The volume of the solid of revolution is \(\frac{1674\pi}{5}\) cubic units.
The volume of the solid of revolution can be determined by the following integral equation:
\(V = 2\pi\int\limits^a_b {|f(x)-g(x)|} \, dx\) (1)
Where:
\(g(x)\) - Lower bound function\(f(x)\) - Upper bound function\(a\) - Upper bound\(b\) - Lower boundIf we know that \(b = 2\), \(b = 1\), \(g(x) = 0\) and \(f(x) = 27\cdot x^{3}\), then the volume of the solid of revolution is:
\(V = 2\pi\int\limits^2_1 {x\cdot |27\cdot x^{3}-0|} \, dx\)
\(V = 54\pi \int\limits^2_1 {x^{4}} \, dx\)
\(V = 54\pi \left(\frac{2^{5}}{5}-\frac{1^{5}}{5} \right)\)
\(V = \frac{1674\pi}{5}\)
The volume of the solid of revolution is \(\frac{1674\pi}{5}\) cubic units.
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Simplify the following expression incorporating order of operations. (6K)
15 – 3 x 4 + 2(3 + 2) + 6 = 2
Answer:
The answer is K= -1/45 if the K isnt supposed to be in there then 19=2
Step-by-step explanation:
what is the dependent variable of the number of packages of hotdog buns needed for a certain number of packages of hotdogs?
Always check the quantity in each package to determine the appropriate number of hotdog bun packages needed for the given number of hotdog packages.
The dependent variable in this situation is the number of packages of hotdog buns needed, as it relies on the number of packages of hotdogs (the independent variable).
We want to know the dependent variable when considering the number of packages of hotdog buns needed for a certain number of packages of hotdogs.
Let me explain this relationship:
First, let's define the terms involved.
The dependent variable is the variable that depends on another variable (called the independent variable).
In this case, we are examining the relationship between the number of packages of hotdogs and the number of packages of hotdog buns needed.
The independent variable is the number of packages of hotdogs.
This is because the number of hotdog buns needed depends on the number of hotdogs you have.
The dependent variable, in this case, is the number of packages of hotdog buns needed.
This variable depends on the number of packages of hotdogs, as you need a certain amount of buns to accommodate the hotdogs.
To determine the relationship between these two variables, we would likely use a proportion or a ratio.
For example, if one package of hotdogs contains 10 hotdogs and one package of hotdog buns contains 10 buns, then the ratio is 1:1, meaning you need one package of hotdog buns for every package of hotdogs.
This relationship may vary depending on the number of hotdogs and buns in each package.
Remember to examine the proportion between the two variables to ensure you have the correct amount of buns for the hotdogs.
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How in statistics the bayesian approach is different from the frequentist approach?.
In statistics, the bayesian approach treats parameters as random variables while in frequentist approach the parameters are fixed.
What is bayesian approach in statistics?There are different approaches in statistics that are used in data analysis they include the following:
Bayesian approach in statistics is defined as the approach that applies probabilities in a statistical procedure by treating the parameters under evaluation, randomly. The variables are being treated randomly but not fixed.
The frequentist approach is defined as the approach in statistics that deals with the frequency or proportion of the data and variables.
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help me graph this plzzzzzz mate
Answer:
Should look like this
Step-by-step explanation:
y-intercept = 2
slope = 1
What is the vertex of the graph of f x )=[ x 5 ]- 6?
The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.
Therefore the answer is (5, -6).
The graph f(x) = |x - 5| - 6 is symmetrical about the axis x = 5.
A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is
(5, -6)
--The question is incomplete, answering to the question --
"What is the vertex of the graph of f(x) = |x - 5| - 6?"
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parking garage has 5 floors. If 117 cars can be parked on each floor, how many total cars can park in the garage? Drag numbers to complete the multiplication. Numbers may be used once, more than once, or not at all.
Answer:
585 cars
Step-by-step explanation:
Given
\(Floors = 5\)
\(Cars = 117\) per floor
Required
Determine the total number of cars
This is calculated by multiplying number of cars per floor by number of floors.
