An equilateral triangle has a side length of $12 \sqrt{3}.$ The triangle is rotated about one of its altitudes as an axis, sweeping out a cone in space. Find the volume of the cone.
The volume of the cone is 254.85 cubic units
How to determine the volume of the cone?The side length of the equilateral triangle is given as:
l = 12√3
Calculate the radius (r) of the cone using:
r = l/2
r = 12/2√3
r = 6√3
Calculate the height of the cone using:
[tex]h = \sqrt{l^2 + (l/2)^2[/tex]
This gives
[tex]h = \sqrt{(12\sqrt 3)^2 + (6\sqrt3)^2[/tex]
Evaluate
[tex]h = \sqrt{540[/tex]
h = 22.24
The volume of the cone is then calculated as:
V = 1/3πr²h
This gives
V = 1/3π * (6√3)² * 22.24
Evaluate
V = 254.85
Hence, the volume of the cone is 254.85 cubic units
Read more about volume at:
https://brainly.com/question/1972490
#SPJ1
Solve for x
58° 22 X
Answer:
x = 13.75 units
Step-by-step explanation:
Right triangle
tan 58 = opposite side / adjacent side
tan 58 = 22/x
x = 22/ (tan 58) = 13.75
John spins a fair spinner with 5 equal sections numbered 1 through 5. His spin lands on the number 2. What is the probability that John's next three spins land on the number 2
Using it's concept, it is found that the probability that John's next three spins land on the number 2 is of [tex]\frac{1}{125}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that out of 5 numbers, one is 2, hence the probability of three consecutive spins landing on two is given by:
[tex]p = \left(\frac{1}{5}\right)^3 = \frac{1}{125}[/tex].
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
The first four terms of a sequence are shown on the graph below.
What can be concluded about the sequence?
The common ratio of the sequence is 2.
The common difference of the sequence is 2.
The next term of the sequence is represented by the point (5, 64).
The next term of the sequence is represented by the point (5, –64).
Answer:
The next term of the sequence is represented by the point (5, –64)
Step-by-step explanation:
From inspection of the graph, the first four terms of the sequence are:
(1, -4)(2, 8)(3, -16)(4, 32)Each x-value increases by 1 for each consecutive term.
Each y-value is the previous y-value multiplied by -2.
Therefore, it is a geometric sequence with a common ratio of -2.
Following the above rule, if the last term in the sequence is (4, 32), then the next term in the sequence will be:
x = 4 + 1 = 5y = 32 × -2 = -64So, the next term of the sequence is represented by the point (5, –64)
What is the volume of the triangular prism?
12 cm
3 cm
8 cm
Answer:
Find the area of the triangle side, then multiply by the length of the prism.Area of triangle = 1/2 x height x baseArea = 1/2 x 2 x 3 = 3 square cmVolume = 3 x 4 = 12 cubic cm.Answer is A)
Step-by-step explanation:
what is the answer ?
The angle B will be equal to ∠B=53.13 degrees.
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
It is given that:-
Three sides of the triangle are:- a= 3, b=4 and c =5
The angle B will be calculated by the following formula;-
[tex]\angle B=Cos^{-1}\dfrac{a^2+c^2-b^2}{2ac}\\\\\\\angle B=Cos^{-1}\dfrac{3^2+5^2-4^2}{2\times 3\times 5}\\\\\\\angle B=Cos^{-1}(0.6)\\[/tex]
∠B=53.13 degrees
Hence the angle B will be equal to ∠B=53.13 degrees.
To know more about triangles follow
https://brainly.com/question/17335144
#SPJ1
What does this math statement tell us?
ΔΑΒC ~ ΔΧΥΖ
PLS HELP I WILL MARK BRAINLIEST
Answer:
B
Step-by-step explanation:
~ symbol refers to similarity. ∆ABC ~∆XYZ means that the two triangles are similar(Same shapes, not the same size).
Find the Surface Area:
A) 144 in^2
B) 102 in^2
C) 17 in^2
D) 180 in^2
E) 68 in^2
Answer:
D 180 in²
Step-by-step explanation:
step 1
2 (l) (w) + 2 (l) (h) + 2(h) (w)
step 2
2×(6)×(3) + 2×(6)×(8) + 2×(8)×(3)
step 3
2×(18) + 2×(48) + 2×(24)
step4
36 + 96 + 48 = 180 in²
344/299 = x
what is x?
Answer:
Mixed Number Form: x = 1 45/299
Decimal Form: x = 1.15050167…
Step-by-step explanation:
In a company's first year in operation, it made an annual profit of $140,000. The profit of the company increased at a constant 20% per year each year. How much total profit would the company make over the course of its first 14 years of operation, to the nearest whole number?
