Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex]
Now, According to the question:
The shell method formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
Take a vertical cross section of the region. The width of the cross section is dx, and the height is [tex]8x^3.[/tex]
Rotate the cross section about the line x = 2. The height of the shell is [tex]8x^3.[/tex] the radius is 2 - x, and the thickness is dx.
Volume of shell = 2π(2-x)([tex]8x^3[/tex])dx = 2π([tex]16x^3 - 8x^4[/tex])dx
Volume of solid = [tex]2 \pi \int\limits^1_0 [16x3 - 8x4]dx[/tex]
[tex]= 2\pi (4x^4 - (8/5)x^5)^1_0[/tex]
= 24π/5
Hence, Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex].
Learn more about Volume of solid at:
https://brainly.com/question/23705404
#SPJ4
Mathematical 8. PRACTICE Model Math Christy purchased 6.75 pounds of licorice. How much licorice does she need to put in each bag if she divides the total amount into 10 equal-sized bags?
Answer:i think it is yes! this )--89+98
Step-by-step explanation:
the school marching band has 328 members. Can the band members march in 8 lines, with an equal numberof band members in each line with no members left over? Explain
Answer:
Yes
Step-by-step explanation:
328/8 = 41
Thus if 41 members are in each line, there should be no members left without a spot and it should be equal all across
The graph below is a transformation of x^2
Give the function in the graph below
G(x)= ?
I first put it as G(x)=(x-2)^2-1
But what I put it at was wrong
The equation of the graph is g'(x) = -(x + 2)² - 1
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = x²
From the graph, we can see that the graph is inverted
This means that
g'(x) = -x²
Next, the graph is shifted left by 2 units
This implies that
g'(x) = -(x + 2)²
Lastly, the graph is shifted down by 1 unit
So, we have
g'(x) = -(x + 2)² - 1
Hence, the equation is g'(x) = -(x + 2)² - 1
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
For counseling groups, it is recommended that the number of members for groups of children, __________, as compared to counseling groups for adults.
decrease
The number of members for counseling groups of children should generally be smaller as compared to counseling groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. Smaller groups also allow for more individualized attention and support.
The recommended number of members for counseling groups of children should generally be smaller than that of groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. This can lead to a lack of engagement and little benefit from the group counseling sessions. Smaller groups also allow for more individualized attention and support, which is important for young people to feel comfortable expressing their thoughts and feelings. Additionally, smaller groups can help create a more intimate environment for participants to safely share their experiences and feelings with one another. As such, reducing the size of the group for counseling sessions with children can help ensure a more successful therapeutic experience.
learn more about number here
https://brainly.com/question/10547079
#SPJ4
What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
Group of answer choices
6
3
0.75
1.5
Answer:
A resposta correta é 6. Esta sequência geométrica, tem uma razão comum de r = 1/2. O 10º prazo o da sequência pode ser encontrado usando a fórmula an = a1 * r-n1, em de n é o número do prazo. Assim, o 10º prazo é: ano = 384 * (1/2)9 = 384 * (1/512) = 6
Points B and D are on the perpendicular bisector of ∠ABC. The measure of ∠ABD is 45°. Find the measure of ∠C.
Answer:
Step-by-step explanation:
Given ∠B=45,∠C=55
So, ∠A=180°−45°−55°
=80°
From △ABD,40°+45°+∠ADB=180°
⟹∠ADB=95°
From△ADC,40°+55°+∠ADC=180°
⟹∠ADC=85°.
A line passes through the point (-6, 5) and has a slope of 2 Write an equation in point-slope form for this line. 0 08
The required point-slope form for the given line is y = 3x/2 + 14.
What is equation of line?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
According to question:
We have,
A line passes through the point (-6, 5) and has a slope of 3/2
Then the equation of line is;
y - 5 = 3/2(x - (-6))
y - 5 = 3/2 (x + 6)
2y - 10 = 3x + 18
2y = 3x + 28
y = 3x/2 + 14
Thus the point slope form of the line is y = 3x/2 + 14.
