm, and 14 cm. the shortest of the corresponding real-life distances is 105 km. find the longest of the real-life distances. round to the nearest unit
The cm units cancel out, leaving: Longest real-life distance = 14 * 15000 km = 210 km So, the longest real-life distance is approximately 210,000km.
To solve this problem, we need to use the concept of scale factor. The scale factor is the ratio of the corresponding lengths in the map and the real world. In this case, we know that the shortest side of the triangle in the map has a length of 7.0 cm, and its corresponding real-life distance is 105 km. Therefore, the scale factor is:
105 km / 7.0 cm = 15,000
This means that every cm in the map represents 15,000 km in real life. Now we can use this scale factor to find the lengths of the other sides of the triangle in real life:
Longest side = 14 cm x 15,000 km/cm = 210,000 km
Therefore, the longest real-life distance is 210,000 km (rounded to the nearest unit).
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Which Expressions are equivalent to -(8/2) ? Select All the Equivalent Expressions.
Answer: B, C, E
Step-by-step explanation:
When multiplying or dividing - and + numbers, rules are as follows:
If the signs are the same, equals +
So for division
[tex]\frac{+}{+} =+[/tex] and [tex]\frac{-}{-} =+[/tex]
If signs are different, equals -
[tex]\frac{-}{+}=-[/tex] and [tex]\frac{+}{-} = -[/tex]
Question [tex]-(\frac{8}{2} )[/tex] the number is negative
A. not the same because [tex]\frac{-}{-} =+[/tex] and your question is -
B. yes it is the same because [tex]\frac{+}{-} = -[/tex] and your question is also -
C. yes it is the same because the parenthesis are ok to remove and it doesn't change your answer
D. not the same [tex]\frac{+}{+} =+[/tex] and your question is -
E. yes it is the same because [tex]\frac{-}{+}=-[/tex] and your answer is also -
Out of 520 randomly selected students, 104 of them dropped an online course. Construct a 90% confidence interval for the true proportion of students that will drop an online course. Find the standard error
The standard error is found to be 0.024, when constructing a 90% confidence interval for the true proportion of students.
The point estimate of the proportion of students (sample) who dropped an online course is:
p' = 104/520 = 0.2
The standard error of the sample proportion is:
SE = √[p'(1 - p') / n]
where n is the sample size.
SE = √[0.2(1 - 0.2) / 520] = 0.024
To construct a 90% confidence interval, we can use the formula:
CI = p' ± z × SE
where z is the desired confidence level's associated z-score. The z-score with a 90% degree of confidence is 1.645.
CI = 0.2 ± 1.645(0.024) = (0.155, 0.245)
Therefore, we can be 90% confident that the true proportion of students who will drop an online course is between 0.155 and 0.245.
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Find the missing side of the triangle. 10 cm and 6 cm. What is X??????? I missed my RSM class and now this?!
The missing side of triangle is 11.66 cm, under the condition that the given triangle is a right angled triangle and the other sides of the triangle are 10cm, 6cm respectively.
In order to evaluate the other side of the triangle, we have to rely on the principles of Pythagorean Theorem which states that in a right triangle, the sum of the square sides are equal to the square of the hypotenuse side.
Then, let us consider that x be the length of the missing side then
x² = 10² + 6²
x² = 100 + 36
x² = 136
x = √(136)
x ≈ 11.66 cm
Then, the missing side of this triangle is approximately 11.66 cm.
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The complete question is
Find the missing siside of the following right triangle in the figure
(will give 50 points) Which graph shows the solution to the system of linear equations?
y equals one half times x
x + 2y = −8
coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1
coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1
coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1
coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3
The graph that shows the solution to the system of equations is given by the image presented at the end of the answer.
How to solve the system of equations?The system of equations for this problem is defined as follows:
y = 0.5x.x + 2y = -8.Replacing y = 0.5x on the second equation, the x-coordinate of the solution is given as follows:
x + 2(0.5x) = -8
x + x = -8
2x = -8
x = -4.
The y-coordinate of the solution is given as follows:
y = 0.5(-4)
y = -2.
Hence the graph will show the two lines intersecting at the point (-2,-4).
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A population has a mean of u = 60 and a standard deviation of a = 12. Find the X value for each of the following z-scores. (4 pts) A. z = .50 (1 pt) لے H. Z = -0.25 (1 pt) What is the probability of randomly selecting a score that is less than z = -0.25? (2 pts)
A. For z = 0.50 = 66; B. For z = -0.25 = 57 and the probability of randomly selecting a score less than z = -0.25, you can use a standard normal (z-score) table or calculator. For z = -0.25, the probability is approximately 0.4013, meaning there's a 40.13% chance of randomly selecting a score less than z = -0.25.
