Answer: 216 small balls
Step-by-step explanation:
The volume of a ball:
[tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]
Let us calculate the volume of a big metallic ball:
[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]
Now let us calculate the volume of a big small ball:
[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]
Thus, the number of identical small balls should work:
[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]
[tex]\sqrt{x} 4=x-3[/tex]
The simplification of the given expression is x² - x + 3.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is √x⁴ = x - 3. The expression will be simplified as,
√x⁴ = x - 3
Solve the radical term first and simplify the expression further,
x² = x - 3
x² - x + 3 = 0
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A triangle has sides with lengths of 54 meters, 78 meters, and 90 meters. Is it a right
triangle?
The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ΔABC
Now , the value of the sides of the triangle is
AB = 54 m
BC = 78 m
AC = 90 m
Now , for the triangle to be right angle triangle , it should satisfy the Pythagoras Theorem
So , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substitute the values in the equation , we get
AC² = AB² + BC²
90² = 54² + 78²
8100 = 2916 + 6084
8100 ≠ 9000
Therefore , the triangle ΔABC is not a right angle triangle
Hence ,
The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle
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Harry's soccer team is trying to raise $2,520 to travel to a tournament in florida, so they decided to host a pancake breakfast. Each person must pay $15 for the breakfast. How many people need to attend their breakfast in order to raise $2520?.
Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
To find the number of people that need to attend the pancake breakfast, we can set up the following equation:
Number of People x Cost per Person = Total Cost
We know that the total cost is $2,520 and the cost per person is $15, so we can substitute those values into the equation:
Number of People x $15 = $2,520
We can solve for the number of people by dividing both sides of the equation by $15:
Number of People = $2,520 / $15
This gives us the number of people that need to attend the pancake breakfast in order to raise the desired amount of money. In this case, the number of people is 168.
Therefore, Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
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Find the missing measures in the parallelogram given below. Also, state the property used.
Answer:
see explanation
Step-by-step explanation:
AD = BC = 8 ( opposite sides of a parallelogram are congruent )
DC = AB = 15 ( opposite sides of a parallelogram are congruent )
Consecutive angles in a parallelogram are supplementary , sum to 180° , so
∠ A + ∠ D = 180° , that is
∠ A + 68° = 180° ( subtract 68° from both sides )
∠ A = 112°
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 68° , and
∠ C = ∠ A = 112°
dr. yung tests a new anti-malaria drug in an asian population and concludes that he cannot reject the null hypothesis, and must conclude he does not have sufficient evidence to conclude that the drug works. in reality, the drug does work. dr. yung has committed a error. group of answer choices logical type i (false positive) type ii (false negative) statistical
Dr. Yung has committed a type l ( false positive) error.
What is a type I error?Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).
A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),
Therefore, the error is a type 1 error.
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8. The speed of an object can be found by taking the distance it travels and dividing it by the
time it takes to travel that distance. An object travels 100 feet in 2.5 seconds Let the speed, be
measured in fleet per second. Write an equation to represent the relationship between the three
quantities (speed, distance, and time).
Speed of object = 40 feet per second
What is speed and its formula?Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar number.Based on the distance travelled in a certain amount of time. These automobiles can travel at speeds of more than 150 kilometres per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.Given data :
Distance cover by object = 100 feetTime taken by object = 2.5 secondsEquation represent speed is s = d/t
Assume;
Speed = S
Time taken = T
Distance cover = D
So,
Speed = Distance / Time
S = D / T
Speed of object = 100 / 2.5
Speed of object = 40 feet per second
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If d/dx (g(x)) = 0
then d/dx (g(x)sin(x)) = ?
Answer:
Step-by-step explanation:
If the derivative of g(x) with respect to x (denoted d/dx g(x)) is equal to 0, then the derivative of the product g(x)sin(x) with respect to x can be found using the product rule for derivatives.
The product rule states that if f(x) and g(x) are two functions, then the derivative of the product f(x)g(x) with respect to x is given by:
d/dx (f(x)g(x)) = f(x) * d/dx g(x) + g(x) * d/dx f(x)
In our case, f(x) is g(x) and g(x) is sin(x). Substituting these values into the equation above, we get:
d/dx (g(x)sin(x)) = g(x) * d/dx sin(x) + sin(x) * d/dx g(x)
Since the derivative of sin(x) with respect to x is cos(x) and the derivative of g(x) with respect to x is 0, we can simplify this expression to:
d/dx (g(x)sin(x)) = 0 * cos(x) + sin(x) * 0
Which simplifies to:
d/dx (g(x)sin(x)) = 0
Therefore, if the derivative of g(x) with respect to x is equal to 0, then the derivative of the product g(x)sin(x) with respect to x is also equal to 0.
How do you find the missing value in an isosceles triangle?
Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .
the sum of triangle is 180, sum of all the interior angles is equal to 180.
so if you know two angles then apply sum of triangles and find out the value of the third triangle.
isosceles triangle
An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.
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5 dogs had long hair out of the 8 dogs at the park. What percent of the dogs had long hair? Round your answer to the nearest whole percent.
Answer:
62.5%
Step-by-step explanation:
5/8 × 100
should give you 62.6%
How many points lie on a line?
Ridgid motions to prove
Answer:
Sequence:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]
. . . . . . . . . . ⭐ please take a ruler and measure the distance from AA', . . . . . . . . BB', CC', DD', and EE', and then write that distance (it should . . . . . . . . be the same for each measurement) in place of 5 in -5. I just . . . . . . . . wrote -5 because it was my best approximation for looking at . . . . . . . . a laptop screen. ⭐
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]
Step-by-step explanation:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.
How do you describe the relationship of the volume between the volume of a sphere and the volume of a cylinder?
The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.
In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.
Consider a cylinder with radius r and height h.
we know that the formula for the volume of cylinder is,
V1 = π * r² * h
Consider a sphere with radius r1.
We know that the formula for the volume of sphere is,
V2 = 4/3 * π * r1³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r
V2 = 4/3 * π * r³
And V1 = π * r² * (2r)
V1 = 2 * π * r³
V1 = 2 * 3/4 * V2
V1 = 3/2 * V2
volume of cylinder = 3/2 * volume of sphere
Therefore, the volume of a sphere = 2/3 * the volume of a cylinder
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how do I convert 5 rows of ribbons to inches
You may use the expression to convert the length of 5 rows of ribbons to inches: length = 5w + (5 - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.
To convert 5 rows of ribbons to inches, you need to know the width of the ribbons and the spacing between the rows.
Let's say the width of the ribbons is w inches, and the spacing between the rows is s inches. In this case, the total length of the ribbons in 5 rows would be 5w + 4s inches, since there are 5 ribbons and 4 spaces between them.
For example, if the width of the ribbons is 0.5 inches and the spacing between the rows is 0.1 inches, the total length of the ribbons in 5 rows would be :5 × 0.5 inches + 4 × 0.1 inches = 2.5 inches + 0.4 inches = 2.9 inches.
In general, to convert the length of n rows of ribbons to inches, you can use the formula: length = nw + (n - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.
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How to find duplicate numbers in an array if it contains multiple duplicates?
The pigeonhole principle can be used to demonstrate that there must be at least one duplicate in the set nums. Each possible number that can appear in nums is a "pigeonhole" in this context, and each number within nums is a "pigeon."
Method or evidence to confirm that Nums must contain multiple duplicate number: Simple Strategy: Utilizing nested loops, it is intended to determine whether or not each element appears in the array more than once for each element.
Put it in a hash-map if it is there. Otherwise, keep looking at the other components.Duplicate data might be valuable in some situations, but it can also make your data more difficult to analyze.Find and highlight duplicate data using conditional formatting.You can then examine the duplicates and determine whether you wish to eliminate them.The duplicate data will be permanently removed when you use the Remove Duplicates functionality. It's a good practice to copy the original data to another worksheet before deleting the duplicates so you don't unintentionally lose any data.Choose the range of cells where the duplicate values should be eliminated.To remove duplicates, select Data, and then Check or uncheck the columns you want to have the duplicates removed from under Columns.Learn more about duplicate number Visit: brainly.com/question/15323323
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What is the relation between area height and volume?
The relation between area, height and volume is: volume = area * height
In this question we need to find the relation between area height and volume.
the formula for area and volume are based on height:
volume = base area * height
Let v represents the volume, A represents area and h represents the height.
V = A * h
As we know the volume of rectangular prism is:
volume = length * width * height
i.e., V = l * w * h
and the base area is:
area = length * width
i.e., A = l * w
Substitute A = l * w in V = l * w * h
Then we get, V = A * h
Therefore, the relation between area, height and volume is: V = A * h i.e., volume = area * height
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Which is a discontinuous process?
The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.
The function is an expression or law that defines a relationship between one variable and the independent variable and another variable the dependent variable
The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control
Some examples of a discontinuous function
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
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A relationship between one variable, the independent variable, and another variable, the dependent variable, is defined by an expression or law known as the function.
The variable being controlled in the problem is the independent variable, and the variable that changes as a result of this control is the dependent variable.
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
I really need help on this page, could anyone help me?
F=9/5C+32 is the required equation and Greg statement is true
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.
C=5/9(F-32)
We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.
F=9/5C+32
The temperature where John leaves has 77 F.
Let us convert to celsius.
C=5/9(77-32)
C=5/9(45)
C=5(5)
C=25 degrees.
25 degress< 30 degrees.
Hence, F=9/5C+32 is the required equation and Greg statement is true.
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What are binomials give five examples?
"A binomial is an algebraic expression which has exactly two terms." The examples of binomials are x² + 3, x + y, x³ + 2x, 9 + 7y, xy² + xy, etc.
A polynomial is of various types like monomial, binomial, trinomial, etc.
Monomial contains only single term.
Trinomial contains exactly three terms. All the three are dissimilar.
A binomial is said to have only positive exponents and no negative exponents.
In x³ + 2x, x³ and 2x are two different terms. The variable is only x. The exponent of x³ is 1, the exponent of x is 1. The coefficient of x³ is 1, the coefficient of x is 2.
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Calculate the approximate degree measure of the angle, given the following expression: cos(y°) = -0.10 Round your answer to the nearest tenth.
Answer:
y ≈ 95.7°
Step-by-step explanation:
To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.
Inverse of tan(y°) = 4.12:
[tex]tan^{-1}(-0.10) = y[/tex]
Next, I used a scientific calculator to find the angle measure of y. I recommend using the Desmos Scientific Calculator.
[tex]95.7 = y[/tex]
Need Help With This Question
(The table represents an exponential function) ( what is the multiplicative rate of change of the function) - the question( picture below)
Answer:
A. [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
⭐ What is the multiplicative rate?
The multiplicative rate is the number each consecutive y-value gets multiplied by.The multiplicative rate can only be found in exponential functions.To find the multiplicative rate of this exponential function, we need to make an equation to see what each y-value gets multiplied by to get the next y-value.
I am picking the y-values 2 and 2/5, but you can choose any two consecutive y-values.
Equation (let x= the multiplicative rate of change):
[tex]2x = \frac{2}{5}[/tex]
Solve for x:
[tex]\frac{2x}{2} = \frac{2}{5}(2)[/tex]
[tex]x = \frac{2}{10}[/tex]
Simplify:
[tex]x = \frac{1}{5}[/tex]
∴ The multiplicative rate of change of the function is 1/5.
What are the 3 lengths of a right triangle?
True or false math. Make sure you are correct though. Thank you!
Answer:
True
Step-by-step explanation:
Most of the function f(x) has the domain is (- infinity, positive infinity), So I think this is true!
In a survey of 118 randomly selected gun owners, it was found that 81 of them said they owned a gun primarily for protection.
Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Report answers to at least 2 decimal places.
Margin of Error (as a percentage)
The margin of error is 0.086 and its C.I is (0.575 , 0.785).
What is margin of error?
Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.n = 117 , x =87
Point estimate for the proportion:
P = x/n
= 81/118
= 0.68644
Confidence = 95%, α = 0.05
From z-table area 0.975 close to z=1.96
Margin of error, E = 1.96 √((0.68*0.55)/130)
= 1.96 * 0.05363
= 0.105
= 0.086
Confidence = P ± E
= 0.68 ± 0.105
=(0.68-0.105 , 0.68+0.105)
= (0.575 , 0.785)
Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).
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Use the quadratic formula to solve x^2+3x-28=0
The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.
What are the solutions to the quadratic equation?The quadratic formula is expressed as;
x = (-b±√(b² - 4ac)) / (2a)
Given the equation;
x² + 3x - 28 = 0
a = 1b = 3c = -28Substitute the values of a, b, and c into the formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -3 ±√( 3² - ( 4 × 1 × -28) )) / (2×1)
x = ( -3 ±√( 9 - ( -112) )) / (2)
x = ( -3 ±√( 9 + 112 )) / (2)
x = ( -3 ±√( 121 )) / 2
x = ( -3 ± 11 ) / 2
x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2
x = -14/2, x = 8/2
x = -7, x = 4.
Therefore, -7 and 4 are the solutions to the equation.
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How do you store 3 values in one variable in Python?
My_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
Now, According to the question:
Create a list containing your 3 variables : my_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
How do I store multiple values in one variable Python?
append()
We use the append() method for this. You can use this to append single values to the list – value, list, tuple.
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What are the 3 steps in graphing linear inequalities in two variables?
The three steps for graphing linear inequalities are consists of solving the variables, plotting the points on graph and bound the region.
How to plot inequalities?while solving the inequalities of two variables the inequal sign are changed by equal sign for a certain time. After determining the unknown value, we plot the points on the XY axis.
why we use solid line or dashed line?while graphing the inequal variables the region that satisfy the inequality is bounded by solid line or dashed line depends on the inequal sign.
hence, we need to plot the linear inequalities on XY axis in three steps.
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I need help on this please someone answer me!
So basically for the first one do 14.0%x 4.6
Write the number 1. 8 in the form , using integers, to show that it is a rational number.
The number 1. 8 in the form a / b, using integers, to show that it is a rational number is 9 / 5 .
Note that the number 1.8 consists of two parts 1 and 0.8.
The decimal 0.8 can be written as the fraction is 8 / 10
Add these two numbers :
= 1 + 8 / 10
multiply and divide by 10
= 10 / 10 + 8 / 10
= 10 + 8 / 10
= 18 / 10
simplify the number
= 2 * 3 * 3 / 2 * 5
= 1 * 3 * 3 / 1 * 5
= 9 / 5
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Solve for x: 7x-22=3x+18
Answer:
x = 10
Step-by-step explanation:
7x-22=3x+18
4x -22 = 18
4x = 40
x = 10
is an integer.
Given that the value of lies between between 29 and 39 Write down the value of .
The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Given that the integers lie between the numbers 29 and 39. The numbers will be,
29, { 30,31,32,33,34,35,36,37,38 }, 39
Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.
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