The volume of the cone which has slant length of 5 and a diameter of 4 is 12.56 cubic units.
What is of volume of solid?Volume of solid is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
The more the volume of a object is obtains the more space. The volume of the cone can be given as,
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Here, (r) is the radius of the base of the cone and (h) is the height of the cylinder.
The diameter of the cone is 4 units. Thus, the radius of the cone is,
[tex]r=\dfrac{4}{2}\\r=2\rm units[/tex]
As the cone has a slant length of 5. Thus, the height of the cone is,
[tex]h=\sqrt{5^2-4^2}\\h=\sqrt{9}\\h=3 \rm units[/tex]
Here, the height is 3 units and the radius 2 units long. Thus the volume of the cone is,
[tex]V=\dfrac{1}{3}\times3.14\times (2)^2\times3\\V=12.56\rm units^3[/tex]
Hence, the volume of the cone which has slant length of 5 and a diameter of 4 is 12.56 cubic units.
Learn more about the volume of solid here;
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A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. Mrs. Johnson picks one without looking, replaces it and picks another one.
What is the probability that she picks two that are NOT orange?
Answer:
75%
Step-by-step explanation:
Because there were 12 marbles and only 3 of them are orange so it is a 75% chance she won't pick one and a 25% chance she will.
Hope it helps Have a great afternoon:)
Suppose P(A) = 0.7, P(B) = 0.8, andP (A n B) = 0.56.Calculate P(A U B).
Answer:
0.94
Step-by-step explanation:
Formula; P(AUB) = P(A) + P(B) - P(AB).
P(A) = 0.7
P(B) = 0.8
P(AB) = 0.56
= 0.7 + 0.8 - 0.56
= 0.94
Hence, P(A U B) = 0.94
[RevyBreeze]
Answer:
P(A ∪ B) = 0.94
Step-by-step explanation:
P(A) = 0.7
P(B) = 0.8
P (A ∩ B) = 0.56
P(A ∪ B) = P(A) + P(B) - (A ∩ B)
⇒ P(A ∪ B) = 0.7 + 0.8 - 0.56
⇒ P(A ∪ B) = 0.94
What is the surface area of the right cone below?
6
O A. 1307 units2
O B. 1267 units2
O C. 5407 units2
O D. 1807 units
HELPPP PLEASE
The solution is, surface area of the given circular cone is 126π units².
Option B is the correct option.
What is surface area of a cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r 2 + π L r , \pi r^2 + \pi L r, πr2+πLr,
where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.
here, we have,
Surface area of a cone is given by the expression,
V = πr(r + l)
Here, r = Radius of the circular base
l = Lateral height of the cone
By substituting the given values in the given expression of volume,
here, given that.
r = 6
l = 15
V = π(6)(6 + 15)
= 126π units²
Therefore, surface area of the given circular cone is 126π units².
Option B is the correct option.
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Lana wants to have $100,000 in 20 years. She plans to invest $8,000 to start and make yearly payments of $1,500 to the account. She will be receiving 7.5% interest compounded monthly on her investment. Will she reach her goal?
No
Yes
Answer:
Yes Lana will reach her goal she'll have 10,414.58 by the end of the 6 years,
Step-by-step explanation:
y=(3x+15)(x-2)
in standard form
Answer:
[tex]y=3x^2+9x-30[/tex]
Step-by-step explanation:
To multiply [tex](3x+15)[/tex] with [tex](x-2)[/tex] we can use a method called the FOIL method. FOIL is an acronym standing for First, Outer, Inner, Last. This is the order in which we need to multiply. The first terms of each multiplier are [tex]3x[/tex] and [tex]x[/tex]. Therefore, we multiply these two terms to get [tex]3x^2[/tex]. The outer terms are [tex]3x[/tex] and [tex]-2[/tex]. Once again, we multiply these terms.
[tex](3x)(-2)=-6x[/tex]
Now, our equation looks like this: [tex]y=3x^2-6x[/tex]. We're not finished yet though. Next, we need to multiply the inner terms, [tex]15[/tex] and [tex]x[/tex]. This comes out as simply [tex]15x[/tex]. Now our equation looks like this: [tex]y=3x^2-6x+15x[/tex]. We just need to multiply the last terms, [tex]15[/tex] and [tex]-2[/tex]. This comes out as [tex]-30[/tex].
Our equation at this point has been fully multiplied:
[tex]y=3x^2-6x+15x-30[/tex]
We can see that we still have two like terms, [tex]-6x[/tex] and [tex]15x[/tex]. These can be combined to simply [tex]9x[/tex]. Our final equation, then, is this: [tex]y=3x^2+9x-30[/tex]
URGENT
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = 10,000 in.
Answer:
h=39
Step-by-step explanation
V = [tex]\pi[/tex]r^(2) h
V = 10,000[tex]\pi[/tex]
radius = diameter / 2
diameter = 32
radius = 32/2
radius = 16
10,000[tex]\pi[/tex]=[tex]\pi[/tex](16)^(2)(h)
Simplify by dividing [tex]\pi[/tex] from both sides and evaluating 16^2
10,000=256h
Simplify again by dividing 256 from both sides to isolate h.
39.06 = h
Round to the nearest whole number:
39 inches.
Determine the distance between points A (3, 5) and B (2, 1) rounded to the nearest tenth.
Answer:
4
Step-by-step explanation:
gradient=vertical distance /Horizontal distance
G=V/H
G = -4/-1
G =4
Which is the graph of y= 3/4 x - 3?
Answer:
Graph A.
Step-by-step explanation:
I graphed it out and my graph is below this text.
Have a great day! :D
Given p | q and 24 = 130°, find the measure of angle 1:
P
34
5 6
78
9
70°
130°
HELP!!
Answer:
p is equal to 130 reason vertical opposite angles
Can someone help me on these to questions ???
What is the area of this shape?
Answer:
144
Step-by-step explanation:
The shape is a trapezoid.
Add 6 and 112, which is eighteen
divide eighteen by 2, which is 9
Finally, multiply 9 and sixteen which is 144
En un edificio de cinco pisos viven las familias grados, sarabia, gutierrez, pardo y castro
which of these functions is linear?
The only linear function is:
y = x - 5
So the correct option is B.
How to identify a linear function?
A linear function is a polynomial of degree 1, and can be written as:
y = a*x + b
So we have a coefficient multiplying the variable and a constant term, nothing else.
By comparing this with the options, we can see that the only linear function given is the one in option B.
y = x - 5
Where a = 1, and b = 5.
If you want to learn more about linear functions, you can read:
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how many sites are in this data set
Answer:
i think 15
Step-by-step explanation:
HI PLEASE HELP PLEASE PLEASEE HELP
Answer:
Step-by-step explanation:
[tex]26) tan \ 56 =\dfrac{opposite \ side }{adjacent \ side}\\\\\\ 1.4826 = \dfrac{BC}{12}\\\\\\1.4826*12 = BC[/tex]
BC = 17.8 cm
[tex]27) Cos \ x =\dfrac{adjacent \ side}{hypotenuse}\\\\Cos \ x = \dfrac{15}{18}\\\\\\Cos \ x = 0.83\\\\x = Cos^{-1} \ (0.83)\\\\[/tex]
x = 33.9°
X, Y and Z form the vertices of an isosceles triangle.
XY = 8.7m, YZ = 13.8m.
Find the angle
∠
XYZ rounded to 1 DP.
Answer:
∠XYZ = 37.5
Step-by-step explanation:
IN THE IMAGE ABOVE
Which function has the same slope as the function on the graph?
PLEASE I REALLY NEED HELP WITH THIS
A. y = -2x - 4
B. y = -1/2 x - 2
C. y = 1/2 x - 3
D. y = 2x - 6
Answer:
D -2x-6
Step-by-step explanation:
Compile a list of words that describe you as a child. Compile a second list that describes you as you are now. How are these lists the same? How are they different?
Alexa always gives a 15% tip when she eats at a
restaurant. She gives a $2.13 tip. What was the
cost of her meal?
the cost of her meal was "x", which is the 100% of her bill, we also know that $2.13 is 15% of that, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 2.13&15 \end{array}\implies \cfrac{x}{2.13}=\cfrac{100}{15}\implies \cfrac{x}{2.13}=\cfrac{20}{3} \\\\\\ 3x=42.6\implies x=\cfrac{42.6}{3}\implies x=14.2[/tex]
pls pls pls help me out
Answer:
4%
Step-by-step explanation:
using a calculator, you can do 5200/130000 and get 0.04
:)
Answer:
4%
Step-by-step explanation:
Given:
Present population = 130,000
Future population = 135,200
Find:
Increase in percent
Computation:
Increase in population = Future population - Present population
Increase in population = 135,200 - 130,000
Increase in population = 5,200
Increase in percent = [Increase in population / Present population]100
Increase in percent = [5,200/130,000] 100
Increase in percent = 4%
The surface area of the block is
Answer:
In this rectangular prism, opposite sides are equal.
So if we find the 3 different sides, we would need to multiply those individual sides by 2 (because opposite sides are equal/have the same area) and then add them to get the surface area.
