Answer:
[tex]1.91\ \text{in}[/tex]
[tex]3.84\ \text{in}[/tex]
Step-by-step explanation:
V = Volume of cylinder = [tex]44\ \text{in}^3[/tex]
h = Height of cylinder
r = Radius of cylinder
Volume of cylinder is given by
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{44}{\pi r^2}[/tex]
Total surface area of a cylinder is given by
[tex]S=2\pi r^2+2\pi rh\\\Rightarrow S=2\pi r^2+2\pi r\times\dfrac{44}{\pi r^2}\\\Rightarrow S=2\pi r^2+\dfrac{88}{r}[/tex]
Differentiating with respect to radius
[tex]\dfrac{dS}{dr}=4\pi r-\dfrac{88}{r^2}[/tex]
Equating with zero
[tex]4\pi r-\dfrac{88}{r^2}=0\\\Rightarrow 4\pi r=\dfrac{88}{r^2}\\\Rightarrow r^3=\dfrac{88}{4\pi}\\\Rightarrow r=(\dfrac{22}{\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.91\ \text{in}[/tex]
Double derivative of S
[tex]\dfrac{d^2S}{dr^2}=4\pi+176>0[/tex]
So [tex]r[/tex] is minimum at [tex]\dfrac{dS}{dr}=0[/tex]
[tex]h=\dfrac{44}{\pi r^2}=\dfrac{44}{\pi 1.91^2}\\\Rightarrow h=3.84\ \text{in}[/tex]
So the radius and height of the cylinder is [tex]1.91\ \text{in}[/tex] and [tex]3.84\ \text{in}[/tex] respectively such that the least amount of metal is used.
20 points.Cynthia has a bag of jellybeans. There are two red jellybeans, one yellow jellybean, and two black jellybeans in her bag. Cynthia grabs two jellybeans and gives them to her friend, Pedro, and he eats them. What is the probability that she gives him two red jellybeans?
Answer:
2/5
Step-by-step explanation:
Answer:
D. This is a dependent event because Pedro ate the jellybeans, and they cannot be replaced.
Step-by-step explanation:
Pretty much, dependent means it can’t be replaced and independent means it can be replaced.
Tony is spending money at a constant rate. Suppose he initially has $1000, and after 4 months, he has $760,
Which of these expresses the rate at which Tony's amount of money is changing?
Answer:
$60 monthlyStep-by-step explanation:
Step one:
The initial amount that Tony has= $1000
final amount =$760
amount spent= 1000-760= $240
time taken is 4 months
Step two:
Required:
the rate of spending
we know that rate= quantity/time
rate= 240/4
rate= $60 per month
Hence Tony's amount is changing at $60 monthly
Answer: -60
Step-by-step explanation:
help pls
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answer:
Step-by-step explanation:
simplify 32 L : 56L with whole numerator and denominator
Answer:
4L/7L
Step-by-step explanation:
32:56 is the same as 32/56
They can be divided by a maximum of 8
32/8=4
56/4=7
4/7
What is the slope-intercept form of a line that contains the point (0,3) and a slope =-2?
PLZ HELPP MEEE!!
Answer:
C.
Step-by-step explanation:
-2 is in front of x so thats gonna be the slope
and +3 is the y-intercept
if 'HOPE' is called 3, ' GOVERNMENT' is called 9, ' PEACEFUL' is called 7, what would HAPPINESS 'be called??
Answer:
8
Step-by-step explanation:
Identifying the Pattern:
We are told that 'HOPE' is called 3
we can see that there are 4 characters in the word HOPE
So, we can see that the number is one less than the number of characters in the given word
Let's see if the observation we made still holds for the other Words:
We are also told that 'GOVERNMENT' is called 9
the number of characters = 10
Here, we once again notice that the code number is one less than the number of characters in our word
We are Given that 'PEACEFUL' is called 7
the number of characters = 8
Once again, our observation holds true
Hence, our observation holds true for all the words
Therefore, we can say with certainty that the pattern is:
code number = (number of characters of the word) - 1
Code number for 'HAPPINESS':
from the above, we know that:
code number = (number of characters of the word) - 1
we can see that 'HAPPINESS' has 9 words, plugging that value:
code number = 9 - 1
code number for 'HAPPINESS' = 8
Find the angle measures.
Justify your responses.
Given: a ||b, m∠6=128°
Find: m∠1, m∠3
Answer:
Step-by-step explanation:
It's given that a║b and m∠6 = 128°
Since, ∠1 and ∠3 are the consecutive interior angles,
m∠6 + m∠1 = 180°
128° + m∠1 = 180°
m∠1 = 180° - 128°
= 52°
Since, ∠6 and ∠3 are the corresponding angles,
Therefore, ∠6 ≅ ∠3
m∠3=52°
8
Find the circumference of the circle pictured above.
Round your answer to the nearest tenth
Example 4: In May 2006, Commonwealth Edison Company supplied electricity to residences for a
monthly customer charge of $7.58 plus $0.08275 per kilowatt-hour (kWhr) for the first 400 kWhr
supplied in the month, and $0.06208 per kWhr for all usage over 400 kWhr in the month. (a) What is the
charge for using 300 kWhr in a month? (b) What is the charge for using 700 kWhr in a month? (c) If Cis
the monthly charge for x kWhr, develop a model relating the monthly charge and kilowatt-hours used.
That is, express C as a function of x.
Answer: monthly customer charge of $7.58 plus $0.08275 per kilowatt-hour (kWhr) for the first 400 kWhr
Step-by-step explanation: I took this test before so I hope this helps gl on the test
a) The charge for using 300 kWhr in a month is $ 32.41
b) The charge for using 700 kWhr in a month is $ 59.30
c) The rule for computing C is
C ( x ) = { 7.58 + 0.08275x if 0 ≤ x ≤ 400
15.848 + 0.06208x if x > 400
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The monthly charge = $ 7.58
The monthly charge for per kWhr = $ 0.08275
The monthly charge per kWhr over 400 kWhr = $ 0.06208
So ,
The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x
The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
Now ,
a)
The charge for using 300 kWhr in a month is calculated by substituting the value of x as 300
So ,
The monthly charge for x kWhr is given by the equation = 7.58 + 0.08275x
The monthly charge for 300 kWhr = 7.58 + 0.08275 x 300
= 7.58 + 24.825
= $ 32.405
Therefore , The monthly charge for 300 kWhr is $ 32.41
b)
The charge for using 700 kWhr in a month is calculated by substituting the value for x as 700
The monthly charge for x kWhr which is more than 400 kWhr is given by the equation = 7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
The monthly charge for 700 kWhr =
7.58 + 0.08275 ( 400 ) + 0.06208 ( x - 400 )
Substituting the value for x as 700 , we get
= 7.58 + 0.08275 ( 400 ) + 0.06208 ( 300 )
= 40.68 + 18.624
= $ 59.304
Therefore , The monthly charge for 700 kWhr is $ 59.304
c)
Let x represent the number of kWhr used and C be the monthly charge for x kWhr.
The model can be split into 2 parts of condition , where
For , 0 ≤ x ≤ 400
The function is 7.58 + 0.08275x
For , x > 400
The function is 15.848 + 0.06208x
Therefore ,
The rule for computing C is
C ( x ) = { 7.58 + 0.08275x if 0 ≤ x ≤ 400
15.848 + 0.06208x if x > 400
Hence , The monthly charge for 300 kWhr is $ 32.41 and the monthly charge for 700 kWhr is $ 59.304
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5(2y-3)-4y=8-2y-15
Justify each step with a property of algebra. Drag the property to the correct row.
Please help me asap this was due 5 days ago
Answer:
do 9.60 divided by 12
Step-by-step explanation:
Answer:
$0.80
Step-by-step explanation:
All that is needed for finding this answer is 9.60 ÷ 12 which gets us 0.80.
Algebra!!!
3 Questions Only take if you know ALL Answers
PLZZZ QUICK
Answer:
1. -7.5
2. $1
3. 40
Step-by-step explanation:
For number 1, it can be solved by using the PEMDAS method, or see explanation below:
6x - 4x - 36 = 6 - 2x
2x - 36= -2x + 6
4x + 36 = 6
4x = -30
x = -15/2 or -7.5
For number 2, substitute 3 into both equations:
f(x) =1.50(3) + 2.00
and
f(x) = 2.00(3) + 1.50
This would get $6.50 and $7.50, which, if subtracted, gets $1.
For number 3, do something similar to the previous problem. Substitute 3 for x. It would be 5(2^3), or 40.
Hope this helps!
ions
How many solutions does this equation have?
1 solution
x + 3 + x + 3 = - (x + 4) + (3x - 2)
No solution
Infinite solutions
Explain your thinking
Answer:
I am not certain but I think it's no solution but how the number of X's their is and won't have it's value, it's by themselves
Why is the distributive property important in solving equations?
Answer:
it helps simplify difficult problems . it breaks down expressions into the difference or the sum
of two numbers.
The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the line tangent to the graph of f at x=−1 ?
Answer:
The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].
Step-by-step explanation:
From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - Intercept, dimensionless.
The slope of the tangent line at [tex]x = -1[/tex] is:
[tex]f'(x) = -3\cdot x +4[/tex] (2)
[tex]f'(-1) = -3\cdot (-1) +4[/tex]
[tex]f'(-1) = 7[/tex]
If we know that [tex]m = 7[/tex], [tex]x = -1[/tex] and [tex]y = 6[/tex], then the intercept of the equation of the line is:
[tex]b = y-m\cdot x[/tex]
[tex]b = 6-(7)\cdot (-1)[/tex]
[tex]b = 13[/tex]
The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].
