For some values, such as the speed of light or the separation between the Earth and the sun, scientists and mathematicians long ago realized they needed a simpler way to write and refer to these large numbers.
They developed/created scientific notation at that time.
For us to estimate the order of magnitude:
Firstly, write the number in scientific notation.
Secondly, Round up to the nearest integer times a power of ten or power of ten.
Thirdly, Apply these estimates to your calculations.
Fourthly, If possible, compare the result to the exact one.
Example question, How many orders of magnitude are there in one million, for instance?
Answer will be, In order to represent the number 1,000,000, we will move the decimal to the left, stopping just before the first digit. The order of magnitude is determined by the quantity of left moves you make. Since we moved it six times, there are six orders of magnitude between ten and one million, which means that ten times six is equal to one million.
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6) A 6-ounce bottle of medicine contains 36 doses. How many doses are in a 15-ounce bottle of the same medicine?
A 15-ounce bottle of the same medicine contains 90 doses.
Unitary method:The unitary method is a method used to solve problems related to proportionality. It involves finding the value of a single unit or the value of a given quantity when the value of one or more units is known.
In the given problem, we will find the number of doses in 1 unit from that will find the number of doses in a 15-ounce bottle.
Here we have
A 6-ounce bottle of medicine contains 36 doses.
Number of doses in a 1-ounce bottle
= 36/6 = 6 doses
Then the number of doses in a 15-ounce bottle of medicine
= 15 × Number of doses in 1 ounce
= 15 × 6
= 90
Therefore,
A 15-ounce bottle of the same medicine contains 90 doses.
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VIDEO GAMES A video game developer determines that the profit, in thousands of dollars, from a new video game can be modeled by the
function P(x) = -2x² + 130x - 2000 when x is the price of each game. The game will be profitable if P (x) > 0.
To make the game profitable, the price should be at least $
and no more than $
P(x) = -2x² + 130x - 2000 when x is the price of each game to make the game profitable, the price should be at least $ 25 and no more than $ 40.
Quadratic equations are polynomial equations of degree 2 in one variable of the form f(x) = ax2 + bx + c = 0, where a, b, c, R, and a 0 are all zeros. It is the generic form of a quadratic equation in which 'a' is referred to as the leading coefficient and 'c' is referred to as the absolute term of f. (x). The roots of the quadratic equation (,) are the values of x that fulfil the quadratic equation.
There will always be two roots to the quadratic equation. Roots might be real or fictitious in nature.
p(x) = -2x² + 130x - 2000
The game will be profitable if P (x) > 0.
-2x² + 130x - 2000 > 0
-x² + 65x - 1000 > 0
x² - 65x + 1000 > 0
x(x-25) - 40(x -25) > 0
x>25 x < 40.
Therefore, price should be at least $ 25 and no more than $ 40.
The values of variables that satisfy the given quadratic equation are referred to as its roots. In other words, if f() = 0, x = is a root of the quadratic equation f(x).
The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
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1000 litros de sangre a mililitros.
Answer:
1000 litros x 1000000 ml/litro = 1 000 000 000 mililitros
jill has a pail of water that holds 6 1/2 quarts. She needs to give some pants 1/8 quart each. How many plants can she water?
Jill can water 52 plants.
One quart has what meaning?A measurement of volume or capacity in the US Customary System that is equivalent to 14 gallons or 32 ounces and is used for liquids (0.95 liter).
We must divide the pail's overall capacity by the quantity of water required by each plant to determine how many plants Jill can water.
Let's first translate 6 1/2 gallons into a mixed number:
6 1/2 = 13/2
Then, we can divide the pail's total capacity by the quantity of water that each plant requires:
(13/2) / (1/8) = (13/2) * (8/1) = 104/2 = 52
Jill is then able to water 52 plants.
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4(3p+3)=60 what does p mean
Answer: p = 4
Step-by-step explanation:
Because 3 * 4 + 3 = 15 which is then multiplied by 4 equaling 60
Answer:
p=4
Step-by-step explanation:
4(3p +3) = 60
12p + 12 = 60
-12 -12
___________
12p = 48
p = 4
Does the Laplace Transform Method apply to the following equations?
a.)y′′′+4y′′−3y′+8y=sin(3t)
b.)3y′′+5y′−10y=0
c.)3y′′+2y′−3y=cos(t)
d.)(e^t)y′′+ty′−5(t^2)y=0
e.)yy′=sin(t)
f.)yy′′+5y′=5
g.)y′=sin(y)
h.)2y′+5y=sin(t)
The Laplace Transform Method can be used to solve all of these equations except for equation (e).
a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.
b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.
c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.
d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.
e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.
f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.
g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.
h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.
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please help ASAP!!!!!!!!
The diameter of the circle is 30 units, and the equation is:
(x + 3)^2 + (y - 3)^2 = 15^2
How to find the equation of the circle?We know that the diameter of the circle is defined by the points (12, 3) and (-18,3)
Notice that the y-value is the same one in both points, then the diameter is the difference between the x-values:
d = 12 - (-18) = 30
The diameter is 30 units.
Then the radius, half the diameter, is 15 units.
To write the circle equation we need to find the center.
Because of the points (12, 3) and (-18,3) we know that the y-value of the center must be y = 3.
And the x-value is the midpoint between x = -18 and x = 12, that is:
x = (-18 + 12)/2 = -6/2 = -3
The center is at (-3, 3)
Remember that the equation for a circle of center (a, b) and radius R is:
(x - a)^2 + (y - b)^2 = R^2
Here the center is (-3, 3) and the radius is 15, so the equation is:
(x + 3)^2 + (y - 3)^2 = 15^2
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The binomial probability distribution is a __________ probability distribution that describes probabilities for experiments in which there are two __________ outcomes.
discrete
mutually exclusive
The binomial probability distribution is a discrete probability distribution that describes probabilities for experiments in which there are two mutually exclusive outcomes.
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
In binomial probability distribution, the number of ‘Success’ in a sequence of n experiments, where each time a question is asked for yes-no, then the boolean-valued outcome is represented either with success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 − p). A single success/failure test is also called a Bernoulli trial or Bernoulli experiment, and a series of outcomes is called a Bernoulli process.
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Which of the following is equal to Square Root of 16*4 (Sort of looks like this v/16*4)
A. v/ 16/4
B. 64
C. 32
D. v/ 16 * v/ 4
The square root of 16*4 can be simplified as follows:
Square root of 16*4 = Square root of (16) * Square root of (4) = 4 * 2 = 8
Therefore, the answer is not A, B, or D. The correct answer is C) 32.
Answer:
The square root of 16*4 can be simplified as follows:
Square root of 16*4 = Square root of (16) * Square root of (4) = 4 * 2 = 8
Therefore, the answer is not A, B, or D. The correct answer is C) 32.
Step-by-step explanation:
Find an equation of the line L that passes through the point
(−2, 4)
and satisfies the condition. (Let x be the independent variable and y be the dependent variable.)
L is parallel to the line
3x − 2y = 6.
Answer:
Para encontrar la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6, primero debemos encontrar la pendiente de la línea 3x - 2y = 6.
La forma estándar de la ecuación de una línea es y = mx + b, donde m es la pendiente y b es la intersección en y. Podemos reescribir la ecuación 3x - 2y = 6 en esta forma:
3x - 2y = 6
-2 años
Por lo tanto, la pendiente de la línea 3x - 2y = 6 es 3/2.
Dado que la línea L es paralela a esta línea, también tiene una pendiente de 3/2. Ente
y - y1 = m(x - x1)
donde m es la pendiente y (x1, y1) es un punto en la línea. Nos
y - 4 = (3/2)(x - (-2))
Simplificando esta ecuación, obtenemos:
y - 4 = (3/2)x + 3
y = (3/2)x + 7
Por lo tanto, la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6 es y = (3/2)x + 7.
Step-by-step explanation:
espero te sirva, traducelo si no puedes español.
what is 24cm in inch?
24 centimeter is approximately equal to 9.4488 inches ( rounded to four decimal places )
To convert 24 cm to inches, we can use the following formula:
1 cm = 0.393701 inches
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in inches = conversion factor × The length in centimeter
Substitute the values in the equation
24 cm = 24 x 0.393701
Multiply the numbers
= 9.4488 inches ( rounded to four decimal places )
Therefore, 24 centimeter is 9.4488 inches
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75% of the employees in a specialized department of a large software firm are computer science graduates. a project team is made up of 8 employees. part a) what is the probability to 3 decimal digits that all the project team members are computer science graduates? 0.013 part b) what is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? part c) what is the most likely number of computer science graduates among the 8 project team members? your answer should be an integer. if there are two possible answers, please select the smaller of the two integers. part d) there are 56 such projects running at the same time and each project team consists of 8 employees as described. on how many of the 56 project teams do you expect there to be exactly 3 computer science graduates? give your answer to 1 decimal place. part e) i meet 30 employees at random. what is the probability that the first employee i meet is the first one who is a computer science graduate? give your answer to 3 decimal places. part f) i meet 33 employees at random on a daily basis. what is the mean number of computer science graduates among the 33 that i meet? give your answer to one decimal place.
The probability that all 8 project team members are computer science graduates is approximately 0.100
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Since 75% of the employees in the department are computer science graduates, the probability that a randomly selected employee is a computer science graduate is 0.75. We want to find the probability that all 8 employees on the project team are computer science graduates. Assuming that the employees are chosen randomly, we can model the situation as a binomial distribution with n = 8 and p = 0.75.
Using the binomial probability formula, the probability that all 8 employees on the project team are computer science graduates is:
P(X = 8) = (8C8) * (0.75)⁸ * (1 - 0.75)⁸⁻⁸
= 1 * 0.1001 * 1
= 0.1001
Therefore, the probability that all 8 project team members are computer science graduates is approximately 0.100, to three decimal places.
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What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Slope of the given graph is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let us take two points to find the slope of line.
The two points are (4, 1) and (6,5)
m=5-1/6-4
m=4/2
m=2
Hence, slope of the given graph is 2.
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Faith is going to use a computer at an internet cafe. The cafe charges $0. 80 for every minute using a computer on top of an initial charge of $3. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of using a computer for tt minutes at the internet cafe. Number of Minutes Total Cost to Use Computer
00 3\hspace{3px}\color{green}{\checkmark}3✓3
11 3. 80\hspace{3px}\color{green}{\checkmark}3. 80✓3. 80
22 4. 60\hspace{3px}\color{green}{\checkmark}4. 60✓4. 60
33 5. 40\hspace{3px}\color{green}{\checkmark}5. 40✓5. 40
Answer: C=C=
The equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3
The cost of using a computer at the internet cafe can be represented by a linear equation, where C is the total cost and t is the number of minutes used. The equation can be written as C = 0.80t + 3, where 0.80 is the cost per minute and 3 is the initial charge.
To make a table of values, we can plug in different values of t into the equation and solve for C
Number of Minutes (t) Total Cost to Use Computer (C)
0 C = 0.80(0) + 3 = 3
1 C = 0.80(1) + 3 = 3.80
2 C = 0.80(2) + 3 = 4.60
3 C = 0.80(3) + 3 = 5.40
So the equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3.
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When can a correlation coefficient based on an observational study be used to support a claim of cause and effect? A. Never B. When the correlation coefficient is close to -1 or +1. C. When the correlation coefficient is equal to -1 or +1. D. When the scatterplot of the data has little vertical variation.
Option A. Never. A correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
However, a strong correlation between two variables does not necessarily mean that one causes the other. This is because there may be other factors, known as confounding variables, that affect both variables simultaneously. Therefore, it is not appropriate to use a correlation coefficient to establish a causal relationship between two variables. In order to establish causality, more rigorous methods such as randomized controlled trials must be used, which attempt to isolate the effect of one variable on another while holding other factors constant.
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A glass case is in the shape of a rectangular prism. The volume of the case is 4/125 cubic foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of glass case?
2
3
4
5
A glass case is in the shape of a rectangular prism where the volume of the case is 4/125 cubic foot. The number of cubic blocks with a side length of 1/5 foot required to find the volume of glass case is option C: 4.
What is the rectangular prism?
A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape that has six faces, where each face is a rectangle.
The volume of the glass case is 4/125 cubic foot. We can write this as:
V = l × w × h = 4/125
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
To find how many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case, we need to find the number of cubic blocks that can fit in the rectangular prism. Since the side length of each block is 1/5 foot, the volume of each block is (1/5)^3 = 1/125 cubic foot.
Therefore, the number of cubic blocks required is:
number of blocks = V / volume of one block
number of blocks = (4/125) / (1/125)
number of blocks = 4
So, we would need 4 cubic blocks with a side length of 1/5 foot to find the volume of the glass case.
Hence, the answer is 4.
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The sum of the digits of an odd 2 digit number is 17 what is the number
Answer:
x+y=17
y can be 1,3,5,7 or 9
Let's start at 9
x+9=17
x=8
So the burner is 89
7, 5, 3 and 1 don't work
For example In order x+7=17, x should be 10, which is a contradiction; x is the one-digit number. If 7 doesn't work, lower numbers shouldn't work as well.
Step-by-step explanation:
A go-kart track is 1 2/10 kilometers long. you complete 8 laps. how many meters do you travel?
Answer:
12800 meters.
Hope that helps!!!
You travel 9600 meters after completing 8 laps on a 1 2/10 kilometers long go-kart track.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
The length of the go-kart track is 1 2/10 kilometers, which can be converted to meters as follows:
1 kilometer = 1000 meters
2/10 kilometer = 2/10 x 1000 = 200 meters
So, the length of the go-kart track in meters is:
1 2/10 kilometers = 1 x 1000 + 2/10 x 1000 = 1200 meters
To find the total distance you travel after completing 8 laps, you need to multiply the length of the track by the number of laps:
Total distance = 8 x 1200 meters = 9600 meters
Therefore, you travel 9600 meters after completing 8 laps on a 1 2/10 kilometers long go-kart track.
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??? HELP im confused
Answer:
a=3
Step-by-step explanation:
the sum of anterior angle of a triangle is =180
57+81+14a=180
138+14a=180
42=14a
42/14=14a/14
3=a
therefore a=3.
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How many minutes in 420 seconds?
Answer: 7 minutes
Step-by-step explanation:
There is 1 minute every 60 seconds
So if we divide the amount of seconds by 60 we will get the answer.
Therefore our equation is: 420/60
420/60=7
SO the answer is 7 minutes
Hope this helps! :)
Use the graph above to determine if the questions below are True, False, or Cannot be determined.
A. (True) (False) (Cannot be determined)
B. (True) (False) (Cannot be determined)
C. (True) (False) (Cannot be determined)
D. (True) (False) (Cannot be determined)
E. (True) (False) (Cannot be determined)
F. (True) (False) (Cannot be determined)
The true and false statements are
True, False, False, True, True, True
How to determine the true and false statementsFrom the question, we have the following parameters that can be used in our computation:
The graph
The maximum from the graph is
y = 4
The graph has real zeros because it crosses the x-axis
Also, it is true that the graph increases from negative infinity to x = -1 and it it true that the y-intercept is 3 (because it intersects the y-axis at this pont)
The vertices are (-1, 4)
Lastly, the function is above 0 at the interval (-3, 1)
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Which expression is equivalent to |x| < 11?
Responses
x > –11 or x < 11
x > –11 or x < 11
x < –11 and x > 11
x < –11 and x > 11
x < –11 or x > 11
x < –11 or x > 11
x > –11 and x < 11
Answer:
x > -11 and x < 11
Step-by-step explanation:
Find the absolute value of a number gives you its distance from zero, which is just the numerical parts of it. From this we can reason that the numbers between -11 and 11 have an absolute value less than 11, as they are the numbers that are less than 11 away from zero. This can be represented as -11 < x < 11, and can be separated into x > -11 and x < 11 (the "and" is because x has to fulfill both conditions of being greater than -11 and less than 11).
Given △PQR ~ △STU, find the missing measures in △STU.
The missing measures in △STU could be 28 degree.
WE have been Given △PQR ~ △STU,
WE need to find the missing measures in △STU.
What is law of sines?For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
[tex]\dfrac{sin\angle Q}{21} = \dfrac{sin\angle T}{6}[/tex]
[tex]\dfrac{sin\angle 64}{21} = \dfrac{sin\angle T}{6} \\\\\dfrac{0.920}{21} = \dfrac{sin\angle T}{6} \\\\{sin\angle T} = \dfrac{0.920 \times 6}{21}[/tex]
Sin angle T = 0.2628
△STU = 28 degree.
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A medium pizza at Benny’s Pizza costs $13.60 plus $2.50 for each topping. At Ricco’s Pizza, a medium pizza costs $14.60 plus $2 for each topping. Which statement is true regarding the price of a medium pizza at the two pizza restaurants?
A.A pizza with three toppings will cost less at Benny's Pizza.
B.A pizza with four toppings will cost less at Ricco's Pizza.
C.A pizza with two toppings will cost more at Ricco's Pizza.
D.A pizza with one topping will cost more at Benny's Pizza.
Answer: A
Step-by-step explanation:
Benny's Pizza
13.60 + 2.50(3)
13.60 + 7.50
21.10
Ricco's Pizza
14.60 + 2(3)
14.60 + 6
21.60
Write an expression that is equivalent to 734+356 − 134that uses addition instead of subtraction.
The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:
734 + 356 + (-134)
Answer:
706+350 = 956
I need help with this question from Geometry...
Answer: B. 240
Step-by-step explanation: Hi there here is why your answer is this:
Area = b × h
= 12 × 20
= 240 feet2
Hope this helps you!
PLEASE HELP ITS DUE ANY MINUTE
The image is an enlargement of the pre-image |s| > 1. The image is a reduction of the pre-image 0 < |s| < 1. The image is the same as the pre-image rotated 180 s = 1.
What is scale factor?We double the length of each of the original shape's sides by a quantity known as a scale factor to enlarge a given shape. The shape will become smaller or larger depending on the scale factor, which can range from 0 to 1. If the scale factor is greater than 1, the shape will become larger. The image, for instance, displays a dilation with a scale factor of two.
The image is an enlargement of the pre-image |s| > 1.
The image is a reduction of the pre-image 0 < |s| < 1.
The image is the same as the pre-image rotated 180 s = 1.
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Manny has 1/2 yard of fabric with which he intends to make bookmarks. Each bookmark is made from 1/8 of a yard of fabric. How many bookmarks can manny make
Manny can make 4 bookmarks from 1/2 yard of fabric, each bookmark is made of 1/8 yard of fabric.
Manny has 1/2 yard of fabric, and each bookmark requires 1/8 of a yard of fabric. To find out how many bookmarks Manny can make, we need to divide the total amount of fabric by the amount of fabric used per bookmark:
1/2 ÷ 1/8
To divide by a fraction, we can flip the second fraction (the divisor) and multiply:
1/2 × 8/1
Multiplying the numerators and denominators gives:
(1 × 8) / (2 × 1) = 8/2
Simplifying the fraction by dividing both the numerator and denominator by the greatest common factor of 8 and 2, which is 2:
(8/2) ÷ (2/2) = 4/1
Therefore, Manny can make 4 bookmarks from 1/2 yard of fabric. This problem involves basic arithmetic operations such as division and multiplication of fractions. To solve it, we can flip the second fraction (1/8) and multiply it with the first fraction (1/2). This gives us the total number of bookmarks that can be made with the given amount of fabric. We then simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor.
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I need help with finding the missing side length
The missing side length of the triangle is:
UT = 54
How to find the missing sidelength?Here we can assume that the two triangles are similar triangles, that means that the quotient between the correspondent sides must be equal.
That means that:
KL/UV = ML/UT
And we know that:
KL = 130
ML = 117
UV = 60
UT = ?
Replacing that we can write:
130/60 = 117/?
Solving for the missing value we will get:
? = 117*(60/130) = 54
That is the missing side length.
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Identify each as function even, odd, or neither. Explain or show your reasoning.
1. the function k shown here:
k
YA
2-1
2. the function f defined by f(x) = 3* +3**
N
X
As k(-x) = -k(x), the function k is indeed an odd function. By switching the words in f, we can observe that f(-x) Equals f(x) (x). Hence, f is an even function.
What is a brief explanation of function?A collection of inputs or one output for each input are referred to as a "function" in this sentence. Simply described, a function is a connection between inputs where each input is connected to exactly one output. Each function has a domain, codomain, or range.
According to the given information:1.The function k is an odd function.
A function is odd if f(-x) = -f(x) for all x. In the case of function k, we have:
k(-x) = 2 - 1(-x) = 1 + 2x
k(x) = 2 - 1(x) = 1 + 2x
Therefore, k(-x) = -k(x), and the function is odd.
2.The function f is an even function.
A function is even if f(-x) = f(x) for all x. In the case of function f, we have:
f(-x) = 3^(-x) + 3^x
f(x) = 3^x + 3^(-x)
We can see that f(-x) = f(x) by swapping the terms in f(x). Therefore, f is an even function.
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