Answer:
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex] meters
[tex]r=10.24[/tex] meters
Step-by-step explanation:
Here is the equation for the volume of a sphere
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].
[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the left side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.
[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]
Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].
[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerators on the left side of the equation. Then multiply the denominators.
[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of 12.
[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the right side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]r^3=\frac{3V}{4\pi }[/tex]
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]
Now we have an equation to find the radius.
Substituting our number for volume gives us
[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
Enter this into a calculator
[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
You can leave the answer in simplest radical form or as a decimal.
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]
[tex]r=10.24[/tex]
A rating/review would be much appreciated. Hope this helps!
Express The Ratio 36 : 42 In it's Simplest Form ?
Answer:
6/7
Step-by-step explanation:
36/42 = 36:6/42:6 = 6/7
PLEASE ANSWER
Write an equation in point-slope form passing through the given point and parallel to the given line:
(- 4, 4)
y = - 7/4x + 2
Answer:
y-4=-7/4(x+4)
Step-by-step explanation:
Point Slope Form: y-y*sub*1=m(x-x*sub*1)
Parallel lines have the same slope as the line to which they are parallel.
y-4=-7/4(x+4)
Hope this helps :)
What’s the pattern? You start with 14 and a half, but then you get 12 and three fourths. How does that happen?
In math, a pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object.
What’s the pattern?A pattern has a rule that identifies the items that are part of the pattern and those that are not. A pattern in mathematics is a series of recurring figures, shapes, or numbers.
Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. A specific set of rules must be taken into account in order to create a full pattern.
We must first comprehend the nature of the sequence and the distinction between the two successive numbers provided in the pattern in order to apply these rules.
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Calculating the median
The following data points represent the number of attendees at each of the private dance events hosted by
Fenel Arrangements.
Sort the data from least to greatest.
49
48
33
51
38
47
42 34
Find the median number of attendees.
attendees
Repon a problems
Stuck? Watch a video or use a hint.
Answer:
Okay so!
Step-by-step explanation:
33, 34, 38, 42, 47, 47, 48, 49, 51.
The median is 47 because it turns up twice.
In the figure, d || m. What is the value of x?
I WILL MARK BRAINLIEST!!
|
———— | ————
(2x - 20°)|
| 86°
———— | ———-
|
Answer: 53
Step-by-step explanation:
2x-20=86 [alternate interior angles theorem]2x=106 [add 20 to both sides]x = 53 [divide both sides by 2]Jeffrey left 4/7 of his estate to his wife and 1/4 of the remainder to his granddaughter.The part of his estate that is not accountefor .given as a fraction is?
plseas someone know this answer and solution I need it in 10 minutes
Answer:
21.888
Step-by-step explanation:
32*1.2*1.9*0.3= 21.888
.The medical practice you are working at has been an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
Answer:
If we're looking for those that don't have insurance, it's 504. If we're looking for those that do, it's 1,512.
Step-by-step explanation:
Multiply 22.4 by 30 because there's roughly 30 days in a month. You'll get 2,016. Divide 2,016 by 4. You'll get 504. Multiply 504 by 3 to get how many have insurance.
PLEASE HELP
All numbers less than 17 and greater than or equal to -8
Answer: C
Step-by-step explanation: it says that it's smaller or equal to x and x is smaller than 17
2 copies of 1/10 write fraction for each statement
2 copies of 1/10 can be written as 2/10
What is a fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here 2 copies of 1/10 thus 2×1/10=2/10
=1/5
Hence, 2 copies of 1/10 can be written as 2/10
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Special right triangles.
Find u.
Please help due in 30 min!
Answer:
u= 2 kilometers
Step-by-step explanation:
[tex] \frac{2 \sqrt{2} }{ \sqrt{2} } = 2[/tex]
Natalie is driving on the freeway. She just passed mile marker 290. The markers have
been increasing as she drives by them. The fastest Cameron will drive is 80 miles per
hour. However, there is a bit of traffic that might slow her down, but she doesn't know
exactly how much it will slow her down.
a. Write an inequality to represent Natalie's position relative to the mile markers
three hours from now.
b. Rewrite this inequality to reveal Natalie's speed.
Need help with this ASAP
On solving the provided question we can say that - the inequality equation which will be formed is 290x [tex]\geq[/tex] -23 + y
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
here,
we have 290x
so the inequality equation which will be formed is
-y + 290x [tex]\geq[/tex] -23
290x [tex]\geq[/tex] -23 + y
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Question 7 of 10
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them? hs
2x – 4y= 5
6x - 3y=10
A. Multiply the top equation by -3 and the bottom equation by 2.
B. Multiply the top equation by 3 and the bottom equation by 4.
o o
C. Multiply the top equation by -2
D. Multiply the top equation by -3.
Answer:
D. Multiply the top equation by -3.
Step-by-step explanation:
2x – 4y= 5 -3(2x – 4y= 5) -6x + 12y= -15
6x - 3y=10 6x - 3y=10
No you can eliminate -6 and 6
Answer:
The answer is D.
Step-by-step explanation:
D. Multiply the top equation by -3.
This works because if you multiply the top equation by -3 then it will be
-3(2x – 4y= 5) which is -6x + 12y = -15
now our equation is : -6x +12y = -15
6x - 3y = 10
As you can see we can eliminate -6x and 6x if we add those two equation together.
Select ALL composite numbers with their correct prime factors(I need help)
Answer:
The answer would be the second and fourth options.
Step-by-step explanation:
This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!
An octagon has a perimeter of 27 feet. If the sides of the octagon shrink by a scale factor of 8/9, what will the perimeter of the new octagon be
The perimeter of the new octagon be 24 feet.
What is the perimeter of octagon?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.
The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.
Given that the perimeter of an octagon is 27 feet
so the length of its side is 27/8 feet
if the side of the octagon shrink by a scale factor of 8/9
The side of new octagon is (27/8) * (8/9)
The side of new octagon is 3 feet.
So the perimeter of new octagon is 8 * side
⇒ the perimeter of new octagon = 8 * 3 feet
⇒ the perimeter of new octagon = 24 feet
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What's the area of the triangle with 9mm 76mm 100mm
9514 1404 393
Answer:
342 mm²
Step-by-step explanation:
The triangle shown has a base of 9 mm and a height of 76 mm. Its area is ...
A = 1/2bh
A = (1/2)(9 mm)(76 mm) = 342 mm²
The triangle shown has an area of 342 mm².
_____
Additional comment
The other leg of the right triangle with one leg 76 mm and hypotenuse 100 mm will be about 65 mm. The base shown is 9 mm, so any triangle with the dimensions shown will be a fairly skinny obtuse triangle, not the acute triangle in the picture. (This makes us suspect an error: the 9 mm dimension maybe should be 90 mm.)
EES
2.6 m
Find the area. Use = 3.14
a. 21.2264 m2
b. 16.328 m2
c. 84.9056 m2
d. 5.3066 m2
Please select the best answer from the choices provided
Ο Α
Answer:
5.3066m²
Step-by-step explanation:
A=πr²=π·1.3²=5.3066m²
Put these in order from least to greatest!: 88/25, 3.551, 3.88, 3 11/20
Rewrite all 4 numbers as decimals to compare them:
88/25 = 3.52
3 11/20 = 3.55
Now arrange them in the correct order:
88/25, 3 11/20, 3.551, 3.88
Answer:
Step-by-step explanation:
all numbers are 3 and some more
start by arranging the decimals from least to greatest
3.551, 3.88
88/25 ( 25, three times is 75) = 3 and (88-75)/25 = 3 and 13/25 =3.52
3 11/12 is almost 4 because 11/12 is almost 12/12
the order is :
88/25, 3.551, 3.88, 3 11/20
A geyser erupts every 25 minutes. A hiker has not consulted a schedule before heading to see the geyser, so the amount of time he spends waiting to see an eruption follows a uniform distribution. What is the probability that he will wait longer than 6 minutes? Give your answer to two decimal places.
Answer:
0.76 = 76% probability that he will wait longer than 6 minutes
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
A geyser erupts every 25 minutes. A hiker has not consulted a schedule before heading to see the geyser, so the amount of time he spends waiting to see an eruption follows a uniform distribution.
This means that [tex]a = 0, b = 25[/tex]
What is the probability that he will wait longer than 6 minutes?
[tex]P(X > 6) = \frac{25 - 6}{25 - 0} = 0.76[/tex]
0.76 = 76% probability that he will wait longer than 6 minutes
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
Define volume.Volume, which is expressed in cubic units, is a unit of measurement for the 3-dimensional space occupied by matter or encircled by a surface. The SI unit of volume = area * height is the cubic metre (m3), which is a derived unit. A "litre" (L) is the name given to the cubic decimeter (dm3).
Here,
The volume of cylinder = πr²h
Given : Diameter = 12 inches
radius = 12/2 = 6 inches
Height = 8 inches
Thus ,
To find the volume we put the all the above values in the formula:
=> V = πr²h
=> V = 22/7 * 6² * 8
=> V =355/113 * (6)² * 8
Therefore , the solution of the given problem of volume comes out to be
V =355/113 * (5)² * 7 thus correct option is V equals 355 over 113 times 6 squared times 8.
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Answer:
V equals 355 over 113 times 6 squared times 8.
Step-by-step explanation:
You have a 1/3 -teaspoon measuring spoon and a 1/2-teaspoon measuring spoon. What are two ways you can measure 3 1/6 teaspoons of salt?
Answer: One way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:
the 1/2 teaspoon measuring spoon 3 times to measure 3/2 = 1 1/2 teaspoons
and use the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons
3 1/2 + 2/3 = 3 1/6
Another way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:
the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons
and use the 1/2 teaspoon measuring spoon 6 times to measure 6 * 1/2 = 3 teaspoons
3 + 2/3 = 3 1/6
So, there are two ways to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2-teaspoon measuring spoon, one is by using 3 times 1/2 teaspoon measuring spoon and 6 times 1/3 teaspoon measuring spoon and the second one is by using 6 times 1/3 teaspoon measuring spoon and 3 times 1/2 teaspoon measuring spoon.
Step-by-step explanation:
George peels and eats 2 whole satsumas.
He then splits another satsuma into 6 equal segments and eats 1 of these segments.
How many satsumas does he eat in total?
Give your answer as an improper fraction.
The total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).
Given is that George peels and eats 2 whole satsumas. He then splits another satsuma into 6 equal segments and eats 1 of these segments.
The total number of satsumas eated by him can be written as -
2 + 1/6
2[tex]\frac{1}{6}[/tex]
Therefore, the total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].
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The National Park Service is interested in comparing the amount of money that visitors in two different national parks spend. They sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample. Analysis for these data will be based on a _______ design.Please type the correct answer in the following input field, and then select the submit answer button or press the enter key when finished.Your answer:
Answer:
Analysis for these data will be based on a __survey__ design.
Step-by-step explanation:
A survey design is a process through which surveys are conducted to acquire enough insight about a given situation or matter of interest. In this case, the National Park Service's interest is finding out the amount of money that visitors in the two different national parks spend. Visitors are sampled from each park to get the required information. The mean spends are calculated and then compared.
Help me please 35 points on the line
Answer shown in bold
401924109147The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.
========================================================
Explanations:
Add up all of the values in the Venn diagram to find the total. Therefore, 9+10+14+7 = 40 students were surveyed.We add the values in the "social interaction activities" circle only. There are 9+10 = 19 students here.This time add up the values in the "technology driven activities" to get 10+14 = 24 students.The answer is 10 because this value is in the overlapped region between the two circles. The answer is 9 since this value is in the "social interaction activities" circle, but outside the other circle. The answer is 14 as this value is in the "technology driven activities" circle, but outside the other circle.The answer is 7 because this value is outside both circles.Let me know if you have any questions.
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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What are the exact values of a and b?
CORRECT ANSWER
WITH EXPLANATION
Step-by-step explanation:
TRY WITH SOME Trigonometric FUNCTION.
IF SOMETHING IS Wrong . I AM STILL A STUDENT
Sixty is 20 percent more than what number?
Answer:
48
Step-by-step explanation:
20 percent off of 60 is 48
Sixty is 20 percent more than 50.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Let's call the unknown number x.
We know that 60 is 20% more than x, which can be written as:
60 = x + 0.2x
Simplifying:
60 = 1.2x
Dividing both sides by 1.2:
x = 50
Therefore, 60 is 20% more than 50.
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Using elimination, what is the solution to the following system?
x+y=4
x-y=8
Answer:
x=6, y=-2. (6, -2).
Step-by-step explanation:
x+y=4
x-y=8
----------
2x=12
x=12/2
x=6
6+y=4
y=4-6
y=-2
What is the value of c in the equation below?
24.22=abc
0 -4
0 -2
O
1
64
O
1
4
Answer:
are the values of a or b given?
Step-by-step explanation:
Solve the following quadratic equation for all values of xx in simplest form.
4(x^2-5)-1=
4(x
2
−5)−1=
\,\,3
3
The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
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