I needs help with this question pls
Answer:
Is it A
Step-by-step explanation:
A weighted coin has a 0.599 probability of landing on heads. What is the probability that it takes 5 flips for the first head to occur?
Answer:
0.411^5 times 0.599
Step-by-step explanation:
0.599 chance of landing on heads.
0.411 chance of not landing on heads.
0.411 times 0.411 times 0.411 times 0.411 times 0.411 (for the 5 flips that do not land on heads) times 0.599 (for the time that it does land on heads).
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Answer:
This is a hw site pls dont post this, if you dont need help. I dont want your account to be deleted. :) Hope u have a great day tho, but in the future dont post this.
Step-by-step explanation:
answer fast!!!
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students filled 32% of the seats in the theater. How many 6th graders went on the trip?
Answer:
992
Step-by-step explanation:
Answer:
38%
Step-by-step explanation:
1178 / 3100 = 0.38
38%
Jose D is looking for a skateboard. He sees one that costs $148. The owner is offering him a 20% discount.. What is the price of the skateboard after the discount and a 7% sales tax?
Answer:
110.112
Step-by-step explanation:
1.5 m =_____ cm
a 15
b 0.015
c 1.5
d 150
Answer:
150
Step-by-step explanation:
Answer:
D.)150
Step-by-step explanation:
Hope I helped
The mean age of several boys in a class is 12. The total is 156. How
many boys are there?
Answer:
13
Step-by-step explanation:
156/12
Please hurry. Please
Answer:
yes
Step-by-step explanation:
12p<=56
12*3<=56
36<=56
Correct.
Hope this helps :D
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Required:
Develop a confidence interval estimate of the population mean rating for Miami.
Answer: 6.8622 ; 8.1778
Step-by-step explanation:
Given the data:
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Assume a confidence interval of 95%
Using calculator :
The mean of the distribution (m) = 7.52
Standard deviation (s) = 2.314
Sample size),
Obtaining the t score ;
Degree of freedom (df) = (n-1) = 50 - 1 = 49
t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)
Margin of Error :
2.01 * s/√n = 2.01 * 2.314/7.0710678
Margin of Error (E) = 0.6578
Confidence interval:
(Mean - E) ≤μ≤ (mean + E)
(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)
6.8622 ≤μ≤ 8.1778
12. Write the EQUATION for 125 is what percent of 200.
A 125 = p x 200
B 125 = p/200
C 125/p = 200
D 125 = 200/2
Answer:
Step-by-step explanation:
125 =200p
125/p=200
So the answer is option D
The correct equation for 125 is what percent of 200 is:
C (125/p = 200).
To write the equation for 125 is what percent of 200, follow these steps:
Step 1: Identify the unknown value.
In this case, looking for the percent, which can represent as p.
Step 2: Set up the equation.
To express the relationship between 125 and 200 as a percent, use the equation: 125 = p/100 * 200.
Step 3: Simplify the equation.
To simplify, divide both sides of the equation by 200 to isolate p:
125/200 = p/100
Step 4: Simplify further.
To simplify the left side, divide both the numerator and denominator by 25:
5/8 = p/100
Step 5: Rewrite the equation.
Finally, rewrite the equation as:
125/p = 200
Therefore, the correct equation for 125 is what percent of 200 is:
C (125/p = 200).
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I will mark Brainliest What is the length of AB
Please help ASAP due soon I need help
Answer: 18
Step-by-step explanatio 18
4) What are all the subsets of (3, 5, 7)?
ANSWER: 1 is a subset of 3,5,7
Answer:
X=(0,3) (3,0) Y=(0,5)(5,0) Z=(7,0) (0,7)
Step-by-step explanation:
suppose ,3=x ,5=y and 7=z
0 is the common number
Find the range of the following piecewise function. [27,3) (-22,3] (27,3] [-22,3)
Answer:
The answer is "(27,3]"
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\to f(-5) = (-5)^2 + 2 = 25 +2 =27\\\\\to f(7)= 7-4 = 3\\\\answer \ is = ( 27, 3]\[/tex]
Answer
(27,3]
Step-by-step explanation:
Correct In HW
A random sample is made of 256 middle managers concerning their annual incomes. The sample mean is computed to be $35,420. If the population standard deviation is $2,050. What is the standard error of the mean?
a. $128.125
b. $138.36
c. $2.050
d. $8.01
Answer: a. $128.125
Step-by-step explanation:
The standard error of the mean is given by :
[tex]SE=\dfrac{\sigma}{\sqrt{n}}[/tex] , where [tex]\sigma[/tex] = population standard deviation , n= sample size.
Given: [tex]\sigma=\$2,050[/tex]
n= 256
Then, the standard error of the mean:-
[tex]SE=\dfrac{2050}{\sqrt{256}}\\\\=\dfrac{2050}{16}=\$128.125[/tex]
Hence, option a. is correct.