Given a volume of 4500π cubic feet, the radius is found to be approximately 15 feet after solving the equation.
To find the radius of a sphere given its volume, we use the formula for the volume of a sphere: V = (4/3)πr³. In this case, the given volume is 4500π cubic feet. To solve for the radius, we can set up the equation as follows:
V = (4/3)πr³
4500π = (4/3)πr³
To isolate r³, we divide both sides by π and then multiply by 3/4:
4500 = (4/3)r³
(3/4) * 4500 = r³
3375 = r³
Now, we take the cube root of both sides to find the radius:
r = ³√3375
r ≈ 15 feet
Therefore, the radius of the sphere is approximately 15 feet.
the radius of the sphere is 15 feet.
The formula for the volume [tex](\( V \))[/tex] of a sphere in terms of its radius [tex](\( r \))[/tex] is:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Given that the volume of the sphere is [tex]\( 4500\pi \)[/tex] cubic feet, we can set up the equation:
[tex]\[ 4500\pi = \frac{4}{3}\pi r^3 \][/tex]
To find the radius [tex]\( r \)[/tex], we need to isolate it in the equation. First, let's cancel out [tex]\( \pi \):[/tex]
[tex]\[ \frac{4500\pi}{\pi} = \frac{4}{3} r^3 \][/tex]
[tex]\[ 4500 = \frac{4}{3} r^3 \][/tex]
Now, to solve for [tex]\( r \)[/tex], we'll multiply both sides by [tex]\( \frac{3}{4} \)[/tex] to isolate [tex]\( r^3 \):[/tex]
[tex]\[ r^3 = \frac{4500 \times 3}{4} \][/tex]
[tex]\[ r^3 = \frac{13500}{4} \][/tex]
[tex]\[ r^3 = 3375 \][/tex]
Now, to find ( r ), we'll take the cube root of both sides:
[tex]\[ r = \sqrt[3]{3375} \][/tex]
[tex]\[ r = 15 \][/tex]
So, the radius of the sphere is 15 feet.
Abbie opened a no-interest bank account with $20, and she de
Carlos opened a no-interest bank account with $28, and he de
Carlos and Abbie do not make any withdrawals from their acco
be used to find w, the number of weeks it will take for the bal
same.
20+14.50w = 28 +12.50w
Answer:
4 weeks
Step-by-step explanation:
Compute the average (mean) from the data shown. (round to the nearest whole number)
{42 , 30 , 79 , 99 , 72 , 24 , 89 , 91 , 78 , 69}
A) 67
B) 68
C) 69
D) 70
Answer:67
Step-by-step explanation:
42+30+79+99+72+24+89+91+78+69=673
673÷10=67.3
You divide by ten because that is how many numbers there are
Choose the ratio that is equivalent to this one. 1/6
A. 3/8
B.4 2/4
C. 2/6
D. 12 / 2
Answer:
Answer is none of these
Step-by-step explanation:
ask questions with correct options.
anyway don't repeate the mistakes again.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Suppose a circle with center (1, −3) passes through point (1, −1). Which equation represents the circle?
Answer:
(2,-4)
Step-by-step explanation:
Answer:
It is C) (x − 1)^2 + (y + 3)^2 = 4
Step-by-step explanation:
The radius is the distance between the center and the point on the circle.
Center: (1, −3); Point: (1, −1)
Distance formula: d = square root of {(x2 - x1)^2 + (y2 - y1)^2}
r = square root of {(1 − 1)^2 + (−1 + 3)^2 }
r = square root of {0 + 4 } = 2
(x − h)^2 + (y − k)^2 = r2 ----> (x − 1)^2 + (y + 3)^2 = 4
Hope this isn't confusing and helps. I also know its right because I just did this on USA Testprep.
Which numbers are irrational? Select all that apply.
StartFraction 9 Over 15 EndFraction
StartRoot 18 EndRoot
StartRoot 9 EndRoot
StartRoot 169 EndRoot
StartRoot 78 EndRoot
Pi
The irrational numbers from the list are [tex]\sqrt{ 18},\ \sqrt{78}[/tex] and [tex]\pi[/tex]
To find: all numbers that are irrational
Irrational numbers are those that cant be expressed as a ratio of integers
[tex]\frac{9}{15}[/tex]: This fraction is written as a fraction of integers 9 and 15. Thus it is a rational number.[tex]\sqrt{18}[/tex]: It can be simplified to [tex]3\sqrt{2}[/tex] and as [tex]3\sqrt{2}[/tex] cant be expressed as a fraction of integers, [tex]\sqrt{18}[/tex] is an irrational number[tex]\sqrt{9}[/tex]: The square root of 9 is 3 and 3 can be expressed as a fraction of integers 3 and 1. So, [tex]\sqrt{9}[/tex] is a rational number.[tex]\sqrt{169}[/tex]: The square root of 169 is 13. 13 can be expressed as a fraction of integers so, [tex]\sqrt{13}[/tex] is a rational number[tex]\sqrt{78}[/tex]: It cannot be simplified further and cant be expressed as a fraction of integers so, [tex]\sqrt{78}[/tex] is irrational [tex]\pi[/tex]: It has a non-terminating and non-repeating decimal expansion and so cannot be expressed as a fraction of integers. Therefore, [tex]\pi[/tex] is an irrational numberThus, the irrational numbers from the list are [tex]\sqrt{ 18},\ \sqrt{78},\ \pi[/tex]
Find the perimeter of the figure to the nearest hundredth.
Answer:
60.00 in^2
Step-by-step explanation:
First focus on the area ABOVE the dotted line. The shape here is that of a trapezoid. The two leg lengths are 12 in and 18 in (18 in is the diameter). At the far right of this trapezoid we can picture a triangle of base 3 in, height h and hypotenuse 5 in. Using the Pythagorean Theorem, we get h = 4 in.
This 4 in measurement is the width of the trapezoid. Thus, we are now ready to apply the formula for the area of a trapezoid: A = (average length of legs)*(width).
Here that area comes out to
12 in + 18 in
A = --------------------- * 4 in = 15 in*4in = 60 in^2, or (to the nearest hundredth)
2 60.00 in^2
What is the value of y
Answer:
31 degrees
Step-by-step explanation:
The 2 angles are vertical and vertical angles are always equal!! So, y=31 degrees. Hope it Helped!!
SOMEONE PLEASE HELP ME WITH THIS PROBLEM I ONLY HAVE 5 MINUTES TO DO IT YOU DONT NEED TO SHOW WORK ON HOW YOU GOT IT JUST THE RIGHT ANSWER IS FINE THANK YOU!
Answer:
234.3
Step-by-step explanation:
You use Law of Cosines:
a^2 = b^2 + c^2 - 2bc(cosA)
Plug in the values
a^2 = 400^2 + 375^2 - 2(400*375)(cos35)
a = sqrt(160000+140625-300000(cos35))
a = sqrt(300625 - 300000cos(35))
a is approx. 234.263498466, which rounds to 234.3
Find the volume of a rectangular prism 3 inches high, 14 inches wide, and 9
inches long.
Answer:
Answer:
378
Step-by-step explanation:
What is the height of the prism? 7 cm 14 cm 21 cm 30 cm
Answer: 61740
Multiply
Answer:
where is the image?
How do u get 100 points?
Answer:
Just keep answering questions :)
Lena buys 3 cans of soft drinks and 5 sandwiches for a picnic. Patrick buys 9 cans of soft drinks and 10 sandwiches for the same picnic. Let c be the cost of a soft drink. Let s be the cost of a sandwich. Write an expression that represents the total cost.
Answer:
3c+5s+9c+10s= total cost
or
12c+15s= total cost
Step-by-step explanation:
Lena bought 3 cans of soft drinks, or 3c
she also bought 5 sandwiches, or 5s
Patrick bought 9 cans, or 9c
he also bought 10 sandwiches, or 10s
if you add them all up you would get the total cost
If the minute hand is 5.25 in. long. What is the circumference of the circle?
In this example, the minute hand is our radius, because it’s half the internal length of the circle.
The circumference of the circle is equal to pi x diameter.
Since diameter is twice the radius, we can do 5.25 x 2 = 10.5.
From there, we can substitute and solve.
pi x diameter
pi x (10.5)
If we’re representing pi as 3.14, the answer will come out to 32.97.
If we’re representing pi in its calculator function form, it’ll be roughly 32.986723.
So either of those could be your answer depending on how pi is represented.
Hope that helps! :)
Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ. What is the area of circle C, which passes though points W and Z? 81Pi units squared 164Pi units squared 324Pi units squared 1296Pi units squared
Answer:
324Pi
Step-by-step explanation:
The total area of the figure is 77 square centimeters. The overall height of the figure is 9 centimeters.
Drag the correct measurements to label the unknown lengths in the figure.
Answer:
5cm and 10 cm
Step-by-step explanation:
Since the overall height of the shape is 9 and the base of the triangle shaped piece is 6, the area of that piece is 6*9/2=27 units. Subtracting this from the total of 77, you know that the rectangle must have an area of 50 units. Out of the options that you have to drag, the only two that multiply together to be 50 units are 5 for the shorter side and 10 for the longer side. Hope this helps!
The correct measurements to label the unknown lengths in the figure 5 cm and 10cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
The overall height of the shape is 9 cm
The base of the triangle shaped piece is 6
The area of triangle is 1/2×base×height
Area of that piece is 6×9/2=27 units.
Now let us subtract this from the total area
Total is 77 units
the rectangle must have an area of 50 units.
the only two that multiply together to be 50 units are 5 for the shorter side and 10 for the longer side.
Hence, the correct measurements to label the unknown lengths in the figure 5 cm and 10cm.
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4x-4 over 5x+10 times 30x+60 over 2x-2
Answer:
The answer is 12
Step-by-step explanation:
[tex]\frac{4x-4}{5x+10}*\frac{30x+60}{2x-2}[/tex] We need to factor the expression
[tex]\frac{2(2x-2)}{5x+10} *\frac{30x+60}{2x-2}[/tex] Now we reduce the expression
[tex]2*6[/tex] Then we multiply the numbers
[tex]12[/tex] Now we have the answer
How likely is it to spin a vowel on this spinner?
A Certain
B Likely
C As likely as not
D Unlikely
E Impossible
Find the perimeter of the parallelogram with these vertices.(-2,2) ,(-2,-2) ,(6,-1) ,(6,-5)
The perimeter of the parallelogram with these vertices.(-2,2) ,(-2,-2) ,(6,-1) ,(6,-5) is 26 units.
In this explanation, we will find the perimeter of a parallelogram using its vertices' coordinates. The perimeter is the total length of all sides of the parallelogram. To find it, we'll apply the distance formula from coordinate geometry.
A parallelogram is a four-sided polygon with opposite sides parallel and equal in length. To calculate its perimeter, we need to find the lengths of all four sides and then add them together.
Step 1: Find the length of side AB.
Using the distance formula, the length of AB is
= √((-2 - (-2))² + (2 - (-2))²)
= √(0² + 4²)
= √16
= 4 units.
Step 2: Find the length of side BC.
Again, applying the distance formula, the length of BC is
= √((-2 - 6)² + (-2 - (-1))²)
= √((-8)² + 1²)
= √(64 + 1)
= √65 units.
Step 3: Find the length of side CD.
By using the distance formula, the length of CD is
= √((6 - 6)² + (-1 - (-5))²)
= √(0² + 4²)
= √16
= 4 units.
Step 4: Find the length of side DA.
Once more, applying the distance formula, the length of DA is
= √((6 - (-2))² + (-5 - 2)²)
= √((8)² + (-7)²)
= √(64 + 49)
= √113 units.
Step 5: Calculate the perimeter.
The perimeter is the sum of all four sides:
= AB + BC + CD + DA
= 4 + √65 + 4 + √113
≈ 4 + 8.06 + 4 + 10.63
≈ 26 units.
Therefore, the perimeter of the parallelogram defined by the given vertices is approximately 26 units.
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The degree of the product is the ____ of the degrees of the factors
Answer:
Sum
Step-by-step explanation:
Its right
The degree of the product is the sum of the degrees of the factors.
What is the degree of a polynomial?The degree of a polynomial is the highest power of the variable in the polynomial.
The length of a box is (4x -1)
The width of a box is x
The height of a box is x³
The volume of the box is determined by
Length * Width * Height
Volume = (4x -1) * x * x³
Volume = 4x⁵ - 4x⁴
The degree of length is 1
The degree of width is 1
The degree of height is 3
The degree of Volume = 5
The degree of the product is the sum of the degrees of the factors.
It seems that your question is incomplete, the complete question is attached with the answer.
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In a randomly generated list of numbers from 0 to 8, what is the chance that each number will occur
Answer:
There is an 11.1111111% chance of each number coming up.
Step-by-step explanation:
100 / 9= 11.1111111
Answer:
1/9
Step-by-step explanation:
A P E X
Find the 8th term in the following geometric sequence. 28,14,7,3.5,...
Answer: 0.21871
Step-by-step explanation:
28
14
7
3.5
1.75
0.875
0.4375
0.21871
Final answer:
To find the 8th term in a geometric sequence, identify the common ratio and use the formula for the nth term. The 8th term of the sequence is 1.75.
Explanation:
Geometric Sequence:
Identify the common ratio: The common ratio is found by dividing any term by the previous term in the sequence. In this case, the common ratio is 0.5 (14/28 = 0.5).
Find the 8th term: Using the formula for the nth term of a geometric sequence [tex](a_n = a_1 * r^{(n-1)}),[/tex] plug in [tex]a_1 = 28[/tex], r = 0.5, and n = 8 to find the 8th term.
The 8th term of the sequence will be equal to 1.75.
The greatest common factor (GCF) of x2, x5, xº is
Answer:
1.
Step-by-step explanation:
That would be x^0 which is 1.
Any number, variable or expression taken to the power 0 is equal to 1.
Answer:
1
Step-by-step explanation:
X2,x5,x°
X2=1,x,x
X5=1,x,x,x,x,x
X^0=1
So when comparing the factor is greater in the 3 give Variables
It was observed that 1 is the greatest variables
the rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?
Answer:
See explanation.
Step-by-step explanation:
Hello, your question is not very clear.
Based on the limited information, this is how we go about it.
If the rate at which people learn about a secret is directly proportional to the number of people who know the secret and 20 people know it on day 2, then the unit rate is 10.
That is the constant of proportionality is 10.
The direct variation equation is
[tex]y = 10x[/tex]
We want to find how long it will take take for a whole school population of 4000 people to know the secret.
We put y=4000 and solve for x.
[tex]4000 = 10x[/tex]
[tex]x = 400[/tex]
Hence it will take 400 days.
Help ASAP ! I’ll mark as brainlist
Answer:
1031 Meters
Step-by-step explanation:
You would use the Pythagorean Theorem to solve it which would be a^2 + b^2 = c^2 and a would be 800 and b would be 650 in this circumstance you would try to find C which would be glenn blvd.
The length of the Glenin Blvd road is 1030.77 m.
Step-by-step explanation:
Given,
Length if Main street (b) = 800 m
Length of Oak street (l) = 650 m
To find the length of Glenin Blvd (h) road
The given diagram forms a right angle triangle where Main street is the base, Oak street is the height and Glenin Blvd road is the hypotenuses.
Formula
Pythagoras theorem: b²+l² = h²
So,
h² = 800²+650²
or, h² = 1062500
or, h = 1030.77 (approx)
Hence,
The length of the Glenin Blvd road is 1030.77 m.
A rocket is launched from a tower. The height of the rocket, y in feet is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=-16x^2+165x+78
To find the maximum height reached by the rocket, we need to find the vertex of the quadratic equation. The maximum height is approximately 270.6 feet.
Explanation:To find the maximum height reached by the rocket, we need to find the vertex of the quadratic equation. The equation is in the form of y = ax^2 + bx + c, where a = -16, b = 165, and c = 78. The x-coordinate of the vertex is given by -b/2a, and the y-coordinate is the value of y when x is the x-coordinate of the vertex. Plugging in the values, we find that the maximum height reached by the rocket is approximately 270.6 feet.
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A cone has a diameter of 18 units and a height of 8 units. What is its volume?
[tex] \bold{answer \: \: : } \\ \rm{volume = \frac{1}{3} \pi{r} ^{2} t} \\ = \frac{1}{3} \times 3.14 \times {(18 \div 2) }^{2} \times 8 \\ = \frac{1}{3} \times 3.14 \times {9}^{2} \times 8 \\ = \frac{1}{3 } \times {3.14} \times 81 \times 8 \\ = \frac{1}{3} \times 254.34 \times 8 \\ = \frac{1}{3} \times 2034.72 \\ = \frac{2034.72}{3} \\ = \boxed{ \boldsymbol{678.24 }\: \: \rm{units}}[/tex]
HELP ME PLEASE I NEED IT 40 PTS
Answer: D
Step-by-step explanation:
10 squared is 100 and 11 squared is 121, and 111 is in between those two numbers.
Answer: 10 and 11
Out of the choices all you have to do it 7x7 or 8x8 and etc.
Until one of the choices are the closest.
A cube has a net with area 600 in2. How long is an edge of the cube?
Answer : The length of an edge of cube is, 10 inches.
Step-by-step explanation :
The formula used for area of cube is:
Area of cube = [tex]6a^2[/tex]
where,
a = edge
We are given that:
Area of cube = [tex]600in^2[tex]
Now put all the given values in the above formula, we get:
Area of cube = [tex]6a^2[/tex]
[tex]600in^2=6a^2[/tex]
[tex]a=10inches[/tex]
Therefore, the length of an edge of cube is, 10 inches.
What is the greatest common factor of 24s^3,12s^4,18s
Answer:
6s
Step-by-step explanation:
Answer:
6s
Step-by-step explanation:
24s^3 = 2 * 3 * 4 * s *s * s
12s^4 = 2 * 2 * 3 * s * s * s * s
18s = 2 * 3 * 3 * s
As we can see, the common factors that both 24s^3, 12s^4, and 18s have are 2, 3, and s. Multiply these common factors, and you get 2 * 3 * s = 6s, which is the greatest common factor of 24s^3, 12s^4, and 18s.
Graph a line with a slope of 2/5 with a point of -2/4
Answer:
See photo
Step-by-step explanation:
To graph a straight line, you need two points, then connect them.
Your first point is given: (-2, 4)
To get the next point, use the slope.
The slope 2/5 is written rise / run.
Rise is the number of units going up, or down if it's a negative number.
Run is the number of units rightwards.
Take the first point (-2, 4), and add the rise to the y-value. Add the run to the x-value.
x = -2, run = 5
New x = 3
y = 4, rise = 2
New y = 6
New point: (3, 6)
Plot the two points on the grid, then connect the dots.
Remember to put arrows at both ends of your graph.
Answer:
I NEED HELP ON A QUESTION LIKE THIS PLEASE
Step-by-step explanation: