Answer:
the volume of the sphere will be 4 times the volume of the cone;
Step-by-step explanation:
The question is on volume comparison
Volume of a sphere=4/3 [tex]\pi[/tex]×r³
Volume of a cone= [tex]\pi[/tex]/3×r²h
where r is the radius and h is the height
Apply the condition
If r=h=1 unit
Then volume of sphere will be= 4/3 × [tex]\pi[/tex]×1³ = 4/3[tex]\pi[/tex]
And volume of the cone will be= [tex]\pi[/tex]/3 ×1²×1 =[tex]\pi[/tex]/3
We can see the volume of the sphere will be 4 times the volume of the cone;
4/3[tex]\pi[/tex] = 4×[tex]\pi[/tex]/3
The volume of the sphere is exactly twice the volume of the cone.
To establish the relationship between the volumes of a cone and a sphere when they have the same radius and height, we need to use the formulas for the volumes of these shapes.
Let's denote the radius of both the cone and the sphere as r and the height of the cone (which is also the diameter of the sphere) as h .
The volume V of a sphere is given by the formula:
[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \][/tex]
The volume V of a cone is given by the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 h \][/tex]
Since the height of the cone is the same as the diameter of the sphere, we have [tex]\( h = 2r \).[/tex]Substituting this into the volume formula for the cone gives us:
[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 (2r) = \frac{2}{3}\pi r^3 \][/tex]
Now, we can compare the volumes of the two shapes:
[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \] \[ V_{\text{cone}} = \frac{2}{3}\pi r^3 \][/tex]
Dividing the volume of the sphere by the volume of the cone, we get:
[tex]\[ \frac{V_{\text{sphere}}}{V_{\text{cone}}} = \frac{\frac{4}{3}\pi r^3}{\frac{2}{3}\pi r^3} = \frac{4}{2} = 2 \][/tex]
Therefore, the volume of the sphere is exactly twice the volume of the cone when they have the same radius and height.
very confused please help asap ( 13 points)
Answer:
2 and a half
Step-by-step explanation:
To solve this, divide the total amount of free time [5/6] by the time it takes to play one video game [1/3]
Remember that dividing 5/6 by 1/3 is the same as multiplying 5/6 by 3/1.
Multiply the numerators
5 x 3 = 15
Multiply the denominators
6 x 1
15/6 = 2 3/6
So, Lamar can play 2 and a half video games
I hope this helps!
The answer is 2 and a half.
Big Ed’s car dealership is running a special on 2008 trucks. Big Ed offers financing at a rate of 6.71% on a loan with a term of 36 months, but he requires the customer to make a down payment of 15% of the cost of the vehicle. You are interested in a Car Crusher truck that costs $25,230. Not including the down payment, how much will you pay over the lifetime of the loan? a. $27,924.84 c. $23,735.88 b. $25,789.32 d. $21,445.50 Please select the best answer from the choices provided A B C D
Answer: C
Step-by-step explanation:
25,230 x .15= 3,784.50
25,230- 3,784.50= 21,535
21,535/36= 598.20833
598.20833 x 1.0671= 638.348109
638.348109 x 36= 22,980.5319
Answer:
Letter C $23,735.84.The result varies a few dollars, because during the solution an adjustment was made to the decimals.
Step-by-step explanation:
1. Define the price of the vehicle you are going to buy with the dealer or seller
Principal: $25230
Rate= 6.71%
N= 36 months
Down payment=15% of the cost of the vehicle= (25230*0.15)=$3784.50
25230-3784.50=21445.5
2. Apply the amortization formula to determine the monthly payments. With this taxation, you will determine the payments applied to the principal and the copper of interest.
A=P*(r(1+r)^{n})/((1+r)^{n}-1).
A= amortization or monthly payments.
P=Principal
R=interest rate
N= the total number of months
a. Calculate the monthly interest rate. The annual interest rate is 6.71% percent. Divide it by 12 to get the monthly interest rate. The monthly interest rate is 0.5592 percent (6.71/12 = 0.5592)
A=21445.5*(0,005592 (1+0,005592)^{{36}})/(1+0,005592)^{{36}}-1.
