Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
_____
Comment on the geometry
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
What is the distance between the coordinates (5,5) and (7,2)? Round your
answer to the nearest tenth.
Answer:
4
Step-by-step explanation:
when you write them down and draw a diaganal line from 7,2 to 5,5 it passes 4 intersections, so it would be 4 units. When you round if it is 4 or less it stays the same and if it is 5 or more then it changes so it would still be 4.
Stay Safe
A pitcher struck out 11 out of 40 batters. Write an equivalent decimal.
Answer:
0.275
Step-by-step explanation:
We want to write 11 out of 40 batters as a decimal.
We can write 11 out of 40 as a fraction to get:
[tex] \frac{11}{40} [/tex]
Note that:
[tex] \frac{11}{40} = \frac{1}{4} \times \frac{11}{10} [/tex]
This implies that:
[tex] \frac{11}{40} = 0.25 \times 1.1[/tex]
This gives us
[tex] \frac{11}{40 } = 0.275[/tex]
What is larger? -1 or -4/3
Answer:
-4/3
Step-by-step explanation:
-4/3 is equal to -1 1/3 which is greater than just -1
Answer: -1 is ;larger
what is 738 divided by 13 in fraction form
Answer:
56.76923076...
Step-by-step explanation:
738 divided by 13 should be [tex]\frac{738}{13}[/tex] as an improper fraction.
As a mixed fraction, it is: [tex]56\frac{10}{13}[/tex]
And as a decimal it is approximately 56.769
I did this problem on a calculator after doing some written work on it.
can you find the simplest form of this math problem.
Answer:
- 7y²
Step-by-step explanation:
(0,01)⁻¹/² × ∛(- 343y⁶/1000) =
= -(1/100)⁻¹/² × ∛( - 7³y⁶/10³)
= - 100¹/² × 7y²/10
= -(10²)¹/² × 7y²/10
= - 10 × 7y²/10
= - 7y²
Answer:
-7y^2
Step-by-step explanation:
(0.01)^(-1/2) = (1/0.01)^(1/2) = 100^(1/2) = 10
(-343 × y^6 ÷ 1000)^(1/3) =
(-343)^(1/3) × (y^6)^(1/3) ÷ 1000^(1/3)
= -7 × y^2 ÷ 10 = -0.7y^2
10 × -0.7y^2
-7y^2
pls help me for part A and B if correct I will mark brainslit :)) !!
Answer:
answer choice b is the correct answer
Step-by-step explanation:
5/8 times 2 1/2
1 3/4
1 3/4 > 1 1/4
30 kg into 5:3 ratio
Answer:
18.75 Kg : 11.25 Kg
Step-by-step explanation:
Sum the parts of the ratio, 5 + 3 = 8 parts
Divide 30 Kg by 8 to find the value of one part of the ratio
30 Kg ÷ 8 = 3.75 Kg ← value of 1 part of the ratio, thus
5 parts = 5 × 3.75 Kg = 18.75 Kg
3 parts = 3 × 3.75 Kg = 11.25 Kg
Jill traced the. three shapes shown out of cardboard for an art project. Select all of the shapes that will give Jill a piece of cardboard with the same total area. Please help!
Answer:
1st and 3rd figures have the same area
Step-by-step explanation:
1st figure is combined figure consisting of 4 m by 5 m rectangle and right triangle with legs
[tex]4-1=3\ m[/tex] and [tex]10-5=5\ m[/tex]
The area of the first figure is
[tex]A_{rectangle}=4\times 5=20\ m^2\\ \\A_{triangle }=\dfrac{1}{2}\cdot 3\cdot 5=7.5\ m^2\\ \\A_{1^{st}\ figure}=20+7.5=27.5\ m^2[/tex]
2nd figure is combined figure consisting of 3 m by 6 m rectangle and right triangle with legs
3 m and [tex]1+3+1=5\ m[/tex]
The area of the second figure is
[tex]A_{rectangle}=3\times 6=18\ m^2\\ \\A_{triangle }=\dfrac{1}{2}\cdot 3\cdot 5=7.5\ m^2\\ \\A_{2^{nd}\ figure}=18+7.5=25.5\ m^2[/tex]
3rd figure is combined figure consisting of 10 m by 2 m rectangle and right triangle with legs
3 m and [tex]10-5=5\ m[/tex]
The area of the third figure is
[tex]A_{rectangle}=2\times 10=20\ m^2\\ \\A_{triangle }=\dfrac{1}{2}\cdot 3\cdot 5=7.5\ m^2\\ \\A_{3^{rd}\ figure}=20+7.5=27.5\ m^2[/tex]
What is 10 +19. +20000000000000
The answer is 20000000000029
Organize the following polynomial expressions from least to greatest based on their degree: (2 points)
I. x + 2xyz
II. 9x3y2
III. 18x2 + 5ab − 6y
IV. 4x4 + 3x2 − x − 4
On arranging from least to greatest based on their degree:
[tex]18x^2 + 5ab - 6y\\\\x + 2xyz\\\\4x^4 + 3x^2 -x-4\\\\9x^3y^2[/tex]
Solution:
Given that,
Organize the following polynomial expressions from least to greatest based on their degree
Degree of polynomial is highest power of the variable in the algebraic expression
For polynomial with more than one variable, find the degree of each monomial and then add them and choose the largest exponent
[tex]I) x + 2xyz \\\\Degree\ of\ x = 1\\\\Degree\ of\ 2xyz = 1 +1 + 1 = 3[/tex]
Thus degree is 3[tex]II) 9x^3y^2\\\\Degree = 3 + 2 = 5[/tex]
Thus degree is 5[tex]iii) 18x^2 + 5ab - 6y\\\\Degree\ of\ 18x^2 = 2\\\\Degree\ of\ 5ab = 1 + 1 = 2\\\\Degree\ of\ 6y = 1[/tex]
Thus degree is 2[tex]iv) 4x^4 + 3x^2 -x-4\\\\Degree\ of\ 4x^4 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ x = 1\\\\Degree\ of\ 4 = 0 (since\ degree\ of\ constants\ is\ 0)[/tex]
Thus degree is 4On arranging from least to greatest based on their degree:
[tex]18x^2 + 5ab - 6y\\\\x + 2xyz\\\\4x^4 + 3x^2 -x-4\\\\9x^3y^2[/tex]
2x-4=10 reverse order algebra
Answer:
7
Step-by-step explanation:
2x-4=10
2x=10+4
2x=14
x=14/2
x=7
One side of a triangle is 2 times the second side. The third side is 5 feet longer than the second side. The perimeter of a triangle is 81 feet. Find the length of each side.
Answer:
The length of the side of the triangles are;
First side = 38 ft
Second side = 19 ft
Third side =24 ft
Step-by-step explanation:
To solve the question we are going to take;
Second side is x ft
Since, the first side is 2 times the second side then;
First side of the triangle is 2x ft
Since the third side is 5 ft less than the second side, then;
The third side is (x+5) ft
But, the perimeter of the triangle is 81 ft
Perimeter of a triangle is given by the sum of sides;
Therefore;
x + 2x +(x +5) = 81 ft
4x + 5 = 81
4x = 76
x = 19 ft
Therefore;
Second side = 19 ft
First side = 38 ft
Third side = 24 ft
What is the slope of the line that contains these points?
x -4, 1, 6, 11
y -3,-2,-1,0
Answer:
slope = 1/5
Step-by-step explanation:
[tex]\frac{0-(-3)}{11-(-4)} =\frac{3}{15} =1/5[/tex]
What is diversification?
A. investing in volatile stocks
B. investing in various types of investments
C. investing in low-risk investments
(20 points!!!!!! )
Answer:
b. investing in various types of investments
Step-by-step explanation:
i hope this helps!
brainliest is appreciated... :}
Answer:
1. diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk.
A. Stock market volatility is arguably one of the most misunderstood concepts in investing.
(B i) Stocks.
(ii) Bounds
(III) mutual funds
(iv) index funds
(C). Bank Savings.
Certificates of Deposit (CDs) ...
Treasury Securities. ...
Money Market Accounts. ...
Stable Value Funds. ...
Fixed Annuities. ...
Immediate Annuities
Which quadrilateral can be inscribed in a circle?
A) A
B) B
C) C
D) D
Answer:
The correct option is A
Therefore the quadrilateral in the option A can be inscribed in a circle.
Step-by-step explanation:
Given:
Four Quadrilateral, A ,B ,C ,D in the figure below.
For a quadrilateral to be inscribed in a circle we required opposite angles must be supplementary, that is it should add up to 180°.
So from the four given quadrilateral we have only in quadrilateral A the opposite angles are supplementary.
Quadrilateral A :
Consider the quadrilateral PQRS where
∠SPQ = 91°
∠PQR = 101°
∠QRS = 89°
∠SPQ and ∠QRS are opposite angles and their sum is 180°
[tex]\angle SPQ+\angle QRS = 91+89 =180[/tex]
Others in option B, C , and D opposite angles are not supplementary hence cannot inscribe in a circle.
Therefore the quadrilateral in the option A can be inscribed in a circle.
Answer:
c Mark me as the brainiest
Step-by-step explanation:
A quadrilateral that can be inscribed in a circle has vertices that lie on a single circle. A distinguishing property of such quadrilaterals is that they have opposite angles adding up to 180°. Non-rectangular parallelograms cannot be inscribed in circles, because their opposite angles are equal rather than supplementary.
Approximately 68% of films are rated R. If 720 films were recently rated, how many were rated R?
Answer:
Approximately 490 films were rated R.
Step-by-step explanation:
Total films recently rated is 720. About 68% of the films were rated R. Thus, 68% of 720 is calculated below.
[tex]68\% \: of \: 720 \: films[/tex]
[tex] = \frac{68}{100} \times 720[/tex]
[tex] = 0.68 \times 720[/tex]
[tex] = 489.6[/tex]
[tex] = 490 \: films \: (approximated)[/tex]
Therefore, if 720 films were recently rated, 68% of films rated R is about 490 films.
How do you find a volume of a sphere? Please explain. (Also if you can please someone answer the other questions I asked but it has not been answered.)
Thanks!
Answer:
V = (4/3)πr³
Step-by-step explanation:
The formula usually used to find the volume of a sphere is ...
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
where r represents the radius of the sphere.
The actual math involved will depend on what information about the sphere you are given. If you are given the radius or diameter (twice the radius), then this formula will be directly useful.
To determine the volume of a sphere, use the formula V = ([tex]\frac{4}{3}[/tex])πr³. Measure the radius, cube it, multiply by pi, and then multiply by 4/3.
To find the volume of a sphere, you use the formula:
V = ([tex]\frac{4}{3}[/tex])πr³
Here, V stands for volume, r represents the radius of the sphere, and π (pi) is approximately 3.14159.