To find the X value for each z-score, we use the formula:
X = u + (z * a)
where u is the mean, a is the standard deviation, and z is the z-score.
A. For z = 0.50:
X = 60 + (0.50 * 12)
X = 66
Therefore, the X value for z = 0.50 is 66.
B. For z = -0.25:
X = 60 + (-0.25 * 12)
X = 57
Therefore, the X value for z = -0.25 is 57.
To find the probability of randomly selecting a score that is less than z = -0.25, we use a z-table or a calculator that can calculate normal distribution probabilities. The probability of a score being less than z = -0.25 is the same as the area under the curve to the left of z = -0.25.
Using a z-table, we find that the probability of a score being less than z = -0.25 is 0.4013.
Therefore, the probability of randomly selecting a score that is less than z = -0.25 is 0.4013 or approximately 40.13%.
A. For z = 0.50:
To find the X value, use the formula X = μ + (z * σ), where μ is the mean and σ is the standard deviation.
X = 60 + (0.50 * 12) = 60 + 6 = 66
B. For z = -0.25:
X = 60 + (-0.25 * 12) = 60 - 3 = 57
To find the probability of randomly selecting a score less than z = -0.25, you can use a standard normal (z-score) table or calculator. For z = -0.25, the probability is approximately 0.4013, meaning there's a 40.13% chance of randomly selecting a score less than z = -0.25.
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If there is a decrease in the money supply that causes prices to fall and leads
to deflation, what happens to money?
A. It changes from commodity money to fiat money.
B. It changes from fiat money to commodity money.
C. It gains purchasing power.
D. It loses purchasing power.
determine the values of the following quantities. (round your answers to three decimal places.) (a) t0.10, 10 (b) t0.05, 10 (c) t0.05, 21 (d) t0.05, 60 (e) t0.005, 60
These values are based on the t-distribution table and represent critical values for the given probabilities and degrees of freedom.
To answer this question, we need to use a t-table. The values we are looking for are the t-values associated with specific probabilities and degrees of freedom.
(a) t0.10, 10 = 1.372 (from the t-table, using 10 degrees of freedom and the probability of 0.10)
(b) t0.05, 10 = 1.812 (from the t-table, using 10 degrees of freedom and the probability of 0.05)
(c) t0.05, 21 = 1.721 (from the t-table, using 21 degrees of freedom and the probability of 0.05)
(d) t0.05, 60 = 1.671 (from the t-table, using 60 degrees of freedom and the probability of 0.05)
(e) t0.005, 60 = 2.660 (from the t-table, using 60 degrees of freedom and the probability of 0.005)
Note that we round all answers to three decimal places, as specified in the question. The values we have found are the t-values for the specified probabilities and degrees of freedom. These values can be used in calculations involving t-distributions.
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find the probability of (a or b)P(a) = 0.21P(b) = 0.35P(a and b) = 0.12
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To find the probability of (a or b), we can use the formula:
P(a or b) = P(a) + P(b) - P(a and b)
Plugging in the given values:
P(a or b) = 0.21 + 0.35 - 0.12
= 0.44
Therefore, the probability of (a or b) is 0.44.
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the average number of miles a person drives per day is 24. a researcher wishes to see if people over age 60 drive less than 24 miles per day. she selects a random sample of 25 drivers over the age of 60 and finds that the mean number of miles driven is 23.4. the population standard deviation is 4.1 miles. At a=0.05 is there sufficient evidence that those drivers over 60 years ild drive less on average than 24 miles per day?
There is sufficient evidence to suggest that drivers over the age of 60 drive less on average than 24 miles per day. To answer this question, we can use a one-sample t-test. The null hypothesis is that the mean number of miles driven by drivers over 60 is equal to 24, while the alternative hypothesis is that it is less than 24.
Using the given information, we can calculate the t-statistic as follows:
t = (23.4 - 24) / (4.1 / sqrt(25)) = -1.95
The degrees of freedom for this test are 24 (n-1).
Using a t-table or calculator, we can find the critical value for a one-tailed test at a significance level of 0.05 with 24 degrees of freedom to be -1.711.
Since our calculated t-value of -1.95 is less than the critical value of -1.711, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that drivers over the age of 60 drive less on average than 24 miles per day.
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