A=21445.5*(0,00683/0,2223)
A=21445.5*0,03072=658.90
Total of the payment= 658.90*36=23720.40
A certain hexagonal prism has a volume of 160 cubic meters. Its base has a perimeter of 30 meters and an area of 64 square meters. What is the surface area in square meters of the hexagonal prism??
Answer:
The surface area is equal to [tex]203\ m^{2}[/tex]
Step-by-step explanation:
step 1
Find the height of the prism
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
we have
[tex]V=160\ m^{3}[/tex]
[tex]B=64\ m^{2}[/tex]
substitute in the formula and solve for h
[tex]160=64h[/tex]
[tex]h=160/64=2.5\ m[/tex]
step 2
Find the surface area
The surface area of the prism is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base
h is the height of the prism
we have
[tex]B=64\ m^{2}[/tex]
[tex]P=30\ m[/tex]
[tex]h=2.5\ m[/tex]
substitute in the formula
[tex]SA=2(64)+(30)(2.5)=203\ m^{2}[/tex]
Plz help me with this
Answer: [tex]A)\quad \dfrac{x^6\ z}{y^{10}}[/tex]
Step-by-step explanation:
[tex].\quad \dfrac{(x^{2}\cdot y^{-3}\cdot z^{4})^2}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\= \dfrac{x^{2\cdot 2}\cdot y^{-3\cdot 2}\cdot z^{4\cdot 2}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4}\cdot y^{-6}\cdot z^{8}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4+2}\cdot y^{-6+6}\cdot z^{8-7}}{x^{-2+2}\cdot y^{4+6}\cdot z^{7-7}}\\\\\\=\large\boxed{\dfrac{x^6\ z}{y^{10}}}[/tex]
the sale of a boatshaped like a right triangle with the dimensions shown below how much material is needed to make the sale
[tex]A=\frac{ab}{2}=\frac{25\cdot12}{2}=\boxed{150}[/tex]
does anybody know this?
Answer:
37
Step-by-step explanation:
To evaluate, substitute x = 10 into g(x) then substitute the value obtained into f(x)
g(10) = 10 - 4 = 6, then
f(6) = 6² + 1 = 36 + 1 = 37
Dave uses the functionP(d) = 20d - 20 to calculate the net profit of his dog walking business. Where P(d) is the net profit in dollars, and "d" the number of dogs he walks. Interpret the meaning of the equation below using the context of the problem
P(3) = 40
When Dave walks three dogs he will earn a net profit of 40 dollars.
P(3) = 40 in the given problem context implies that Dave makes a net profit of 40 dollars from walking three dogs.
Explanation:In the given problem context, the equation P(3) = 40 means that when Dave walks three dogs (d=3), he makes a net profit of 40 dollars. Dave's profit function is P(d) = 20d - 20. By substituting d with 3 in his profit function, we obtain P(3) = 20*3 - 20, which gives us P(3) = 60 - 20 = 40. Thus, Dave earns a net profit of 40 dollars from walking 3 dogs.
Learn more about Profit Function Interpretation here:
https://brainly.com/question/32638481
#SPJ3
Which expression is equivalent to this one? 1/6(x - 18)
A)1/6x - 18
B)1/6x • (-18)
C)1/6x - 3
D)1/6 + x - 18
C, because you distribute the 1/6 to x and 18 which ends up being 1/6x - 3
[tex]\frac{1}{6}(x-18)[/tex] Distribute 1/6(multiple 1/6 to x and -18)
[tex]\frac{1}{6}(x) -\frac{1}{6} (18)[/tex] Simplify
[tex]\frac{1}{6}x -3[/tex] Your answer is C
For the direct variation such that when y = 2 then x = 3 , find the constant of variation ( k) and then find the value of y when x = - 0.5.
Answer:
k is 2/3 and y is -1/3 when x is -0.5.
Step-by-step explanation:
The direct variation relationship is y = kx, where k is the const. of var.
Subbing 3 for x and 2 for y, 2 = 3k, or k = 2/3.
Now, if x = -0.5, y = (2/3)(-1/2) = -1/3
k is 2/3 and y is -1/3 when x is -0.5.
