Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
Answers
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]Related Questions
Two angles are supplementary. The measure of one angle is 54 more than the measure of the other angle. What is the measure of the bigger angle?
Answers
The measure of the bigger angle is 117°
What are Supplementary Angles?
Two angles are said to be supplementary if their sums total 180 degrees.
Let, x be the angle
and, x + 54 other angle measure.
we know, sum of Supplementary angle is 180°
so, the equation will be
x + (x + 54) = 180°
2x + 54 = 180
2x = 180 - 54
2x = 126
x = 63°
x + 54 = 63 + 54 = 117°
Therefore, The measure of the bigger angle 117°
To read more about Supplementary Angles.
https://brainly.com/question/12919120
#SPJ9
Can you help me pls this was very hard for me
Answers
Given:
The equation is,
[tex]\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}[/tex]Explanation:
Simplify the right hand side of equation.
[tex]\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}[/tex]From left side and right side of equationn it can be observed that,
[tex]-8ax^2=24x^2\text{ and (-3a+16)x=}25x[/tex]Simplify the equation for a.
[tex]\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}[/tex]OR,
[tex]\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}[/tex]So value of a is -3.
Option B is correct.
A chemist is using 363 milliliters of a solution of acid and water. If 13.6% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answers
If 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
In the question;
it is given that
the total solution of acid and water is 363 milliliters .
and also it is given that 13.6% of the solution is acid ,
which means
the amount of acid in solution = 13.6% of total solution
Substituting the values , and
on solving further ,
we get
amount of acid in solution = 0.136×363 ......as 13.6% = 0.136
= 49.368
≈ 49.4 milliliter
Therefore , if 13.6% of the solution is acid ,then 49.4 milliliters of acid are there .
Learn more about Percent here
https://brainly.com/question/8413511
#SPJ1
Which graph represents data used in a linear regression that produces a correlation coefficient closest to -1?
Answers
What does the letter "L" stand for in the simulation?
Answer: d
Step-by-step explanation: ion know man but i looked it up and got it right
4560=12 ÷ y
What is y equal to?
Answers
Answer:y=1/380
Step-by-step explanation:
if you are trying to do y divided by 12 it would be 4560x12
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
Answers
As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution.
In the theory of probability, the central limit theorem states that the distribution of a sample mean approximates a normal distribution as the size of the sample increases. For the central limit theorem to hold, it is necessary that the sample size at least cross a margin of 30. Having a sufficiently larger sample size can predict the characteristics of the sample more accurately. The central limit theorem is applicable when we are analyzing large data sets.
Read more about normal distribution at
https://brainly.com/question/12421652?referrer=searchResults
#SPJ4
product of (-12)(-8)
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{GUIDE TO FOLLOW: }[/tex]
• [tex]\large\textsf{2 negatives equal positive}[/tex]
• [tex]\large\textsf{2 positives equal positive}[/tex]
• [tex]\large\textsf{1 negative \& 1 positive equal negative}[/tex]
• [tex]\large\textsf{1 positive \& 1 positive equal negative}[/tex]
[tex]\large\textsf{SOME OPERATIONS MAY BE DIFFERENT THAN OTHERS!}[/tex]
[tex]\large\textsf{ANYWHO, LET US ANSWER THIS QUESTION, SHALL WE? }[/tex]
[tex]\mathsf{(-12)(-8)}[/tex]
[tex]\mathsf{= 12(8)}[/tex]
[tex]\mathsf{= 96}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{96}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
4/y+2 = 10/5y
solve for y
Answers
Answer:
y = - 1
Step-by-step explanation:
[tex]\frac{4}{y}[/tex] + 2 = [tex]\frac{10}{5y}[/tex]
multiply through by 5y to clear the fractions
20 + 10y = 10 ( subtract 20 from both sides )
10y = - 10 ( divide both sides by 10 )
y = - 1
simplify the following 22e- 5e- 8e- 4e
Answers
Answer:
5e?
Step-by-step explanation:
so if i help let me know this please
[tex]22e - 5e - 8e - 4e = 5e[/tex]
Give an example of a percent problem involving the simple interest formula. Then solve your problem.
