Answer:
A) The volume of the cylinder is 1017.9 in³.
B) The volume of the enlarged cylinder is 27,482.7 in³.
Step-by-step explanation:
What is the volume of the cylinder?The radius of the cylinder is r = 6 in and the height is h = 9 in.
The volume of a cylinder can be found using the formula:
V = πr²hSubstitute r = 6 and h = 9 into the formula.
V = π(6)²(9)V = π(36)(9)V = π(324)V = 1017.876The volume of the cylinder is 1017.876 in³.
What is the volume of the enlarged cylinder?If the cylinder is enlarged by a factor of 3, this means that each dimension is getting increased by 3.
Therefore, we need to multiply the original volume by a factor of three cubed; 3³.
V_enlarged = V · 3³V_enlarged = 1017.876 · 27 = 27482.652 in³The volume of the enlarged cylinder is 27,482.652 in³.
the length of the hypotenuse of a 45°-45°-90° triangle with a leg of 12, what the length
Answer:
The length of the other two legs are 6√2.
since the hypotenuse is one of the legs multiplied by √2.
dividing the hypotenuse by √2 will get the length of one leg. since it is a 45 45 90 triangle, the length of the two legs are the same.
12/√2= 12√2/2= 6√2
68. What is the value of x?
Type your answer and then click or tap Done.
The number of seconds is equal to 60 times the
number of minutes. Write the direct variation
equation that represents this situation. Let xbe the
independent variable. Let y be the dependent
variable.
Answer:
See below
Step-by-step explanation:
x(x-2y)-(y-x)2
Final result :
-y2
Step by step solution :
Step 1 :
Equation at the end of step 1 :
x • (x - 2y) - (y - x)2
Step 2 :
2.1 Evaluate : (y-x)2 = y2-2xy+x2
Final result :
-y2
Answer:
y=60x
Step-by-step explanation:
Let x be the number of minutes, y be the
number of seconds
4=60x
{Direct variation}
In an isosceles triangle the length of the base is 10 cm
The computation shows the radius of the circle that is inscribed in the isosceles triangle will be 3.33cm.
How to calculate the radius?From the information given, the isosceles triangle the length of a base is 10 cm and the length of a leg is 13 cm.
Let A = area of the triangle
Let S = semi perimeter of the triangle.
The radius will be: = A/S
where,
[tex]S = \dfrac{(a + b + c)}{2} = \dfrac{(13 + 13 + 10)}{2} = 18[/tex]
The radius will be:
[tex]=\dfrac{(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{10})} { 18}[/tex]
= 3.33cm
In conclusion, the radius is 3.33cm.
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In a town, 15% of the population is unemployed. what is the
total population, if number of people who are employed is
8381
Answer:
1479 people
Step-by-step explanation:
If the amount employed is 8381, that means 8381 is 85% of the population. 8381/85 = 98.6
Every 1% of the population is 98.6, so we can just do 15 x 98.6 to get 1479
Answer:
9,860
Step-by-step explanation:
100% - 15% = 85 % = 85/100
85/100 * 8381/x
85x = 838,100
838,100/85 = 9,860
determine the volume of a sphere if it has a radius of 5 inches
Answer:
V ≈ 523.6in³
Step-by-step explanation:
Using the second sphere volume equation results in:
4/3 x 3.14159 x 53 = 4.1866 x 125 = 523.6in3
Help me find the mean (average) of these numbers! (Also I don’t have them lined up in order from smallest to largest)
Answer:
[tex] \frac{5}{4} [/tex]
Step-by-step explanation:
To find the average of any amount of numbers, just add all the given numbers together and then divide by the amount of numbers given, in this case it would be :
[tex]( \frac{3}{4} + \frac{13}{5} + \frac{14}{10} + \frac{6}{24} ) \div 4[/tex]
(S-6) + (8s +4) simplify
Step-by-step explanation:
[tex] = (s - 6) + (8s + 4)[/tex]
[tex] = s - 6 + 8s + 4[/tex]
Combine the like terms..
[tex] = s + 8s - 6 + 4[/tex]
[tex] = \boxed{\sf{9s - 2}}[/tex]
hence the answer is 9s - 2 .....
hope it helped !!!
Casey is buying snacks for a class trip. She has 16 snacks left over from the last trip. She buys snacks by the case to get a good price. Each case holds 24 snacks. How many cases will she have to buy if she wants to have a total of 160 snacks?
Answer:
Your answer is 10
Step-by-step explanation:
160 devided by 16 = 10
Angela needs volume of a sphere. Which formula is correct?
The diameter of the sphere is d=17
A 4/3 pi 17 cubed
B 4/3 pi 17 squared
C 4/3 pi 8.5 cubed
D 4/3 pi 8.5 squared
Answer:
C-------------------------------------------------
Which words mean the same thing as 5/8
Answer:
c) Five out of 8 equal parts of a whole
Step-by-step explanation:
The statement "Five out of 8 equal parts of a whole" means the fraction of 5/8. Hence, option (c) is the correct answer.
Answer:
"Five out of eight equal parts of a whole"
Step-by-step explanation:
In a fraction, the numerator (top part) is saying "this number out of the number below it."
The denominator (lower part) is the number below it that we are taking the proportion out of.
A denominator is ALWAYS equal parts, so if we match up the phrase: "5 out of eight equal parts of a whole"
the vertex of triangle DEF are D(1,3) ;E(-1,0) ;F(2,-1) find the coordinate of orthocenter for this triangle
please with clear explanation I will give brainliest
Answer:
[tex]\sf \left(\dfrac{1}{11},\dfrac{3}{11}\right)[/tex]
Step-by-step explanation:
The orthocenter is the point of intersection of the altitudes of a triangle.
(The altitude is the line that passes through the vertex and is perpendicular to the side opposite the vertex).
**Refer to attached diagram**
DC, EA and FB are the perpendicular lines drawn from the three vertices D, E and F.
[tex]\sf Let\:(x_1,y_1)=D\implies(x_1,y_1)=(1,3)[/tex]
[tex]\sf Let\:(x_2,y_2)=E\implies (x_2,y_2)= (-1,0)[/tex]
[tex]\sf Let\:(x_3,y_3)= F\implies (x_3,y_3)=(2,-1)[/tex]
G (x, y) is the intersection point of the three altitudes of the triangle, i.e. the orthocenter.
To find the point of intersection (orthocenter), we need to create linear equations for the altitudes, then equate them to find the point of intersection.
We only need to work with 2 altitudes.
Calculate the slopes of two sides of the triangle.
[tex]\sf \implies Slope\:of\:EF=\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{-1-0}{2-(-1)}=-\dfrac{1}{3}[/tex]
[tex]\sf \implies Slope\:of\:DF=\dfrac{y_3-y_1}{x_3-x_1}=\dfrac{-1-3}{2-1}=-4[/tex]
As the slopes of the altitudes are perpendicular to the slopes of the sides:
[tex]\textsf{Slope of DC}=\sf \dfrac{-1}{\textsf{slope of EF}}=\dfrac{-1}{-\frac{1}{3}}=3[/tex]
[tex]\textsf{Slope of EA}=\dfrac{-1}{\textsf{slope of DF}}=\sf \dfrac{-1}{-4}=\dfrac{1}{4}[/tex]
Using point D (1, 3) and the slope of DC to create a linear equation for DC using the point-slope form of a linear equation:
[tex]\sf \implies y-y_1=m(x-x_1)[/tex]
[tex]\sf \implies y-3=3(x-1)[/tex]
[tex]\implies \sf y=3x[/tex]
Using point E (-1, 0) and the slope of EA to create a linear equation for EA using the point-slope form of a linear equation:
[tex]\sf \implies y-y_1=m(x-x_1)[/tex]
[tex]\sf \implies y-0=\dfrac{1}{4}(x-(-1))[/tex]
[tex]\sf \implies y=\dfrac{1}{4}x+\dfrac{1}{4}[/tex]
To find the x-value of the point of intersection (the orthocenter), equate the equations and solve for x:
[tex]\implies \sf 3x=\dfrac{1}{4}x+\dfrac{1}{4}[/tex]
[tex]\implies \sf \dfrac{11}{4}x=\dfrac{1}{4}[/tex]
[tex]\implies \sf 11x=1[/tex]
[tex]\implies \sf x=\dfrac{1}{11}[/tex]
To find the y-value of the point of intersection (the orthocenter), substitute the found value of x into the equation for line DC:
[tex]\implies \sf y=3\left(\dfrac{1}{11}\right)[/tex]
[tex]\implies \sf y=\dfrac{3}{11}[/tex]
Therefore, the orthocenter is at point:
[tex]\sf \left(\dfrac{1}{11},\dfrac{3}{11}\right)[/tex]
A man is twice as old as sum of ages of his two sons. After ten years the sum of his age and ages of his sons is equal to 105 then present age of man is:
50
60
70
80
The present age of the man is 70
What are the linear equations that represent the question?a = 2b equation 1
105 = a + b equation 2
Where:
a = man's age b = sum of his son's ageWhat is the man's present age?Substitute for a in equation 2
105 = 2b + b
105 = 3b
3b = 105
b = 35
Substitute for b in equation 1 : a = 2 x 35 = 70
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solve the inequility 3x - 3 <9
Answer:
x<4
Step-by-step explanation:
Here, hope this helped!
A quick tip, just think that the sign is an equal sign, that helps.
Answer: [tex]x < 4[/tex]
Step-by-step explanation:
Our inequality is [tex]3x-3 < 9[/tex]
We will add 3 to both sides. (addition property of equality)
Simplify [tex]9 + 3 9+3 9+3 ~to ~12[/tex].
Then divide both sides by 3. (division property of equality)
[tex]3x[/tex]÷[tex]3 < 12[/tex]÷[tex]3[/tex]
[tex]\frac{3x}{3} < \frac{12}{3}[/tex]
Simplify [tex]312~to~4[/tex].
Famous (and not so famous) Mathematicians Escape Room(Slide 3)
Can someone put the events in the correct order pls
(when they are in the correct order the letters in the corner form a CODE not a WORD so dont look for that)
I WILL GIVE BRAINLIEST
The chronological organization allows us to organize the events sequentially according to the date of their occurrence.
What is seen in the image?The image shows several tables that refer to historical events around the world that we must organize chronologically.
How to organize events chronologically?To organize the events chronologically we must know the date on which they occurred, for this we must search for complementary information and establish the date of each one of them, especially the year.
Later, we can organize them and we have two alternatives, from the most recent to the oldest or from the oldest to the most recent. In this case we are going to organize them from the most recent to the oldest, so they would look like this:
1992 - Mae Carol Jemison, First African American woman to visit space.1854 - 1856 - Florence Nightingale develops the polar area diagram during the Crimean war.1202 - Leonardo Bigollo discovered the Fibonacci sequence.499 - At the age of 23 Aryabhata writes his book aryabhatiya.400 - Hypatia becomes the outstanding head of the Platonic school in Alexandria.650 BC - First evidence of the development of the Chinese Lo Shu magic square.Note: This question is incomplete because the image is missing. Here is the image.
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The lines that appear tangent are tangent. What is the value of x, to the nearest tenth.
Answer:
x ≈ 10.7
Step-by-step explanation:
Is given in the picture that x is the radius of the circle.
The radius of a circle and the tangent line to the circle form a right angle, therefore our triangle is a right triangle.
We can apply the Pythagorean Theorem to find one equation that will have one unknown x.
(x+12)² = x² +20² , use that (a+b)² = a²+b²+2ab
x²+12²+2·x·12 = x² +20², subtract x² from both sides of the equation
12² + 24x = 20², subtract 12² from both sides of the equation
24x = 20²-12², raise to power and combine like terms
24x = 256, divide by 24 both sides of the equation
x = 10.6666666..., round to the nearest tenth
x ≈ 10.7
A line passes through the point and has a slope of .
Write an equation in point-slope form for this line.
Answer:
oringns
Step-by-step explanation:
Use DESMOS: What is the equation
that represents a line that is
perpendicular to the graphed line and
passes through the point (-6, 6)?
y=mx+c
I picked the points (0, -4) and (-2,-10) to find the gradient of the line
M= rise/run
= 6/2
=3
Y-intercept is at - 4
Y= 3x - 4 is equation of the line given
Reciprocal of 3 is 1/3
(m1 x m2 = - 1)
So, to make - 1, our second gradient should be negative.
Gradient of the perpendicular line will be - 1/3
Y= - 1/3x + c
Substitute value of x & y into the equation
(-6,6) means x = - 6, y = 6
y = - 1/3x +c
6 = - 1/3 x - 6 + c
6 = 2 + c
-2
4 = c
Thus, final equation we're after will be:
y= - 1/3x + 4
Hope this helps!
what is the fraction of the recurring decimal 0.1 in its simplest form
Answer:
1/10
Step-by-step explanation:
I believe the answer is 1/10
To win a lottery, 7 numbers are drawn at random from a pool of 21 numbers. Numbers cannot repeat. If a person has one ticket, what is the probability that they have the winning ticket?
Answer:
the answer should be 3....this is not right btw
the probability of having a winning raffle ticket is 15%.
You told your friend that you could eat 78 of a large pizza. If you only ate 23 of what you said you could eat, what fraction of a large pizza did you eat?
Answer:
5/16
Step-by-step explanation:
Fraction of claim is 5/8
But you actually eat 1/2
Fraction of large pizza actually eaten 5/16
Hopefully this is correct and it can help you!
The scatter plot with trend line below shows the data comparing wind speed and wind chill. Wind Chill (˚F) Wind Speed (mph) The trend line passes through (10, 9) and (35, 0). Write an equation for the trend line. The equation of the trend line is y = x + .
The trend line passes through (10, 9) and (35, 0) will be 9x + 25y = 315.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
The scatter plot with the trend line below shows the data comparing wind speed and wind chill. Wind Chill (˚F) Wind Speed (mph). The trend line passes through (10, 9) and (35, 0).
Write an equation for the trend line.
(x₁, y₁) → (10, 9)
(x₂, y₂) → (35, 0)
Then we have
y - 9 = -9/25(x - 10)
25y - 225 = -9x + 90
9x + 25y = 315
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please answer question below asap!!
Answer:
44 boots
Step-by-step explanation:
24/6=4
that means we have to multiply all the numbers by 4 as well
2*4=8
3*4=12
24+8+12=44
A filing cabinet measures 5 feet is 18 inches wide and 2 feet deep what is the volume of the filing cabinet
Answer:
15 feet
Step-by-step explanation:
From the question above,we are asked to find the volume of a cabinet with the following dimensions:
Height is five feet
Width is eighteen inches
And a depth of two feet.
Here it is quite obvious that we ate dealing with a cuboidal object since its dimensions differ from one another.
So volume of a cuboid as we all know is :
Length multiplied by width and then height
We should head straight away to the calculations, but we need to remember that the width is in inches and needs to be converted to feet
1 inch = 1/12 feet
18 inches = 18× 1/12
= 1.5 feet
L×W×H
= 1.5×5×2
= 15 feet
I need help please I don’t get it
Answer:
ask your teacher for help. learn more today.
Step-by-step explanation:
Can someone help me? :D
answer: b and a cannot be points on the unit circle so there for the answer is b and a
option A and option D
hope it helps...!!!
helpppppppppppppppppp
asapppppppppppppp!!!!!!!!
Answer:
1st and 3rd statements are true
Step-by-step explanation:
2u + 9v + 1
the constant term is the term with only a numeric value
in this case the constant term is 1
the coefficient of the term 2u is 2 ( the value in front of the variable u )
the coefficient of the term 9u is therefore 9
there are 3 terms in the expression 2u , 9v , 1
these terms are being added together , thus
2u + 9v + 1 is the sum of three terms
If a1 = 5 and 5 and an = -3an-1 then find the value of a5. WILL GET BRAINLIEST
Answer:
405
Step-by-step explanation:
Given
a₁ = 5aₙ = -3aₙ₋₁Solving
a₂ = -3a₁ = -3(5) = -15a₃ = -3a₂ = -3(-15) = 45a₄ = -3a₃ = -3(45) = -135a₅ = -3a₄ = -3(-135) = 405a_1=5
a_2=-3a_1=-3(5)=-15a_3=-3a_2=-3(-15)=45a_4=-3a_3=-3(45)=-135a_5=-3a_4=-3(-135)=405HELP!!!!!!!! Select an expression that id equivalent to 4squareroot of 2x^2 • 4squareroot of 2x^3
Answer:
B
Step-by-step explanation:
[tex]\sqrt[4]{2x^2} *\sqrt[4]{2x^3} =(2x^2)^{1/4}*(2x^3)^{1/4}\\= 2^{1/4}*(x^2)^{1/4} *2^{1/4} * (x^3)^{1/4}\\[/tex]
combine like terms
[tex]= 2^{2/4} *x^{2/4}*x^{3/4}\\= 2^{2/4} * x^{5/4}[/tex]
these steps use exponent laws
a few key ones i used:
(x^y^z) = x^(y*z)
x^y * x^z = x^(y+z)
let me know if you have any questions!
Demand and supply in a market are described by the following equations: qd = 66-3p qs = -4 2p find the equilibrium price and quantity
The equilibrium price is $14 and the quantity is 24.
What is the equilibrium price?Equilibrium is the place in the market where there is no trend for change.
Buyers’ and sellers’ plans accord, and consequently quantity demanded equals quantity supplied.
The equilibrium price occurs when the quantity demanded equals the quantity supplied.
The demand and supply functions are, respectively:
Demand and supply in a market are described by the following equations: QD = 66-3p and qs = -4 + 2p.
The equilibrium price and quantity are;
QD = QS
66-3p = -4 + 2p
66 + 4 = 2p + 3p
70 = 5p
p = 70/5
p = 14
QD = 66-3p
QD = 66-3 × 14
QD = 66- 42
QD = 24
Hence, the equilibrium price is $14 and the quantity is 24.
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