Step-by-Step Explanation:
Measure the radius r of the sphere.Cube the radius (multiply it by itself three times): r³.Multiply the cubed radius by π (pi).Multiply the result from step 3 by 4/3.The scale of a railroad train set is 3.5 mm to 1 foot if the link of the model car in this it is 150 mm what is the approximate length of an actual car
The actual length of car is 42.857 foot
Solution:
Given that,
The scale of a railroad train set is 3.5 mm to 1 foot
The link of the model car in this it is 150 mm
To find: Length of actual car
Let "x" be the length of actual acr
From given,
Scale is:
3.5 mm : 1 foot
Then, given that link of the model car in this it is 150 mm
Then we get,
3.5 mm : 1 foot
150 mm : x foot
This forms a proportion and we can solve the sum by cross multiplying
[tex]3.5 \times x = 1 \times 150\\\\x = \frac{150}{3.5}\\\\x = 42.857[/tex]
Thus the actual length of car is 42.857 foot
Annabella has a cup of raisins. She gave equal portions of 1/2 cups of the raisins to her for siblings which diagram could Annabella used to find the fraction of the love the each sibling receives
Answer:1/4
Step-by-step explanation:
Evaluate f(5):f(x) = x2 - 16x - 48
Answer:
f(5)=-103
Step-by-step explanation:
f(x) =x^2-16x-48
x=5
f(5)=5^2-16*5-48
f(5)=25-80-48
f(5)=-103
A cylinder has a height of h meters, and the base has a radius of 7 meters. If the volume of the cylinder is 539π find the height
Answer:
Therefore,
The Height of Cylinder is 11 meters.
Step-by-step explanation:
Given:
Cylindrical Shape
Radius = r = 7 meter
Volume of Pipe = 539π
To Find:
Height = ?
Solution:
Formula for Volume of Cylinder is given by
[tex]\textrm{Volume of Cylinder}=\pi (Radius)^{2} \times Height[/tex]
Substituting the given values we get
[tex]539\pi=\pi(7)^{2}\times Height\\\\Height=\dfrac{539}{49}=11\ meter[/tex]
Therefore,
The Height of Cylinder is 11 meters.
there are 25 animals in the field. Some are horses, some are ducks. There are 84 legs in all. How many of animal are in the field?
Answer:
Ducks = 8
Horses = 17
Step-by-step explanation:
From the question;
Total number of animals = 25 Total number of legs = 84 legsWe are required to determine the number of ducks and horses;
We need to know that;
A duck has two legs while a horse has four legs;
Assuming there were x ducks and y horses
Then;
x + y = 25 ................................Eqn 1
And;
2x + 4y = 84 .............................Eqn 2
Solving the two equations simultaneously we can get the number of each animal.
x + y = 25
2x + 4y = 84
Multiplying the first equation by 2, we get
2x + 2y = 50
2x + 4y = 84
Subtracting the two equations;
2x + 2y = 50
2x + 4y = 84
........................................................
- 2y = -34
y = 17
Solving for x
x = 25 -17
= 8
Therefore; there were 8 ducks and 17 horses in the field
2x246-2x3-194 add brackets to make the question right.
Answer:
(2*246)-(2*3)-194=492-6-194=292
Step-by-step explanation:
3. Bill's baseball bag weighs 4 pounds. If he takes out a pair of cleats
that weigh 6 ounces, how much will his bag weigh?
Answer:
58 ounces
Step-by-step explanation:
16 x 4=64 - 6=58 ounces
Final answer:
After converting the weight of the cleats from ounces to pounds, the new weight of Bill's baseball bag is determined to be 3.625 pounds by subtracting 0.375 pounds (weight of the cleats in pounds) from the original 4 pounds.
Explanation:
The subject of this question is Mathematics, specifically dealing with unit conversion and simple subtraction of weights. To determine the new weight of Bill's baseball bag after removing the cleats that weigh 6 ounces, we need to first convert the ounces to pounds, since the weight of the bag is given in pounds.
There are 16 ounces in one pound. Therefore, 6 ounces is equivalent to 6 ounces \/ 16 ounces per pound = 0.375 pounds. Starting with the original weight of the bag which is 4 pounds, subtracting the weight of the cleats in pounds will give us the new weight of the bag.
4 pounds - 0.375 pounds = 3.625 pounds. This is the weight of Bill's baseball bag after the cleats are removed.
Family room measures 23 feet by 28 feet. They are covering the floor with tiles that measure 1 foot on a side and cost $0.94 each. How many will they spend on the tile?
Answer:
$605.36
Step-by-step explanation:
They will spend 644* 0.94 = 605.36
Sure you can write in one line
23*28*0.94 = $605.36
Factor completely 8y^2+6y+1
8y² + 6y + 1 = (4y + 1)(2y + 1)
Find the Sum.
213,857 +43,762
Solve the following by using mathematical Induction. For >/ 1
1^2+2^2+3^3+......+ n^2 = 1/6 n(n+1)(2n+[)
Answer:
See explanation
Step-by-step explanation:
Prove that
[tex]1^2+2^2+3^3+...+n^2=\dfrac{1}{6}n(n+1)(2n+1)[/tex]
1. When [tex]n=1,[/tex] we have
in left part [tex]1^2=1;[/tex] in right part [tex]\dfrac{1}{6}\cdot 1\cdot (1+1)\cdot (2\cdot 1+1)=\dfrac{1}{6}\cdot 1\cdot 2\cdot 3=1.[/tex]2. Assume that for all [tex]k[/tex] following equality is true
[tex]1^2+2^2+3^3+...+k^2=\dfrac{1}{6}k(k+1)(2k+1)[/tex]
3. Prove that for [tex]k+1[/tex] the following equality is true too.
[tex]1^2+2^2+3^3+...+(k+1)^2=\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)[/tex]
Consider left part:
[tex]1^2+2^2+3^2+...+(k+1)^2=\\ \\=(1^2+2^2+3^3+...+k^2)+(k+1)^2=\\ \\=\dfrac{1}{6}k(k+1)(2k+1)+(k+1)^2=\\ \\=(k+1)\left(\dfrac{1}{6}k(2k+1)+k+1\right)=\\ \\=(k+1)\dfrac{2k^2+k+6k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+7k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+4k+3k+6}{6}=\\ \\=(k+1)\dfrac{2k(k+2)+3(k+2)}{6}=\\ \\=(k+1)\dfrac{(k+2)(2k+3)}{6}[/tex]
Consider right part:
[tex]\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)=\\ \\\dfrac{1}{6}(k+1)(k+2)(2k+3)[/tex]
We get the same left and right parts, so the equality is true for [tex]k+1.[/tex]
By mathematical induction, this equality is true for all n.
What are all of the Angle measures
Answer:Type of Angle Description
Acute Angle is less than 90°
Right Angle is 90° exactly
Obtuse Angle is greater than 90° but less than 180°
Straight Angle is 180° exactly
Step-by-step explanation:
Answer:
∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Step-by-step explanation:
Solving for xWe can say that angle ABC and angle DBE are vertically opposite angles because there are only two intersecting lines. Vertically opposite angles are equal so we can form an equation:
4x + 2 = 5x - 13
5x - 4x = 2 + 13
x = 15
Angles ABC and DBENow we can substitute x into the equation and find out the value for angles ABC and DBE.
4(15) + 2 = 60 + 2 = 62°, just to make sure we need to substitute x into the other equation to see whether we get the same answer:
5(15) - 13 = 75 - 13 = 62°, now we can confirm that angles ABC and DBE are 62°.
Angles CBE and ABDNow we can use the rule, angles on a straight line add up to 180°, to find the other two angles, because these two angles are vertically opposite, they are also equal to each other.
180 - 62 = 118°
Angles CBE and ABD are both 118°
Determine the equation of the linear function that has a slope of -4 and passes through the point (2,-4). Write the equation in slope-intercept form and draw/graph the equation
Answer:
Part 1) [tex]y=-4x+4[/tex]
Part 2) The graph in the attached figure
Step-by-step explanation:
Part 1)
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=-4\\point\ (2,-4)[/tex]
substitute in the linear equation
[tex]-4=-4(2)+b[/tex]
solve for b
[tex]-4=-8+b\\b=8-4\\b=4[/tex]
substitute
[tex]y=-4x+4[/tex]
Part 2) Draw the equation
we know that
To graph a line we need two points
we have the y-intercept (0,4) and (2,-4)
Plot the points, connect them and join to draw the line
see the attached figure