Answers
The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?
What is simple interest?
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Solution for the above problem is:
The formula to calculate simple interest is:
[tex]S.I. = P \times I \times T[/tex]
Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time
Given in the question:
P = $2500
I = 6% = 0.06 (in decimals)
T = 2
Putting the value in the question:
S.I. = 2500(0.06)(2)
S.I. = 300
Therefore, the simple interest is $300.
To know more about simple interest, go to link
https://brainly.com/question/25793394
#SPJ13
Find the perimeter pf the regular polygon.
5 (x+2)
7x+4
Answers
The perimeter of the regular polygon is 108 units.
How to find the perimeter of a regular polygon?A regular polygon is a polygon that has all its sides equal to each other.
Therefore,
5(x + 2) = 7x + 4
5x + 10 = 7x + 4
5x - 7x = 4 - 10
-3x = -6
x = -6 / -3
x = 2
The perimeter of a regular polygon is the sum of the whole sides of the polygon.
Therefore,
each side of the regular polygon = 7(2) + 4
each side of the regular polygon = 14 + 4
each side of the regular polygon = 18
Hence the regular polygon has 6 sides
perimeter of the regular polygon = 18 × 6
perimeter of the regular polygon = 108 units
learn more on regular polygon here: https://brainly.com/question/356990
#SPJ1
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. based on a 19 bag sample where the mean is 437 grams and the varicance is 441, is there sufficent evidence at the 0.025 level that the bags are underfilled?
Answers
Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .
In the given question, we shall check the bag is underfilled at given level or not .
We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :
H₀ : u = 411 : the bags are not underfilled
Hₜ : u < 411 : the bags are underfilled
Check it now using statistic Z-test and the test Statistic formula is given by
= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .
From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21
Including all of the above variables in formula
Z = (437-411)/21/√19
= 26/21/√19
= 5.395
This is right -tail test in statistic Z -test
P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )
The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025
P- value >α , this implies that Null hypothesis is not Rejected .
There is sufficient evidence to suggest that bag is not underfilled.
To learn more about Hypothesis testing, refer:
https://brainly.com/question/580970
#SPJ4
Which equation has no solution?
Answers
Answer:
The answer is the third one down
Step-by-step explanation:
l5-3xl = -8
Absolute value cannot equal a negative number.
Step-by-step explanation:
l5-3xl = -8
the | | is absolute value to it so it cant be negative number
Find the measure of the missing arc (dont worry about the degree symbol)
Answers
The formula to calculate the missing arc is,
[tex]m\angle T=\frac{1}{2}\times m\angle arcTS[/tex]where,
[tex]m\angle arcTS=146^0[/tex]Therefore,
[tex]\begin{gathered} m\angle T=\frac{1}{2}\times146^0=73^0 \\ \therefore m\angle T=73^0 \end{gathered}[/tex]Hence, the answer is
[tex]\begin{equation*} m\angle T=73^0 \end{equation*}[/tex]Evaluate if x = 4. x² + x = [?]
Answers
Answer: The answer is 0.
X = 0 when evaluated.
Step-by-step explanation:
The value of x^2 - 2x for x = 4 is calculated as below
Now, substituting x=4 in the given equation, we get
x^2 - 2x = 4^2 - 2 x 4
= 16 - 8
= 8
Therefor, the answer is 8
A and B are supplementary angles. If mA = (3x - 28)° and
m/B = (x − 4)°, then find the measure of A.
Answers
Answer:
A = 131°
Step-by-step explanation:
Supplementary angles sum 180°
A + B = 180°
(3x - 28) + (x - 4) = 180
4x - 28 - 4 = 180
4x - 32 = 180
4x = 180 + 32
4x = 212
x = 212/4
x = 53
Then:
A = 3x - 28
A = 3*53 - 28
A = 159 - 28
A = 131°
B = x - 4
B = 53 - 4
B = 49°
Check:
131° + 49° = 180°
Answer:m∠A=33
Step-by-step explanation:
(x^4/7^-8)^7
Solve asap pls
Answers
Answer: x=2
Step-by-step explanation: (x^4/7^-8 )^7
(4x/-56)^7 (7×8=56)
4x/-8
x/-2
x = 2
C)
to make the total value equal to 2. Re-write the statement 19 + 7 + 2 x 6 + 1 by including two pairs
of brackets
Answers
If you place brackets or parenthesis around the numbers 19+7 and 2*6+1. It would appear as follows: (19+7)/(2*6+1) = 26/13 = 2. It takes special parenthetical treatment to express the mathematical expression 19+7/26+1 to get a result of 2.
What is expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
y=19+7/2×6+1
becomes
y=(19+7)/(2×6+1)
y=26/(12+1)
y=26/13
y=2
If you enclose the numbers 19+7 and 2*6+1 in parenthesis or brackets. It would look like this: (19+7)/(2*6+1) = 26/13 = 2. The mathematical expression 19+7/26+1 must be expressed with special parenthetical treatment to yield the number 2.
To know more about expression,
https://brainly.com/question/1859113?referrer=searchResults
#SPJ13
84 minutes for 32 songs = 42 minutes for _____
songs
Answers
Answer: 84 minutes for 32 songs= 42 minutes for 16 songs.
Step-by-step explanation: All I had to do was divide 84 by two and divide 32 by 2.
84/2=42
32/2= 16 songs.
Answer: 16 songs.
84 dived by 2 equals 42.
Do 32 divided by 2 and it gives us 16.
step by step explanation 6 divided by 396 show work
Answers
The value of 6 divided by 396 is 0.1515.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.
The steps include:
Step 1: Take the first digit of the dividend from the left.
Step 2: Divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and then write the difference below.
Step 4: Bring down the next digit of the dividend.
In this case, 6/396 will give the value illustrated above.
Learn more about division on:
https://brainly.com/question/25289437
#SPJ1
The United States flag has a height : width ratio of 10 : 19. If a U.S. flag is 25 inches high, what is its area?
Answers
The area of the given flag is 1187.5 square inches.
Given that, the United States flag has a height : width ratio of 10 : 19.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Let the sum of Height and width of flag be x.
Now, 10+19=29
⇒ 10/29 ×x = 25
⇒ 10x=29 × 25
⇒ x=72.5
So, width = 72.5-25 =47.5
Area of flag = Length × Width
= 25 × 47.5
= 1187.5 square inches
Therefore, the area of the given flag is 1187.5 square inches.
To learn more about the ratio visit:
brainly.com/question/13419413.
#SPJ1
The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x-4, y-1), give the vertices of △A′B′C′.
Answers
Answer:
A' = (-2, -4)
B' = (-7, -6)
C' = (0, 0)
Step-by-step explanation:
Vertices of triangle ABC:
A = (2, -3)B = (-3, -5)C = (4, 1)Given mapping rule:
(x, y) → (x - 4, y - 1)
This notation tells you that the x-coordinate is translated 4 units to the left, and the y-coordinate is translated 1 unit down.
Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':
⇒ A' = (2 - 4, -3 - 1) = (-2, -4)
⇒ B' = (-3 - 4, -5 - 1) = (-7, -6)
⇒ C' = (4 - 4, 1 - 1) = (0, 0)
Is the commutative or associative property being shown in the problem below?
(3 x 5) x 8 = 3 x (5 x 8)
Answers
Associative Property
Answer:
Associative
Step-by-step explanation:
Suppose a ray of sunlight bounces off a window at a point P, and that
line mis perpendicular to the window at point P. Angles of inflection
and reflection are created as shown.
Write an equation and then solve for x.
m
-
(3x - 10)°
(2x + 5)°
P
Answers
By applying the law of reflection to the ray of sunlight, the value of x is equal to 5.
What is the law of reflection?The law of reflection is a theorem which states that the magnitude of the angle of incidence is equal to the magnitude of the angle of reflection when a ray of light is reflected off a surface such as a plane mirror.
Mathematically, law of reflection can be represented or modelled by this mathematical expression:
sinθi = sinθr
Where:
sinθi represents the angle of incidence.sinθr represents the angle of reflection.By applying the law of reflection to the ray of sunlight (see attachment), we have the following equation:
(3x - 10)° = (2x + 5)°
3x + 2x = 10 + 5
5x = 15
x = 15/3
x = 5.
Read more on law of reflection here: https://brainly.com/question/16158899
#SPJ1
Tiana made lemonade for a party. Her family drank half of the lemonade. After the party, she gave one-third of the remaining lemonade to her neighbors. If Tiana has 210 ounces of lemonade remaining after the party and giving some away to her neighbors, how many ounces of lemonade did she start with? Show your work.
Answers
The amount of lemonade Tina made in the starting is 630 ounces.
Given that:-
Fraction of lemonade drank by her family = 1/2
Fraction of lemonade given to neighbors = 1/3 of remaining
Amount of lemonade left with her at the end = 210 ounces
We have to find the amount of lemonade Tina made in the starting.
Let the amount of lemonade Tina made in the starting be 6x.
Hence,
Amount of lemonade drank by her family = (1/2)*6x = 3x
Remaining lemonade = 6x - 3x = 3x
Amount of lemonade given to neighbors = (1/3)*3x = x
Remaining lemonade = 3x - x = 2x = 210 ounces
Hence,
x = 210/2 = 105 ounces
Amount of lemonade Tina made in the starting = 6x = 6*105 = 630 ounces.
To learn more about Fraction, here:-
https://brainly.com/question/10354322
#SPJ1
Which graph represents the reflection of AABC over the line y = 0?
-54-3 -2 -1
S ON
CH
-3
LO
*
C
A
2 3
A
B
12
X
Answers
Answer:
The graph represents the reflection of triangle ABC over the line y=0 in graph (C).
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Step-by-step explanation:
hope this helps I hope
The graph C represents the reflection of triangle ABC over the line y = 0
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
The coordinates after applying rule
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Hence, the graph C represents the reflection of triangle ABC over the line y = 0
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ5
arlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
Write an equation to describe the relationship between m, the amount of minerals, and w, the number of workers.
Answers
The required equation is m/w = 900/18
What is meant by an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Differential equations are equations in which one or more functions and their derivatives are involved. They are solved by locating a function expression that does not use derivatives. Differential equations are used to represent processes with variable rates of change in fields such as physics, chemistry, biology, and economics.
The required equation is m/w = 900/18
To know more about an equation, click on then link
https://brainly.com/question/27893282
#SPJ9
Is the ordered pair a solution of the equation?
y = -6x - 14, (-5,16)
a. yes
b. no
Answers
Answer:
a. Yes
Step-by-step explanation:
If you plug in the ordered pairs, the -5 is x and 16 is y.
The equation would look like this:
16=30x-14
Add 14 on both sides
14+16=30
30=30x
divide by 30 on both sides
1=1
a. Yess
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29,
2005, the national debt was 4.974 x 10^12 dollars. Find the amount of increase in the national debt from September of 2005 to September of 2015.
Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
Answers
The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.
What is scientific notation?Scientific notation simply means a way of expressing numbers that are either too large or too small.
The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,
2005, the national debt was 4.974 x 10^12 dollars.
The increase will be the difference between the two notations. This will be:
= 1.815 x 10^13 - 4.974 x 10^12
= 1.3176 × 10^13
The increase is 1.3176 × 10^13.
Learn more about scientific notation on:
brainly.com/question/1767229
#SPJ1
The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.
Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.
So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³
Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
Learn more about scientific notation here:
https://brainly.com/question/18073768
#SPJ1
a bakery uses 3 3/5 cups of oats to make 2 4/7 pounds of oatmeal cookies how many cups of oats are required per pound of cookies
Answers
Answer: 7/5 or 1 2/5
Step-by-step explanation:
Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.
You need to find the unit price.
So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7
You need to do the same thing to 3 3/5 cups.
3 3/5 as an improper fraction is 18/5
2 4/7 as an improper fraction is 18/7
Now to divide you need to keep, change, and flip
keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18
18/5*7/18=7/5
7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies