The formula for a solid sphere is V = 4/3πr³
A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. It is a group of points in three dimensions that are all situated at the same r-distance from one another. The supplied point is the sphere's centre, while the letter r stands for the sphere's radius. It has a spherical, symmetrical shape.
It is a three-dimensional solid with equal distances between each surface point and the centre. On the basis of its radius, it has a surface area and a volume. There are no faces, corners, or edges on this geometrical figure. The formula for a solid sphere is V = 4/3πr³. Here V is the volume of the shape and r is the radius of the shape.
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a) what additional info is needed to prove the triangles are congruent by ASA postulate, explain.
b) what additional info is needed to prove the triangles are congruent by the HL theorem, explain.
Answer:
See below
Step-by-step explanation:
A) If [tex]DF\cong GH[/tex], then both triangles will be congruent by the ASA postulate
B) If [tex]DE\cong GI[/tex], in addition to one of the corresponding leg pairs being congruent to each other (so EF+IH or DF+GH), then the triangles will be congruent by the HL theorem
For a project in her Geometry class, Aria uses a mirror on the ground to measure the height of her school building. She walks a distance of 11.45 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.25 meters to the other side of the mirror, until she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answer = 10.53m
The height of the school building is approximately 9.69 meters or 10.53 meters (rounded to the nearest hundredth).
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the studies of relationships between angles and sides of triangles.
Let's denote the height of the school building as "h".
From the given information, we can draw a right triangle with the mirror on the ground, the top of the school building, and Aria's eyes as the vertices. The distance from Aria to the mirror is 1.25 meters, and the distance from the mirror to the school building is the unknown height "h". The distance from Aria's eyes to the mirror is 1.15 meters.
We can use similar triangles to set up an equation to solve for "h".
In the smaller triangle formed by Aria's eyes, the mirror, and the point directly below the top of the school building, we can see that:
h/1.25 = (h + 1.15)/11.45
This equation comes from the fact that the ratios of corresponding sides in similar triangles are equal.
Simplifying this equation gives us:
1.45h = 14.06875
Dividing both sides by 1.45 gives us:
h ≈ 9.6931
Hence, The height of the school building is approximately 9.69 meters or 10.53 meters (rounded to the nearest hundredth).
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write an expression that represent dived 0.04 by n
The expression that refers the operation "0.04 divided by n" is written as 0.04/n
An expression is a mathematical statement that contains operators, variables, and constants.
In this case, we want to write an expression that will represent the division of 0.04 by n.
The expression for this would be 0.04/n, where n is the number being divided by 0.04.
This expression shows that when 0.04 is divided by n, the result is 0.04 divided by n.
The expression can be used to calculate the result of any division problem involving 0.04 and n
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HELP PLSSS ineed all of these!!!!!!!
The unknown variables in parallelograms above include the following:
x = 8 units.
y = 27 units.
x = 20°
x = 9°
What is a parallelogram?In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
In this context, we have:
2x - 5 = 11
2x = 11 + 5
2x = 16
x = 8 units.
y + 1 = 28
y = 28 -1
y = 27 units.
Generally speaking, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:
(7x - 1)° = 139°
7x = 139° + 1°
7x = 140°
x = 140/7
x = 20°
For parallelogram b, we have:
(7x - 10)° = (6x - 1)°
7x - 6x = -1 + 10
x = 9°
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what is 3 to the 2 power?
The equivalent to the expression 3², which equals 9.
An exponent is a mathematical operation that involves raising a number to a certain power. In this case, you are curious about what 3 to the 2 power means. Let's explore this concept further.
When we write 3 to the 2 power, it means that we are multiplying 3 by itself two times. This can also be written as 3 raised to the power of 2, which is represented by the notation 3².
To illustrate this concept, let's use an example. Consider the expression 3². This means that we need to multiply 3 by itself twice, as indicated by the exponent of 2. In other words:
3² = 3 x 3 = 9
So, 3 to the 2 power is equal to 9. Another way to think about this is to imagine a square with sides of length 3. The area of this square would be 3 x 3, or 9.
