(i) To find the total internal surface area, we need to calculate the area of the curved surface and the areas of the top and bottom circles.
The curved surface area of the cylinder is given by the formula:
A_curved = 2πrh
The area of the top and bottom circles is given by the formula:
A_circles = 2πr²
The total internal surface area is the sum of the curved surface area and the areas of the top and bottom circles:
A = A_curved + A_circles
= 2πrh + 2πr²
Given that the volume of the flask is 1000 cm³, we have the equation:
πr²h = 1000
Solving for h, we get:
h = 1000 / (πr²)
Substituting this value of h into the equation for A, we have:
A = 2πrh + 2πr²
= 2πr(1000 / (πr²)) + 2πr²
= 2000/r + 2πr²
Simplifying further, we get:
A = 2000/r + 2πr²
= 2πr² + 2000/r
(ii) To find the value of r for which A has a stationary value, we differentiate A with respect to r and set the derivative equal to zero.
dA/dr = 4πr - 2000/r² = 0
Multiplying through by r², we get:
4πr³ - 2000 = 0
Solving for r, we have:
4πr³ = 2000
r³ = 2000 / (4π)
r = (2000 / (4π))^(1/3)
Calculating this value to one decimal place, we get:
r ≈ 3.4 cm
To verify that the flask is most efficient when r takes this value, we need to check the second derivative of A with respect to r.
d²A/dr² = 12πr² + 4000/r³
Substituting the value of r, we have:
d²A/dr² = 12π(3.4)² + 4000/(3.4)³
Calculating this value, we find that it is positive, indicating a minimum. Therefore, the flask is most efficient when r ≈ 3.4 cm.
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
Solve for x. Round your answer to the nearest tenth.
42
37
X=
units
Answer:
10
Step-by-step explanation:
That little square gives you a hint that it's an 90 degree angle/ acute angle First add 42 and 37 and you will get 79. Next subtract 79 from 90 and you will get 11. (5 or more, raise the score, for or less, let it rest.) 11 equals 10.
Numarical form:
47 + 37 = 79
90 - 79 = 11
11 = 10
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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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
A quadrilateral has four angles.
Each angle is 90°
(6) Write down the mathematical name of this quadrilateral.
Square and Rectangle
I hope this helps you
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
which expressionis 4 times as large as the expression 34 minus 15
Answer:64?
Step-by-step explanation:
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
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
Elvin has three sails of different sizes for his model ships. Which of the sails are congruent, and which are similar?
45°
15 in.
3x in.
9 in.
- 10x)
5 in 4593 in.
Fly - 10x)"
EK IF
z in.
255
55°
BK
A 80
R
OR
4 in.
4 in.
Sail 1
Sail 11
Sail III
Similar means angles are the same
Congruent means angles and sides are the same.
Sail 1 and sail 2 have the same angles but the sides are not the same.
So sail 1 and sail 2 are similar.
Pllllllllllllllllllllllllllllssssssssssssssssssssssssssss
Answer:
50.24 units^2
Step-by-step explanation:
Area of circle formula: [tex]\pi[/tex]r^2
r = 4, [tex]\pi[/tex] = 3.14
3.14 * (4^2) = 3.14 * 16 = 50.24
Answer:
Step-by-step explanation:
3.14*4^2
3.14*16= 50.24
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]
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
Write the additive inverse and multiplicative inverse of 3-7i?
Step-by-step explanation:
additive inverse means multiplying 3-7i by it's conjugate which would be
(3-7i)(3+7i)=3^2+7^2=9+49=58
the multiplicative inverse of a number z is 1/z
1/(3-7i)
multiply numerator and denominator by 3-7i's conjugate and it equals 58
(3-7i)/58
3/58-7/58i
Hope that helps :)
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:
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
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
During the flight of a projectile the x component of the velocity is
A.same during its whole journey
B.maximum when it hits the ground
C. Zero at the highest point
D. Maximum when it leaves the ground
Answer:
D. Maximum when it leaves the ground
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
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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VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
(3, -2)
Step-by-step explanation:
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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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
-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)
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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A landscaping company charges a $12 fee to make a house call plus an hourly rate for labor if the total bill for a job that takes two and a half hours comes to $95.75 write an equation that can be used to solve for the hourly labor rate use R to represent the rate then solve the equation and explain all steps
12 multiplied by 2.5=30=95. 75-30=65.75
Helppp meeeee plssss I would me the world
Answer:
its 3 trust me
Step-by-step explanation:
Answer:I’m thinking it’s the first one but someone else might know for sure sorry
Step-by-step explanation:
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.
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° :)
PLS ANSWER QUICK, HELP
Answer:
6 inches of paper:)!
Step-by-step explanation: