The exponential of 16, also known as [tex]e^{16[/tex], is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 16.
To calculate e^16, we would use the following formula:
[tex]e^{16[/tex] = e x e x e x e x e x e x e x e x e x e x e x e x e = 8.222838 x [tex]10^6[/tex]
So, the exponential of 16 is approximately 8.222838 x [tex]10^6[/tex].
It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.
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use the distributive property to simplify the expression
1/2( 2n +4+6m)
Answer:
n + 2 + 3m
Step-by-step explanation:
[tex]\frac{1}{2} (2n+4+6m) = (\frac{1}{2}*2n)+(\frac{1}{2}*4)+(\frac{1}{2}*6m)\\ =n+2+3m[/tex]
When Angel left his house in the morning, his cell phone battery was partially charged. Let
B
B represent the charge remaining in Angel's battery, as a percentage,
t
t hours since Angel left his house. A graph of
B
B is shown below. Write an equation for
B
B then state the
x
x-intercept of the graph and determine its interpretation in the context of the problem.
B =
The x intercept of the function is
Which represents
1.the charge of the battery when Angel woke up
2.the charge of the battery when Angel left his house
3.the number of hours until Angel’s phone dies
4.the percentage charge that Angel’s phone loses each hour
The slope of -6 means that the battery reduces by 6% each hour
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
The slope of -6 means that, the battery reduces by 6% each hour and the equation is B = -6t + 48
The points
The points on the graph are represented using the following ordered pair (1, 42) and (5,18)
The slope
Start by calculating the slope (m) using:
m = (B2 - B1)/(t2 - t1)
So, we have:
m = (18 -42)/5-1
m = -24/4
m = -6
The equation
The equation is then calculated as:
B = m(t - t1) + B1
This gives
B = -6(t - 1) + 42
B = -6t + 6 + 42
B = -6t + 48
Hence, The slope of -6 means that the battery reduces by 6% each hour
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Find the value of each variable in the following parallelogram
So on solving the provided question we can say that we know that all angles of Quadrilateral is 90, 4x - 2 = 90; x = 22
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
we know that all angles of Quadrilateral is 90
4x - 2 = 90
4x = 88
x = 22
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A map has a scale of 1 cm to 10 km. What would the distance be in kilometres if the distance displayed on the map is 7.211102550928 cm?
The real distance by means of scales used in the map that is described in the statement is approximately equal to 72.11102550928 kilometers.
How to predict the real distance from a map by using scales
Scales are a useful resource to represent any system in a size different than real. Maps are usually created from application of scales. Mathematically speaking, scales are described by following mathematical ratio:
r = s / R
Where:
r - Map scale, in centimeters per kilometer.s - Scale distance, in centimeters.R - Real distance, in kilometers.If we know that r = 0.1 centimeters per kilometers and s = 7.211102550928 centimeters, then the real distance derived from the distance shown in the map that is described in the statement is:
R = s / r
R = (7.211102550928 cm) / (0.1 cm / km)
R = 72.11102550928 km
By using scales on the map, the real distance is approximately equal to 72.11102550928 kilometers.
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Write a paragraph proof of the corollary interior angles theorem.
A corollary is a theorem that connects to an established theorem in mathematics with a brief proof. As opposed to statement or theorem, the term "corollary" is inherently arbitrary.
Explain about the corollary interior angles theorem?A corollary may be unquestionably true if the idea or theory it is founded on is correct. Any triangle's internal angles, for instance, add up to 180 degrees in all cases. Each interior angle of an equilateral triangle is 60 degrees, which is a corollary of the aforementioned theorem.
A triangle is equiangular if it is equilateral, which is a corollary to the Base Angles Theorem. Converse of Base Angles Theorem Corollary: If a triangle is equiangular, it is also equilateral.
The sum of the measurements of the two distant interior angles determines how large an exterior angle of a triangle must be. the triangle's angle-sum Corollaries: A right triangle's acute angles are complimentary. A theorem whose proof naturally follows from another theorem is called a corollary.
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The corollary interior angles theorem is a mathematical result that relates to the number of sides in a polygon and the sum of the interior angles of that polygon.
What is corollary interior angles theorem?The corollary interior angles theorem states that if a polygon has n sides, then the sum of its interior angles is equal to (n-2) times 180 degrees. This theorem is a direct result of the interior angle theorem, which states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. To prove the corollary interior angles theorem, we first consider a triangle with three sides. The sum of the interior angles of a triangle is equal to 180 degrees, which confirms that the interior angle theorem holds for a triangle. We can then use this result to extend the theorem to polygons with more sides by induction. If we add one more side to the polygon, the sum of the interior angles increases by 180 degrees. By continuing this process and adding sides to the polygon, we can conclude that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. This confirms the corollary interior angles theorem.
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NEED HELP ASAP - Algebra 2
Identify the first step that shows an error in the problem below.
Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵
Step-by-step explanation:
The exponential form of a logarithm should be the other way around.
if In = 5 x" (1+x)0.5 dx ,n= 0,1,2....
where the integral is for x e [0,1].
By first finding a bound on the integrand, which of these is an upper bound on In?
Pick ONE option
O 1/(n+1)
O 1/2(n+1)
O 1/(n+1) + 1/(n+2)
O N^N
The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).
To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
0
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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What are the 3 types of 3D modeling?
Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.
1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.
2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.
3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.
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What is a 3-dimensional vector?
A 3-dimensional vector is a line segment running from a point called head to the point called tail in 3-Dimensional space.
Vectors are mathematical or geometrical quantity that has two independent properties i.e., direction and magnitude. There are many types of vectors like unit vectors, equal vectors, etc.
The magnitude of the vector is the length of the line segment without it the direction has no power, Similarly unit vectors help us to find the direction of vectors and their magnitude is 1.
A 3-dimensional vector has majorly 3 components i.e., it has projections in the x, y, and z axes. For a three-dimensional vector A(a1,a2,a3), the formula for its magnitude is ∥a∥=√a21+a22+a23.
Along with magnitude and directions, the 3-D vectors also have angles and they are formed from the vector directly to each of the 3 positive axes.\ i.e., x, y, z axes. The formula used to calculate angle is θ = cos-1 [ (a · b) / (|a| |b|) ]
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The functions approximate the velocities (in meters per second) of an object
dropped from a height of x feet right before it hits the ground on Earth and Venus.
What is the velocity of an object dropped from a height of 100 feet right before it
hits the ground on Venus?
Earth: E(x) = 4.4√x
Venus: V(x) = 0.9 x E(x)
The velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: V(x)=0.9×4.4√x
Thus if x=100feet or 30.47 m putting this value in the equation we get
V(30.47)=0.9×4.4√30.47
= 21.86 m/sec
Hence, the velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec
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WILL GIVE BRAINLEST, DUE TODAY, A system of linear equations is shown in the graph. How many solutions does the system have?
a coordinate plane with one line that passes through the points 0 comma 4 and 3 comma 5 and another line that passes through the points 0 comma negative 1 and 6 comma 1
No solution
One solution at (0, −1)
One solution at (3, 0)
Infinitely many solutions
The number of solutions which the system of equations has is: A. no solution.
How to determine the number of solutions?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (0, 4), a linear equation of the first line can be calculated in slope-intercept form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4 = (5 - 4)/(3 - 0)(x - 0)
y = x/3 + 4
For the second line, we have:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 1 = (1 + 1)/(6 - 0)(x - 0)
y = x/3 + 1
In conclusion, the system of linear equations has no solution because it represents parallel lines.
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Can 7 cm 5 cm and 3 cm form a triangle?
Yes, the triangle can be easily formed for the sides 7 cm, 5 cm and 3 cm.
According to the side side side rule of triangle, if the sum of the any two sides of triangle is more than third side, it will form a triangle. Let us check the same by assuming side a to be 7 cm, side b to be 5 cm and side c to be 3 cm.