\(Total = Floors*Cars\)
\(Total = 5 * 117\)
\(Total = 585\)
Hence, there are 585 cars in total
A certain forest covers an area of 3000 km^2. Suppose that each year this area decreased by 8%. What will the area be after 15 year? Round answer to nearest square kilometer
if you start at 89 degrees and it decreases 5% each hour what would it be at in 3 hours
Answer:
A = 76.3 degrees after 3 hours
Step-by-step explanation:
An exponential function is needed here:
A = P(1 - 0.05)^3, where this (1 - 0.95) reflects a DECREASE of 5%/hour.
Then: A = (89 degrees)(0.95)^3, or
A = 76.3 degrees after 3 hours
Question 12 (16 points) Below is a sample of times (in minutes) that it takes students to complete an exam. Data: 23.2, 50.1, 57.6, 54.5, 52.7, 55.6, 52.9, 58.3, 19.5, 55.6, 58.3 Calculate the five nu
The five-number summary for the given data set is: Minimum: 19.5, Q1: 51.4, Q2 (Median): 54.5, Q3: 56.6, Maximum: 58.3
To calculate the five-number summary for the given data set, we need to find the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum.
1. Arrange the data in ascending order:
19.5, 23.2, 50.1, 52.7, 52.9, 54.5, 55.6, 55.6, 57.6, 58.3, 58.3
2. Obtain the minimum:
The minimum value is 19.5.
3. Obtain Q1 (the first quartile):
Q1 is the median of the lower half of the data set.
In this case, we have 11 data points, so the lower half consists of the first 5 data points:
19.5, 23.2, 50.1, 52.7, 52.9
To obtain Q1, we need to calculate the median of these data points:
Q1 = (50.1 + 52.7) / 2 = 51.4
4. Obtain Q2 (the median):
Q2 is the median of the entire data set.
In this case, we have 11 data points, so the median is the middle value:
Q2 = 54.5
5. Obtain Q3 (the third quartile):
Q3 is the median of the upper half of the data set.
In this case, we have 11 data points, so the upper half consists of the last 5 data points:
55.6, 55.6, 57.6, 58.3, 58.3
To obtain Q3, we need to calculate the median of these data points:
Q3 = (55.6 + 57.6) / 2 = 56.6
6. Obtain the maximum:
The maximum value is 58.3.
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IS THERE ANYONE WHO HASNT GOT ANYTHING TO DO AT THE MOMENT BECAUSE I NEED HELP!!! :(
Answer:
me
Step-by-step explanation:
Answer:
I can try to help whats ur question?
Match each quadratic function in factored form with its solutions on the right.
1) f(x) = (x - 2)²
2) g(x) = (x + 2)(x - 1)
3) y = (2x-1)(3x + 4)
4) y = 3x(x-3)
A) x = 1/2,-
B) x = 0,3
C) x = 2
D) x = -2,1
We can match the quadratic functions in factored form with their solutions in this way:
1) 1) f(x) = (x - 2)² is C) x = 2.
2) g(x) = (x + 2)(x - 1) is D) x = -2, 1
3) y = (2x-1)(3x + 4) is A) x = 1/2, -4/3
4) y = 3x(x-3) is B) x = 0, 3
How to solve the quadratic functions?Here, the quadratic functions are already in factored form. So, we shall use the zero product property to solve the functions.
1) f(x) = (x - 2)²
x = 2 (multiplicity 2)
Let's set the expression equal to zero and solve for x:
(x - 2)² = 0
x - 2 = 0
x = 2
2) g(x) = (x + 2)(x - 1)
Here, we will use the zero product property again:
(x + 2)(x - 1) = 0
x + 2 = 0, x - 1 = 0
x = -2, x = 1
3) y = (2x-1)(3x + 4)
Also, we apply the zero product property and solve for x:
2x-1 = 0, 3x + 4 = 0
2x = 1, 3x = -4
x = 1/2, x = -4/3
4) y = 3x(x-3)
We will use the zero product property:
3x = 0, x - 3 = 0
x = 0, x = 3
Therefore, the solutions to the quadratic functions are:
1) f(x) = (x - 2)² is C) x = 2
2) g(x) = (x + 2)(x - 1) is D) x = -2, 1
3) y = (2x-1)(3x + 4) is A) x = 1/2, -4/3
4) y = 3x(x-3) is B) x = 0, 3
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please please pleaseeeee help me!!
Answer:
wanna see my pokemon cards
Step-by-step explanation:
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
A (-2, 5)
Step-by-step explanation:
The attached shows the rectangle and the offered points. The point not on the rectangle is A(-2, 5).
__
If we examine the coordinates, we see that the y-values must be -2 or 3 for a point to be on the rectangle. Similarly, the x-values must be -2 or 5.
The offered point A has an appropriate x-value, but not an appropriate y-value. Point A is not on the rectangle.
Wesimann Co. Issued 13-year bonds a year ago at a coupon rate of 7.3 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 5.6 percent, what is the current bond price?
Answer:
Current Bond price = $1155.5116
Step-by-step explanation:
We are given;
Face value; F = $1,000
Coupon payment;C = (7.3% x 1,000)/2 = 36.5 (divided by 2 because of semi annual payments)
Yield to maturity(YTM); r = 5.6%/2 = 2.8% = 0.028 (divided by 2 because of semi annual payments)
Time period;n = 13 x 2 = 26 years (multiplied by 2 because of semi annual payments)
Formula for bond price is;
Bond price = [C × [((1 + r)ⁿ - 1)/(r(r + 1)ⁿ)] + [F/(1 + r)ⁿ]
Plugging in the relevant values, we have;
Bond price = [36.5 × [((1 + 0.028)^(26) - 1)/(0.028(0.028 + 1)^(26))] + [1000/(1 + 0.028)^(26)]
Bond price = (36.5 × 18.2954) + (487.7295)
Bond price = $1155.5116
Which of the of the following statements is true with respect to a simple linear regression model? a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1. O b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative. O C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant. O d. all of the above is true. e. none of the above is true.
Answer:
d. All of the above are true
Step-by-step explanation:
All of the following statements,
a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.
b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.
C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.
are true
Solve for x. Figures are not necessarily drawn to scale.
Check the picture below.
\(\cfrac{x}{10}=\cfrac{24.5}{14}\implies x=\cfrac{(10)(24.5)}{14}\implies x=\cfrac{245}{14}\implies x=17.5\)
what should i do to feel less lonely
For a result to be considered _____, the chances of its occurring as a result of random error are often less than 5 percent.
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
What is Random error?A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).
It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.
Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.
According to the given data,
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
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Choose the correct description of the graph of the compound inequality: (5 points) x − 3 < −7 or x + 5 greater than or equal to 8
Answer:
the answer would be a number line with an open circle on -4, a closed circle on 3, and shading in between.
Step-by-step explanation:
Find the probability that a randomly selected point within the circle falls in the red shaded area
The probability that a randomly selected point within the circle falls in the red shaded area is 15.9%
How to determine the probability?The radius is given s:
r = 4 cm
So, the area of the triangle is
A1 = 0.5r^2
Similarly, the area of the circle is
A2 = πr^2
The probability that a randomly selected point within the circle falls in the red shaded area is
P = A1/A2
This gives
P = 0.5r^2/πr^2
Evaluate
P = 15.9%
Hence, the probability that a randomly selected point within the circle falls in the red shaded area is 15.9%
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1100 students attend Ridgewood Junior High School. 20% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answer:
20% of 1100 is 220, so two hundred and twenty students brought their lunch to school on Thursday (and every other school day).
Step-by-step explanation:
The day of the week is a distraction. All you need to know is that 20% of 1100 students bring their lunch to school every day. 20% of 1100 is 200 + 20, or 220. So 220 students bring their lunch to school every day.
If this couple has four children, what is the probability that the first two children will be color-blind boys and the last two children will be girls with normal vision?
The probability of having the first two children as color-blind boys and the last two children as girls with normal vision is 1/16 or approximately 0.0625, assuming equal probabilities of gender and independent events.
To calculate the probability of having the described sequence of children, we need to consider the probability of each individual event occurring and then multiply them together.
Assuming the probability of having a color-blind boy is p(CB) and the probability of having a girl with normal vision is p(GNV), the desired probability can be calculated as follows:
Probability of the first child being a color-blind boy: p(CB) = 1/2 (assuming an equal probability of a child being a boy or a girl, and the probability of color blindness is independent of gender).
