Answer:
The average function [tex]f_{avg}[/tex] value = 4
Step-by-step explanation:
Given that:
[tex]f(x,y,z) = 3x^2z+3y^2z[/tex]
The enclosed region [tex]z = 4 -x^2 -y^2[/tex] and the plane z = 0.
Over an area E, the average value of a function f(x,y,z) is:
[tex]f_{avg} = \dfrac{1}{V_{E}} \iiint_E f(x,y,z) dV ------ (1)[/tex]
where;
[tex]V_E[/tex] = volume of region E
To find the volume use cylindrical coordinates;
[tex]x=rcos \theta; \ \ \ y = rsin \theta; \ \ \ z = z[/tex]
Then;
E = 0 ≤ r ≤2, 0 ≤ θ ≤ 2π, 0 ≤ z ≤ 4 - r²
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} \int^{4-r^2}_{0} \ rdzdrd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} r(4-r^2) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} (4r-r^3) \ drd \theta[/tex]
[tex]V_E = \int^{2 \pi}_{0} \Big(2r^2- \dfrac{r^4}{4} \Big)^2_0 \ d \theta[/tex]
[tex]V_E = 4(2 \pi)\\\\ V_E = 8 \pi[/tex]
However, from equation (1):
[tex]f_{avg} = \dfrac{1}{V_E} \iiint_E f(x,y,z) \ dV \\ \\ = \dfrac{1}{8 \pi} \iiint_E (3x^2z + 3y^2 z) dV \\ \\ = \dfrac{1}{8 \pi } \int^{2 \pi}_{0} \int^{2 }_{0} \int^{4 - r^2}_{0} \ \ 3zr^2 \ rdzdrd\theta \\ \\ = \dfrac{3}{8 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} \Big(\dfrac{z^2}{2}\Big)^{4-r^2}_{0} \ r^3 drd\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (4-r^2)^2 \ r^3 \ dr d\theta[/tex]
[tex]= \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16-8r^2 + r^4)r^3 \ dr d\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16r^3 -8r^5 + r^7) \ dr d \theta \\ \\ = = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \Big (4r^4 - \dfrac{8}{6}r^6 + \dfrac{r^8}{8} \Big)^2_0 \ d \theta \\ \\ = \dfrac{3}{16 \pi } (2 \pi) \Big (64 - \dfrac{8}{6} \times 64 \times \dfrac{256}{8} \Big) \\ \\ = \dfrac{3}{16 \pi} (2 \pi) (\dfrac{32}{3}) \\ \\ = 4[/tex]
I NEED HELP WITH A PROBLEM
Answer:
64
Step-by-step explanation:
Volume of one sugar cube = 1x1x1= 1cm³
Volume of dish = 4x4x4 = 64cm³
Divide volume of dish by volume of one cube to find out how many can fit:
64/1 = 64
Please help! I need this answer fast!
Frank left his house at 7 am and drove to the airport at a speed of 50 mph. Lance left his house at 6 am and drove to the same airport at a speed of 55 mph. Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport.
At what time did Lance arrive at the airport?
Answer:
87
Step-by-step explanation:
Answer: 10:00 AM
This is the answer, and it’s correct. I did this problem and it’s 10:00 AM
-7x+4y=32
-5x-2y = -16
elimination method explain please
Answer:
(0,8)
Step-by-step explanation:
-7x+4y=32
-10x-4y=-32
-17x=0
x=0
-5×0-2y=-16
y=8
(0,8)
A computer randomly puts a point inside the rectangle. What is the probability that the point lands in triangle T?
Answer:
87.5%
Step-by-step explanation:
The area of the entire rectangle is 8 by 6,
8x6=48 so the area is 48 units^2.
The area of the triangle is A=1/2bh
A=1/2(2)(6)
A=1(6)
A=6 units^2
6/48=0.125
0.125=12.5%
You need to find the percent it will not land in the triangle, so subtract 12.5 from 100.
100-12.5=87.5
There is an 87.5% chance it will not land in the triangle
A company issues a general knowledge test to its potential employees as part of its recruitment procedures. The company does not invite the lowest scoring 20% back for a second interview. If the scores on this test are normally distributed with a mean of 60 and a standard deviation of 17. What mark (to the nearest whole number) must a candidate achieve in order to secure a second interview
Answer:
46
Step-by-step explanation:
Given :
Lowest scoring 20% ; this corresponds to score below (1 - 0.2) = 0.8
Mean, m = 60
Standard deviation, s = 17
Zscore = (x - mean) / standard deviation
Therefore, the Zscore for the bottom 20% equals ; P(x > Z) = 0.8
Using a Z probability calculator ;
The Zscore = -0.842
Therefore to Obtian the score, x
Zscore = (x - mean) / standard deviation
-0.842 = (x - 60) / 17
-0.842 * 17 = (x - 60)
-14.314 = x - 60
-14.314 + 60 = x
x = 45.686
To secure a second interview, candidate must score, 46 (nearest whole number).
The marks (to the nearest whole number) must a candidate achieve in order to secure a second interview is 46 and this can be determined by using the z-score formula.
Given :
A company issues a general knowledge test to its potential employees as part of its recruitment procedures.The company does not invite the lowest scoring 20% back for a second interview.If the scores on this test are normally distributed with a mean of 60 and a standard deviation of 17.Let 'x' be the mark must a candidate achieve in order to secure a second interview.
So, through the z-score formula, the value of 'x' can be determined.
[tex]\rm z_{score} = \dfrac{x-mean}{Standard\; Deviation}[/tex]
[tex]\rm -0.842 = \dfrac{x-60}{17}[/tex]
[tex]17\times -0.842 = x - 60[/tex]
x = 60 - 14.314
x = 45.686
So, the marks (to the nearest whole number) must a candidate achieve in order to secure a second interview is 46.
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tony completes one lap of a track every 20 seconds. diana completes one lap of the same track every 55 seconds. suppose tony and diana start at the starting line at the same time. how many seconds will it be before they cross the starting line at the same time again?
Answer:
220 seconds.
Step-by-step explanation:
55, 110, 165, 220.
20,40,60,80,100,120,140,160,180,200,220.
Both have 220 in common so will cross at 220 seconds at the same time.
Evaluate. 72 - 3 + 9 × 8 ÷ 2 w =
Answer:
Step-by-step explanation:
Request of activities so increase then division, at that point deduction and expansion.
9*8 = 72
72/2 = 36
72-3 = 69
69+36 = 105
Another way of saying it is:
Utilize the request for tasks to improve on mathematical articulations. The request is brackets, types and roots, augmentation and division, expansion and deduction. Duplication and division are "something similar" so you would utilize the first that happens from left to right.
Bit by bit clarification:
7^2 - 3 + 9 x 8 ÷ 2
49 - 3 + 9 x 8 ÷ 2
49 - 3 + 72 ÷ 2
49 - 3 + 36
49 - 39
W=10
Brainliest?
Write the equation of the line that passes through (7,-4) and (-1,-2) in slope-intercept form.
Answer:
y = -1/4x - 5/2
Step-by-step explanation:
-2- -4 /-1-7 = 2/-8 = -1/4
y+2 = -1/4(x+2)
y+2 = -1/4x - 1/2
y = -1/4x -5/2
Solve 24y + 0.2 = 29.6
Answer:
[tex]y=1.225[/tex]
Step-by-step explanation:
[tex]24y+0.2=29.6[/tex]
Subtract 0.2 from both sides:
[tex]24y+0.2-0.2=29.6-0.2\\24y=29.4[/tex]
Divide both sides by 24:
[tex]\frac{24y}{24} =\frac{29.4}{24} \\y = 1.225[/tex]
y = 1.225 is your final answer.
In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 95% confident that your sample mean is within 11 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 202 min. The minimum sample size required is_______computer users. (Round UP to the nearest whole number.)
Answer:
1568
Step-by-step explanation:
The computation of the minimum sample size is shown below:
Given that
Error E = 11
The population standard deviation [tex]\sigma[/tex] =217
Confidence level 1-α = 95%
Now following formula should be used
n > (Zalpha ÷ 2 × sigma ÷ E)^2
As we know that
Zalpha ÷ 2= 1.96
Now the sample size is
n> (1.96 × 202 ÷ 10)^2
= 1568
In a business meeting, every person at the meeting shakes every other person's hand exactly one time. The total number of 1/2 -n(n-1). - handshakes for n people at the meeting is given by an Evaluate a15 and interpret its meaning in the context of this problem. a15 If 15 people are present at the meeting, there will be handshakes.
We get : Handshakes = (15*(15-1))/2Handshakes = 105In a meeting with 15 people, there will be 105 handshakes in total
The handshake problem is a classic problem of combinatorial mathematics that gives the number of handshakes in a meeting where each individual shakes hands with each other individual.
The handshake problem can be expressed as follows:In a business meeting, every person at the meeting shakes every other person's hand exactly one time. The total number of 1/2 -n(n-1). - handshakes for n people at the meeting is given by an.
Evaluate a15 and interpret its meaning in the context of this problem. We need to find out the total number of handshakes that take place in a meeting of n people, and the formula for that is given as:Handshakes = (n*(n-1))/2Putting n = 15, .
It's important to keep in mind that this formula assumes that every person shakes hands with every other person exactly once.