Answer:
2/3 and y is -1/3 when x is -0.5.
Step-by-step explanation:
Hope I helped
If M = N, the diameter of M = 148, and AB = 140, what is the length of NQ?
Answer:
[tex]NQ=24\ units[/tex]
Step-by-step explanation:
we know that
Triangles ABM and CDN are congruent
so
CD=AB
AB=2AL ----> because the diameter divide the circle into two equal parts
CQ=AL=140/2=70 units
NC----> is the radius
NC=148/2=74 units ----> the radius is half the diameter
Applying Pythagoras Theorem find the value of NQ
[tex]NC^{2}=NQ^{2}+CQ^{2}[/tex]
substitute the values
[tex]74^{2}=NQ^{2}+70^{2}[/tex]
[tex]NQ^{2}=74^{2}-70^{2}[/tex]
[tex]NQ^{2}=576[/tex]
[tex]NQ=24\ units[/tex]
(15 points) please help asap!!!
(4, 2) and (4, -5)
(Look at the photo. They have the same x-coordinates, but different y-coordinates; one is positive the other is negative, resuting in different quadrants)
I hope this helps!
What is the factored form of x^3-1
Answer:
the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]
Step-by-step explanation:
We need to find factors of x^3 -1
[tex]x^3-1 \\(x)^3 -(1)^3\\We \,\, know\,\, a^3 -b^3 = (a-b) (a^2 +ab + y^2) \\So, \,\, using\,\, the \,\, formula\,\,\\Here\,\, a= x \,\,and\,\, b= 1\\(x)^3 -(1)^3 = (x-1) (x^2 +x+1)\\[/tex]
So, the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]
There is a 52% chance that a player will win a certain carnival game. Which statement describes the likelihood that a player will win the game?
A. The player will definitely win the game.
B. It is unlikely that the player will win the game.
C. It is likely that the player will win the game.
D. It is neither likely nor unlikely that the player will win the game.
It’s A. Hope you already got it✨
The answer is actually D or C
The function H(t) = −16t^2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answer:
see the attachment for a table
Step-by-step explanation:
A. The table is shown in the attachment. The solution to h(t) = g(t) is at a value of t that lies between 6 and 7. At t=6, h(t) > g(t). At t=7, h(t) < g(t). Since both functions are continuous, they must have equal values somewhere between t=6 and t=7. (Intermediate value theorem.)
__
B. The solution means the cannon balls will have the same height at a value of t between 6 and 7.
Answer:
b
Step-by-step explanation:
Find the value of x for which line a is parallel to line b
Answer:
20
Step-by-step explanation:
Since we are told that line a is parallel to line b, even if it's not visible in the image, we can say that ∠5 = ∠1, since they are formed by the same line crossing parallel lines.
So, we have
∠4 = 3x
∠5 = ∠1 = 6x
Since ∠4 and ∠5 are complementary angles formed by line t, we know their sum is 180 degrees. So,
∠4 + ∠5 = 180
3x + 6x = 180
9x = 180
x = 20
Answer is 20.
Solve for 3/4u = 12
.
Simplify your answer as much as possible.