One side (the front and back side);
The width is 8 and the height is 7, so (8 x 7) = 56. Though, it's opposite side is the same as well so we multiply 56 by 2, (56 x 2) = 112
Second side (the left and right side);
The width is 18 and the height is 7, so (18 x 7) = 126. Though, it's opposite side is also the same as well, so we multiply 126 by 2, (126 x 2) = 252
Third side (the top and bottom side);
The width is 8 and the height is 18, so (8 x 18) = 144. Though, it's opposite side is also the same as well, so we multiply 144 by 2, (144 x 2) = 288
Now, we add all the areas we've gathered:-
112 + 252 + 288 = 652 square cm
find the length of missing side in the triangle, give answer 1 decimal place
giving brainliest
Please help! I will give brainliest.
Answer:
the awnser is d bc it passes through the line
You have a puppy named Fido and 60 feet of fencing. You want to make him the largest play area possible. What are the dimensions of the rectangular area that has the greatest area? Show why this is the biggest with diagram or charts
Answer:
15 feet x 15 feet
Step-by-step explanation:
I'm worried about Fido, so I'll use three different approaches to maximizing his play space: Graphing, Chart, and First Derivative. This is perhaps more than Fido wants, but it hopefully offers ideas on how these types of problems can be answered.
=========================
Fido is limited to 60 feet of fence, which will form the perimeter. The area of a rectangle is (length)*(width). Let's set length to L and width to W. I'll use A for area.
Therefore A = L*W
The rectangle's perimeter will be 2L + 2W, and this is equal to 60 feet:
2L + 2W = 60
Let's rearrange this equation to isolate either W or L. I chose L:
L + W = 30
L = 30 - W
Now let's use this definition of L in the Area equation:
A = L*W
A = (30-W)*W
A = 30W - W^2
Graphing
We can graph this function (A = 30W - W^2) to find the maximum area. See the attached image. We find a maximum area of 225 ft^2 when the width is 15 feet. 15 feet would mean that Fido's roaming pen will be in the shape of a square; 15 feet for each side equals 60 feet total fence.
Chart
One can also find a maximum by calculating a variety of conditions set by L = 30 - W. I randomly picked lengths from 2 to 24 feet and calculated the resulting width and then the resultant area for each condition. See attached image. Although I did not pick 15 feet, we can see that the area increases until the length transitions from 14 to 16 feet. It reverses direction at that point. A closer inspection around those values will show that 15 feet is, in fact, the optimum value to produce a pen with the most area.
First Derivative
One could also take the first derivative of the equation A = 30W - W^2 and set it equal to zero. The fist derivative tells us the slope of the line at any point (for a value of W in this example). The slope is zero only when the curve hits a maximum.
A = 30W - W^2
A' = 30 -2W
0 = 30 - 2W
2W = 30
W = 15 feet
The slope is zero when the width is 15 feet. 15 feet is the optimum for creating a pen with the most area possible with 60 feet of fence.
===
All three approaches yield the same result. Graphing is fun when you have access to DESMOS. Charts are fun if you like Excel. Derivatives can also be fun, mostly because I always ponder "Who had the audacity to think this might work?" (Didn't they have something more important to do? Raid a village, etc.?).
====
Arf
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Sipho travelled 480km for 6 hours .Calculate his average speed
Answer:
Average speed = 80km
Step-by-step explanation:
[tex]AS = \frac{480km}{6} \\ AS = 80km[/tex]
as means average speed
Sipho travelled 480km in 6 hours -> In an hour, Sipho travelled 1/6 of the distance.
So, in an hour, Sipho travelled : 480 x 1/6 = 80km
In an hour, he travelled 80km -> his average speed is 80km/h
Nabin is twice as old as Kiran. Two years hence he will be six years older then Kiran. Find there present age
Answer:kiran is 2 and Nabin is 4
Step-by-step explanation:
A plumber charged x dollars per hour for a 4-hour job plus $175 for parts. The to- tal charge for the service call was $415.00. Which equation can be used to deter- mine how much the plumber charged per hour?
Answer:
4x + 175 = 415
Step-by-step explanation:
4 is the hours, so it should be multiplied by x to see how much you get every hour (and a total of 4 hours).
175 is the constant and should be added to the equation so that all fees are included.
415 is the total amount so the equation should equal that number.
Hope this helps!
HELP!
50pts. + Brainly for the best answer.
Answer:
let s = number of buttons on a shirt
let j = number of buttons on a jacket
Create 2 equations from the given information:
Equation 1: 36s + 42j = 842
Equation 2: 6s + 7j = 137
If we multiply equation 2 by 6 we get:
⇒ 36s + 42j = 822
Comparing this with equation 1, we can see that the number of shirts and jackets is now the same BUT the number of buttons is different
Therefore, her hypotheses is incorrect and we cannot solve to determine the number of buttons on a shirt and/or jacket.
HELP ASAP
Determine the x-intercepts of the graph with the function
f(x) = x²+6x-7
A (-7,0) & (1,0)
B (0,-7) & (0,1)
D (6,0) & (1,0)
D (7,0) & (-1,0)
Step-by-step explanation:
hope that helps. explanation is on the paper :)
