Answer:
17,964.9 cubic meters
Step-by-step explanation:
Hey there!
The formula for finding the area of a sphere is:
[tex]V=(4/3)\pi r^3[/tex]
Where V is volume, and r is radius
The question already tells us that the diameter is 32.5m
*Remember, the diameter isn't the radius. It is the radius times two*
Now, we have to divide 32.5 by 2 to get the radius
32.5/2 is 16.25
Now we can plug this into the formula
16.25 cubed is 4291 after being rounded to the nearest tenth
Now we multiply 4291 by 3.14 (pi)
4291 x 3.14 is 13473.7 after being rounded to the nearest tenth
Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere
13473.7 x 4/3 is 17964.93333333...
Since it is asking us to round to the nearest tenth of a cubic meter;
The volume of the sphere will be 17,964.9 cubic meters
[tex]\rule{300}{1}[/tex]
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
We are asked to find the volume of a sphere, which we can find using the following formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Where:-V=volumeπ=pi (3.14…)r=radiusProvided information:-diameter (d)=32.5 mWhat we need in order to find the volume:-radiusWhat we need in order to find the radius:-Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-[tex]\bold{r=d\div2}[/tex]
Replace d with 32.5:-
[tex]\bold{r=32.5\div2}[/tex]
Therefore, the sphere's radius is as follows:-
[tex]\bold{r=16.25}[/tex] m
[tex]\rule{300}{1}[/tex]
Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Replace r with 16.25:-
[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex] Next, we replace π with 3.14:-
[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]
On simplification,
[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]
On further simplification,
[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Why is 10^15/10^4 equal to 10^11
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 10¹⁵/10⁴ equals 10¹¹.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 10¹⁵/10⁴ can be simplified as,
[tex]\dfrac{10^{15}}{10^4}\\\\= 10^{15} \cdot 10^{-4}\\\\= 10^{15-4}\\\\=10^{11}[/tex]
Hence, the value of the expression 10¹⁵/10⁴ equals 10¹¹.
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A cube has a surface area of 486 inches square. Can the length of each side of the cube be 11 inches? Explain
Answer:
The volume of cube whose total surface area is 486 cm² is 729 cm³
Step-by-step explanation:
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answer:
See below ~
Step-by-step explanation:
Finding the proportionality constant, k :
y = kxTake the point (0.5, 3)3 = 0.5kk = 6Table :
[tex]\left[\begin{array}{ccc}0.5&3\\1.5&9\\4.5&27\end{array}\right][/tex]
4^3 times 4^? = 4^-3. what number is ?
Answer:
x = -6
Step-by-step explanation:
Let[tex] \: 4^3\times 4^{x}=4^{-3}[/tex][tex] \implies 4^{3+x}=4^{-3}[/tex][tex] \implies {3+x}= {-3}[/tex][tex] \implies {x}= {-3-3}[/tex][tex] \implies {x}= {-6}[/tex][tex] \implies\huge{\red{ 4^3\times 4^{-6}=4^{-3}}}[/tex]An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. it asks a group of 85 randomly selected people in the town about their age.
select the statement that is true.
a. the sample is 2,534 people. the population is 85 people.
b. the sample is 85 people. the population is 2,449 people.
c. the sample is 85 people. the population is 2,534 people.
d. none of the answer choices are true.
Using sampling concepts, it is found that the correct statement is given by:
c. the sample is 85 people. the population is 2,534 people.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.
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hey guys. question posted in the picture. will award brainliest.
Answer:
x=80
that is because a straight angle value is 180 and that angle is already 100 sooo i guess you get the point
Complete the sentence.
------- is 4 times as much as 9.
Answer:
36
Step-by-step explanation:
4 x 9 = 36
36 / 4 = 9
Therefore, 36 is 4 times as much as 9.
[tex]{\sf Hello!}[/tex]
The answer is 36
⇢ 4 × 9 = 36
8x+21=3 need the answer please
Answer:
[tex]x=-\frac{9}{4}[/tex]
Step-by-step explanation:
Step 1: Subtract 21 from both sides
[tex]8x + 21 = 3[/tex]
[tex]8x + 21 - 21 = 3 - 21[/tex]
[tex]8x = -18[/tex]
Step 2: Divide 8 from both sides
[tex]8x = -18[/tex]
[tex]\frac{8x}{8}=-\frac{18}{8}[/tex]
[tex]x=-\frac{9}{4}[/tex]
Answer: [tex]x=-\frac{9}{4}[/tex]
Find the arc length of the circle with a central angle of 30 degrees and a radius 12. Leave the answer in terms of π.
[tex]\text{Arc length,}\\\\s = r \theta \\\\~~=12\cdot \left(30 \times \dfrac{\pi}{180} \right)\\\\~~=12\cdot \dfrac{\pi}6\\\\~~=2\pi[/tex]
1. Find the least common multiple of x² + x-12 and x² + 2x - 15
Least Common Multiple = (x-3) (x+5) (x+4)
Step-by-step explanation:
First we solve for x² + x-12
Factorise=> x² + 4x - 3x - 12
Taking common=> x ( x+4 ) - 3 (x+4 )
=> (x-3) (x+4)
Now we will solve for x² + 2x - 15
Factorise=> x² + 5x - 3x - 15
Taking common=> (x-3) (x+5)
we see here (x-3) is common in both the equations so We write it only 1 time as we have to find least common multiple .
Ans. Lest common multiples are = (x-3) (x+5) and (x+4)
PLEASE SOLVE FOR X AND Y!!!! I WILL MARK BRAINLIEST!!!!
opposite sides and diagonals of a parallelogram are equal
+ diagonals of a parallelogram meet eachother in the middle so:
10x+14=x+77
10x-x=77-14
9x=63
x=63÷9
x= 7
y+8=4y-19
y-4y=-19-8
-3y=-27
y=-27÷-3
y=9
2z+3=37
2z=37-3
2z=34
z=34÷2
z=17
PLEASE HELP WILL GIVE BRAINLEST!
Answer:
5[tex]\pi[/tex]/12 rad
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
75(π/180) = 5π/12 radians
arc length = central angle (2πr)
360
measure of the inscribed angle = 75º
measure of the central angle = 150º
arc length = 150 (2π1000)
360
arc length = (5/12)
PLEASE HELP MEEEEE I DONT LIKE PI
Answer:
I did the work and uploaded the picture i hope it helped!!
PLS help i will give you 26 points and brainly pls i need this for tomorrow i don't understand the question that i left blank. It Math thanks. :)
Answer:
145 is the outlier
Step-by-step explanation:
When compared to the other values, 145 is an exceeding highly value. Hence, it can be considered an outlier in the data set.
If 35 boxes equals to 21 dollars in total, how much does each box cost?
PLS ANSWER FAST TYYYYYSMMM!!!
Answer:
option 3, [tex]972\pi in^{3}[/tex]
Step-by-step explanation:
The formula to find the volume of a sphere is [tex]\frac{4}{3} \pi r^{3}[/tex]
where r os the radius
given: diameter = 18in
radius = diameter / 2
radius = 18 / 2
r = 9in
Plug in radius:
[tex]\frac{4}{3} \pi (9)^{3}\\\\\frac{4\pi (9)^{3}}{3} \\\\Factor (9)^{3}: (3)^{6}\\\\\frac{(3)^{6} * 4\pi }{3} \\\\[/tex]
cancel common factor: 3
[tex]3^{5} * 4\pi \\3^{5} = 243\\243 * 4\pi\\972\pi[/tex]
Let me know if you have any questions !
in how many ways can 4 people be seated in a row of 12 chairs
Answer:
11,880.
Step-by-step explanation:
This is given by the number of permutations of 4 from 12
= 12P4
= 12!/(12-4)!
= 12!/8!
= (12*11*10*9*8*7*6*5*4*4*2*1) / (8*7*6*5*4*4*2*1)
= 12^11*10*9
= 11,880.
Find the amount of sheet metal needed to form a conical funnel of base radius 30 cm and vertical height 50 cm, allowing for a 0.5 cm overlap at the join
The amount of sheet metal needed to form the conical funnel is 5525 cm²
How to determine the amount of sheet?The given parameters are:
Radius, r = 30 cmVertical height, h = 50 cmOverlap = 0.5 cmStart by calculating the slant height (l) of the cone using:
l = √(r² + h²)
This gives
l = √(30² + 50²)
Evaluate
l = 58.31
The lateral surface area of the conical funnel including the overlap is then calculated as:
A = πrl + Overlap * l
This gives
A = 3.142 * 30 * 58.31 + 0.5 * 58.31
Evaluate
A = 5525.4556
Approximate
A = 5525
Hence. the amount of sheet metal needed is 5525 cm²
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I need this done fast please
hope this helps :)
............
I need help asap please
When Digitalis knows that it'll sell many of the processors, it's expected to make money since there's a higher probability that it's not defective.
How to illustrate the probability?Since the processor is sold for $3300 and a profit of $429 is made, the selling price will be:
= $3300 - $429
= $2871
In this case, there's a 13% chance that it's defective and 87% that's it's not defective. Therefore, it's expected to make money since there's a higher probability that it's not defective.
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Two similar spheres have a scale factor of 2:5. What is the ratio of their surface areas?
Answer:
4:25
Step-by-step explanation:
Sphere surface area = 4 pi r^2
now change r to 2.5 r ( to maintain the 2:5 ratio)
area2 = 4 pi (2.5 r)^2 = 6.25 * 4 pi r^2
so ratio of surface areas is 1 : 6.25 = 4:25
If two similar spheres have a scale factor of 2:5. Then the ratio of their surface areas will be 4 / 25.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Two similar spheres have a scale factor of 2:5.
Let the r₁ and r₂ be the radius of the spheres. Then we have
r₁ / r₂ = 2 / 5
Then the surface area of the sphere is given as
Surface area = 4πr²
Then the ratio of their surface areas will be
[tex]\rightarrow \dfrac{4\pi r_1^2 }{4\pi r_2^2} = \left (\dfrac{r_1}{r_2} \right )^2[/tex]
Then we have
→ (2 / 5)²
→ 4 / 25
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(I will mark brainliest) Will 3/8 + 2/8 be closer to 1/2 or 1? How do you know?
Answer:
1/2
Step-by-step explanation:
3/8 + 2/8 is 5/8, 1/2 is equal to 4/8, so 5/8 is only 1/8 away from 1/2 while 5/8 is also 3/8 away from 1 or 8/8 therefore, it is closer to 1/2
Find the measure of the missing angles.
Answer:
d = 105° , e = 32° , f = 43°
Step-by-step explanation:
d and 105° are vertically opposite angles and are congruent , then
d = 105°
e and 32° are vertically opposite angles and are congruent , then
e = 32°
105° , e and f lie on a straight line and sum to 180° , that is
105° + e + f = 180°
105° + 32° + f = 180°
137° + f = 180° ( subtract 137° from both sides )
f = 43°
Answer:
d= 105° f= 43° e= 32°
Step-by-step explanation:
angle d = 105° ( vertically opposite angles are equal)
f°+d°+32°= 180 (angles on a straight line)
f+105+32= 180
f+137=180
f= 180-137= 43°
f= 43°
angle .d+f+e = 180° (angles on a straight line)
105+43+e = 180°
148+ e = 180°
e = 180-148
e = 32°
therefore,
d= 105° f= 43° e= 32°
FIND B ONLY
WILL GET BRAINLIEST
Answer:
the answer is RATIONAL
Step-by-step explanation:
why u ask
becasue the number is less than 1
please mark brainiest
If each of the numbers in the following data set were multiplied by 12, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
Answer:
answer: 336!!
Step-by-step explanation:
have a good day!
Find the dependent value
for the graph
y = 12 + 5x
when the independent value is 3.
y = [?]
Answer:
Y = 27
Step-by-step explanation:
In the equation (y = 12 + 5x) the X is the independent value. When you replace this by 3 you will multiply 3*5 which will give you 15 and then you will want to add 12 as that is your y intercept. Giving the value of your Y a 27, or the point would be (3,27)
What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)? x 2 x – 2 x – 8 x 8
The quotient of the given expression is x-2. The correct option is the second option- x – 2
Simplification of fractionsFrom the question, we are to determine the quotient
The given expression is
[tex]\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}[/tex]
The numerator can be expressed as
[tex](x-2)(x^{2} +5x+6)[/tex]
Then, the fraction becomes
[tex]\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}[/tex] = [tex]\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6}[/tex]
Simplifying
[tex]\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6} = x-2[/tex]
Hence, the quotient of the given expression is x-2. The correct option is the second option- x – 2
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Here is the complete and correct question:
What is the quotient of (x cubed + 3 x squared minus 4 x minus 12') divided by (x squared + 5 x + 6)? x + 2 x – 2 x – 8 x + 8
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Explain how you would graph the inequality, "b ≤ 0
Answer:
the inequality, b ≤ 0 has interval Notation of -∞,0
Step-by-step explanation:
the inequality, b ≤ 0 has interval Notation of -∞,0
please help!!!
Find an equation for this graph.
During a sale the regular price of an item is reduced by 20 percent if the sale price is $600 what is the regular price