Answer:
$8,287,429
Step-by-step explanation:
The total profit will be the sum of a geometric series. The formula for that sum is ...
Sn = a1 × (r^n -1)/(r -1)
where a1 is the first term, r is the common ratio, and n is the number of terms.
__
Here, the series has first term $140,000, common ratio 1+0.20 = 1.2, and we want the total of 14 terms. The total profit is ...
S14 = ($140,000) × (1.2^14 -1)/(1.2 -1) ≈ $8,287,429
In the first 14 years of operation, the total profit would be $8,287,429.
In ΔRST, = 93 inches, ∠S=123° and ∠T=28°. Find the length of r, to the nearest 10th of an inch
Answer:
<r=29
Step-by-step explanation:
Im honestly so confused and need help with it because i just want to go on to the next question♀️
Answer:
1.05 (0.2x + 1/2y + 0.75z)
Step-by-step explanation:
Finding the cost of each item :
1 Sweatshirt
Cost = $xDiscount = 80% offPrice = (100% - 80%)(x)Price = 0.2x2 T-shirts
Cost = $yDiscount = Buy one, get one 50% offPrice = (50%)(y)Price = 1/2y1 Pair of Pants
Cost = $zDiscount = 25% offPrice = (100% - 25%)(z)Price = 0.75zNow, the final cost (after applying sales tax) is :
1.05 (0.2x + 1/2y + 0.75z)Option #1ST is tangent to OQ. What is m
Sum of the interior angle of any triangle must equal to 180 degrees thus :
[tex]53 + 90 + t = 180[/tex]
[tex]143 + t = 180[/tex]
[tex]t = 37[/tex]
Thus angle T has a measure of 37° .
Answer: 37
Explanation: Angle S is a right triangle because ST is tangent to circle Q.
180 - 90 - 53 = 37
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a
scale factor of 3/4. Find the perimeter of the preimage, the original triangle, before its
dilation. Round your answer to the nearest tenth, if necessary.
If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.
Then the perimeter of the preimage, the original triangle, before its
dilation will be
Let c be the perimeter of the original triangle.
Then we have
[tex]\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67[/tex]
Then the perimeter of the original triangle is 66.67 units.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
Expand and simplify 3(x-4)(2x+5)
3(x-4)(2x+5)
= 3×(x-4)×(2x+5)
= (3x-12)(2x+5)
= 6x²+15x-24x-60
= 6x²-9x-60
[tex]3( {2x }^{2} + 5x - 8x - 20) \\ 3( {2x}^{2} - 3x - 20) \\ {6x}^{2} - 9x - 60 \\(6x + \frac{5}{2} )(x - 4)[/tex]
g(t)=-3t +2 h(t)=t-4 find (g o h)t)
Answer:
3t-10
Step-by-step explanation:
g(h(t))=g(t-4)
=3(t-4)+2
=3t-12+2
=3t-10
Ms Hieronymus goes through 1/2 a package of pencils every 1/8 a month for her students How many packages does Ms Hieronymus need for 10 months
Answer:
Every 1/8 month (ie about 4 days) she uses 1/2 a package
So every month she will use 8 x (1/2) = 4 packages
So in 10 months she will use 4 x 10 = 40 packages
the jar contains 22 marbles 12 purple 8 red and 2 green one marbles drawn and put back then a 2nd marble is drawn, what is the probability that both marbles were red?
Explanation:
There are 8 red marbles out of 22 total
8/22 = 4/11 is the probablity of randomly selecting red.
If the first marble is put back, then that probability will not change.
The probability of two red marbles in a row is (4/11)*(4/11) = 16/121
Side note: 16/121 = 0.1322 = 13.22% approximately
A(2,-3), P(2,9)Find the slope of the line through the pair of points
Answer:
Step-by-step explanation:
(9 + 3)/(2 - 2)= 12/0= undefined
What is the sum of the solution 4|3x-5|-5=-1
4|3x-5|-5=-1
|12x-20|-5= -1
|12x-20|= -1+5
|12x-20|= 4
x1-> 12x-20= 4
12x= 4+20
x= 24/12
x=2
x2-> -12x+20 = 4
-12x = 4-20
-12x= -16
x= -16/-12
x= 4/3
Handedness: 18 left-handed
22 right-handed
The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. if there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)
A) 0.410
B) 0.357
C) 0.333
D) 0.250
If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
Answer:
Let x be the number of left handed female students and let y be the number of left handed male students.
Then the number of right handed female students will be 5x and the number of right handed male students will be 9y. Since the total number of left handed students is 18 and the total number of right handed students is 122, the following system of equations must be satisfied.
x+y=18 and 5x+9y=122
Solving this system gives x=10 and y=8.
Thus, 50 of the 122 right handed students are female. Therefore, the probability that a right handed student selected at random is female is the fraction 50/122
which to the nearest thousandth is 0.410.
T is average time spend by shoppers in minutes
N average number of shoppers.
Here, shoppers/hour =84.
Hence r=
60
84
T=5
Hence N=rT=
60
84
×5=7
Average number of shoppers waiting at checkout =7
Answer:
EMMA ITS KAIDN. text back.
Step-by-step explanation:
I had already answered this.
I need help with this ASAP
At Josie’s job, she is paid $12 for every hour she works. Write a
recursive and explicit formula to describe this sequence.
Im also giving Brainlist
Answer:
It would be y=12x
Step-by-step explanation:
I think
Answer:
if x=24°and y = 54°
sin x + sin y
Which of the following statements is true for a sphere?
A sphere is the set of all points in space equidistant from a line segment called the radius.
Answer A: A sphere is the set of all points in space equidistant from a line segment called the radius.
A
A sphere is the set of all points in space equidistant from a point called the center.
Answer B: A sphere is the set of all points in space equidistant from a point called the center.
B
A sphere is the set of all points in a plane equidistant from a line segment called the radius.
Answer C: A sphere is the set of all points in a plane equidistant from a line segment called the radius.
C
Answer D : A sphere is the set of all points in a plane equidistant from a point called the center.
The answer choice which is true of a sphere; A sphere is the set of all points in space equidistant from a point called the center.
What is a Sphere?A sphere is a geometrical entity that is characterized as a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space. The given point in discuss is the centre of the sphere, and distance, r is the sphere's radius.
Read more on sphere;
https://brainly.com/question/16693593
#SPJ1
i just dont know the answer
Answer:
(3,7) (4,4) (1,2)
Step-by-step explanation:
180 degrees: (x, y) —> (-x, -y)
mary drove for four hours on an interstate highway at a constant rate of 60 miles per hour. during the next hour, she drove on a state road at a slower rate of 40 miles per hour. how many miles did mary travel on her trip?
Step-by-step explanation:
speed = distance/time
distance = speed × time.
so, for the first 4 hours
distance = 60 m/h × 4 h = 240 miles
and for the next hour
distance = 40 m/h × 1 h = 40 miles
she traveled therefore
240 + 40 = 280 miles
the answer was 280, Take your chances with it, I did it on edgeinuity but it wont let me show the screenshot i took
A bag of dry costs $2.85. Alka pays for the bag with a $5.00 bill. How much change does Alka get back?
Answer:
$2.15
Step-by-step explanation:
$5 - $2.85 = $2.15
this is the explanation
The cost of dry bag is $2.85 then the change does Alka get back will be $2.15.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the mentioned information in the question,
Cost of dry bag = $2.85
Money given by Alka for the bill = $5.00
Then, the amount she will get back,
($5.00 - $2.85) = $2.15
To know more about arithmetic operations:
https://brainly.com/question/25277954
#SPJ2
alfredo va a comprar 850 dolares si cada dolar cuesta en promedio 2945 pesos cuanto dinero en pesos debe llevar alfredo
Answer:
He will need $2,503,250 pesos.
Step-by-step explanation:
2,945 x 850 = 2,503,250
Which is the next step in the following construction of an equilateral triangle?
circle with center P and point A along circles edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
Circle with centre P and point A along the circle's edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C.
A triangle with three sides that are all the same length and three angles that are all the same size (60°) is called an equilateral triangle.
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
Thus, connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
1-Find the measure of
1. 226 degrees
2. 113 degrees
3. 134 degrees
4. 67 degrees
2-Find the circumference of the circle 7 cm. Use 3.14 for pi.
1. 21.98 cm
2. 38 cm
3. 3.5 cm
4. 7 cm
3-Classify the triangle by its sides and angles: 15.5 in, 15.5 in and 15.5 in.
1. Scalene, right
2. Equilateral, right
3. Equilateral, acute
4. Isosceles, acute
4-What are the coordinates of the image of point L(4,2) after a reflection over the line y = -1.
1. (-5,2)
2. (4,-4)
3. (3,1)
4. (4,-2)
5-A point P has coordinates (3.2). What are it’s new coordinates after reflecting point P over the y-axis.
1. (-3,-2)
2. (3,-2)
3. (3,2)
4. (-3,2)
Someone help please answer question 1
Answer:
Reflection in line x=1
Step-by-step explanation:
If you draw a line of all values where X = 1. It forms a line between the 2 shapes and by reflecting in that line, you will get Shape B from shape A