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What is the surface area of the right rectangular prism?
Enter your answer in the box.
ft²
8 ft
18 ft
7 ft
Why is x = y2 - 9 not a function?
because y=3 has 2 corresponding x-values
because y = 0 has 2 corresponding x-values
because x = 0 has 2 corresponding y-values
because x = -9 has 2 corresponding y-values
Answer:
Step-by-step explanation:
The statement "x = y² - 9" is not a function because for some values of y, there are multiple corresponding values of x.
What is a Function ?A relation between a set of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
Now in the given question ,
In particular, when y = 3, there are two possible values of x (x = 0 and x = 6), so (3, 0) and (3, 6) are two points on the graph of this equation. This violates the definition of a function, which states that for each input (in this case, y), there can only be one output (x). The other statements are not relevant to determining whether the equation is a function.
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What is the end behavior of the polynomial
Answer:
As x --> ∞, then y --> - ∞
Step-by-step explanation:
As the value of x increases(as the graph goes right), the graph seems to go down, meaning the y-values are getting more an more negative. This means that as x approached infinity, the y values approach negative infinity ( x --> ∞, y --> - ∞ ).
As the value of x decreases(going to the left), the graph seems to go higher and higher. Therefore, as x approaches negative infinity, the y-value approach infinity. ( x --> - ∞, y --> ∞ )
Out of the options given, the one As x --> ∞, then y --> - ∞ is true.
Select all equations that are true. A. 3/4 − 1/2 = 1/4 B. 9/16 − 4/8 = 5/8 C. 7/8 − 3/4 = 1/8 D. 7/15 − 1/3 = 6/15 E. 1/2 − 1/20 = 10/20
The correct expression after subtraction is,
⇒ 7/8 - 3/4 = 1/8
Option C is true.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We can all the expressions as,
A). 3/4 - 1/2 = 1/4
LHS;
⇒ 3/4 - 1/2
⇒ (6 - 4) / 8
⇒ 4/8
⇒ 1/2 ≠ 1/4
Hence, It is not true.
B. 9/16 - 4/8 = 5/8
LHS;
⇒ 9/16 - 4/8
⇒ (9 - 8)/16
⇒ 1/16 ≠ 5/8
Hence, It is not true.
C. 7/8 − 3/4 = 1/8
LHS;
⇒ 7/8 - 3/4
⇒ (7 - 6)/8
⇒ 1/8
Hence, It is true.
D. 7/15 − 1/3 = 6/15
LHS;
⇒ 7/15 - 1/3
⇒ (7 - 5)/15
⇒ 2/15 ≠ 6/15
Hence, It is not true.
E. 1/2 − 1/20 = 10/20
LHS;
⇒ 1/2 - 1/20
⇒ (10 - 1)/20
⇒ 9/20 ≠ 10/20
Hence, It is not true.
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Jim is 4 more than twice the age of his
cousin Mark. If the sum of their ages is
34. How old is Jim?
Answer:
24 years old
Step-by-step explanation:
Jim = 2x + 4
Mark = x
Sum of their ages = 34
2x + 4 + x = 34
2x + x = 34 - 4
3x = 30
3x / 3 = 30 / 3
x = 10
Mark = 10 years old
Jim = 2x + 4
= 2 ( 10 ) + 4
= 20 + 4
= 24
Therefore, Jim is 24 years old
Instructions & Problem in picture
What are the three double angle identities?
The three double-angle identities are :
1.[tex]$\cos(2\theta) = \cos^2\theta - \sin^2\theta$[/tex]
2. [tex]$\sin(2\theta) = 2\sin\theta\cos\theta$[/tex]
3. [tex]$\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}$[/tex]
The three double angle identities are equations that relate the cosine, sine, and tangent of twice an angle to the cosine, sine, and tangent of the original angle. these identities are useful in trigonometry, as they make it possible to express a double angle in terms of its simpler angle components.
The first identity states that the cosine of twice an angle is equal to the square of the cosine of the original angle, minus the square of the sine of the original angle. the second identity, states that the sine of twice an angle is equal to twice the product of the sine and cosine of the original angle.
The third identity states that the tangent of twice an angle is equal to twice the tangent of the original angle, over one minus the square of the tangent of the original angle,
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Draw in all lines of symmetry in the shape below. If there are no lines of symmetry, submit an answer without drawing them in.
It should be noted that the line of symmetry for the shape will be 5.
What is a line of symmetry?A line of symmetry is a line that divides a shape into two congruent parts that are mirror images of each other. In other words, if you fold the shape along the line of symmetry, the two halves will perfectly overlap.
Here are some examples of shapes and their lines of symmetry:
Square: A square has four lines of symmetry, which are the vertical, horizontal, and two diagonal lines.
Rectangle: A rectangle has two lines of symmetry, which are the vertical and horizontal lines.
Circle: A circle has an infinite number of lines of symmetry, because you can draw a line through the center in any direction.
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Ernesto measured a house and its lot and made a scale drawing. The scale of the drawing was 5 inches : 6 feet. The house's driveway is 35 inches long in the drawing. How long is the actual driveway?
With the provided scale, the driveway's true length is 7/6 feet, and 1 and 1/6 feet.
Inch Calculator: What is It?The height of any unit can be converted to inches using the free online tool known as an inch calculator. Both inches and centimetres are units used to measure length; inches are abbreviated as "in" and centimeters as "cm".
To determine the real length of the driveway, we can use the provided scale.
The scale indicates that 5 inches just on illustration corresponds to 6 feet in everyday life.
Now, let's change 35 inches just on picture to feet:
35 inches / 5 inches for every 6 feet equals 7/6 feet.
The driveway is therefore 7/6 feet in length in actuality. We can condense.
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Help me with this question please
The coordinate of point C which is 7 / 8 of the distance from M to J is 16 .
How to find the coordinates ?The first step is to find the distance between M and J to be :
= Coordinate of J - Coordinate of M
= 18 - 2
= 16
The distance that is 7 / 8 between M and J is :
= 16 x 7 / 8
= 14
The coordinate of C would be :
= Coordinate of M + 7 / 8 distance
= 2 + 14
= 16
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What is the domain and range of R(c)
The domain of the function; R (c) as required is; [0, 150].
The range of the function; R (c) as required is; [0, 450].
Which intervals represent the domain and range of the function?As evident in the task content; the given function is; R (c) = 3c and the class has a maximum of 150 bags to sell.
In Essence, the possible values of c are such that; 0 ≤ c ≤ 150.
The domain is therefore; [0, 150].
Hence, the range is; 3(0) ≤ R(c) ≤ 3(150).
Ultimately, the range of the function is; 0 ≤ R (c) ≤ 450.
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Please help me for 30 points!!.
Answer: Correct option is B
Step-by-step explanation: 3/6 + 2/6 = 5/6
What would the location of the 83 percentile be for a data set with 40 observations? Click the answer you think is right. 33.20 34.03 40.00 32.00
The location of the 83rd percentile for a data set with 40 observations would be 34.03.
What is data?Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.
A percentile is a value on a scale of one hundred that indicates the percentage of a distribution that is equal to or below it. For example, the 83rd percentile for a data set with 40 observations would indicate that 83% of the observations in the data set are equal to or less than 34.03. To calculate the location of a given percentile, the formula is (p/100) * n, where p is the given percentile and n is the total number of observations. Therefore, for a data set with 40 observations and an 83rd percentile, the formula would be (83/100) * 40 = 33.2, which would be rounded up to 34.03.
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Please help what’s the answer for what the question is asking me
Answer:
Unit rate = 0.6
y = 0.6x
x= 24
Step-by-step explanation:
I cannot see the headings to the table, but on examining the questions, the first column contains the values for variable x and the second column the values for variable y
Unit Rate
Unit rate = increase in y for a unit increase in x
We see that the rate is constant for every unit increase in x and is = 0.6
Unit rate = 0.6
Equation
The equation therefore is y = 0.6x
Value of x when y = 14.4
When y = 14.4, plugging into the equation gives:
14.4 = 0.6x
or
0.6x = 14.4 by switching sides - no effect on equation
Divide both sides by 0.6
0.6x/0.6 = 14.4/0.6
x= 24
Describe all solutions of Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix.[1−3−85012−4][1−3−85012−4]
The parametric vector form of the matrix is AX = < t 0 3/5t> where t is any real number.
Matrices are an important mathematical tool that can be used to represent and solve a wide array of problems.
In this problem, we are given a matrix A, which is row equivalent to the given matrix [1 -3 -8 5 0 12 -4] and asked to describe all solutions of Ax = 0 in parametric vector form.
To answer this question, we first need to use row operations to transform the given matrix into row-echelon form. After applying row operations, the matrix becomes [1 0 -5/3 0 2/3 0 1].
We can now use this matrix and the equation Ax = 0 to identify the solutions in parametric vector form.
The first column of the matrix has a coefficient of 1, indicating that x₁ is free and can take on any real value.
The second column has a coefficient of 0, indicating that x₂ = 0.
The third column has a coefficient of -5/3, indicating that x₃ = 3/5t, where t is a real number.
Then the resulting vector form is written as,
=> AX = < t 0 3/5t> where t is any real number.
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how do I do this step by step?!
Answer:
[tex]2x^{2}[/tex] + [tex]2x[/tex] + [tex]2[/tex]
Step-by-step explanation:
1. In the expression: C - 3D, we plug in the values of C and D
2. So we get the expression: [tex](2x^{2} + 5x -1) - 3(x - 1)[/tex]
3. Then we simplify this even more: [tex](2x^{2} + 5x -1) - (3x + 1)[/tex] by multiplying 3 to the numbers in the parentheses
4. Now we can remove the parentheses: [tex]2x^{2} + 5x - 1 - 3x + 3[/tex]
5. Now we can put the like terms next to each other: [tex]2x^{2} + 5x - 3x + 3 - 1[/tex]
6. FINALLY we simplify: [tex]2x^{2} + 2x + 2[/tex]
Hope this helps! <3
The functions below represent the cost some homeowners pay for water and sewer usage. This is based on the number of 100-gallon units
of water used, defined by x.
Water usage: W(x) = 0.129x
Sewer usage: S(x) = 0.158x + 16.22
Based on this information, approximately what is the total amount a homeowner will pay if the water and sewer usage for one month is 3800
gallons?
A. $10.91
B. $21.12
C. $27.13
D. $43.35
Since the given functions represent the cost for water and sewer separately, the total cost will be the sum of both.
For water usage, W(x) = 0.129x, where x is the number of 100-gallon units of water used. So, for 3800 gallons, we have:
W(x) = 0.129 * (3800/100) = $4.91 (rounded to the nearest cent)
For sewer usage, S(x) = 0.158x + 16.22, where x is the number of 100-gallon units of water used. So, for 3800 gallons, we have:
S(x) = 0.158 * (3800/100) + 16.22 = $21.12 (rounded to the nearest cent)
Therefore, the total amount a homeowner will pay for 3800 gallons of water and sewer usage for one month is:
Total cost = W(x) + S(x) = $4.91 + $21.12 = $26.03 (rounded to the nearest cent)
So, the closest answer choice is C. $27.13.
8 chairs for every 2 desks, how many chairs for 5 desks?
Answer:
Step-by-step explanation:
40 desks
how to convert 0.5625 as a fraction?
The value 0.5625 as a fraction is 9/16 .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
.5625*100/100 = 9/16
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scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what is the minimum score you would need to be in the top 7%?a. 0.93b. 1.48c. 85.4d. 81.4
Answer:
I don’t understand
Step-by-step explanation:
I had the same one
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
help me...
