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!
mr doyle shares 1 roll of bulletin board paper equally with 8 teacher.The total length of the roll is 72 meters. How
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer: x = 13 and x = –29
Step-by-step explanation:i hope i help you
Answer:
To find the values of x that make the equation (x – 7)^2 = 36 true, you can start by undoing the square on the left side of the equation. Since (x – 7)^2 = (x – 7)(x – 7) = x^2 - 14x + 49. Then we know that x^2 - 14x + 49 = 36.
Now, you can add 14x and 49 to both sides to get x^2 = 50.
To find the values of x that make this equation true, we need to find the square root of both sides. So x = ±sqrt(50).
And the two values of x that will make the equation true are x = ±sqrt(50) = ±7sqrt(2). And it is not in the options given, which are x = 13, x = 1, x = -29, x = 42.
Step-by-step explanation:
In JKL, KL = 14, LJ = 3, and JK =12. Which statement about the angles of JKL must be true?
Answer:
D. [tex]L > J > K[/tex]
Step-by-step explanation:
Givenwe are given the vertecies (angles) of the trianglewe are given the side lengths of the triangleWhat to UtilizeThus, we have to utilize the angle relationships in a triangle.
Angle Relationships in a Triangle⭐The largest side is always opposite of the largest angle
⭐The smallest side is always opposite of the smallest angle
Application1. Identify the side lengths of triangle JKL
KL = 14LJ = 3JK = 122. Determine which vertecies are opposite of each side length (draw the figure)
Angle L is opposite of JK (14)Angle K is opposite of LJ (3)Angle J is opposite of KL (12)3. Determine which angles are the greatest, smallest, and in-between
Angle L is the LARGEST angle because it is opposite of the LARGEST side lengthAngle K is the SMALLEST angle because it is opposite of the SMALLEST side lengthWe know that angle J isn't the LARGEST or SMALLEST, but is in the middle4. Write what you found in #3 in terms of inequalities
∠L > ∠J > ∠K
angle L is greater than angle J, and angle J is greater than angle Kif this response helped you, please mark it the "brainliest"!
People at a local festival were asked if their favorite dessert was cake or pie. The probability of each result are as follows: • Probability of 0.42 that people liked pie • Probability of 0.90 that people liked cake or pie • Probability of 0.12 that people liked both cake and pie Use a Venn Diagram to support your calculations for the following questions:
a) Determine the probability that a person will like cake.
B) Determine the probability that a person at the festival does not like either of these two desserts.
C) Are the event liking cake and liking pie mutually exclusive or non-mutually exclusive? Justify your answer.
a) The probability that a person will like cake is given as follows: 0.6 = 60%.
b) The probability that a person does not like any of the two desserts is given as follows: 0.1 = 10%.
c) The events are non-mutually exclusive, as the probability of liking both is different of zero.
What is a Venn probability?In a Venn probability, two events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
The events for this problem are given as follows:
Event A: person likes pie.Event B: person likes cake.The probabilities for this problem are given as follows:
P(A or B) = 0.9, P(A) = 0.42, P(A and B) = 0.12.
Hence the probability that a person likes cake is given as follows:
0.9 = 0.42 + P(B) - 0.12
0.3 + P(B) = 0.9
P(B) = 0.6.
Probability of 0.90 that people liked cake or pie, hence the probability that a person likes neither is of:
1 - 0.9 = 0.1 = 10%.
(or means at least one of them, and neither is complementary to at least one).
As P(A and B) = 0.12 is different of zero, the events are non-mutually exclusive.
More can be learned about Venn probabilities at https://brainly.com/question/7965468
#SPJ1
-2(x+5)=4 math homework help
Answer:
-7
Step-by-step explanation:
-2(x+5)=4
First, distributive property,
-2x-10=4
Add 10 to both sides,
-2x=14
Divide both sides by -2
-7
3 2/3 Divided by 1 2/7
Answer:
[tex]2 \frac{23}{27} [/tex]
I wish you luck in your assignments.
hat is the following sum?
0 7(10√/x²y)
O
O
0 7(²√x²¹x²)
The sum of the given equation is 7[tex]\sqrt[5]{x^{2} y}[/tex].
What is fractional equation?A fractional equation is one in which one or more of its terms have the unknown as their denominator. Equations involving fractions can be resolved using the Cross-Product property.Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers. In other words, we choose the greatest number that the top and bottom have in common and divide them by that.Equations using fractions require the solution of equations in which the unknown variable is a component of the fraction's numerator or denominator. To solve fractional equations, we must determine the value of the undetermined variable.Given data :
4 ([tex]\sqrt[5]{x^{2} y}[/tex].) + 3 ([tex]\sqrt[5]{x^{2} y}[/tex].)
Add similar elements
= 7[tex]\sqrt[5]{x^{2} y}[/tex].
Learn more about fractional equation refer to :
https://brainly.com/question/20323470
#SPJ1
The price of a house was #2.3, 400,006 in 201 At the end of each year, the price was increases by 6% find the price of the house after 3 years Find the price of the house after 5 years
After 3 years, the price of the house would be $2,494,822.48. After 5 years, the price of the house would be $2,830,530.94.
What is price?Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.
To calculate the price of the house after 3 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 3. Therefore, the price of the house after 3 years is P x (1 + 0.06)^3, which equals to $2,494,822.48.
To calculate the price of the house after 5 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 5. Therefore, the price of the house after 5 years is P x (1 + 0.06)^5, which equals to $2,830,530.94.
To know more about price click-
https://brainly.com/question/19104371
#SPJ1
two equivalent ratios for 17:5?
Answer:
34/10 is equivalent to 17/5 because 17 x 2 = 34 and 5 x 2 = 1051/15 is equivalent to 17/5 because 17 x 3 = 51 and 5 x 3 = 1568/20 is equivalent to 17/5 because 17 x 3 = 68 and 5 x 3 = 20
Step-by-step explanation:
hii, how are you
I need help with this PLEASE!!!
Answer:
See the image for marked congruences.
1. JM ≅ LM | Given
2. △JML is isosceles | definition of isosceles
3. ∠MJL ≅ ∠MLJ | isosceles triangle theorem
4. m∠MJL = m∠MLJ | definition of ≅
5. JK ≅ LK | Given
6. △JKL is isosceles | definition of isosceles
7. m∠KJL = m∠KLJ | isosceles triangle theorem
8. m∠MJL + m∠KJM = m∠KJL | adjacent angle theorem
9. m∠MLJ + m∠KMJ = m∠KLJ | adjacent angle theorem
10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM | transitive property of =
11. m∠MJL + m∠KJM = m∠MJL + m∠KLM | substitution
12. m∠KJM = m∠KMJ | subtraction
13. ∠KJM ≅ ∠KLM | definition of ≅
14. △KJM ≅ △KLM | SAS theorem
15. ∠JKM ≅ ∠LKM | CPCTC
16. KM bisects ∠JKL | definition of bisector
find -2/6 + (5/6) model the expression on the number line
The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).
Modelling -2/6 + (5/6 on the number lineTo correctly model the expression -2/6 + (5/6) on a number line, we can use the following steps:
Start at 0 on the number line.Move to the left by 1/3. This represents the value of -2/6 which is equivalent to -1/3.Move to the right by 5/6. This represents the value of 5/6.The final point on the number line will be 2/3 to the right of the point (-1/3) which we reached in step 2, this represents the sum of -2/6 and 5/6, which is the final result.So to model the expression -2/6 + (5/6) on a number line, we start at 0 and move 1/3 to the left, to represent -2/6, and then move 5/6 to the right to represent 5/6. The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).
Learn more on number line here: https://brainly.com/question/22046767
#SPJ1
A flexible metamateria/ is developed for use in robotics and prosthetics. A block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters. What is the edge length of the block of metamaterial?
The edge of a block of metamaterial is 10 centimeters.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, a block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters.
Here, 6a²=600
a²=100
a=10 centimeters
Therefore, the edge of a block of metamaterial is 10 centimeters.
Learn more about the surface area of a cube here:
https://brainly.com/question/23273671.
#SPJ1
Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price. f
WILL MARK BRAINLIEST given angles A and B in quadrant I with tan = 7/24 and tan B = 15/8, find tan (A + B), find the exact value of each expression by applying the identity.
Using PEMDAS to resolve the trigonometric identity which involves trigonometric function, the value of tan A + tan B is 416 / 87
What is Trigonometric IdentityA trigonometric identity is an equation that is true for any value of the variables involved. These identities are useful in solving problems involving trigonometric functions. Examples include the Pythagorean identity, the sine and cosine addition formulas, and the double angle formulas.
In the given problem, we have a compound angle problem and we can solve it as;
tan A + tan B = [(tan A + tan B)] / [1 - tan A * tan B]
tan A = 7/24tan B = 15 / 8Substituting the values into the expression and solve;
tan A + tan B = [(7/24 + 15/8)] /[1 - (7/24)(15/8)]
Applying the rules of PEMDAS;
tan A + tan B = (13 / 6) / (29 / 64)
tan A + tan B = 416/87
Learn more on trigonometric identity here;
https://brainly.com/question/24496175
#SPJ1
The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have an equal monthly salary of P7200, P7600, P6900, P8200, P7800 and P7400 respectively. What is the mean monthly salary of all the employees of the company?
The average monthly wage for the entire workforce of the business is $7489.09.
What is Mean?
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.
First, calculate the total monthly salary
22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200 dollars.
Total monthly salary = $823,800
Then divide this sum by the total number of employees
22 + 32 + 18 + 16 + 10 + 12
Total number of employees = 110
the mean monthly salary of all the employees = [tex]\frac{Total salary}{total number of employee}[/tex]
the mean monthly salary of all the employees = 823800/ 110
the mean monthly salary of all the employees = 7489.0909
Therefore, the mean monthly salary of all the employees of the company is $7489.09.
Learn more about mean here:
https://brainly.com/question/10853033
#SPJ1
A new pair of shoes you would like to purchase is 65% off. If you paid $135 for the shoes, how much was the original cost?
Solving the equation the original cost of the shoes before the discount will be obtained as $385.
To find the original cost of the shoes before the discount, you can use the following equation:
original cost = final cost÷ (1 - discount percentage)
In this case:
original cost = $135 ÷ (1 - 0.65)
To find the final cost you need to multiply 135 by 1 - 0.65.
0.65 is the equivalent to 65% when it's represented as a decimal.
0.65 represents the proportion of the original price that was removed (65% or 0.65)
So:
original cost = $135 ÷ (1 - 0.65)
original cost = $135 ÷ (1 - 0.65) = $135 ÷ 0.35 = $385
The original cost of the shoes before the discount was $385.
Learn more about equation:
https://brainly.com/question
How do you find the equation of the midline for a function?
Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Here,
The midline equation is y = M+m /2
when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.
When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)
It is solely constrained from above (or below)
Any line is midline if a function has the values (-∞, +∞)
Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
To know more about equation , visit
https://brainly.com/question/649785
#SPJ1
NTP2PS
Write 3 equivalent ratios.
For the given ratio.
12/14
Answer:
4 7
Step-by-step explanation:
If f(x) = 2x4 - 3x + 3, then what is the remainder when f(x) is divided by x - 1?
The remainder on dividing 2x⁴-3x+3 by x-1 is 2
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: 2x⁴-3x+3 by x-1
The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a)
∴ The remainder would is f(1) = 2×1-3+3
=2
Hence, The remainder on dividing 2x⁴-3x+3 by x-1 is 2
Learn more about functions here:
https://brainly.com/question/28303908
#SPJ1
Help me pleaseeeeeee
Line segment AB = 12, its image after a dilation is 36. What is the scale factor of the dilation?
The scale factor of the dilation is 3
How to determine the scale factor of the dilation?From the question, we have the following parameters that can be used in our computation:
Line segment AB = 12 units
After the dilation = 36 units
The scale factor of the dilation is then calculated as
Scale factor of the dilation = After the dilation/Line segment AB
Substitute the known values in the above equation, so, we have the following representation
Scale factor of the dilation = 36/12
Evaluate
Scale factor of the dilation = 3
Hence, the scale factor is 3
Read more about scale factor at
https://brainly.com/question/15891755
#SPJ1
The time t in seconds that it takes a car to accelerate to ask mph can be described by T=0.001×0.7 32X^2 +15.417X +603.738 how fast in miles per hour is the car going after 8.55 seconds
The miles per hour that the car is going after 8.55 seconds is 610.79 miles per hour.
How to calculate the time taken?From the information Illustrated, it should be noted that the t in seconds that it takes a car to accelerate to ask mph can be described by T = 0.001 × 0.732X² + 15.417X + 603.738.
In this case, it is important to note that x in the function simply represents the seconds.
Therefore, based on the information, the miles per hour is the car going after 8.55 seconds will be:
T = 0.001 × 0.732X² + 15.417X + 603.738.
T = 0.001 × 0.732(8.55)² + 15.417(8.55) + 603.738
T = 0.001 × 53.511 × 131.815 + 603.738
T = 610.79
Learn more about time on:
brainly.com/question/26046491
#SPJ1
Let p be the statement "He is tall" and let q be the statement the following statements in symbolic form using p and q. He is handsome". Write each of /1/ He is tall and handsome. /2/ He is tall but not handsome. /3/ He is false that he is short or handsome. /4/ He is neither tall nor handsome. /5/ He is tall, or he is short and handsome /6/ It is not true that he is short or not handsome
On solving the provided question we can say that by logarithm the statement is true he is short.
what is logarithm?The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).
He is tall, or he is short and handsome
It is not true that he is short or not handsome
by logarithm,
the statement is true he is short.
To know more about logarithm visit:
https://brainly.com/question/30085872
#SPJ1
A square board is attached to a wall. The board is divided into four squares and each square is painted either black or white. In how many ways can the board be painted if we can rotate the given board about its center? The answer is not 14 or 16.
The board can be rotated in 4 different ways (0, 90, 180, 270 degrees) and each of the four squares can be painted in 2 different ways (black or white). Since we can rotate the board, the order in which the squares are painted does not matter, so we must divide by the number of ways to rearrange the squares. So, there are (2^4) / 4 = 6 ways the board can be painted when we take rotations into account.
How to calculate the Rotation rate?To calculate turnover, it is necessary to consider the departures and additions of people to the company in the period. Calculating turnover is quite simple: you need to add the number of admissions and the number of dismissals, then just divide by 2 and then divide by the total number of employees within your company.
Learn more about Rotation rate in brainly.com/question/30066959
#SPJ1
-15 POINTS-
How many sides does a regular polygon have if one interior angle measures 144°
Answer: 10 sides
Step-by-step explanation:
You can always use the given formula to calculate but I (personally) find it much easier to calculate the number of sides using the exterior angle.
To calculate the exterior angle, it is 180 - the interior angle.
In this example, the exterior angle would be 180-144 = 36°
Because it is a regular polygon, we know that all the angles in the shape are the same.
In all polygons, the exterior angles always add up to 360 degrees.
So divide 360 by 36 (the size of each exterior angle), and you get 10.
360/36 = 10
write the missing digits to make this addition correct
_2_+_2=200
Answer:
128 + 72 = 200
Step-by-step explanation:
Start from the ones. And go next to tens and last find the hundreds.
see image.
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile. She decides to remove this value from further analysis.
What might happen to the mean, median, and mode of the data set after the value's removal?
(select all right answers)
The mode will increase.
The median may stay the same.
The mean will increase.
The mode will stay the same.
The median may decrease.
The mean will decrease.
The required correct options of data set after the value's removal.
1. The mean will increase. 3. The median may stay the same. 5. The mode will stay the same.
What is the value's removal?The Index Sponsor computes the Removal Value in the same way that Fund Interests in the linked Fund are valued.
Here,
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile.
As for the properties of statistics, Change in the IQR does affect the median and mode, So options 3 and 5 are correct.
And also mean will increase.
Thus, the correct options are shown above.
Learn more about value's removal here:
https://brainly.com/question/15396995?referrer=searchResults
#SPJ1
1000(9x-10)=50(976+100x)
Input 8-2n
I’m getting confused
Thanks
Answer:
4,2,0
Step-by-step explanation:
the rule is subtract 2 so 0 and 8 , 1 and 6 , 2 and 4 , 3 and 2 , and then finally 4 and 0
Please help will mark Brainly
The graph of the given inequality y < 4x - 5 is attached below.
What is graph of inequality?
Treat the <, ≤, >, ≥ or sign as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either < or >. Graph the equation as a solid line if the inequality is either ≤ or ≥.
A region on one side of a line can be used to graphically represent an inequality. For the purpose of indicating that a line is not a part of the region, inequality plots that use the < or > symbols have a dashed line. Plotting a solid line indicates that an inequality that uses the symbol
"≤ or ≥" is included in the region.
To learn more about graph of inequality, click on the link
https://brainly.com/question/24372553
#SPJ1