If there are any deviations from this rule (e.g. someone doesn't shake hands with everyone, or someone shakes hands with someone else more than once), then the formula may not be accurate.
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Find the measure of the red arc or angle
The measure of the intercepted arc PS in the circle is 80 degrees.
What is the measure of arc PS?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the diagram:
Inscribed angle R = 40 degrees
Intercepted arc PS = ?
Plug the given value into the above formula and solve for arc PS.
Inscribed angle = 1/2 × intercepted arc.
40 = 1/2 × intercepted arc PS
Intercepted arc PS = 40 × 2
Intercepted arc PS = 80°
Therefore, arc PS measure 80 degrees.
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Help me please. This is due later today.
Answer:
2:5 i THINK
Step-by-step explanation:
what interest rate is the local credit union giving you on a car loan of 25,000 for 5 years if they will collect 1500 in interest? ASAP i only have 5 minutes
Answer:
1.2%
Step-by-step explanation:
find the value of x
help please !
Answer:
56°
Triangles are supposed to equal 180° when all the degrees inside are added, and when you add 44 and 80 it equals 124
Now you subtract 124 from 180 and then you get 56
So the answer would be 56° :)
4/12×1/8 in simplest form
Answer:
[tex]\frac{1}{24}[/tex]
Step-by-step explanation:
[tex]\frac{4}{12} *\frac{1}{8} =\frac{1}{24}[/tex]
A school district is considering moving the start of the school day at Groveland High from 8:00 a.m. to 9:00 a.m. to allow students to get more sleep at night. They want to estimate how many more hours of sleep teens get if their school starts at 9:00 a.m. compared to teens whose schools start at 8:00 a.m. The district takes random samples of 50 of students from Groveland High and 39 students from Phillips High School, which starts at 9:00 a.m., and surveys them about their sleep habits. The sample mean number of hours of sleep per student at Groveland is 7.1 hours, and the standard deviation is 1.7 hours. At Phillips, the sample mean is 8.3 hours of sleep, with a standard deviation of 1.9 hours. What is the 90% confidence interval for the difference in mean hours of sleep for students at the two high schools
Answer:
The answer is "[tex]\bold{(7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} }\\\\[/tex]"
Step-by-step explanation:
Given values:
[tex]\bar{x_1}=7.1\\\\\bar{x_2}=8.3\\\\s_1=1.7\\\\s_2=1.9\\\\n_1=50\\\\n_2=39[/tex]
Using formula:
[tex]\to (\bar{x_1} -\bar{x_2}) \pm t \sqrt{\frac{(s_1)^2}{n_1}+\frac{(s_1)^2}{n_2}} \\\\[/tex]
Put the values in the above formula:
[tex]\to (7.1-8.3) \pm 1.665 \sqrt{\frac{(1.7)^2}{50}+\frac{(1.9)^2}{39}} \\\\[/tex]
7).
2. Hot Text: For each graph, choose the correct sentence to describe the graph.
The graph represents a proportional relationship.
The graph does not represent a proportional relationship.
a. The graph represents a proportional relationship.
b. The graph does not represent a proportional relationship.
c. The graph does not represent a proportional relationship.
d. The graph represents a proportional relationship.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:
y = kx.
Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.
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What is the name for an upward trend for an exponential function?
Exponential Growth
Scientific Notation
Growth-Decay Notation
Exponential Decay
Answer:
Step-by-step explanation:
Exponential growth
PLZ HELP 3 MINUTES LEFT WIL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
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2 Easy 7th Grade questions but its due in 7 min HELP ASAP
A cylinder-shaped beaker is 6 inches tall and its base measures 4 inches across. For a science experiment, Gloria must fill 1/3 of the beaker with water. How much water will Gloria use for the experiment?
What is the height of the cone if the volume is 12 pie ft ? And radius is 3ft
Answer:
Step-by-step explanation:
Problem One
V = pi r^2 h
V = 3.14 * (4/2)^2 * 6
V = 3.14 * 4 * 6
V = 75.36
However, that is not the answer. The answer is 1/3 of that amount.
V1 = 1/3 * 75.36
V1 = 25.12
Problem 2
V= `12 pi
r = 3 feet
Formula
V = 1/3 pi r^2 h
12* pi = 1/3 * pi * 3^2 * h Cancel the pi s.
12 = 1/3 * 9 * h
12 = 3 h Divide by 3
12/3 = h
h = 4
PLEASE HELP!!
All measurements are in inches when not given. Find the area of the
following: *
12
15
180 inches ^2
100 inches 12
300 inches ^2
Answer:
180 inches ^2
Step-by-step explanation:
12 x 15 = 180
also i like your profile
Two chords, AC and DE, intersect inside of circle O at point X. AX=15 cm, CX= 12 cm, and EX= 21 cm. Find DE
Answer:
DE = 29.57
Step-by-step explanation:
Given:
AX = 15 cm,
CX = 12 cm,
EX = 21 cm.