Probability of the second child being a color-blind boy: p(CB) = 1/2 (assuming independent events).
Probability of the third child being a girl with normal vision: p(GNV) = 1/2 (assuming an equal probability of a child being a boy or a girl).
Probability of the fourth child being a girl with normal vision: p(GNV) = 1/2 (assuming independent events).
To calculate the combined probability, we multiply the individual probabilities together:
\(p(2CB-2GNV) = p(CB) \timesw p(CB) \times p(GNV) \times p(GNV) = (1/2) \times (1/2) \times (1/2) \times (1/2) = 1/16.\)
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Find the circumference of a circle when the area of the circle is 64πcm²
Answer:
50.27 cm
Step-by-step explanation:
We Know
The area of the circle = r² · π
Area of circle = 64π cm²
r² · π = 64π
r² = 64
r = 8 cm
Circumference of circle = 2 · r · π
We Take
2 · 8 · (3.1415926) ≈ 50.27 cm
So, the circumference of the circle is 50.27 cm.
Answer: C=16π cm or 50.24 cm
Step-by-step explanation:
The formula for area and circumference are similar with slight differences.
\(C=2\pi r\)
\(A=\pi r^2\)
Notice that circumference and area both have \(\pi\) and radius.
\(64\pi=\pi r^2\) [divide both sides by \(\pi\)]
\(64=r^2\) [square root both sides]
\(r=8\)
Now that we have radius, we can plug that into the circumference formula to find the circumference.
\(C=2\pi r\) [plug in radius]
\(C=2\pi 8\) [combine like terms]
\(C=16\pi\)
The circumference Is C=16π cm. We can round π to 3.14.
The other way to write the answer is 50.24 cm.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
11r+2
Step-by-step explanation:
combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2
What is the area of this parallelogram?
A= 19 1/2 ft
A= 42 ft
A= 61 1/2 ft
A= 71 3/4 ft
Step-by-step explanation:
Parallelogram formula: \(A=b(base)h(height)\)
The value 6 is meant to trick you.
The height is 7, and the base is 10 1/4.
Multiply the base and height:
\(7 \times 10\frac{1}{4} = 71\frac{3}{4}\)
The area equals: \(71\frac{3}{4}\) \(ft^{2}\)
evaluate 5/6 x 4 x equals 7
Answer:
x= 2 1/10
Step-by-step explanation:
What you have to do is to multiply the 4x*5/6 so 4*5/6 = 20/6. Now we have 20/6x - 7 now just solve normally
20/6x=7
x = 7 / 20/6
7/1*6/20
x = 42/20 or 2 2/20 === 2 1/10
Annabelle's initial balance in her checking account was $95.62. She deposited $35.79 and then withdrew $45. What is the final balance for her checking account?
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation 2x-2/5x+2 < 0
Answer:
Step-by-step explanation:
kristy asks lonnie to think of a number, add 3 to it, multiply the sum by 2 and then subtract 6 . let n stand for lonnies starting number . which expression represents lonnies final number ?
The expression that represents Lonnie's final number is 2(x + 3) - 6
Writing an expressionFrom the given information, we are to write the expression that represents Lonnie's final number
From the given information,
"kristy asks lonnie to think of a number, add 3 to it"
Let the number be x
Then,
The statement becomes
x + 3
"multiply the sum by 2" we get
2×(x +3)
= 2(x + 3)
" subtract 6",
The expression becomes
2(x + 3) - 6
This is the expression that represents Lonnie's final number
Hence, the expression that represents Lonnie's final number is 2(x + 3) - 6
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a) Using a 2-year moving average, the forecast for year 6= miles (round your response to the nearest whole number). b) If a 2-year moving average is used to make the forecast, the MAD based on this = miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.40 and 0.60 (the weight of 0.60 is for the most recent period) =3,740 miles (round your response to the nearest whole number). The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.40 and 0.60= miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) d) Using exponential smoothing with α=0.20 and the forecast for year 1 being 3,100 , the forecast for year 6=3,468 miles (round your response to the nearest whole number).
a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.
a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.
b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.
c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.
The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.
d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.
In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.
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