we know that
The volume of the ball (sphere) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
In this problem we have
[tex]V=4.19\ in^{3}[/tex]
Find the radius of the sphere
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Substitute the value of V
[tex]r=\sqrt[3]{\frac{3*4.19}{4\pi}}=1\ in[/tex]
for the calculation of the total volume I will assume that each ball is a cube
The volume of each ball is
[tex]V=b^{3}[/tex]
where
b is the diameter of the ball
[tex]b=1*2=2\ in[/tex]
Substitute
[tex]V=2^{3}=8\ in^{3}[/tex] ------> volume of each ball in the shape of cube
so
Multiply by [tex]64[/tex]
[tex]64*8=512\ in^{3}[/tex]
therefore
the answer is
[tex]512\ in^{3}[/tex]
Which of the following represents 6 x to the 3 fourths power in radical form?
Answer:
[tex]\\ 6x^{\frac{3}{4}} = 6\sqrt[4]{x^{3}}[/tex]
Step-by-step explanation:
When a number is raised to a rational number like [tex]\\ {\frac{3}{4}}[/tex], that is, a fraction, the denominator represents the index of the radical (or commonly known as the root nth of the radical), and the numerator represents the number to which the radicand (the part of the expression inside the radical sign) is about to be raised.
Looking at [tex]\\ 6x^{\frac{3}{4}}[/tex], the index (root) of the radical is 4 and the numerator raises the value of x to the third power, that is, [tex]\\ x^{3}[/tex]. That explains the answer: six (6) times [tex]\\ \sqrt[4]{x^{3}}[/tex]. The six (6) only multiplies the expression.
Likewise, a radical of index 5, with a radicand [tex]\\ (x + 8)[/tex] raised to the ninth power is represented by [tex]\\ \sqrt[5]{(x + 8)^{9}}[/tex], which is equivalent to [tex]\\ (x+8)^{\frac{9}{5}}[/tex].
By the way, a particular case is when the index is 2, that is, [tex]\\ x^{\frac{1}{2}}[/tex]. Here, the number 2 is omitted from the radical symbol and is represented by [tex]\sqrt{x}[/tex].
Find the value of the 100th and 1000th term in the sequence { 3,-5,7,-9,...}
Paul will pay for his new car in 36 monthly payments.if his car loan is for $19,061,then about how much paul will pat each month? Round your answer to the nearest cent if necessary.
Paul will pay approximately $529.47 each month for his new car.
Explanation:To calculate how much Paul will pay each month for his new car, we need to divide the total car loan amount by the number of monthly payments. In this case, the car loan is $19,061 and the number of payments is 36. So, the monthly payment can be calculated as:
Monthly payment = Car loan amount / Number of payments
Substituting the given values, we get:
Monthly payment = $19,061 / 36
Running this calculation, we find that Paul will pay approximately $529.47 each month for his new car, rounded to the nearest cent.
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ramon has a rope that is 25 1/2 feet long. he wants to cut it into 6 pieces that are equal in length. how long will each piece be?
Tati suffered severe stroke damage near the rear of both sides of her brain. She is now unable to perceive
Write an equation for a line perpendicular to y = 2 x + 5 y=2x+5 and passing through the point (-6,1)
Boat takes 3 hours to go 6 miles upstream. it can go 18 miles downstream in the same time. find the rate of the current and the rate of the boat in still water
Which equation shows y = − 12x +4 in standard form?
A. x + 2y = 8
B. 2x + y = 8
C. x + 2y = − 8
D. 2x − y = 8
Answer: The equation that shows y=-(1/2)x+4 is standard form is x+2y=8
Option A. x+2y=8
Solution:
y=-(1/2)x+4
Standard form of the equation Ax+By=C, with A, B, and C integer numbers
The coefficient of x is a fraction. To simplify the fraction, let's multiply both sides of the equation by 2:
2y=2 [ -(1/2)x+4]
2y=-2(1/2)x+2(4)
2y=-(2/1)(1/2)x+8
2y=-[(2*1)/(1*2)]x+8
2y=-(2/2)x+8
2y=-1x+8
2y=-x+8
The two variables must be on the left of the equation, then adding x both sides of the equation:
2y+x=-x+8+x
x+2y=8
This is you correct answer
A line passes through (−1, 7) and (2, 10).
Which answer is the equation of the line?
−3x+y=4−3x+y=4
−3x+y=16−3x+y=16
−x+y=8−x+y=8
−x+y=12
How do you write algebraic expressions to model quantities?
Algebraic expressions to model quantities
A businessman produces x Biscuits made up of wheat and rice daily, and another Business person produces y Snacks made up of vegetables daily.There is another person who manufactures z , drinks daily.Find total number of Biscuit,snack and Drink produced after 8 days.
So, Algebraic Expression will be
=8 x+8y+8z
As, there are three terms,so we call it Trinomial Expression.
the length of a rectangle is 2 cm less than 7 times the width. the perimeter is 62 cm. find the length and width
Factor this expression completely and then place the factors in the proper location on the grid.
ab + 2a + 3b + 6
Answer:
This was a little confusing. I had trouble getting the right answer, but it is all there. It was (a+3) *(b+2) for me.
Thanks BenjaminG123
If y varies inversely as x, and y = 10 as x = 7, find y for the x-value of 10.
Whats 0.87 repeating as a fraction?
If 5 people share 1 2 pound of jelly beans equally, what amount will each person receive?
1/10.
Hope this helps!
A small school has 55 students. if 10 of the students are boys what is the ratio of girls to boys
Type the domain and range values for the corresponding variables that make these relations inverses of each other.
Answer:
The domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0
Step-by-step explanation:
Consider the provided table:
The domain of the function becomes the range of the inverse function and the range of the function becomes the domain of the inverse function.
Now consider Figure 1:
The x value of table 1 becomes the y value of table 2 and the y value of table 1 becomes the x value of table 2.
Therefore, the domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0
1) One equation of a system of equations is 5x + 2y = 10. What is the second equation such that the system is independent?
A) x = -2/5y + 2
B) y = -5/2x + 15
C) y = 5/2x + 5
D) y = -5/2x + 5
2) What is the equation of y = |x| translated 1 unit up and 6 units to the left?
A) y = |x + 6| + 1
B) y = |x – 1| + 6
C) y = |x – 6| + 1
D) y = |x + 1| + 6
3) Which statement describes the relationship between the graph of the equation
y=|x/2| and the graph of the equation y=|x/2| +4 ?
A) The graph of y=|x/2| was shifted 4 units to the right.
B) The graph of y=|x/2| was shifted 4 units to the left.
C) The graph of y=|x/2| was shifted 4 units up.
D) The graph of y=|x/2| was shifted 4 units down.
Answer all questions and please show work :)
What are some prime numbers between 80 and 90?
How would you solve 5x+3y=12 by graphing it?
A 10 foot ladder reaches a window 8 feet above the ground, how far from the wall is the base of the ladder
To find the distance from the wall to the base of the ladder, use the Pythagorean theorem. The distance is 6 feet.
Explanation:To find the distance from the wall to the base of the ladder, we can use the Pythagorean theorem. The ladder, the ground, and the wall form a right triangle. Let's call the distance from the wall to the base of the ladder x. According to the Pythagorean theorem, the square of the ladder's length (10 feet) is equal to the sum of the squares of the distances from the base of the ladder to the wall (x) and the height of the window (8 feet).
x^2 + 8^2 = 10^2
Simplifying the equation, we get:
x^2 + 64 = 100
Subtracting 64 from both sides:
x^2 = 36
Taking the square root of both sides:
x = 6
Therefore, the distance from the wall to the base of the ladder is 6 feet.
Inequalities:
The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus $55 for an assistant. The committee wants to keep the total cost under $555. What is the maximum amount of hours the DJ will play at the dance?
The maximum amount of hours the DJ will play at the dance is 4 hours.
Explanation:To find the maximum amount of hours the DJ will play at the dance, we need to set up an inequality. Let x represent the number of hours the DJ will play. The total cost is given by $125 per hour plus $55 for an assistant, so the cost function is C(x) = 125x + 55. We want the total cost to be less than or equal to $555, so the inequality is 125x + 55 ≤ 555.
To solve this inequality, we need to isolate x. First, subtract 55 from both sides to get 125x ≤ 500. Then, divide both sides by 125 to get x ≤ 4. Therefore, the maximum amount of hours the DJ will play at the dance is 4 hours.
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What are the coordinates of the vertex of the graph of f(x)=−3|x−1|?
Number 19. Answer to number 19) the figure shows a game...
1. If you want to create a cone or cylinder by spinning a 2–dimensional shape about an axis of symmetry, what shapes would you need to use?
2. Describe how the volume formulas for a cone, cylinder and pyramid derived. What are the similarities between the volume of a cone and pyramid?
3. What is the relationship between mass, density and volume? Provide and example that involves calculating population density.
4. Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes (prisms, cylinders, cones and spheres) will affect the volume of these shapes.
5. The concept of volume is something you experience everyday in your life. Provide a specific example in which you could solve a real-world application using volume
Answer: if a cone and a cylinder have the same base and same height then the volume of the cone is the volume of the cylinder.
Step-by-step explanation: its right edge 2021
Jessica made 2 pounds of fudge. How many 1/6 -pound servings are in the 2 pounds of fudge?
Using the knowledge of fractions, the number of 1/6-pound servings in 2 pounds of fudge is: 12.
What are Fractions?Fractions are numbers that represent part of a whole number. They have a denominator and a numerator.
The fraction of a pounds servings is given as 1/6.
Therefore, number of 1/6 pound servings in 2 pounds of fudge would be:
2 ÷ 1/6 = 2 × 6/1 = 12.
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GUYS PLEASE HELP QUICK I'M OFFERING 10 PTS AND BRAINLIEST ANSWER
the length of a rectangle is twice its width. The area of the rectangle is 32 square feet. what are the length and width? which equation models this problem?
A) 32w = 2w + w
B) w - 2w = 32
C) 2w x w = 32
D) 2w+w = 32
Find the slope of the line.
Write the following in scientific notation:
1) 12 756 =
2) 116 464 =
3) 142 984 =
4) 1 392 000 =
5) 59 770 000 =
6) 903 500 000 =
7) 2 644 800 000 =
fifteen more than half a number is 9