The volume of a sphere is a function of its radius, V=4/3(pie)(r^3). Evaluate the function for the volume of a volleyball with radius 11.4cm
Given:
Volleyball (sphere) volume[tex]=\bold{\frac{4}{3} \pi r^2}[/tex]
[tex]\to \bold{r=11.44\ cm}[/tex]
putting the value into the formula:
[tex]=\bold{\frac{4}{3} \times 3.14 \times 11.4^2}\\\\=\bold{\frac{4}{3} \times 3.14 \times 1481.544}\\\\=\bold{\frac{4}{3} \times 4652.04816}\\\\=\bold{4 \times 1550.68272}\\\\=\bold{6202.73}\\\\[/tex]
The final volume of volleyball (sphere) "[tex]\bold{6202.73\ cm^3}[/tex]".
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To find the volume of a volleyball with a radius of 11.4 cm, we plug the radius into the formula for the volume of a sphere, V=4/3(pi)(r^3), resulting in an approximate volume of 6185.7 cubic centimeters.
Explanation:The question asks to evaluate the volume of a sphere using the given formula, which is V=4/3(pi)(r^3), where V represents the volume and r is the radius of the sphere. To find the volume of a volleyball with a radius of 11.4 cm, we substitute r with 11.4 in the formula and calculate the volume accordingly.
The calculation would be:
V = 4/3 × pi × (11.4 cm)^3
V = 4/3 × 3.14159 × 11.4 cm × 11.4 cm × 11.4 cm
V = 4/3 × 3.14159 × 1481.784 cm^3
V ≈ 4/3 × 3.14159 × 1481.784 cm^3
V ≈ 6185.7 cm^3
Therefore, the volume of the volleyball is approximately 6185.7 cubic centimeters.
Two more than 4 times a number is -18
What is the solution of the following system? -3x-2y=-12 9x+6y=-9
Answer:
No solution.
Step-by-step explanation:
Use elimination.
Multiply the equation by the opposite equation's x coefficient.
9(-3x - 2y = -12) = -27x - 18y = -108
Again, multiply by the other x coefficient.
-3(9x + 6y = -9) = -27x - 18y = 27
Add the second equation to the first.
-27x - 18y = -108
+27x + 18y = -27 The x and y will cancel each other out.
0 ≠ 135. Since 0 does not equal 135, there is no solution.
Elimination gives an equation that is always false. The two equations in the system represent parallel lines. This is an inconsistent system. It has no solutions.
Two cards are randomly selected from a 52-card deck. what is the probability that the draw will yield an ace and a face card?
If x + 2 has a value of 5 then which of the following is the value of X(x+2)+3(x+2)
The solution of the equation "[tex]x(x+2)+3(x+2)[/tex]" will be "[tex]5(x+3)[/tex]".
According to the question,
[tex]x(x+2)+3(x+2)[/tex]and,
[tex]x+2=5[/tex]By substituting "5" in place of "(x+2)" in the above given equation i.e.,
[tex]x(x+2)+3(x+2)[/tex], we get
= [tex]x(x+2)+3(x+2)[/tex]
= [tex]x(5)+3(5)[/tex]
By applying multiplication, we get
= [tex]5x+15[/tex]
= [tex]5(x+3)[/tex]
Thus the response above is appropriate.
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Solve 2x2 + x − 4 = 0.
x^2 + ____x+____ = 0
Answer:
1/2 -2
Step-by-step explanation:
The solution of 2x² + x − 4 = 0 is x = ( -1 ± √33 ) / 2.
What is a Quadratic Equation?A quadratic equation is what can be written in the form of ax²+bx+c=0
The equation is,
2x² + x − 4 = 0
To solve the equation, the equation needs to be factorized.
It can be also solved using the formula for determining roots.
x = ( -b ± √ (b² -4ac)) / 2a
Comparing it with the standard equation ax²+bx+c=0.
a = 2, b = 1, c = -4
Substituting the values
x = ( -1 ± √ (1² -4*2*-4)) / 2 * 2
x = ( -1 ± √ (1 + 32)) / 2 * 2
x = ( -1 ± √33 ) / 2
The solution of the given quadratic equation is x = ( -1 ± √33 ) / 2.
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Hard math question!
What is the inverse matrix of [tex] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]?
Please show work!
what is the product of −4 1/2 and 2 1/2 ?
