Answer:
Step-by-step explanation:
A vacuum flask (for keeping drinks hot) is modelled as a closed cylinder in which the internal radius is r cm and the internal height is h cm.
The volume of the flask is 1000 cm³. A flask is most efficient when the total internal surface area, A cm², is a minimum.
(i) Show that A = 2π2²+ 2000/2
(ii) Given that r can vary, find the value of r, correct to 1 decimal place, for which A has a stationary value and verify that the flask is most efficient when r takes this value.
(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.
HELP ASAP!!! A spinner has three sections colored green, purple, and pink. If the spinner is spun twice, how many branches would the tree diagram that represents this situation have? 6 5 9 12
Answer:
The answer is 9.
Answer:
The answer is 9
Step-by-step explanation:
I got it right on the quiz
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
Coordinates switch, and the new y-coordinate changes sign
Explanation:
We have point A with the coordinates (-1,2), when we rotate it c90º it becomes (2,1).
What happened? The coordinates switched and the x-coordinate of A (-1) became the y-coordinate of A' (1) and it changed its sign.
Answer:
A. The coordinates switch and the new x-coordinate changes sign
Step-by-step explanation:
Hope this helps! ✌️
A study was performed to investigate whether teens and adults had different habits when it comes to consuming meat-free meals. In particular, the researchers were interested in the relationship between p1, the proportion of teens who would report eating at least one meat-free meal in the past week, and p2, the proportion of adults who would report eating at least one meat-free meal in the past week. A random sample of 875 teens and a separate random sample of 2,323 adults found that 555 of the teens and 1,601 of the adults reported eating at least one meat-free meal in the past week. The conditions for inference were checked and verified. What is the correct set of hypotheses the researchers should test in this scenario
Answer:
H₀ should be rejected at CI 95% .
Then the proportion of adults with 95 % CI is bigger than the proportion of teen
Step-by-step explanation:
From adult sample:
n₂ = 2323
x₂ = 1601
p₂ = 1601 / 2323 p₂ = 0,689 or p₂ = 68,9%
From teen sample:
n₁ = 875
x₁ = 555
p₁ = 555/ 875 p₁ = 0,634 or p₁ = 63,4
Values of p₁ and p₂ suggest that the proportion of adults consuming at least one meat free meal per week is bigger than teen proportion.
To either prove or reject the above statement we have to develop a difference of proportion test according to:
Hypothesis test:
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₂ > p₁
So is a one-tail test to the right
We can establish a confidence interval of 95 % then α = 5 %
or α = 0,05
As the samples are big enough we will develop a z test
Then z(c) for α = 0,05 from z table is z(c) = 1,64
To calculate z(s)
z(s) = ( p₂ - p₁ ) / √p*q* ( 1/n₁ + 1/n₂ )
where p = ( x₁ + x₂ ) / n₁ + n₂ p = 555 + 1601 / 875 + 2323
p = 2156/3198 p = 0,674
and q = 1 - 0,674 q = 0,326
z(s) = ( 0,689 - 0,634 ) / √0,674*0,326 ( 1/875 + 1 / 2323
z(s) = 0,055/ √ 0,2197 ( 0,00114 + 0,00043)
z(s) = 0,055/ √0,2197* 0,00157
z(s) = 0,055/ √ 3,45*10⁻⁴
z(s) = 0,055 / 1,85*10⁻²
z(s) = 5,5/1,85
z(s) = 2,97
Comparing z(s) and z(c) z(s) > z(c)
Then z(s) is in the rejection region we reject H₀.
We can claim that the proportion of adult eating at least one meat-free meal is bigger than the proportion of teen
A population of bacteria in a petri dish is modeled by the function p(x)=88x , where x is the number of hours that have elapsed since the bacteria was introduced to the petri dish.
When will there be fewer than 512 bacteria?
Enter your answer rounded to the nearest hundredth in the boxes.
Answer:
3.14
Step-by-step explanation:
The answer is going to be 3.14
Hope it helps!
For 3-7, Open Response
For 3-7, Determine whether the linear
relationship is proportional. Show
work.
3. Gabrielle is buying bananas. Each
banana costs 9 cents.