To know more about equation visit:
brainly.com/question/21511618
#SPJ1
The scatterplot shows the relationship between the number of yards allowed by teams in the National Football League and the number of wins for that team in a recent season, along with the least-squares regression line. Computer output is also provided.
2 Calculate and interpret the residual for the Seattle Seahawks, who allowed 4668 yards and won 10 games.
If the residual is negative, it means the observed number of wins is lower than the predicted number of wins, indicating that the team performed worse than expected based on their yards allowed.
What is the interpret the residual for the Seattle sea hawks?The residual for a data point in a regression analysis represents the difference between the observed response (number of wins) and the predicted response (value on the regression line).To calculate the residual for the Seattle Sea hawks, we need to find the value of the regression line at the number of yards allowed (4668), then subtract the observed number of wins (10).Interpretation of the residual: if the residual is positive, it means the observed number of wins is greater than the predicted number of wins, indicating that the team performed better than expected based on their yards allowed. If the residual is negative, it means the observed number of wins is lower than the predicted number of wins, indicating that the team performed worse than expected based on their yards allowed.To learn more about interprets refer:
brainly.com/question/1638242
#SPJ1
the quartiles of a dataset are the three values that divide the data into four equal groups, each group representing 25% of the data. the first quartile (q1), also known as the lower quartile, is the value that separates the lowest 25% of the data from the rest of the data. the second quartile (q2), also known as the median, is the value that separates the lowest 50% of the data from the highest 50% of the data. the third quartile (q3), also known as the upper quartile, is the value that separates the lowest 75% of the data from the highest 25% of the data. together, the three quartiles can give a sense of the distribution of the data and the spread of the values
A dataset's quartiles are critical summary statistics that split the data into four equal groups. The first quartile (q1), often known as the lower quartile, splits the data into the bottom 25% and the remainder.
The second quartile (q2), commonly known as the median, splits the data into the lowest and highest 50%. The third quartile (q3), often known as the upper quartile, divides the data into the lowest 75% and the highest 25%. These quartiles give useful information regarding the data distribution and value spread.
The quartiles may also be used to find outliers in the dataset. Understanding the quartiles is an important element of data analysis and may assist inform data-driven decision making.
To learn more about Dataset quartiles:
https://brainly.com/question/28168026
#SPJ4
HELP PLEASE FAST i'm not understanding how to do this (i'll give brainiest to whoever has best answer) The bar below is 7 inches long and divided into 2 equal parts. What is the length of one of those parts? Fill in the blanks in the equation using fractions or mixed numbers to show the length of one of the parts. X 7 inches = inches
The length of each bar is given as follows:
3.5 inches.
As a mixed number, the length of each bar is given as follows:
3 and 1/2 inches.
How to obtain the length of each bar?The length of each bar is obtained applying the proportions in the context of this problem.
The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:
7/2 = 3.5 inches.
The fraction equivalent to a decimal of 0.5 is given as follows:
1/2.
(which is used to construct the mixed number).
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
A three-column table is given.
Part A C D
Part 25 35 50
Whole B 56 80
What is the value of B in the table?
44
40
36
30
Answer:
(b) 40
Step-by-step explanation:
You want the value of the "whole" corresponding to a "part" of 25 in the given table.
PartsBased on the relationships in the 2nd and 3rd columns, it appears that the parts on the second line are 5/8 of the whole.
This means that 25 is 5/8 of B, or ...
B = 8/5 × 25 = 40
The value of B in the table is (b) 40.
__
Additional comment
The parts on the first line will be 3/5 of the value of the parts on the second line. The sum of the two parts in each column is equal to the whole.
<95141404393>
If Y is a random variable with moment-generating function m(t) and U is given by U = aY + b, a) Show that the moment-generating function of U is e tbm(at). b) If Y has mean µ and variance σ 2 , use the moment-generating function of U to derive the mean and variance of U. c) Suppose that the moment-generating function of a normally distributed random variable, Y , with mean µ and variance σ 2 is m(t) = e µt+(1/2)t 2σ 2 . Derive the moment-generating function of X = −3Y + 4. What is the distribution of X? Why?
a) E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).
b) µ is the mean of Y and σ^2 is the variance of Y.
c) the moment-generating function of X =e^((−3µ + 4)t + (9/2)σ^2t^2) and The distribution of X is normal.
a) If Y is a random variable with moment-generating function m(t), and U is given by U = aY + b, then the moment-generating function of U is e^(tb)m(at). This can be shown by using the definition of a moment-generating function:
E(e^(tU)) = E(e^(taY + tb)) = E(e^(taY)e^(tb)) = e^(tb)E(e^(taY))
Since E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).
b) To find the mean and variance of U using the moment-generating function, we can take the first and second derivatives of e^(tb)m(at) and set t = 0. The first derivative with respect to t evaluated at t = 0 is:
(d/dt)e^(tb)m(at) = be^(tb)m(at) + ae^(tb)m'(at)
Setting t = 0, we get the mean of U:
E(U) = be^(0)m(a0) + ae^(0)m'(a0) = b + a*(m'(0)) = b + a*µ
Where µ is the mean of Y.
The second derivative of e^(tb)m(at) is:
(d^2/dt^2)e^(tb)m(at) = b^2e^(tb)m(at) + 2abe^(tb)m'(at) + a^2e^(tb)m''(at)
Setting t = 0, we get the variance of U:
Var(U) = b^2e^(0)m(a0) + 2abe^(0)m'(a0) + a^2e^(0)m''(a0) = b^2 + 2ab*(m'(0)) + a^2*(m''(0)) = b^2 + 2abµ + a^2σ^2
Where µ is the mean of Y and σ^2 is the variance of Y.
c) If the moment-generating function of a normally distributed random variable Y with mean µ and variance σ^2 is m(t) = e^(µt + (1/2)t^2σ^2), then the moment-generating function of X = −3Y + 4 is e^((−3µ + 4)t + (1/2)(−3)^2σ^2t^2) = e^((−3µ + 4)t + (9/2)σ^2t^2)
The distribution of X is normal with mean (-3µ + 4) and variance (9/2)σ^2. This can be deduced by the fact that if Y is normally distributed, then a linear transformation of Y (such as X = aY + b) is also normally distributed with mean aµ + b and variance a^2σ^2.
To learn more about function here:
https://brainly.com/question/12431044
#SPJ4
jake has 16 toy cars. lydia has five fewer toy cars than jake. how many toy cars do they have in all?
write a system of linear equations whose solution is (6,19)
Step-by-step explanation:
[tex] \alpha + \beta = \frac{ - b}{a} = 6 \\ \alpha \beta = \frac{c}{a} = 19 \\ p(x) = k( {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )) = 0\\ = k( {x}^{2} - 6x + 19) \\ polynomial \: = {x}^{2} - 6x + 19 = 0[/tex]
it takes so much tume to solve and type it here and its so hard so plzzz mark me as brainliest plz .
Estimate the distance in feet that your car travels on the entrance ramp to a freeway as it accelerates from 30 mph to the freeway speed of 70 mph. During this motion what is the average acceleration of the car?
The Average Acceleration of the car will be 14.67 ft/[tex]s^{2}[/tex].
What is Acceleration?
The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.
Formula: a = (v(final) - v(initial))/t
In the given formula, it is given that:
v(initial) = 30mph = 44 ft/s
v(final) = 70mph = 102.67 ft/s
t(time) = 4s
Putting these values in our formula, we get:
a(acceleration) = (102.67 - 44)/4
a = 14.67 ft/[tex]s^{2}[/tex].
Therefore as per the given problem, the acceleration of the given car is 14.67 ft/[tex]s^{2}[/tex].
To learn more about Acceleration, visit: https://brainly.com/question/12550364
#SPJ4
Convert 4/15 to a decimal and a percent.
The percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given a fraction number 4/15
To convert it into decimals we need to divide 4 by 15
Thus, the Decimal value = 0.2666...
the Decimal value = 0.267
To convert it into a percentage we need to multiply it with 100
So,
The percentage values of the given fraction = 4/15 * 100
The percentage values of the given fraction = 26.67%
Therefore, the percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
What is the result from the expression[tex](6x-3)[/tex] is subtracted from [tex](-3x+2)[/tex]
Answer:
9 x - 5
Step-by-step explanation:
Simplify the following:
6 x - 3 - (-3 x + 2)
-(-3 x + 2) = 3 x - 2:
6 x - 3 + (-2 + 3 x)
Grouping like terms, 6 x - 3 - 2 + 3 x = (6 x + 3 x) + (-3 - 2):
(6 x + 3 x) + (-3 - 2)
6 x + 3 x = 9 x:
9 x + (-3 - 2)
-3 - 2 = -(3 + 2):
9 x + (-(3 + 2))
3 + 2 = 5:
Answer: 9 x - 5
ANYONE GOOD IN MATH PLEASE HELP!
Answer: 15
Step-by-step explanation:
The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15
What is a perimeter of a rectangluar drive way measuring 20 feet long and 15 feet wide?
The vector u is shown below. Find the component form of u. Round your final answers to the nearest hundredth. ū=( , ) IL 105°
According to the given vector, the component form of u is (−3.87, 1.048)
The term vector in math is known as a quantity or phenomenon that has two independent properties such as magnitude and direction
Here we have given that the value of the following are obtained through the given diagram.
θ = 165°
Then the value of |u| is calculated by using the formula,
=> ∣u∣ = 4θ
When we apply the value on it, then we get,
=> ∣u∣=4
Now, we have to calculate the value of
=> ∣u∣cos165° = −3.864
=> ∣u∣sin165° = 1.035
Then the component form of the vertor u is written as,
=> u = (∣u∣cos165°, ∣u∣sin165°)
When we apply the values on it, then we get the resulting form as,
=> u = (−3.87, 1.048)
Complete question:
The vector u is shown below. Find the component form of u.
To know more about vector here.
https://brainly.com/question/29740341
#SPJ4
Rewrite this number in appropriate scientific notation:
459,000
Answer:
4.59 × 10^(5)
Step-by-step explanation:
Answer: 4.59 x 10^5
Step-by-step explanation:
If we move the decimal place over 5 times in the answer we get 459,000.
I hope this was able to help you :D
4. Write the expression in
words.
h - 3
Answer:
h minus three
Step-by-step explanation:
Consider the following frequency table representing the scores on a test.
Scores on a TestClass Frequency
30–46
10
47–63
3
64–80
13
81–97
12
98–114
12
Step 3 of 5 :
Determine the class width of each class.
The class width of each class is 17.
What is the class width?Class width is the distance between a class's upper and lower bounds (category). It may also refer to one of the following more precisely, depending on the author:
the difference between the upper and lower limits of two (nearby) consecutive classes, or the lowest and higher limits of two classes.
The width of each class in a frequency distribution table must be the same. Due to the fact that you are only working with a single width, this makes calculating the class width relatively simple (as opposed to varying ones).
To find the class width in this, we subtract the lower limits of two consecutive class. i.e.
47 - 30 = 17
64 - 47 = 17
81 - 64 = 17
98 - 81 = 17
So that, The class width of each class is 17.
To learn more about class width visit:
https://brainly.com/question/20462969
#SPJ1
the triangle below js equilateral. find the length of side x in the simplest radical form with a rational denominator
The length of side x is given as follows:
[tex]x = \frac{11\sqrt{3}}{3}[/tex]
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have that:
The angle is of 60º.The adjacent side is of x.The opposite side is of 11.Applying the tangent, the length x is obtained as follows:
tan(60º) = 11/x
x = 11/tan(60)º
[tex]x = \frac{11}{\sqrt{3}}[/tex]
[tex]x = \frac{11\sqrt{3}}{3}[/tex]
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Can someone help me thank you
EASY just say THANK YOU!!!
Answer:
1. 3 ones
2. 3
3. 3 tens
4. 3
5. 3 hundreds
6. 3
7. 3 halves
8. 3 (not 3/2)
9. 3 fourths
10. 3
11. 3
12. 2
13. 1/2
14. 3
15. 5/2
16. 3/4
17. 3
18. 3/2
19. 3/4
20. 7/2
21. 2/3
22. 4/11
NOTE: Read the step-by-step explanation on how we arrive on these final answers. Don't just copy-paste it and try to understand the concept so that next time you already know how to solve this type of expressions.