Solve each inequality
3t-2<5
-6<5b-4
The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
Write a quadratic equation having the given solutions -8
Answer:
[tex]y=x^2+16x+64[/tex]
Step-by-step explanation:
A quadratic needs 2 solutions, but since you only have 1, I am to assume that x = -8 twice (or multiplicity of 2). If x = -8, then in factor form, it's (x + 8). Muliplying that by itself twice:
(x + 8)(x + 8):
[tex]x^2+8x+8x+64=0[/tex]
Simplifying gives you:
[tex]x^2+16x+64=y[/tex]
Use substitution. 2x + 3y = 5 4x - y = 17 Use linear combinations: 2x + 3y = 5 4x - y = 17
Jerome earns $200 per month plus $12 for each bike he sells at the bike shop. This month, he wants to earn at least $400. What is the least amount of bikes that Jerome can sell to reach his goal
Suppose you start with at least $82 in your savings account and deposit $32 each week. Write, solve, and graph an inequality to describe how much money, m, you have after 10 weeks, w.
Answer:
m ≥ 82 + 32w
m ≥ 402
Step-by-step explanation:
Here, w represents the number of weeks and m represents the total amount in the account after w weeks,
The amount of money saved in each week = $ 32,
So, the total amount saved after weeks = 32w dollars,
Since, the original amount in the account = $ 82
The total amount in the account = 82 + 32w
Thus, the required inequality would be,
m ≥ 82 + 32w
If w = 10,
The amount in the account after 10 weeks = 82 + 32(10) = 82 + 320 = $ 402
⇒ m ≥ 402
That is, the closed circle on 402 and shaded right in the number line ( shown below )
What is the value of X? Remember to show calculations and formulas used for credit.
You have $9, one of your friends has $10, and two of your other friends each have $13. you combine your money to buy arcade tokens. you use a coupon to buy 8 tokens for $1. the cost of the remaining tokens is four for $1. you and your friends share the tokens evenly. how many tokens does each person get? each person gets 65 tokens.
The required number of tokens distributed in each of them is 46 tokens.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Total money = 9 + 10 + 13 + 13 = $45
Total number of persons = 4
For the first $1 there are 8 token
And after that cost of 4 tokens is $1,
Total tokens = 8×1 + 4×(45 - 1)
Total tokens = 8 + 176
Total tokens = 184
Now,
Distribution among the fours,
= 184 / 4
= 46 tokens
Thus, the required number of tokens distributed in each of them is 46 tokens.
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If it takes about 20 minutes to grade a student paper how long in hours does it take to grade palers for a class of 25 people
Final answer:
It takes about 20 minutes to grade one student's paper, so for a class of 25 students, it would take a total of 500 minutes, which is approximately 8.33 hours to grade all the papers.
Explanation:
If it takes about 20 minutes to grade a student paper, to find out how long it takes to grade papers for a class of 25 students, we need to multiply the number of students by the time taken to grade each paper.
Step-by-Step Calculation:
Multiply the number of students (25) by the minutes per paper (20 minutes): 25 students * 20 minutes per student = 500 minutes.
Convert minutes to hours. Since there are 60 minutes in an hour, we'll divide the total minutes by 60: 500 minutes ÷ 60 minutes per hour = 8.33 hours.
Therefore, it takes approximately 8.33 hours to grade papers for a class of 25 students. Please note that this is an ideal situation without any breaks or interruptions accounted for.
find the range of the data set: 28, 11, 25, 4, 24
Solve the system of linear equations in two variables by elimination or substitution.
3x+y=7
-2x-y=9
Answer:
x=16, y=-41
Step-by-step explanation:
Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did sunny earn this week?
Answer: [tex]12x-15[/tex]
Step-by-step explanation:
Given: Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week.
The total earning for this week = [tex]12x[/tex]
Also, she was charged $15 for a late delivery on Tuesday.
It means, The total earning for this week =[tex]12x-15[/tex]
So if Sunny earns $12 per hour delivering cupcakes. She worked for x hours this week and was charged $15 for a late delivery on Tuesday then her earning for this week = 12x-15
What larger conclusion can you reach by stringing together the sentences given below?If the restaurant is closed, we will eat at home.If we eat at home, we will save money.If we save money, we will become rich.
An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ___________ plane
The Cartesian plane is where an ordered pair of real numbers can be represented in a rectangular coordinate system.
In a rectangular (Cartesian) coordinate system, an ordered pair of real numbers can be represented in the Cartesian plane. The Cartesian plane is formed by the xy plane, where the x and y axes are perpendicular and intersect at the origin.
seven less than the quotient of a number, x, and twelve is five times the number. which answer represents this situation? x/12−7 5x 7−x/12=5x 7−x/12 5x x/12−7=5x
Dahlia is simplifying (3t)^4 using these steps:
(3t)^4= 3t*3t*3t*3t=3*3*3*3*t*t*t*t
Although Dahlia is correct so far, which step could she have used instead to simplify the expression ?
A. 3t^4=3t^4
B.3^4t=81t
C. 4(3t)=12t
D.3^4t^4=81t^4
Dahlia could have raised both the coefficient and variable to the power of 4
Simplifying exponential functionsGiven the exponential expression as shown below;
(3t)^4
This shows that we are to multiply 3t in 4 places to have;
(3t)^4 = (3t) * 3t * 3t * 3t
(3t)^4 = 3^4 * t^4
(3t)^4 = 81t^4
This shows that Dahlia could have raised both the coefficient and variable to the power of 4
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If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be parallelogram? True or False?
It's true If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be a parallelogram.
What are the four types of parallelograms?
Rectangles, rhombus, and squares are parallelograms. A trapezoid has as a minimum one pair of parallel facets. The parallel aspects are referred to as the bases and the non-parallel sides are called the legs. There are three kinds of trapezoid - isosceles, right-angled, and scalene trapezoids.
How do you discover a parallelogram?
To identify a parallelogram, the shape has to fulfill one of the following standards:
It has two pairs of parallel contrary aspects.It has pairs of the same opposite angles.It has two pairs of equal and parallel contrary facets.Its diagonals bisect each other.Learn more about parallelogram here: https://brainly.com/question/970600
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which number is between -30 and 025
A. negative square root of 1610
B. negative sqare root of 680
C. negative square root of 410
D. negative square root of 27
sqrt(1610) = 40.12 = -40.2
sqrt(680) = 36.08 = -36.08
sqrt(410) = 20.25 = -20.25
sqrt(27) = 5.20 = -5.20
is that supposed to be 025 or negative 25?
the way the question is written
the answer is C & D
Lori purchases a new set of watercolor paints and some canvases to create art for her next exhibit. The watercolor paint set costs $15 and the canvases are $24.50 each. If Lori buys 6 canvases, what is the total amount of money she spends for her next exhibit?
A $211.00
B $162.00
C $237.00
D $147.00
The answer is B.) $162.00
Bella's score on a spelling test is a function of the number of hours she studies. Which expression represents Bella's score on a spelling test if she studies for 3 hours?
A. 3(score)
B. Score(3)
C. Score + 3
D. 3 - score
Answer:
B. Score(3)
Step-by-step explanation:
Given,
Bella's score on a spelling test is a function of the number of hours she studies.
Let x represents the number of hours and S represents her score after x hours,
Thus, her scoring after x hours = S( x )
If she studies for 3 hours,
That is, x = 3,
Then her score would be S(3) or we can say that score(3).
Hence, option 'B' is correct.
What operation does the power 1/2 represent? Can you think of operations that other fractional powers represent, such as 1/3, 1/4 and 2/3?
Which expression has an estimated product of 45?
Answer with explanation:
We have to find that expression , which has an estimated product of
1.→44.7 x 2.1
2.→7.5 x 8.4
3.→8.7 x 5.28
4.→38.1 x 7.3
We will start from option 1.
→44.7 x 2.1
44.7 when estimated to nearest tenth=45
2.1, when estimated to nearest tenth=2
44.7 × 2.1=45×2=90
Option 2
7.5 x 8.4
7.5 when estimated to nearest tenth=8
8.4, when estimated to nearest tenth=8
⇒7.5 × 8.4=8×8=64
Option 3
8.7 × 5.28
8.7, when estimated to nearest tenth=9
5.28, when estimated to nearest tenth=5
⇒8.7 × 5.28=9×5=45
Option D
38.1 × 7.3
38.1 when estimated to nearest tenth=38
7.3, when estimated to nearest tenth=7
⇒38×7=266
Option C:⇒8.7 × 5.28 has an estimated product of 45