The linear relationship is proportional
Determining whether the linear relationship is proportionalFrom the question, we have the following parameters that can be used in our computation:
Gabrielle is buying bananas. Each banana costs 9 cents.Using the above as a guide, we have the following:
Unit rate = Cost of banana/Number of banans
substitute the known values in the above equation, so, we have the following representation
Unit rate = 9/1
Evaluate
Unit rate = 9 cent per banana
This means that the linear relationship is proportional
Read more about proportional relationship at
https://brainly.com/question/28651666
#SPJ1
9. Complete the following equation using <,>, or =
100% _1
O A. >
O B. <
O C. =
Answer:
C. =
Step-by-step explanation:
Two ways to think about this problem:
1st way: 100% and 1 are all a whole, therefore, they are equal.
2nd way: 1=1/1. Multiply the denominator and the numerator by 100, 1/1=100/100=100%
what is the place value of 5 in . number 4 256
Answer:
4 2 5 6
Ones : 6
Tens : 5
Hundreds : 2
Thousands : 4
Step-by-step explanation:
hope I'm right
8 men can complete the project in 24 days in how many days 12 men can complete the same project
Answer:
16days
Step-by-step explanation:
This is an inverse proportionality
Let the number of men be m
Let the time taken in days be d
Hence m ∝ 1/d
m = k/d
If 8 men can complete the project in 24 days, then;
8 = k/24
k = 8*24
k = 192
To determine the time it will take 12 men to complete the same job, we will say;
m = k/d
12 = 192/d
d = 192/12
d = 16
Hence it will take 12men 16days to finish the same job
How many cups are in 5/1/2 pints
Answer:
11 cups
Step-by-step explanation:
Answer:
11 us cups are in 5 1/2 pints
Step-by-step explanation:
hope this helps
You have collected weekly earnings and age data from a sub-sample of 1,744 individualsusing the Current Population Survey in a given year. Given the overall mean of $434.49and a standard deviation of $294.67, construct a 99% confidence interval for averageearnings in the entire population. State the meaning of this interval in words, ratherthan just in numbers. If you constructed a 90% confidence interval instead, would itbe smaller or larger? What is the intuition?
Answer:
The 99% confidence interval for average weekly earnings in the entire population is between $416.42 and $452.66. This means that we are 99% sure that the true population mean weekly earnings is between these two values.
Due to the smaller margin of error, the confidence interval would be smaller, that is, less likely to contain the true population mean.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{294.67}{\sqrt{1744}} = 18.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 434.49 - 18.17 = $416.42
The upper end of the interval is the sample mean added to M. So it is 434.49 + 18.17 = $452.66
The 99% confidence interval for average weekly earnings in the entire population is between $416.42 and $452.66. This means that we are 99% sure that the true population mean weekly earnings is between these two values.
If you constructed a 90% confidence interval instead, would it be smaller or larger? What is the intuition?
For a 90% confidence interval, we would have z = 1.645.
Looking at the margin of error formula, M and z are direct proportional, that is, as z decreases so does M. Due to the smaller margin of error, the confidence interval would be smaller, that is, less likely to contain the true population mean.
In the right triangle shown, find x.
PLEASE HELP!!!!
What part of a
a dozen is 8?
Answer:
8 Dozen eggs would mean, 8 X 12 = 96 eggs
Step-by-step explanation:
Answer:
[tex]\frac{2}{3}[/tex]
or
0.67
Step-by-step explanation:
a dozen is 12
12/4 = 3
8/4 = 2
8 is 2/3 of a dozen(12)
2/ 3 = 0.66666666666667 which is about 0.67
4z + 8 - 6=
7z ÷ 4 + 5x=
y² ÷ (3z) =
I NEED HELP :(
Answer:
1: 14z+2
2: 7z/4 + 5x
3: y²/3z
Given the data set, calculate the range and the mode:
{9, 3, 1, 8, 3, 6}
Use a formula to find the are.
Karyn has 11/8 pounds of chili to put into three bowls. The amount of chili in each bowl does not have to be the same. How much chili could Karyn put into each bowl? Solve this
Answer:
bowl a: 11/8 pounds of chili
bowl b: 11/24 pounds of chili
bowl c: 33/48
The lengths of nails produced in a factory are normally distributed with a mean of 4.95 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 5% and the bottom 5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
The length that separates the bottom 5% is of 4.87 centimeters.
The length that separates the top 5% is of 5.03 centimeters.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 4.95 centimeters and a standard deviation of 0.05 centimeters.
This means that [tex]\mu = 4.95, \sigma = 0.05[/tex]
Bottom 5%:
The 5th percentile, which is X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 4.95}{0.05}[/tex]
[tex]X - 4.95 = -1.645*0.05[/tex]
[tex]X = 4.87[/tex]
The length that separates the bottom 5% is of 4.87 centimeters.
Top 5%:
The 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 4.95}{0.05}[/tex]
[tex]X - 4.95 = 1.645*0.05[/tex]
[tex]X = 5.03[/tex]
The length that separates the top 5% is of 5.03 centimeters.
Can someone help me with this pls [cry]
Answer: B
Step-by-step explanation:
JUST DID A QUIZ WITH IT
someone please help me answer this!!!
Answer:
15 using the Pythagorean theorem.
hope it helps, plz mark me as brainliest.
Answer:
15 units is the answer.
Step-by-step explanation:
points are (-3,-4) and (6,8)
Pythagorean theorem can be written as,
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(6-(-3))^2 + (8-(-4))^2}\\\\d=\sqrt{(9)^2+(12)^2} \\\\d=\sqrt{81+144} \\\\d=\sqrt{225} \\\\d=15[/tex]
∴ d = 15 units is the distance between the points.
The quadratic function h is shown on the graph. If the graph is h(x) = (3/5 ) (x – d)(x + 6), what is the value of d?
Answers ↓
(A) -14
(B) 14
(C) -60
(D) 42/5
9514 1404 393
Answer:
(B) 14
Step-by-step explanation:
"d" is a value that makes the function be zero. The x-intercepts (zeros) of the function are at x=-6 and x=14, corresponding to factors (x +6) and (x -14). The (x+6) factor is already given in the equation, so we must conclude d=14.
PLZ HELP I WILL MAKE YOU BRAINLIEST NO FAKE LINKS
Answer:
1/30 of an hour
Step-by-step explanation:
SOMEONE PLZZ HELP ME! THIS IS DUE TODAY (I WILL GIVE BRAINLIEST)
This is the graph of f(x). What is the value of f(2)?
10-+
Ο Α. 16
Β. 2
C. 4
D. 8
Answer:
b
Step-by-step explanation:
Please help me i really need help
Answer:
[tex]A=745.06[/tex]
[tex]C=96.76[/tex]
Clumsy Carl is running a marathon. There are 3 dangerous areas on the course, and Clumsy Carl approximates
that he has a 50% chance of falling at each spot, independent of if he falls at the other spots.
The table below shows the total number of people that will see Carl fall based on how many times he falls.
What is the expected total number of people that will see Carl fall?
Round your answer to the nearest hundred.
Answer:600
Step-by-step explanation: Khan Academy
I need help and it’s due soon
Answer:
Point A
Step-by-step explanation:
Answer:
point A
Step-by-step explanation:
The point A is opposite with the point R and the x-axis is between them.
A pair of jeans is on sale for 20% off. The sale price is $55.00. What is the original amount of the pair of jeans?
Answer:
$86.75 i think
Step-by-step explanation:
Subtract 14y + 375 from 8(2y − 1)
Answer:
2y + 367
Step-by-step explanation:
8(2y - 1) - 14y + 375
16y - 8 - 14y + 375
2y + 367
The area of a triangle is 174 square inches. The base is 29 inches. What is the height in inches? Do not include units in your answer.
Answer:
Your answer would be 6
Step-by-step explanation:
Area=174
Base=29
174 divided by 29
Equals 6
6 times 29
Equals 174
So since 29 times 6 gave you 174 which is your area, your answer would be 6 since it is the missing height to your problem.
:)
Answer: 12
Step-by-step explanation:
We can use the formula for the area of a triangle, to help us find the height:
Area=12⋅b⋅h
Using the formula for area, we can solve for the height by plugging in the information we have about the area and the base:
174=12⋅29⋅h
Isolate h by multiplying both sides by 2 and dividing both sides by 29.
hh=2⋅17429=12
The height is 12 inches.