Step-by-step explanation:
This is a simple mathematic problem which requires basic strategies to be solved. People should already know on how to calculate these simple mathematic tasks. Most especially to the first 7 items, we will just use division to get the final answer (numerator/denominator).
[tex]\frac{9}{3}[/tex] = 3 or
9 ÷ 3 = 3
Similar, with the rest of items that includes fractions. We will just reciprocate the denominator and multiply it to the numerator to get the final answer.
Example was the item 8:
= [tex]\frac{9}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex]
= [tex]\frac{9}{2}[/tex] x [tex]\frac{2}{3}[/tex]
= [tex]\frac{18}{6}[/tex]
= 3
il 5 star your comment and thanks it and brainlist if u help me
Answer:
the 4 represents how many times 5 can go into 20
Gianna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Gianna will earn $50 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Gianna's songs were played on twice as many commercials as movies and her total earnings on the royalties from all commercials and movies was $800. Graphically solve a system of equations in order to determine the number of commercials, x,x, and the number of movies, y,y, on which Gianna's songs were played.
A graph of each function is shown in the image attached below.
The number of commercials (x) is equal to 8 commercials while the number of movies (y) is equal to 4 movies.
How to write and solve the system of equations graphically?In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of commercials.Let the variable y represent the number of movies.Since Gianna would earn $50 every time one of her songs is played in a commercial and $100 every time one of her songs is played in a movie, an equation which models it is given by;
50x + 100y = 800
Additionally, Gianna's songs were played on twice as many commercials as movies;
x = 2y
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (8, 4) as shown in the image attached below.
Read more on a graph here: brainly.com/question/4546414
#SPJ1
Work with a partner. Baby manatees are about 4 feet long at birth. They
grow to a maximum length of 13 feet.
a. Which of the following can represent a baby manatee's growth?
What does x represent? Explain your reasoning.
x + 4 < 13
x + 4 ≤ 13
x-4> 13.
x-4 ≥ 13
An equation which can represent a baby manatee's growth include the following: B. x + 4 ≤ 13.
The variable x represent the baby manatee's growth after birth.
How to write and solve the required inequality?In order to write and solve an inequality that represents a baby manatee's growth, we would take note of the following important information;
The maximum length is equal to 13 feet.Baby manatees are typically about 4 feet long at birth.Let the variable x represent the baby manatee's growth after birth.Now, we can write an inequality that represents the value of x for which a baby manatee's growth as follows;
x + 4 ≤ 13
By subtracting 4 from both sides of the inequality, we have the following:
x + 4 - 4 ≤ 13 - 4
x ≤ 11
Read more on inequality here: brainly.com/question/19732652
#SPJ1
can someone give me the answer asap
Answer:
Rise: 2
Run: 1
Slope: 2
At what point does the line intersect the y-axis? (0,-1)
Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a % confidence level. What does the confidence interval tell about the population of all college students in the state?
Question content area bottom
Part 1
What is the confidence interval for the population mean ?
The 95% confidence interval for the population mean is given as follows:
(3.64, 4.18).
It tells that we are 95% sure that the true population mean rating is between these two bounds.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 15 - 1 = 14 df, is t = 2.1448.
The remaining parameters for this problem are given as follows:
[tex]\overline{x} = 3.91, s = 0.48, n = 15[/tex]
Hence the lower bound of the interval is of:
[tex]3.91 - 2.1448\frac{0.48}{\sqrt{15}} = 3.64[/tex]
The upper bound of the interval is of:
[tex]3.91 + 2.1448\frac{0.48}{\sqrt{15}} = 4.18[/tex]
Missing InformationThe sample is given as follows:
3.9
3.1
3.7
4.4
3.2
4.1
3.3
4.4
4.3,
4.4
4.5
3.9
3.2
4.2,
4.0
More can be learned about the t-distribution at https://brainly.com/question/17073112
#SPJ1