Step-by-step explanation:
Let V be the volume of the cone.
The student says that, the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius.
If diameter is 4 inch, radius = 2 inch
Volume of the cone,
[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] .......(1)
If radius, r = 2 inch
New volume,
[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] ....(2)
We can see that the volume in both case is same. Hence, the student is correct.
If an earthquake measures 10^4, what does it measure on
the Richter scale?
Answer:
The Richter scale and how it measures earthquake magnitude. The Richter scale calculates an earthquake's magnitude (size) from the amplitude of the earthquake's largest seismic wave recorded by a seismograph. ... (That is, an earthquake measuring 5.0 releases 31 times more energy than an earthquake measuring 4.0.)
Find the volume of each figure. Simplify your answers.
Please help ASAPPPP
thank you so much!!!!
Answer:
[tex]98.28\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is the width of the prism, and [tex]h[/tex] is the height of the prism.
Substituting given values, we get:
[tex]V=2.5\cdot 4.25\cdot 9.25=98.28125\approx \boxed{98.28\:\mathrm{ft^3}}[/tex]
Since "Simplify your answers" is very subjective, I've rounded to the nearest hundredth as that is reasonably universal, but you may need to adjust the rounding as desired.
1.
For the graph of the function, identify the axis of symmetry, vertex and the formula for the function.
A. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = –x2 + x
B. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = x2 + x + 1
C. Axis of symmetry: x = –0.5; Vertex: (–0.5, –0.75); f(x) = x2 – x + 1
D. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = x2 + 2x + 1
Answer:
D. Axis of symmetry: x = –0.5; Vertex: (–0.5, 0.75); f(x) = x2 + 2x + 1
Step-by-step explanation:
A. Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
( 1 /2 , 1 /4 )
Focus:
( 1 /2 , 0 )
Axis of Symmetry:
x
=
1
2
Directrix:
y
=
1
2
x
y
− 2
− 6
− 1
− 2
1
2
1
4
1
0
2
− 2
B. Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
( − 1 /2 , 3 /4 )
Focus:
( − 1 /2 , 1 )
Axis of Symmetry:
x
=
−
1
2
Directrix:
y
=
1
2
x
y
− 2
3
− 1
1
− 1
2
3
4
1
3
2
7
C. Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
( 1 /2 , 3 /4 )
Focus:
( 1 /2 , 1 )
Axis of Symmetry:
x
=
1
2
Directrix:
y
=
1
2
x
y
− 2
7
− 1
3
1
2
3
4
1
1
2
3
D. Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
( − 1 , 0 )
Focus:
( − 1 , 1 /4 )
Axis of Symmetry:
x
=
− 1
Directrix:
y
=
− 1
4
x
y
− 3
4
− 2
1
− 1
0
0
1
1
4
What is the median of the following numbers?
10, 6, 4, 4, 6, 4, 1
Answer:
4
Step-by-step explanation:
Simplify the expression. Write your answer in positive exponent form:
(1/4) ^3 x (1/4) ^7
Answer:
1/4¹⁰
Step-by-step explanation:
this is the the simplified version for the question
Which expression is equivalent to – 2x²y3 ( 4x2 + 3xy – 5y3)?
A. -8x4y3 - 6x3,4 + 10x2,6
B. _8x4 y3 - 6x2y3 + 10x2,9
OC. 2x4 y3 + x3y4 – 7x2,6
O D. 2x4y3 + x2y3 – 7x2y9
Quicklyyyy please
Answer:
A. -8x⁴y³ - 6x³y⁴ + 10x²y^6
Step-by-step explanation:
Given:
– 2x²y³ ( 4x² + 3xy – 5y³)
Open the parenthesis
= (– 2x²y³ * 4x²) + (– 2x²y³ * 3xy) - (– 2x²y³ * 5y³)
= -8x⁴y³ + (-6x³y⁴) - (- 10x²y6^6)
= -8x⁴y³ - 6x³y⁴ + 10x²y6^6
The correct answer is
A. -8x⁴y³ - 6x³y⁴ + 10x²y^6
what is the result of subtracting the second equation from the first?
2x+7y=-8 - 2x-5y=-1
Answer:
12y = -7
Step-by-step explanation:
A cylinder has a height of 5 feet. Its volume is 1,271.7 cubic feet. What is the radius of the cylinder?
Answer: [tex]9\ ft[/tex]
Step-by-step explanation:
Given
Height of the cylinder [tex]h=5\ ft[/tex]
Volume of the cylinder [tex]V=1271.7\ ft^3[/tex]
The volume of the cylinder is given by [tex]V=\pi r^2h[/tex]
Consider r be the radius of the circle
[tex]\Rightarrow 1271.7=\pi r^2\cdot 5\\\\\Rightarrow r^2=\dfrac{1271.7}{3.142\times 5}\\\\\Rightarrow r^2=80.948\\\Rightarrow r=8.99\approx 9\ ft[/tex]
Thus, the radius of the cylinder is [tex]9\ ft[/tex]
please hurry i need this done asappppp
Answer:
11,25
Step-by-step explanation:
5w-8/3 =4w+2
Please solve with steps
Answer:
5w-8/3=4w+2
-8/3=-1w+2
-8=-1w+6
-14=-1w
14=w
Hope this helps, have a great day :)
What is the volume of a hollow ball whose other radius is 200m and inner radius of
100m.
What is the mass if it is iron*
Answer:
The volume of the hollow ball will be equal to the difference between the volume of a sphere with the outer radius and the volume of a sphere with the inner radius.
Remember that the volume of a sphere of radius R is given by:
V = (4/3)*pi*R^3
where pi = 3.14
Then if R is the outer radius, and r is the inner radius, the volume of the hollow ball is:
V = (4/3)*pi*( R^3 - r^3)
In this case, we have:
R = 200m
r = 100m
Then the volume of the hollow ball is:
V = (4/3)*3.14*( (200m)^3 - (100m)^3)
V = 29,306,666.67 m^3
Now, if this hollow ball is made of iron, we want to find the mass.
Remember the relation:
Mass = Density*Volume.
We know that the density of the iron is:
D = 7300 kg/m^3
Then the mass of this hollow ball is:
M = (7300 kg/m^3)*(29,306,666.67 m^3) = 213,938,666,666.6 kg
Molly and her friends just dined at a restaurant and left a tip of $20.54, which was equal to exactly 30% of the total bill. What was the total bill in dollars? Round your answer to two decimal places.
Answer:
68.47
Step-by-step explanation:
30%=0.3
20.54/0.3=68.4666……
A car travels a distance of 360 km in a time of 3 hours.
What is the car's average speed?
Answer:
convert km into m
1 km=1000m
360 km=1000*360m
=360000m
again,convert 3 hours into seconds
3 hours=60*60*3
=10800 second
average spped=total distance /time taken
=360000/10800
=33.33 m/s
Step-by-step explanation:
Using the unit circle, determine the value of sin(-240°).
A) -1/2
B) √3/2
C) 1/2
D) -√3/2
Answer:
B. √3/2.
Step-by-step explanation:
If we follow the circle from (1,0) clockwise through 240 degrees we end up at 120 degrees.
sin(120)
= √3/2
What is the value of a?
a+36°
a-27°
Answer:
hope this will help you more
All I need to know is what X is for this problem
Answer:
x = 19°
Step-by-step explanation:
We know that ∠UTV and ∠RTS are vertical angles, therefore is the measure of ∠UTV = 85, then the measure of ∠RTS would also be 85, by the "Vertical angles are congruent theorem.
=> ∠UTV ≅ ∠RTS
=> ∠UTV = 85°
=> ∠RTS = 85°
Now that we know all three angles of within the triangle, we can say that the sum of all three angles within the triangle is 180, we can conclude;
∠R + ∠T + ∠S = 180°
(3x) + (85°) + (2x) = 180°
5x + 85° = 180°
5x = 180° - 85°
5x = 95
x = 95/5
x = 19°
Hence, there is you're answer! x = 19°
Hope this helps!
Help please !!!Tomas has 135 more songs downloaded than Carl. Together they have 623 songs downloaded.
Part A
What system of equations could be used to determine how many songs each has downloaded?
Answer:
t + c = 623
t = c + 135
thomas has 379 songs downloaded, and carl has 244
Step-by-step explanation:
togheter they have 623 songs, aka the sum of thomas (t) and carl (c) is 623.
t + c = 623
thomas has 135 more than Carl. so Carl plus 135 is equal to thomas
t = c + 135
now you can solve it:
t + c = 623
(c+135) + c = 623
c + c = 488
2c = 488
c = 244
carl has 244 songs downloaded
t + 244 = 623
t = 379
thomas has 379 songs downloaded
The system of equations represents t + c = 623 and t = c + 135 and Tomas has 379 while Carl has 244 downloaded.
What is the equation?An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
As per the given,
Together they have 623 songs downloaded.
t + c = 623
Tomas has 135 more songs downloaded than Carl.
t = c + 135
By substitution,
c + 135 + c = 623
2c = 488
c =244
And , t = 244 + 135 = 379
Hence "The equations in the system show that Tomas has 379 while Carl has 244 downloaded and that t + c = 623 and t = c + 135 are represented".
For more about the equation,
brainly.com/question/10413253
#SPJ2
Which table represents an exponential function
Answer:
Step-by-step explanation:
table3 represents exponential function
Kelly is making a rectangular garden that has a width of (2x + 3) and length of (2x - 4)
How much fencing does she need to enclose the garden (perimeter)?
I need help immediately, you’ll receive brainlest if answered correctly!!!
Answer: 120
Step-by-step explanation:
Answer:
120°
Step-by-step explanation:
The triangles are similar, find the length of the unknown side. Round your answers to the nearest tenth (0.1), if necessary.
please help me
Answer:
[tex]22[/tex]
Step-by-step explanation:
Similar shapes must have corresponding sides in a constant proportion. Therefore, we can set up the following equation and solve for [tex]?[/tex]:
[tex]\frac{28}{42}=\frac{?}{33}[/tex] (divide corresponding sides)
[tex]\frac{28}{42}=\frac{?}{33},\\\\?=\frac{28\cdot 33}{42}=\boxed{22}[/tex]
Testing a robot. The robot is 17 inches tall and weighs 4 pounds. The employees of the company marked a grid on the floor and set the robot at (5,3). They programmed the robot to walk 2 yards east and 6 yards north each minute. What will
Answer:
After 7 steps, co-ordinate would be (35, 21) in the N-E direction
Step-by-step explanation:
Complete question
Testing a robot. The robot is 17 inches tall and weighs 4 pounds. The employees of the company marked a grid on the floor and set the robot at (5,3). They programmed the robot to walk 2 yards east and 6 yards north each minute. What will the co-ordinate after 7 steps
Solution
The grid on the floor is (5, 3)
5 is the X -co-ordinate and 3 is the y co-ordinate
Since the robot is walking in the north and east direction , it will be in the first co-ordinate only
After seven steps, in east direction, the co-ordinate would be 7 * 5 = 35
After seven steps, in north direction, the co-ordinate would be 7 * 3 = 21
So the co-ordinate would be (35, 21)
The figure below is a regular pentagon. If mZBAE = 5x + 3, find the value of x.
Answer:
x = 21
Step-by-step explanation:
For a pentagon, n = 5.
Each angle measures:
(n - 2)180/5 = (5 - 2)(180)/5 = 108
5x + 3 = 108
5x = 105
x = 21
Write in standard form: forty-seven hundredths
Answer:
0.47
Step-by-step explanation:
0.47
47 hundredths is equal to 0.47.
If this helps please mark as brainliest
Answer:
The standard form of forty-seven hundredths is 0.47.
Step-by-step explanation:
Have a nice day! :-)
TeamRocket3
A rectangular prism has a length of 6 inches, a height of 7 inches, and a width of 10
inches. What is its volume, in cubic inches?
Answer:
420
Step-by-step explanation:
just multiply all the numbers together
Answer: 420 cubic inches
Step-by-step explanation:
Use the formula V = lwh to solve.
V = L * W * H
V = 6 * 7 * 10
V = 420 cubic inches
3h - j when h = 8 and j = 11
plzzz help
Answer:
13
Step-by-step explanation:
3h - j
3(8) - 11
24 - 11
13
Find the value of:x^0+3
Answer:
4
Step-by-step explanation:
x^0 means 1. so 1+3=4
6 $44 is shared between David, Jo and Mary in the ratio 2:3:5
How much does each receive?
Answer:
David=$8.8
Jo=$13.2
Mary=$22
Step-by-step explanation:
2+3+5=10
44/10=4.4
David=4.4x2=$8.8
Jo=4.4x3=$13.2
Mary=4.4x5=$22
8.8+13.2+22=44
the dimensions of a right rectangular prism are 8/5cm 10/3cm & 7/4cm what the volume of the prism
Answer:
16/3
Step-by-step explanation:
Resh's gross pay is $1300 per fortnight. Fortnightly deductions from her gross pay are: PAYE: $31.85 FNPF: 5% HEALTH INSURANCE: $20.50 calculate her fortnightly net pay??
Answer:
$1182.65
Step-by-step explanation:
Given :
Fortnight gross pay = $1300
Given :
PAYE: $31.85 FNPF: 5% HEALTH INSURANCE: $20.50 calculate her fortnightly net pay
FNPF = 5% = 0.05 * $1300 = $65
PAYE = $31.85 ; HEALTH INSURANCE = $20.50
Total deduction = $(65 + 31.85 + 20.50) = $117.35
Net pay :
Gross pay - deduction
$1300 - $117.35 = $1182.65