The required value for the lamina of uniform density [tex]\bar x\\[/tex] and [tex]\bar y[/tex] are written below,
[tex]\bar x = \dfrac{5}{8}\\[/tex]
[tex]\bar y = \dfrac{5}{14}[/tex]
Given that:
The density of lamina: ρThe graph for the lamina: [tex]y = x^{\frac{2}{3}}[/tex], y = 0, and x = 1Calculus's core idea of integration entails determining a function's integral. It is a reverse process of differentiation that enables us to compute cumulative numbers, find the area under a curve, solve differential equations, and more.
The function can be written as,
[tex]m = \rho\int_0^1x^{\frac{2}{3}}dx\\= \rho\left[\dfrac{x^{\frac{5}{3}}}{\frac{5}{3}}}\right]\\=\dfrac{3}{5}\rho[/tex]
The value of Mx can be calculated as,
[tex]M_x = \rho\int_0^1\dfrac{x^{\frac{2}{3}}}{2}}\times x^{\frac{2}{3}}dx\\=\dfrac{\rho}{2}\left[\dfrac{x^{(\frac{2}{7})}}{\frac{7}{3}}\right]_0^1\\=\dfrac{3}{14}\rho[/tex]
Calculate the value of My,
[tex]M_y =\rho \int_0^1 x\times x^{\frac{2}{3}}dx\\=\rho \left[\frac{x^\frac{8}{3}}{\dfrac{8}{3}}\right]\\=\dfrac{3}{8}{\rho[/tex]
The value of [tex]\bar x\\[/tex] will be calculated as,
[tex]\bar x = \dfrac{M_x }{m}\\=\dfrac{ \dfrac{3}{8}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{8}[/tex]
The value of [tex]\bar y\\[/tex] is calculated as,
[tex]\bar y= \dfrac{M_y }{m}\\=\dfrac{ \dfrac{3}{14}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{14}[/tex]
Therefore, the required values are [tex]\bar x = \dfrac{5}{8}\\[/tex] and [tex]\bar y = \dfrac{5}{14}[/tex].
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A magazine includes a report on the energy costs per year for32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.42 . Assume the sample is taken from a normally distributed population. Construct 98 % confidence intervals for (a) the population variance sigma squared and (b) the population standard deviation sigma .
Interpret the results. (a) The confidence interval for the population variance is (___,___ ). (Round to two decimal places as needed.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98 % confidence, you can say that the population variance is less than ___.
B. With 2 % confidence, you can say that the population variance is between nothing and ___ .
C. With 98 % confidence, you can say that the population variance is between ___ and ___ .
D. With 2 % confidence, you can say that the population variance is greater than ___
(b) The confidence interval for the population standard deviation is (n___,___). (Round to two decimal places asneeded.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
B. With 98% confidence, you can say that the population standard deviation is greater than ___ dollars per year.
C. With 2% confidence, you can say that the population standard deviation is less than ___ dollars per year.
D. With 2% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
Answer:
a
The confidence interval for the population variance is [tex] 5.49 < \sigma^2 < 37.02 [/tex]
The correct option is C
b
The confidence interval for the population standard deviation is [tex] 2.34 < \sigma < 6.08 [/tex]
The correct option is A
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The standard deviation is [tex]s = \$3.42[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = 14 -1[/tex]
=> [tex]df = 13 [/tex]
Given that the confidence level is 98% then that level of significance is
[tex]\alpha = (100 -98) \%[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally the 98% confidence interval for the variance is mathematically represented as
[tex]\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}} < \sigma^2 < \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}[/tex]
=> [tex]\frac{(14- 1) (3.42)^2}{x^2 _{[\frac{0.02 }{2} , 13]}} < \sigma^2 < \frac{(14- 1) (3.42)^2}{x^2 _{[1- \frac{0.02 }{2} , 13]}}[/tex]
From the chi -distribution table
[tex]x^2 _{[1- \frac{0.02 }{2} , 13]} = 4.107[/tex]
and
[tex]x^2 _{[\frac{0.02 }{2} , 13]} = 27.689[/tex]
So
=> [tex]\frac{(14- 1) (3.42)^2}{27.689} < \sigma^2 < \frac{(14- 1) (3.42)^2}{4.107}[/tex]
=> [tex] 5.49 < \sigma^2 < 37.02 [/tex]
Generally the 98% confidence interval for the standard deviation is mathematically represented as
[tex]\sqrt{\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}} < \sigma <\sqrt{ \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}}[/tex]
=> [tex]\sqrt{5.49} < \sigma < \sqrt{37.02 }[/tex]
=> [tex] 2.34 < \sigma < 6.08 [/tex]
If 5/9 of a tank can be filled in 2minutes , how many minutes will it take to fill the whole tank?
Answer:
4 1/2 minutes
Step-by-step explanation:
.
Multiply 3/5 by 10/21 Express your answer in simplest form
Answer:
2/7
Step-by-step explanation:
Answer:
3/5 * 10/21= 2/7
64 mi/h to ft/s HELP HELP HELP HELP NOW!!!! WILL PUT 5 STARS AND MARK BRAINLIEST!!!
Answer:
Multiply 64 x 5280
Step-by-step explanation:
You will get your answerhelloAnswer:
64 mi/h = 93.9 ft/s I have the answer guide
What is the quotient of 1 1/4 divided by 21 1/4
Answer:
quotient of 11/4 to be divided by 21 /1/4
gives you 7/8/11
Given the equation y=12x, x representing number of hours worked, y representing amount of money earned, how much would John earn if he worked 6 hours?
9514 1404 393
Answer:
72
Step-by-step explanation:
Substitute 6 for x in the equation and do the arithmetic.
y = 12x
y = 12·6 = 72
John earns 72 money units in 6 hours.
Dominique has $13.75 in her piggy bank. All of the money are quarters. How many quarters are in the piggy bank?
Answer: I think its 0.55
Step-by-step explanation: if you do 25 times 0.55 because quarter's are 25 cents it equals 13.75
The number of quarters in the piggy bag will be 55.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.
Given that Dominique has $13.75 in her piggy bank. All of the money is quarters.
The number of the quarters will be calculated as:-
1 dollar ⇒ 4 quarters
13.75 dollars ⇒ 13.75 x 4 quarters
13.75 dollars ⇒ 55 Quarters
Therefore, the number of quarters in the piggy bag will be 55.
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HELP ASAP PLEASE
Given x^2=81, select all possible values of x.
A. -9
B. -3
C. 0
D. 3
E. 9
Answer:
A and E
Step-by-step explanation:
x² = 81
~Take the square root of both sides
x = ±9
Best of Luck!
Answer:
The answer is a and e
Step-by-step explanation:
Can someone help me out and fast?
Answer:
yes, lets see...no that is not a function.
Step-by-step explanation:
no explanation...that's where your on your own, sorry. (its very hard to explain,
but i know that its impossible to have a function like THAT)
Answer:
no because there are 2 lines on the same x axis
Step-by-step explanation:
A bug starts at the origin of the coordinate plane. The bug moves One-fourth units right and One-fourth units down to point A. Which graph shows the location of point A?
Answer:
the answer would be d
Step-by-step explanation:
i took the test on edge2020
Answer:
D
Step-by-step explanation:
Edg 2020
t> -5
can someone show step by step how to solve this equation?
Answer: The equation cannot be simplified any further.
Explanation: The variable(t) is greater than any number than negative five.
Plz mark brainliest:)
how long does it take an airplane if it files a distance of 2000 miles at a rate of 500mph
Answer:
4 hours
Step-by-step explanation:
We can find the time using the formula [ t = d/s ] where d = distance and s = speed.
t = 2000/500
t = 4 hours
Best of Luck!
As shown in the table, prizes are awarded to students who Benjamin, a student in the class, answers 80 math probalems correctly. His grandmother pays $0.25 per correct answer. His uncle gives him a donation. If benjamin receives $45 from his grandmother ans uncles, how much money does his uncles give him? Explain.
Yousef typed a 36-word paragraph in 23 minute. What is his typing speed, in words per minute?
Answer:
1.5652173913 words per minute.
Step-by-step explanation:
When you divide 36 words/ 23 minutes, you get 1.5652173913.
HELP! WILL MARK BRAINLIEST!
Answer:
The answer to this question is C.
Step-by-step explanation:
All that you have to do is multiply the exponents.
How many 3-digit natural numbers are there?
Answer:
900
Step-by-step explanation:
natural numbers are all positive numbers that dont include 0
Match each equation with its solution equation n-13=-12
Answer:
n=1, :) :P UwU TwT -_-
Answer:
n = 1
Step-by-step explanation:
n-13=-12
n-13-(-12)=0
n-1=0
n=1
The Dean of the Business School at State University would like to test the hypothesis that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course. A random sample of eight students who took both courses was selected and their final exam grades for each course are shown below.
Student 1 2 3 4 5 6 7 8
Marketing 82 86 74 93 90 76 87 100
Finance 76 91 70 79 96 70 85 81
If Population 1 is defined as the Marketing exam scores and Population 2 is defined as the Finance exam scores. Which of the following test is appropriate for Dean's hypothesis?
a. One-way ANOVA
b. Paired samples t- test
c. One sample t- test
d. Independent samples t-test
Answer:
Paired samples t- test is appropriate for Dean's hypothesis
Step-by-step explanation:
Given Data :
Student 1 2 3 4 5 6 7 8
Marketing 82 86 74 93 90 76 87 100
Finance 76 91 70 79 96 70 85 81
We are supposed to find the test which is appropriate for Dean's hypothesis
We are given the grades of two different subjects for same student
We perform the paired t test because the final grades for the Marketing and Finance is taken for the same student.
So, Option B is correct
Hence Paired samples t- test is appropriate for Dean's hypothesis
17-6r=25-3r answer it please
Answer: r = - 8/3
Step-by-step explanation: im pretty sure thats the write answer
Six and forty-two ten-thousandths as a decimal
True or False: A triangle can be formed with sides 3inches, 3inches, 6inches. Explain your choice.
Answer: It's true because 3+3+6 = 12 and a triangle has 3 sides and 12/3 is 4 that's why a triangle can be fored with these measurments.
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
It would be classified as an isosceles triangle.
Hope this helps!
James is studying different kinds of weather. Rain has water drops that are larger than 0.02 inch in diameter. Small hailstones are less than 14 inch in diameter. Complete the statement that best represents the different kinds of weather James studied. Select one correct answer from each box to complete the sentence.
Answer:
wheres the stament
Step-by-step explanation:
Answer:
huh
Step-by-step explanation:
The endpoints of EF¯¯¯¯¯ are located at E (−3, 2) and F (3, 8). Point D divides EF¯¯¯¯¯ such that ED : DF is equal to 1 : 3. For each box, select the values in the dropdown that make the statement true. The x-coordinate of point D is and the y-coordinate of point D is
Answer:
[tex]D(x,y) = (-1.5,3.5)[/tex]
Step-by-step explanation:
Given
[tex]E = (-3,2)[/tex]
[tex]F = (3,8)[/tex]
[tex]ED: DF = 1 : 3[/tex]
Required
Determine the coordinates of D
This is calculated as thus:
[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where:
[tex](x_1,y_1) = (-3,2)[/tex]
[tex](x_2,y_2) = (3,8)[/tex]
[tex]m:n = 1:3[/tex]
[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]D(x,y) = (\frac{1 * 3 + 3 *-3}{1+3},\frac{1 * 8 + 3 * 2}{1+3})[/tex]
[tex]D(x,y) = (\frac{-6}{4},\frac{14}{4})[/tex]
[tex]D(x,y) = (-1.5,3.5)[/tex]
Pleaseeeeeee I rlly need help y’all help me out PLEASE HELP ASAP WILL GIVE BRAINLEIST
Mr. Velasquez wants to make a scale drawing of a set for an upcoming play. If the actual width of the stage is 18 feet and the scale he is using is LaTeX: \frac{1}{2}in
1
2
i
n
: 15 feet. What would the width of the stage be in the scaled drawing?
Answer as a decimal.
Answer:
0.6 in
Step-by-step explanation:
Scale of drawing = ½ inch to 15 ft (½ in : 15 ft)
That is, ratio of the width on paper to actual width.
Given an actual width of 18 ft, the width of the stage on paper can be calculated as shown below:
½ in : 15 ft = x in : 18 ft
[tex] \frac{\frac{1}{2}}{15} = \frac{x}{18} [/tex]
[tex] \frac{1}{2}*\frac{1}{15} = \frac{x}{18} [/tex]
[tex] \frac{1*1}{2*15} = \frac{x}{18} [/tex]
[tex] \frac{1}{30} = \frac{x}{18} [/tex]
Cross multiply
[tex] 30*x = 18*1 [/tex]
[tex] 30x = 18 [/tex]
Divide both sides by 30
[tex] \frac{30x}{30} = \frac{18}{30} [/tex]
[tex] x = \frac{18}{30} = \frac{6}{10} [/tex]
[tex] x = 0.6 [/tex]
Width of the stage in scale drawing = 0.6 in
what divide by -1/2 equals -7/3
is this a keep, change, change?
-9-8
Answer:
Yes, they cancel each other out.
Step-by-step explanation:
Personally never liked the keep, change, change method. Pemdas is what I use, however this is an easy one so nothing so major.
Find the midpoint of the line segment joining the points R(3,3) and S(-2,6).
Answer: 2,9
(3,3) & (-2,6) midpoints
Answer:
(0.5,4.5)
Step-by-step explanation:
Use the midpoint formula to find the answer: ((x1+x2/2),(y1+y2/2))
((3-2/2),(3+6/2))
((1/2),(9/2))
(0.5,4.5)
I need to find the missing angle of this triangle or whatever it is
Answer:
×=126+28
=154 degrees
2
10x2 - 724
100x2 + 140xy + 4972 10x + 7y
Answer:
14xy/(10x+7y)^
Step-by-step explanation:
(11 points!) PLEASEEEEEEEEE Find the value of x for numbers 6,7,8,and 9 and please attach work or a good explanation thank you sm in advance!❤️
(6) 2xº = 86º ==> x = 43
(7) 108º = 3xº ==> x = 36
(8) 72º = 4xº ==> x = 18
(9) 111º = (x + 21)º ==> x = 90
Answer:
1.
2x=86
x=43
2.
3x=108
x=36
3.
4x=72
x=18
4.
x+21=111
x=90