2000 / 100 = 20
20 * 6 = 120 liters total gas
120 * 1.20 = $144 total for gas
144 / 3 = $48 each
A wheel turns 1,800 revolutions per minute. How fast does it turn in radians per second?
A wheel turn 60π radians per second.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A wheel turns 1,800 revolutions per minute.
Now,
Since, A wheel turns 1,800 revolutions per minute.
Hence, Number of revolution in one seconds = 1800 / 60
= 30
We know that;
⇒ 1 revolution = 2π radian
So, Number of revolution in radian per second = 30 × 2π
= 60π
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ2
Simplify. 1/4 (-12+4/3)
The simplification of 1/4 (-12+4/3) first involves simplifying the operation in the parentheses which gives -10.67. Multiplying this by 1/4 we get -2.67.
Explanation:To simplify the expression 1/4 (-12+4/3), first simplify the operation in the parentheses.
-12 + 4/3 equals -12 + 1.33 (approx.), which simplifies to -10.67.
Then, multiply this result by 1/4. So, 1/4 of -10.67 equals -2.67 (approx.).
So, 1/4 (-12+4/3) simplifies to -2.67.
Learn more about Mathematical Simplification here:https://brainly.com/question/33857870
#SPJ2
Jack has 702 acres of land which requires 1.2 acre-feet of water to grow crops successfully. Currently it cost 12.95 per acre-foot to purchase water. How much will it cost to water all his crops
A) 9,090.90
B) 10,909.08
C) 15,540.00
D) none
round 26,891 to the nearest ten-thousands place
A heap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters.
Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.
---------------------
The volume of a cube of edge e is given by:
[tex]V = e^3[/tex]
In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.
[tex]V = e^3[/tex]
[tex]125 = e^3[/tex]
[tex]e = \sqrt[3]{125}[/tex]
[tex]e = 5[/tex]
Now, for the rate of change, we need to apply the implicit differentiation, thus:
[tex]V = e^3[/tex]
[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]
Volume decreases at a rate of 4 cubic meters per minute, thus:
[tex]\frac{dV}{dt} = -4[/tex]
The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:
[tex]-4 = 75\frac{de}{dt}[/tex]
[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]
[tex]\frac{de}{dt} = -0.0533[/tex]
The rate of change is of -0.0533 cubic meters per minute.
A similar problem is given at https://brainly.com/question/24158553
In the game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. a winning "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. the two cards can be in any order. find the probability of being dealt a blackjack hand. what approximate percentage of hands are winning blackjack hands?
We are given here that a blackjack hand consists of:
1 of the 4 aces = 4 / 52
1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52
So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:
P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace
P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)
P = 0.04827 = 4.83%
Therefore there is a 4.83% probability to get a blackjack hand.
Final answer:
The probability of being dealt a blackjack hand with a single deck is approximately 0.0483, which translates to about 4.83% of the hands.
Explanation:
To find the probability of being dealt a blackjack hand in a single-deck game, we need to calculate the chances of drawing an ace and a 10-point card (10, Jack, Queen, or King) in any order. There are 4 aces and 16 cards worth 10 points in a deck of 52 cards. The probability of drawing an ace first is 4/52, and then drawing a 10-point card is 16/51, giving us (4/52)*(16/51). Conversely, if a 10-point card is drawn first (16/52) followed by an ace (4/51), the probability is (16/52)*(4/51). Adding the two probabilities gives us the chance of a blackjack in either order:
P(Blackjack) = (4/52)*(16/51) + (16/52)*(4/51) = (64/2652) + (64/2652) = 128/2652 ≈ 0.0483
The approximate percentage of hands that are winning blackjack hands is about 4.83%.
Daniel is completing a home project. He needs 13 pieces of wood, each 112 feet long, to complete the project. How much wood does Daniel need to complete his home project? 823 ft
Answer:
its a
Step-by-step explanation:
Answer:
19 1/2 ft
Step-by-step explanation:
hope this helped
A solid lies above the cone z = x2 + y2 and below the sphere x2 + y2 + z2 = z. write a description of the solid in terms of inequalities involving spherical coordinates
The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).
Explanation:In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).
The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.
The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.
In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).
Learn more about spherical coordinates here:https://brainly.com/question/31745830
#SPJ12
The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.
Explanation:To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.
Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.
As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).
Therefore, the solid can be described using the following inequalities in spherical coordinates:
0 ≤ r ≤ cos(θ) 0 ≤ θ ≤ 2π 0 ≤ ϕ ≤ π Learn more about Solid described in spherical coordinates here:
https://brainly.com/question/31850328
#SPJ11
Suppose Georgette buys 400 shares of Google at $250 a share. She sells them at $350 a share. What is her capital gain?
a. 400 times $100
b. 400 times $250
c. 400 times $350
d. 400 times $600
Answer: A
Step-by-step explanation:
How do you find absolute extrema for a function?
f(x)= (8+x)/(8-x); Interval of [4,6]
tiffany and Adele sold cookies and brownies to raise money for their school. They sold a total of 25 sweets. If each cookie costs 1$ and the brownies cost a 1.50 each and they made a total of 32$, how many did each sell?
By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.
To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.
The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.
Solving this system of equations will give us the number of each type of sweet sold.
To solve the system of equations, we can use substitution or elimination. I'll use substitution:
From the first equation, we can express y as y = 25 - x.Next, we substitute y in the second equation: 1*x + 1.50*(25 - x) = 32.Simplify and solve for x: X + 37.50 - 1.50x = 32, which simplifies further to 0.50x = 5.50. Divide both sides by 0.50 to find x = 11.Now that we have the value for x, substitute it back into the equation for y: y = 25 - 11 = 14.Tiffany and Adele sold 11 cookies and 14 brownies.
A family has five children. the probability of having a girl is 1/2. what is the probability of having at least 4 girls?
Every week, Mr. Kirkson uses 316 gallon of water to water every 13 square foot of his garden. How many gallons of water does Mr. Kirkson use per square foot to water his garden each week? Enter your answer in the box as a fraction in simplest form.
Is It A Fraction If So Then The Answer Is [tex]\frac{9}{16}[/tex]
If Not Then The Other Guy Is Right
HoPe It HeLpS PlEaSe MaRk Me ThE BRAINlYEST!!!!!!!!!!!!
What is the solution of the equation f(x) = g(x) ?
A. x = -4
B. x = -2
C. x = 2
D. x = 4
solve the system of linear equations. separate the x- and y- with a coma.
6x=-14-8y
-12x=20+8y
Answer:
-16 81 19
Step-by-step explanation:
A manufacturing company has developed a cost model, C(X)= 0.15x^3 + 0.01x^2 +2x +120, where X is the number of item sold thousand. The sales price can be modeled by S(x) + 30- 0.01x. Therefore revenues are modeled by R(x)= x*S(x).
The company's profit, P(x) = R(x)-C(x) could be modeled by
1. 0.15x^3+ 0.02x^2- 28x+120
2. -0.15x^3-0.02x^2+28x-120
3. -0.15x^3+0.01x^2-2.01x-120
4. -0.15x^3+32x+120
What is the cytoplasm? A. a fluid in which organelles are suspended B. a type of organelle that assembles proteins C. the exterior envelope surrounding the nucleus D. the inner surface of the cell's wall
What is 2 3/4 - 1/2? A. -2 1/4 B. 1 1/4 C. 2 1/4 D. 3
A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder
The shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?
What is the matter with this number: .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Is it real?
Which are zeros of the following polynomial?
6x 2 - 11x - 10 = 0
A x = 6, x = 10
B x = ; x =
C x = -2; x = 5
D x = ; x =
Answer:
x = -2/3; x = 5/2.
Step-by-step explanation:
6x 2 - 11x - 10 = 0
Use the 'ac' method:
6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.
That would be -15 and +4. So we write:
6x^2 - 15x + 4x - 10 = 0 Factor by grouping:
3x(2x - 5) + 2(2x - 5) = 0
(3x + 2)(2x - 5) = 0
x = -2/3; x = 5/2.
can someone help me please
to convert feet to miles you would use a ratio of feet over miles
so the answer would be B
The rectangular sandbox at the local community park has a width of 24.5 meters and its length is 31.7 meters. What is the perimeter, in meters, of the rectangular sandbox?
To calculate the perimeter of the rectangular sandbox, use the formula P = 2l + 2w, where l is the length and w is the width. For the given dimensions, 31.7 meters in length and 24.5 meters in width, the perimeter is 112.4 meters.
Explanation:The question asks us to calculate the perimeter of a rectangular sandbox. The formula to calculate the perimeter of a rectangle is 2 times the length plus 2 times the width, often written as P = 2l + 2w.
Given the dimensions of the sandbox, the length (l) is 31.7 meters, and the width (w) is 24.5 meters.
We calculate the perimeter as follows:
Perimeter = 2 × Length + 2 × WidthPerimeter = 2 × 31.7 m + 2 × 24.5 mPerimeter = 63.4 m + 49.0 mPerimeter = 112.4 metersTherefore, the perimeter of the rectangular sandbox is 112.4 meters.
Julian is 10 years younger the Thomas. The sum of their ages is 74. What is Thomas’s age?
Thomas = x
Julian = x-10
x +x-10 = 74
2x-10 = 74
2x = 84
x = 84/2 = 42
Thomas is 42
Julian is 32
Describe the transformation of the graph from f(x) to g(x)
1) f(x)=2x+1
g(x)=2x+4
2) f(x)=x+3
g(x)=-x+1
3) f(x)=x^2
g(x)=(x-1)^2 +3
Transformations of the functions include a vertical shift, reflection and vertical shift, and a horizontal and vertical shift for three different pairs respectively. Specific (x, y) data pairs demonstrate these transformations on the graphs.
Explanation:We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:
Vertical Shift: For the functions f(x)=2x+1 and g(x)=2x+4, g(x) represents a vertical shift up by 3 units from f(x).Reflection and Vertical Shift: For f(x)=x+3 and g(x)=-x+1, g(x) is f(x) reflected across the x-axis (due to the negative sign before x) and then a vertical shift down by 2 units.Horizontal Shift and Vertical Shift: Lastly, from f(x)=x^2 to g(x)=(x-1)^2+3, the graph of g(x) is the graph of f(x) shifted to the right by 1 unit and then up by 3 units.The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.
If 5x=3x-8, evaluate 4x+2
Round 10,386.145 to the nearest tenth
The department store where you work is having a sale. Every item is to be marked down 15% What will the sale price of a $152 coat be
multiply 152 by 15%
152 * 0.15 = 22.80 ( amount of discount
152 - 22.80 = 129.20 ( sale price)
What is the gcf for 84