Use a linear model to predict the amount of jet fuel that is present on the Jet after it has been in flight for 18 hours without stopping to refuel. In two or more complete sentences, explain your answer.
The maximum distance as function of the quantity of gallons of gasoline the required expression is: x = 0.2272 . n
What is distance?Distances between two things or places can sometimes be measured qualitatively and sometimes quantitatively. A physical length or an estimate based on other criteria might be referred to as distance in physics or everyday language. The entire movement of an item, independent of direction, is called distance. No matter where an item starts or ends, distance may be described as the amount of ground it has covered.
The maximum distance as function of the quantity of gallons of gasoline is estimated by the following linear model:
x = (14,430 km / 63500 gallons) . n
Finally, the required expression is:
x = 0.2272 . n
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Show the ratios are equivalent by simplifying any 4 of them.
The ratios are equivalent by simplifying is shown below.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
We have first ratio 3:1
and, second 6:2 on simplifying we get 3:1.
and, third 9: 3 on simplifying we get 3:1.
and, Fourth 12:4 on simplifying we get 3:1.
So, all the ratio gave same value on Simplification which shows the ratios are Equivalent.
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One important use of the regression line is to do which of the following? a) To make predictions about the values of y for a given x-value. b) To determine the strength of a linear association between two variables. c) To determine if a distribution is unimodal or multimodal. d) Both A and B are correct.
A regression line is defined as an estimate of the line that describes the actual line, which is unknown. It represents a linear relationship between the two variables, that is the dependent and the independent variable.
In other words, the equation of the regression line is used to estimate the value of the dependent variable from a specified value of the independent variable.
Correlation coefficient is used to determine the strength of linear association between two variables, that is the dependent and the independent variable. (Correlation shows what kind of relation two variables have.)
Regression line's important use is to make predictions about the values of y for a given x-value.
Hence option a is correct.
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what is teh numpy matrix inverse?
The NumPy matrix inverse is a function that calculates the inverse of a given square matrix.
The NumPy matrix inverse function is a strategy that works out the opposite of a square grid involving the NumPy library in Python. The inverse of a matrix is a matrix that, when duplicated by the first grid, creates the identity matrix.
In NumPy, the matrix inverse function is executed as the linalg.inv() technique, which takes a NumPy cluster as information and returns its converse as an exhibit. The matrix should be square and invertible, the importance of its determinant isn't equivalent to nothing. The matrix inverse is utilized in different fields of math, designing, and science to solve systems of linear equations, track down the eigenvalues and eigenvectors of a network, and perform different procedure on matrices.
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Need help ASAP!! Struggling with these word problems... D:
You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively.
x + y + z = (total investment)
0.045x + 0.05y + 0.09z = (annual return)
2y − z = 0
Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.)
Total Investment Annual Return
$10,300 $620
The amount invested in AAA - bonds is $5353, amount invested in
A - bonds is $1681 and amount invested in B - bonds is $3369. The solution has been obtained by using matrices.
What are matrices?
The term "matrix of order m by n," sometimes known as "m × n matrix," refers to a rectangular array of m × n numbers (real or complex), organised into m rows and n columns.
Such a range is bounded by [ ] or ( ).
We are given equations as
x + y + z = $10300
0.045x + 0.05y + 0.09z = $620
2y − z = 0
From this, we get the matrix as
[tex]\left[\begin{array}{ccc}1&1&1\\0.045&0.05&0.09\\0&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]
This shows that AX = B
X = A⁻¹B
[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}2.42&-31.57&-0.42\\-0.47&10.52&0.47\\-0.94&21.05&-0.05\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}10300\\620\\0\end{array}\right][/tex]
On solving this, we get
[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] [tex]=\left[\begin{array}{ccc}5353\\1681\\3369\end{array}\right][/tex]
Hence, the amount invested in AAA - bonds is $5353, amount invested in A - bonds is $1681 and amount invested in B - bonds is $3369.
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