Answer:
u = 16
Step-by-step explanation:
Given
[tex]\frac{3}{4}[/tex] u = 12
Multiply both sides by 4 to eliminate the fraction
3u = 48 ( divide both sides by 3 )
u = 16
if x is 5, then what does 6x =
Answer:
x=30
Step-by-step explanation:
The vertices of ABC are A(-2,2), B(6,2), and C(0,8). The perimeter of ABC
Answer:
The perimeter of the triangle ABC is 22.8 units
Step-by-step explanation:
* Lets study the information in the problem
- There is Δ ABC with vertices:
A (-2 , 2) , B (6 , 2) , C (0 , 8)
- The perimeter of the triangle is the sum of the length of its
three sides
* We must to find the lengths of AB , BC and CD
- The rule to find the distance between 2 points (x1 , y1) and (x2 , y2) is
√[(x2 - x1)² + (y2 - y1)²]
* Lets find the lengths of the three sides
- Length of AB
∵ A = (-2 , 2) and B = (6 , 2)
∴ AB = √[(6 - -2)² + (2 - 2)²] = √8² = 8 units
- Length of BC
∵ B = (6 , 2) and C = (0 , 8)
∴ BC = √[(0 - 6)² + (8 - 2)²] = √[6² + 6²] = √72 = 6√2 units
- Length of AC
∵ A = (-2 , 2) and C = (0 , 8)
∴ AC = √[(0 - -2)² + (8 - 2)²] = √[2² + 6²] = √40 = 2√10 units
* Now lets find the perimeter of the triangle
∵ The perimeter = AB + BD + AC
∴ The perimeter = 8 + 6√2 + 2√10 = 22.8 units
* The perimeter of the triangle ABC is 22.8 units
Answer:
The perimeter of triangle ABC = 22.78 units
Step-by-step explanation:
Formula:-
The length of line segment with end points (x₁, y₁) and (x₂, y₂) is given by,
Length = √ [(x₂ - x₁)² + (y₂ - y₁)²]
To find the each side of triangle
We have A(-2,2), B(6,2), and C(0,8).
AB = √[(6 - -2)² + (2 - 2)²] = √64 = 8
BC = √[(0 - 6)² + (8 - 2)²] = √(36 + 36) = 8.48
AC = √[(0 - -2)² + (8 - 2)²] = √(4 + 36) = 6.3
To find the perimeter of triangle ABC
Perimeter = AB + BC + AC
= 8 + 8.48 + 6.3 = 22.78 units
You'll find lots of clouds over _____________ climates and practically no clouds over ___________ climates.
these are your answers : tropical, desert, polar, maritime. ( they will work for both)
(this is science)
Answer:
you'll find lots of clouds over tropical climates and practically no clouds over desert clmates.
Answer:
encontrará muchas nubes sobre climas tropicales y prácticamente ninguna nube sobre climas desérticos.
Step-by-step explanation:
An important postulate in geometry states: "Through Point P, there is only one line parallel to ". What is the equation of line l, parallel to AB that passes through Point X?
Answer:
y=(-5/12)x+(95/12)
Step-by-step explanation:
step 1
Find the slope of the line AB
m=(3-8)/(2+10)=-5/12
step 2
Find the slope of the line parallel to AB
we know that
If two lines are parallel then their slopes are the same
so
the slope is m=-5/12
step 3
Find the equation of the line l parallel to AB that passes through Point X
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
substitute
y-10=(-5/12)(x+5)
y=(-5/12)x-(25/12)+10
y=(-5/12)x+(95/12)
ANSWER NEEDED ASAP!!!!!!!!
1. 428 pages: There are a total of 428 pages that you can flip to.
2. 1/428: Page 45 is only one page out of the total sample space.
3. 1/2: Since the last page is 428, there is an even number of pages. That means that there are 214 page numbers that are even. 214/428 = 1/2.
Answer:
1. What is the sample space for this experiment?
A: 1 to 428
2. What is the probability that you will turn to page 45?
A: There is a 1 out of 428 chance you will turn to page 45.
3. What is the probability that you turn to an even numbered page?
A: There is a 1 out of 2 chance you will turn to an even numbered page.
The students in Mr. Taylor's class are part of different clubs. 8 boys in reading club 4 girls in reading club 2 boys in drama club 12 girls in drama club Which of the following statements is correct? A. For every boy in the drama club, there are two boys in the reading club. B. For every boy in the drama club, there are six boys in the reading club. C. For every girl in the reading club, there are three girls in the drama club. D. For every girl in the reading club, there are four girls in the drama club.
Answer:
The answer is D. For every girl in the reading club, there are four girls in the drama club. It is not B. For every boy in the drama club, there are six boys in the reading club.
Pls make me brinlyest .
Hope this helped
The correct statement is, C. For every girl in the reading club, there are three girls in the drama club.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, 8 boys in reading club 4 girls in reading club 2 boys in drama club 12 girls in drama club.
Going through the given options (given statements so multiple options would be correct).
For every girl in the reading club, there are three girls in the drama club,
As 12 is a multiple of 4 and 3.
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
Select "Growth" or "Decay" to classify each function.
Final answer:
Classifying functions involves identifying whether a population is experiencing growth, depicted by exponential or J-curve growth models, or decay, which is often described through logistic or S-curve models. Exponential growth shows unrestricted rapid increases, while logistic growth accounts for environmental limits and a carrying capacity. Age structure diagrams provide further context for the type of population change being observed.
Explanation:
Growth and Decay in Biological Functions
When classifying functions as growth or decay, one must consider the nature of the function in relation to the context of time and population size. For instance, when discussing bacterial growth, Curve A depicting exponential growth is characterized by a population size that increases rapidly over time, often without any constraints. This curve represents a J-curve model on a graph where population size skyrockets as time progresses. On the other hand, Curve B illustrates logistic growth, which follows an S-curve model where the population grows rapidly at first and then slows down as it reaches carrying capacity, a point where growth rate starts to decline.
Different time intervals on a growth curve represent various phases, such as the lag phase, where growth is slow or negligible; the log phase or exponential phase, where the number of cells increases dramatically; the stationary phase, where growth rate is zero due to resource depletion or waste accumulation; and the death phase, where the number of live cells declines.
Various types of growth in organisms can be identified by their structural adaptations or ecological contexts, such as whether they are terrestrial or aquatic, or whether they are deciduous or evergreen plants. Additionally, age structure diagrams for populations can reveal if a population is rapidly growing, growing slowly, stable, or in decline.
The radius of the circle whose equation is (x-3)^2 + (y+1)^2 = 16 is
Answer:
4
Step-by-step explanation:
The general equation of a circle with center (a, b) and radius r is given by the equation;
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
The constant in the right hand side of the equation is simply the square of the radius;
We have been given the following equation;
(x-3)^2 + (y+1)^2 = 16
Comparing this with the general equation above;
[tex]r^{2}=16\\\\r=\sqrt{16}=4[/tex]
Simplify the following expression
7x^2 - 15x + 5 - 2x - 8x^2
Answer:
[tex]\large\boxed{7x^2-15x+5-2x-8x^2=-x^2-17x+5}[/tex]
Step-by-step explanation:
[tex]7x^2-15x+5-2x-8x^2\qquad\text{combine like terms}\\\\=(7x^2-8x^2)+(-15x-2x)+5\\\\=-x^2-17x+5[/tex]
And buys a pencil for $0.45 draw and label coins. Ann could use to make $0.45
Answer:
You could use one quarter and two dimes... that will equal $0.45
(I'm not sure what you are asking for)
Answer:
You could use 9 nickels
You could use 45 pennies
You could use 1 quarter and 2 dimes
You could use 4 dimes and 1 nickel
You could use 2 dimes and 5 nickels
You could use a lot more combination that equal 45...
Steve can train 48 dogs in 6 hours. How many dogs can Steve train in 10 hours?
Answer:
80
Step-by-step explanation:
Steval train 80 dogs in 10 hours because 48÷6 = 8 so if you do 10 times a day you get 80 so you will get a total of 80 dogs in 10 hours
what is 26.553 rounded to the nearest hundred?
Answer:
26.55
Step-by-step explanation:
When rounding to the nearest whatever, you always look at the digit to the right of it. In this case, you look at the thousandth digit. 3 is not equal to or less than five, so you round 3 to 0 and you get 26.55
If f(x) = 5x + 40, what is f(x) when x = -5?
the answer to this problem is 15
I believe 15 is correct ^^
Which side lengths form a right triangle 30 POINTS!!
Answer:
A. 3, 4, 5
Step-by-step explanation:
Option A:
LHS = 3² + 4² = 9 + 16 = 25
RHS = 5² = 25
(3, 4, 5) is a right triangle.
Option B:
LHS = 7² + 8² = 49 + 64 = 113
RHS = 9² = 81
(7, 8, 9) is NOT a right triangle.
Option C:
LHS = 3² + 9² = 9 + 81 = 90
RHS = √95² = 95
(3, 9, √95) is NOT a right triangle.
Hope this help!!!
Have a nice day!!!