Required:
Find DE
Solution:
AX and CX are segments of chord AC
DX and EX are segments of chord DE
Therefore,
DE = DX + EX
DE = DX + 21
We are not given the value of DX, so we need to find DX
Based on the intersecting chords theorem:
AX*CX = DX*EX
Plug in the values
15*12 = DX*21
180 = DX*21
Divide both sides by 21
180/21 = DX
8.57142857 = DX
DX ≈ 8.57
✅DE = DX + 21 = 8.57 + 21 = 29.57
Which data set could be represented by the box plot shown below?
10
12
14
16
18
20
22
24
26
Answer:
B
Step-by-step explanation:
12, 15, 15, 17, 19, 19, 20, 22, 24
The data set { 12, 14, 16, 18, 20, 22, 24, } is represented by the box plot above the number line.
Which data set could be represented by the box plot shown is to be determined.
Range, it is the set of the values that come out to an outcome for a certain mathematical operation.
A number line is defined as a line is a horizontal line that has equally distributed number offsets. The numbers contained on the line will determine, the number on the line that can be answered. The query that reaches the numeral resolves how it will be used, eg, planning a point.
Since the box only represent the data set of the interval of its length,
so from 12 to 24 on the number line is a set of values that are represented by the box.
Thus, The data set { 12, 14, 16, 18, 20, 22, 24, } is represented by the box plot above the number line.
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Which NCAA college basketball conference has the higher probability of having a team play in a college basketball's national championship game? Over the last 20 years, the Atlantic Coast Conference (ACC) ranks first by having a team in the championship game 10 times. The Southeastern Conference (SEC) ranks second by having a team in the championship game 8 times. However, both conferences have had teams in the championship game only one time, when Arkansas (SEC) beat Duke (ACC) 76–70 in 1994 (NCAA website, April 2009). Use these data to estimate the following probabilities.
a. What is the probability the ACC will have a team in the championship game?
b. What is the probability the SEC will have team in the championship game?
c. What is the probability the ACC and SEC will both have teams in the championship game?
d. What is the probability at least one team from these two conferences will be in the championship game? That is, what is the probability a team from the ACC or SEC will play in the championship game?
e. What is the probability that the championship game will not a have team from one of these two conferences?
Answer:
A)P(ACC has a team in the championship game) = 0.5
B)P(SEC has a team in the championship game) = 0.4
C)P(both ACC & SEC having teams in the championship games) = 0.05
D)P(ACC or SEC) = 0.85
E)P(not ACC or SEC) = 0.15
Step-by-step explanation:
A) We are told that in the last 20 years, ACC has had a team in the championship game for 10 times.
Thus;
P(ACC has a team in the championship game) = 10/20 = 0.5
B) SEC has a team in the championship game 8 times in the last 20 years;
Thus;
P(SEC has a team in the championship game) = 8/20 = 0.4
C) since both ACC and SEC have had teams in the championship game for the past 20 years, then;
P(both ACC & SEC having teams in the championship games) = 1/20 = 0.05
D) Addition rule of probability is that;
P(A or B) = P(A) + P(B) - P(A & B)
Applying it to this question, we have;
P(ACC or SEC) = P(ACC) + P(SEC) - P(ACC & SEC)
Plugging in the relevant values, we have;
P(ACC or SEC) = 0.5 + 0.4 - 0.05
P(ACC or SEC) = 0.85
E) from complement rule, we can find the probability that the championship game will not a have team from one of these two conferences.
Thus;
P(ACC not SEC) = 1 - P(ACC or SEC)
P(ACC not SEC) = 1 - 0.85
P(ACC not SEC) = 0.15
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Answer: 4/18
Step-by-step explanation:
The ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
Xavier writes a ratio out of 18 as the decimal 0.22222222.
Let's suppose the x out of 18 can be written as 0.22222222
x/18 = 0.22222222
x = 3.999999 ≈ 4
It means 4/18 can be written as 0.22222222
Thus, the ratio 4:18 can be written as the decimal 0.22222222, so the value in the numerator is 4.
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PLS ANSWER QUICK, HELP
Answer:
6 inches of paper:)!
Step-by-step explanation:
which expressionis 4 times as large as the expression 34 minus 15
Answer:64?
Step-by-step explanation:
Solve for mZIJL.
K
\100°
52°
o
Answer: mZIJL
Submit Answer
Answer:
m<IJL = 48
Step-by-step explanation:
<IJL = x
100 - 52 = x
x = 48
Subtract y from 5....
Answer:
5y-y= 5? I don’t know I’m not totally sure.
Step-by-step explanation: