The volume of the sphere is 4/3 times the volume of the cylinder.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
The volume of the cone is 1/3 the volume of a cylinder.
The volume of a cone is given as:
V = (1/3)πr²h ____(1)
The volume of a cylinder is given as:
V = πr²h _____(2)
From (1) and (2) we get,
(1/3)πr²h = 1/3 πr²h
The volume of a sphere:
V = 4/3 πr³
Since the height of the sphere and the radius is the same we can have
V = 4/3πr²h
So,
Volume of sphere = 4/3 x πr²h
The volume of the sphere = 4/3 x the Volume of the cylinder.
Thus,
The volume of the sphere is 4/3 times the volume of the cylinder.
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If you write every whole number from I to
100. how many times will you write the digit
"2"?
Answer:
20 times
Step-by-step explanation:
Digit 2 appears 20 times in first 100 natural numbers
What is the perimeter of this 48" by 60" rug?
How do you solve this problem?
The area of the figure given below is 56.6 units² .
In the question ,
a figure is given
where there is one rectangle and two semicircles .
the length of the rectangle is given as 11 units
and the breadth of the rectangle is = 4 units
we know that the area of the rectangle is = length × breadth
on substituting the values ,
we get
area = 11 × 4
area = 44 units²
the radius of the semicircle = 2 units
the are of the semi circle = (1/2)*π*r²
since there are two semicircle , the area of the two semi circle will be
= 2 * (1/2)πr²
= π*r²
On substituting , the value of radius = 2 ,
we get the area is = 3.14*(2)² = 12.56 using π = 3.14
so the area of the complex figure is = 44 + 12.56 = 56.56
≈ 56.6
Therefore , The area of the figure given below is 56.6 units² .
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Write the equation in slope intercept form: -6x+4y=20
Answer:
[tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]
Find the smallest whole number bu which 512 must be multiplied in order to give a perfect square
Answer:
2
Step-by-step explanation:
512÷2=256
256÷2=128
128÷2=64
64÷2=32
32÷2=16
16÷2=8
8÷2=4
4÷2=2
2÷2=1
=(2^2)+(2^2)+(2^2)+(2^2)+2
When 2 is multiplied it will make it a perfect square.
512×2=1024
√1024
=32
What is the absolute value of the number plotted on the number line?.
A. -1.75
B. -1.25
C. 1.25
D. 1.75
Answer:
D. 1.75
Step-by-step explanation:
Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.
What is the value of x+ y in the system of equations below?
8x + 9y = 4.92
9x + 14y = 6.93
The value of x + y in the system of equations is 0.82125.
Given system of equations:-
8x + 9y = 4.92 ...(1)
9x + 14y = 6.93 ...(2)
We have to find the value of x + y in the system of equations.
Multiplying (1) by 9 and (2) by 8, we get,
72x + 81y = 44.28 ...(3)
72x + 112y = 55.44 ...(4)
(4) - (3), we get,
0x + 31y = 11.16
31y = 11.16
y = 11.16/31
y = 0.36
Putting the value of y in (1), we get
8x + 9*(0.36) = 6.93
8x + 3.24 = 6.93
8x = 6.93 - 3.24
8x = 3.69
x = 0.46125
Hence,
x + y = 0.46125 + 0.36 = 0.82125
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1 (Express 360° into centesimal system.)
Answer: 400 gradians
Reason:
100 gradians = 90 degrees
4*100 gradians = 4*90 degrees
400 gradians = 360 degrees
An athlete swims at a constant rate. After 12 minutes, the swimmer swims 16 laps. A. Graph this relationship. B. Is this a proportional relationship? Explain.
Answer:
Step-by-step explanation:
1. Jack buys small tins of tomatoes every week. They usually cost 50¢ each. Last week,
however, Jack saw that the shop was selling six large tins of tomatoes plus a bag of
pasta for $7.50. He worked out that the pasta was normally $2. Jack decided that he
could use one large tin of tomatoes instead of two small tins so he bought 18 large tins
of tomatoes together with three bags of pasta.
This week, however, the small tins of tomatoes are on offer at $1.60 for a pack of four.
How much more did Jack pay last week for tinned tomatoes than if he had bought them
this week?
Answer is in what unit?
Jack paid $ 2.10 more than last week for tinned tomatoes.
The answer is in dollars.
Given that:-
Price of small tomato tins = 50 cents
Price of pasta packet = $ 2
Price of large tomato tins = 2*50 cents = $ 1
Total price of 6 large tins and a pasta packet = $ 7.50
Price of 4 small tins of tomatoes this week = $ 1.60
Price paid by Jack last week for 18 large tins and 3 pasta packets = 7.50*3 = $ 22.50
Price of 18 large tins = 22.50 - 2*3 = 22.50 - 6 = $ 16.50
As 18 large tins equals 36 small tins, we can write,
Price Jack would have paid this week = 36*1.60/4 = $ 14.40
The amount Jack paid more for tinned tomatoes = 16.50 - 14.40 = $ 2.10
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Write the equation 2(x + 3 )= 2x + 6 as a system of equations
Answer:
y=2x+6
y=2x+6
Explanation:
Given the equation:
[tex]2\mleft(x+3\mright)=2x+6[/tex]The equation written as a system of equations is:
[tex]\begin{gathered} y=2\mleft(x+3\mright) \\ y=2x+6 \end{gathered}[/tex]Opening the bracket in the first equation gives:
[tex]\begin{gathered} y=2x+6 \\ y=2x+6 \end{gathered}[/tex]A house is bought for $75000 and then resold for $87000. Calculate the percentage profit
Write an equation of a parabola with a vertex at the origin and a directrix at y=5
SOLUTION
The equation of the parabola is defined using
[tex]y=\frac{1}{4(f-k)}(x-h)^2+k[/tex]Since the vertex is at the origin the equation becomes
[tex]\begin{gathered} y=\frac{1}{4(f-0)}(x-0)^2+0 \\ y=\frac{1}{4f}x^2 \end{gathered}[/tex]Since the directrix is y=5
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix
It follows
[tex]\begin{gathered} f-k=k-5 \\ f=-5 \end{gathered}[/tex]Thus the equation becomes
[tex]\begin{gathered} y=\frac{1}{4\times-5}x^2 \\ y=-\frac{x^2}{20} \end{gathered}[/tex]Therefore the equation of the required parabola is
[tex]y=-\frac{x^2}{20}[/tex]Answer: Y=-1/20x^2
Step-by-step explanation:
Solve the system of one linear- one Quadratic equations algebraically.
x-y=3
x^2-3y=19
Answer:
x=-2 y=-5
x=5 x=2
Of the ice cream cones sold yesterday at Zeke's Ice Cream Shop, 3/10 were chocolate and another 3/10 were vanilla. What fraction of the ice cream cones sold were either chocolate or vanilla?
The fraction of ice cream cones sold that are either chocolate or vanilla is 3/5.
What is the fraction?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/5. 3 is the numerator and 5 is the denominator.
In order to determine the fraction of ice cream cones sold that are either chocolate or vanilla, add the fraction of chocolate cones sold and vanilla cones sold together. Addition is the process of determining the sum of two or more numbers.
Fraction of ice cream cones sold that are either chocolate or vanilla = 3/10 + 3/10 = 6/10 = 3/5.
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Pls help me. I'm struggling so bad
The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
in the question ,
it is given that the
formula to find , "gravitational force" between two objects is
[tex]F_{g}[/tex] = (G*M₁*M₂)/r²
to express the formula in terms of M₁ ,
we first multiply both the sides by r² ,
on multiplying , we get
[tex]F_{g}[/tex]*r² = G * M₁ * M₂
On dividing both sides by G ,
we get
( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂
we have to find the formula for M₁ ,
we divide both sides by M₂,
So , on dividing both sides by M₂ , we get
( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁
hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )
Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
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A machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate, in
pounds per hour, does the machine make nails? Show your work.
The rate of pounds per hour of the machine is 1.5 pounds per hour
How to determine the rate of pounds per hour?From the question, we have the following parameters:
Pounds of nails = 2 1/4 pounds of nail
Number of hours = 1 1/2 hour
From the above parameters, the rate of pounds per hour can be calculated using the following formula of constant of proportionality
The constant of proportionality is calculated as
Constant of proportionality = Pounds of nails/Number of hours
In this case, we have
Rate of pounds per hour = Pounds of nails/Number of hours
Substitute the known values in the above equation
Rate of pounds per hour = (2 1/4)/(1 1/2)
So, we have
Rate of pounds per hour = 1.5
Hence, the rate is 1.5 pounds per hour
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Answer:
1 1/2
Step-by-step explanation:
2 1/4 divide 1 1/2 is 1 6/12
1 6/12 simp —-> 1 1/2 (1.5)
What is the slope of -2,1 and 2,1
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
pls help me super confused on inequality
Help me please I don’t know the answer
Answer:
Classification by Angles: Obtuse
Classification by Sides: Scalene
Step-by-step explanation:
➜ This triangle has an obtuse angle, or an angle greater than 90°, so it is an obtuse triangle. This is the classification by angles.
➜ This triangle's sides are all different lengths, as shown by the three different angle measurements. This means this triangle is scalene, and scalene is the classification by sides.
which plan will result in the prive of feed reaching 12 faster
In plan B the price rises by 10%.
Thus the price rise is per week is $0.8
In plan A the price rise per week is $0.1
In plan C the price rise per week is
[tex]\frac{12-8}{8}=\frac{4}{8}=0.5[/tex]In plan D the price rise per week is $0.25
Considering all the plan the maximum price rise for each week is 0.8.
So the plan that would lead to $12 fastest is plan B.
The answer is plan B.
PLS HELP DUE NOWWWWWWWWWW
The correct statement will be:
A. The rate of change is the number of inches grown per month, and the initial value is the starting height.
We can form the following equation from the given data:
H(m) = 13 + 41m,
Where H ( Height ) is a function of the number of months ( m ).
We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.
The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.
So, option A will be the ultimate explanation for the data given.
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Answer:
Step-by-step explanation:
This is a linear function of time, as mentioned.
A linear function is always in the form of:
[tex]y=mx+b[/tex]
The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.
The initial value is when [tex]x=0[/tex].
[tex]x=0[/tex] means at the very beginning.
At the very beginning, the height would be the starting height, so the initial value would be the starting height.
The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].
Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.
You could also write it as the number of inches grown per month.
The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).
I’m not english person. I cannot understand those. Can someone explain some of them please? I’m trying to pass an english math exam..
Step-by-step explanation:
lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer
A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
If a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.
Determining whether the triangle is a right triangleWe would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.
In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides
Longest side
45² = 2025
Other side
30 ² + 35 ²
900 + 1,225
= 2125
Hence,
2025 ≠ 2125
Based on the above it is not a right triangle because the longest side did not equate the other side.
Therefore it is not a right triangle.
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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.
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i need help please help tysm
Answer:
(2, 3)
Step-by-step explanation:
the work is all in the pic go check it out I am so sorry if it's incorrect also have a nice day:)
Hello, I’m struggling with my geometry homework. It’s number 2
An inscribed circle is the largest circle contained in the polygon (triangle):
• Bisects two angles of the triangle.
,• The angle bisector will intersect at the intercenter.
Procedure
To draw the inscribed circle, we have to use the intercenter (O, in our case) as the center, pointing one of the compass points in O, and draw the circle touching the edges.
if it takes 3/4 of an hour to fill 3/5 of a pool how many hours will it take to fill the pool completely
The time taken to completely fill the pool is 5/4 hour
How to determine the time to fill the pool?From the question, the given parameters are:
Time =3/4 hour
Size of the pool = 3/5
The time to fill the pool is then calculated as
Time = Given time/Proportion of the pool
Substitute the known values in the above equation
So, we have the following equation
Time = 3/4 hour ÷ 3/5
Express the quotient as product
So, we have the following equation
Time = 3/4 hour x 5/3
Evaluate the products
Time = 5/4 hour
Hence, the time taken is 5/4 hour
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PLS HELP!!!
The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the
cat population on each island is changing.
year
01 2 3
number of cats on Meow Island 2 6 18, 54 162
2 3 4
number of cats on Purr Island 2 6 10 14 18
B I
year
Type your response in the space below.
Type here
01
t
Step-by-step explanation:
Meow island get's their population multiplied by 3 per year
Purr island get's and additional 4 cats per year
The population of cats on each island in the mathematical form is:
Meow island:
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
y = 4x + 2
Where x is the number of years from x = 0, 1, 2, 3 ,,,,
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
We will make ordered pair of number of years x and number of cats y as
(x, y).
Meow island:
We see that the number of cats is increasing 3 times the previous number of cats.
So,
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
(0, 2), (1, 6), (2, 10), (3, 14) ....
The equation for the table.
y = mx + c
m = (6 - 2) / (2 - 1) = 4/1 = 4
(0, 2) = (x, y)
2 = 4 x 0 + c
c = 2
Now,
y = 4x + 2
Thus,
The population of cats on each island in mathematical form is given above.
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Answer fast
Which of the following is used to identify outliers in a set of data?
1.5(IQR)
1.5(range)
2(mean)
2(median)
The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).
What is the Interquartile range (IQR)?We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.
To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.
Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.
Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.
Hence, the correct answer would be option (A).
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Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. The speed of the tennis ball is...
The speed of the tennis ball is 6.2 metres per seconds.
How to find the speed of the tennis?Speed is measured as the ratio of distance to the time in which the distance was covered.
Therefore, speed can be represented mathematically as follows;
speed = distance / time
Hence, the table tennis travels 12.4 metres south in 2 seconds.
The speed of the tennis can be computed as follows:
distance = 12. 4 metres
time = 2 seconds
Therefore,
speed = 12.4 / 2
speed = 6.2 meters per seconds.
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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given that,
Katie and her best friend Liam play tennis every Saturday morning.
When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.
The speed of the tennis can be found by using formula
speed=distance/time
distance = 12. 4 metres
time = 2 seconds
Now speed=12.4/2
speed=6.2
Hence speed of the tennis ball is 6.2m/s
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