Side a + side b > side c
7 + 5 > 3
Add the digits in Left Hand Side of the equation
12 > 3
Side b + side c > side a
5 + 3 > 7
Add the digits in Left Hand Side of the equation
8 > 7
side c + side a > side b
3 + 7 > 5
Add the digits in Left Hand Side of the equation
10 > 5
We see that the two sides of the triangle are greater than third side, hence, it is possible to form the triangle.
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If the bu travel more than 28 mile, how much dieel i left? Expre your anwer in the form of an inequality
The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.
If a vehicle uses diesel fuel, the amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality by saying that the diesel remaining will always be greater than or equal to 0.
diesel remaining ≥ 0
The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.
The amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality, which states that the diesel remaining will always be greater than or equal to 0. This means that no matter how far the vehicle has traveled, there will always be some diesel left in the tank.
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d/4-9=-3
show work
show check
Answer:
d = 24
Step-by-step explanation:
d/4 - 9 = -3
d/4 - 9 + 9 = -3 + 9
d/4 = 6
d/4 * 4 = 6*4
d = 24
Check:
(24)/4 - 9 = -3
6 - 9 = -3
-3 = -3 (Correct)
Hope this helps!
Determine whether the point (1, 1) is a solution to the system of equations. Explain your reasoning in complete sentences. graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2
(1, 1) is not solution of system of equations.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We need to check the point (1, 1) is a solution to the system of equations.
graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one.
y = 3x + 2
g = |x-1| +1
We obtain the intersection point
(0,2)
The only point of intersection of the graphs is (0, 2).
The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection
Hence, (1, 1) is not solution of system of equations.
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6 x. _. = 3 what is the missing number
Answer:
1/2
Step-by-step explanation:
6 x __ = 3
We divided by 6 into both sides
x = 3/6 = 1/2
So, the missing number is 1/2
Find the range for the measure of the third side of a triangle when the measures of the other two sides are 18 ft and 23 ft.
Answer:
The measure of the third side of a triangle, when the measures of the other two sides are 18 ft and 23 ft, must be greater than the difference between the measures of the other two sides (which is 18 ft - 23 ft = -5 ft) and less than the sum of the measures of the other two sides (which is 18 ft + 23 ft = 41 ft).
This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.
Therefore the range of the measure of the third side of a triangle with side lengths 18 ft and 23 ft is:
(-5 ft < x < 41 ft)
or
[x > -5 ft and x < 41 ft].
It is also important to note that any value of x within this range will produce a valid triangle, however, any value less than -5 or greater than 41 will not.
Step-by-step explanation:
Write an equation of the perpendicular bisected of the segment with endpoints (3,7) and (-1,-5)
The equation of perpendicular line that bisects the line segment is y = - (1 / 3) · x + 4 / 3.
How to find the equation of the perpendicular line that bisects a line segment
In this problem we must determine the equation of the line that is perpendicular to a line segment and partitions the line segment in two parts of equal length, it happens when the perpendicular line passes through the midpoint of the line segment.
The equation of the line in explicit form is shown below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableIn addition, two lines are perpendicular to each other when the following relationship is observed:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.Besides, the slope of a line can be determined by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.And lastly, the midpoint of a line segment is determined by this formula:
M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)
First, find the midpoint of the line segment:
M(x, y) = 0.5 · (3, 7) + 0.5 · (- 1, - 5)
M(x, y) = (1.5, 3.5) + (- 0.5, - 2.5)
M(x, y) = (1, 1)
Second, determine the slope of the line related to line segment:
m = (- 5 - 7) / (- 1 - 3)
m = (- 12) / (- 4)
m = 3
Third, calculate the slope of the perpendicular line:
3 · m' = - 1
m' = - 1 / 3
Fourth, find the intercept of the equation of perpendicular line:
b = y - m · x
b = 1 - (- 1 / 3) · 1
b = 1 + 1 / 3
b = 4 / 3
Fifth, write the equation of perpendicular line:
y = - (1 / 3) · x + 4 / 3
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If the scale factor of figure A
too figure B is 7:2 find the perimeter of figure A
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
What is perimeter?
A boundary is a closed path that encompasses, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's perimeter is its outermost portion. Numerous applications in real life involve the perimeter calculation. The radius of a shape's edge is known as the perimeter. By summing the lengths of the sides of various forms, discover how to calculate the perimeter. By multiplying the lengths of the sides, one can always get a shape's perimeter. The area surrounding an object is called its perimeter. An enclosed garden is one example at your home. The distance around anything is called its perimeter. A 200-foot fence will be needed for a yard that is 50 feet by 50 feet.
Ratio factor of A to B = 7:2
Proportion between the perimeters = 7/2
We now understand that a shape's perimeter equals the sum of all its sides. Consequently, using the values from the provided figure, enter the following expression:
A1 / 9+5+9+12 = 7/2
A1 = (7*35)/2
A1 = 122.50 units.
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
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where
h (t) = 5+40t - 16t²
. tis in seconds after being thrown in the air
• height is measured in feet above the ground.
We can use this model to answer some questions like how high the ball will reach.
As a reminder, the velocity of the ball at time t is v(t) = h' (t) and the acceleration is at a (t) = h" (t).
(Side note on projectile motion: there are variations on this model, for example, if the ball is not thrown st
will not focus on those in this example.)
Question 1
1 point possible (graded)
When is the ball the highest?
To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;
dh(t) = d (-16[tex]t^{2}[/tex] + 40t +5 )
dt dt
dh(t) = -32t + 40
dt
with t= 2:
h'(2) =-32 (2) +40
h'(2) =-24 ft/s.
What is velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude. The direction of a velocity vector can be expressed in various ways, depending on the number of dimensions involved.Velocity is relative. Consider a car moving at 20 m/s with respect to the surface of a highway, traveling northward. If you are driving the car, the velocity of the car relative to your body is zero. If you stand by the side of the road, the velocity of the car relative to you is 20 m/s northward. If you are driving a car at 15 m/s with respect to the road and are traveling northward, and another car moving 20 m/s with respect to the road passes you in the same direction, that other car's velocity relative to you is 5 m/s northward. But if that other car passes you going the opposite way on the road, its velocity relative to you is 35 m/s southward.To learn more about Velocity refer to:
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Two students can eat 4 doughnuts in 6 minuts. At this rate, how many doughnuts will be eaten by 8 students sin 9 minutes?.
By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.
The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:
2 students can eat 4 doughnuts in 6 minutes
By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes
It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes
In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut
This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:
X = 8 x 9 x (1/3) = 24 doughnuts
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Is root 1 and 1 are equal?
No, the square root of 1 is 1, but 1 is not equal to the square root of 1. The square root of a number, represented by the symbol √, is a value that, when multiplied by itself, gives the original number.
For example, the square root of 4 is 2, because 2 x 2 = 4. In the case of 1, the square root is also 1, because 1 x 1 = 1.
In mathematics, the square root of a number is always non-negative, real number. It is positive for positive numbers and zero for zero. So, in short, the square root of 1 is 1, but 1 is not equal to the square root of 1. It is just a value that gives 1 when multiplied with itself.
It's important to note that the square root is not a number but an operator, an action which you perform on a number. The square root of a number is a value that, when multiplied by itself, gives the original number.
In this case, the square root of 1 is 1, which means that 1 multiplied by 1 is 1.
Also, it's worth mentioning that there are two types of square roots: principal square root and non-principal square roots. Principal square root is the positive value of the square root and non-principal square roots are the negative value of the square root.
In this case, the square root of 1 is 1, which is the positive value of the square root.
In conclusion, the square root of 1 is 1, and it is the positive value of the square root, but 1 is not equal to the square root of 1, as the square root is a value that gives the original number when multiplied by itself.
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Two factories, National Food Inc. and Anderson's Mill, produce canned food. There is a proportional relationship between the amount of time each factory runs and the amount of food it produces.
The number of the cans that is produced is 5832.
What is a direct proportion?
We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.
We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;
x = Number of hours
y = Number of cans
After 24 hours, we have;
y = 243(24)
y = 5832
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need answer asap <3 ! thank you so much to anyone that answers !
Answer:
A. -1
Step-by-step explanation:
imma human calculator and no one can stop me
please help with this question in the screenshot !!!
The Volume of shape Q is 25,600 cm³.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared.
Let z be the scale factor
x be the surface area of shape Q
and, y be the surface area of shape P
So, z²=x/y
we have,
x = 2880 cm², y= 720 cm²
z² = 2880/720
z² = 4
z = 2
Now, If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
z³ = x/y
We have z= 2 and y = 3200 cm³
So, 2³ = x/3200
x = 8×3200
x = 25,600 cm³
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How do the functions from part a differ from functions you have used in algebra in the past?
The functions differ from functions that we have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
An output variable and one or more input variables are the minimum number of variables in a function.
An equation can have any number of variables and declares that two expressions are equal (none, one, or more). Although not all equations are functions, a function is frequently expressed as an equation.
It should be recalled that a function is merely an equation in which the x inserted produces precisely one from the equation.
In this instance, the functions are different from the ones we have used in algebra in the past since they may be coupled and focus more on rotation than on where they travel.
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Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS)
The grouping symbols commonly used in mathematics are the following:
( ), [ ], { },Parentheses: ( )Brackets: [ ]Braces: { }Bar:Now, According to the question:
What are the 4 types of grouping symbols?
The grouping symbols commonly used in mathematics are the following:
( ), [ ], { },Parentheses: ( )Brackets: [ ]Braces: { }Bar:The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
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can someone show mw how to do liner programming on desmos :)?
tara has 3 boxes of books each box has 48 books tara divides the books amongst 3 friends how many books will each friend get
Each friend will get 48 books. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
Addition(‘+’): This operation deals with finding the sum.Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product.Division(‘÷’): This operation deals with finding the quotient.Now, Tara has 3 boxes of books and each box contains 48 books.
So, the total books that Tara has is equal to 3×48= 144.
Thus, Tara has total 144 books.
Tara divides the books among 3 friends.
So, the number of books that each friend will get is equal to 144÷3= 48
Hence, each friend of Tara will get 48 books.
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What are the mathematical concepts used to calculate insurance premiums?
The mathematical concepts used to calculate insurance premiums include probability, actuarial science, risk assessment, pricing models, financial models, and statistical analysis.
Probability:
To calculate premiums, insurance companies use statistical data to determine the likelihood of a claim occurring. Probability is used to estimate the likelihood of certain events happening, such as accidents, illnesses, or natural disasters, and to determine the likelihood of a claim being made.
Actuarial Science:
Actuarial science is the application of mathematical and statistical methods to assess risk and uncertainty in insurance, finance, and other industries. Actuaries use mathematical models to analyze data and make predictions about future events, which is crucial in determining insurance premiums.
Risk Assessment:
Insurance companies use risk assessment to determine the level of risk associated with insuring a particular individual or group. Factors such as age, health, occupation, and location are considered when assessing risk, and premiums are adjusted accordingly.
Pricing models:
Pricing models are used to determine the cost of insurance based on the perceived level of risk. Pricing models like Loss Ratio, Pure Premium, and Captive pricing are used to arrive at the insurance premium.
Financial Models:
Financial models are used to determine the long-term financial stability of an insurance company and to ensure that the company has enough funds to pay out claims. Actuaries use financial models to calculate the amount of money an insurance company needs to set aside in order to pay claims and to determine the long-term financial health of the company.
Statistical Analysis:
Insurance companies use statistical analysis to evaluate data on claims and losses, and to identify patterns that can be used to predict future claims and losses. This analysis is used to identify trends in claims, to identify high-risk groups, and to set premiums.
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