A geometric sequence begins with 72, 36, 18, 9,
Which option below represents the formula for the sequence?
Of(n) = 72(2)-1
Of(n) = 72(2)+1
Of(n) = 72(0.5)-1
Of(n) = 72(0.5)+1
A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.
How should a geometric sequence be calculated?The ratio of any term to the term before it is constant in a geometric series. When r is used as the common ratio, the explicit formula for a geometric sequence is of the form a = a1r-1.Due to the shared ratio between each term, this sequence is geometric. The subsequent term is obtained in this instance by multiplying the previous term in the sequence by 12.The a1=72 a 1 = 72 and r=23 r = 2 3 should be substituted into the sequence.A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.To learn more about geometric sequence refer to:
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Answer:
f(n) = 72(0.5)n−1
Step-by-step explanation:
Got right.
a personnel director for a corporation has hired ten new engineers. if three (distinctly different) positions are open at a cleveland plant, in how many ways can she fill the positions?
There are 720 ways that personnel director for a corporation fills the positions
What is permutation?It is the ordered arrangement of members belonging to a set with no repeats.
To solve this problem the formula and the permutation procedure we must use is:
nPr = n! / (n-r)!
Where:
nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
n = 10r = 3Applying the permutation formula we have:
nPr = n! / (n-r)!
10P3 = 10! / (10-3)!
10P3 = 10! / 7!
10P3 = 10*9*8*7! / 7!
10P3 = 10*9*8
10P3= 720
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-3(x+2)^2-4=5 solve by factoring
Answer: To solve the equation -3(x+2)^2-4 = 5 by factoring, we can follow these steps:
Move all the terms to one side of the equation by adding 3(x+2)^2 and 4 to both sides: -3(x+2)^2-4+3(x+2)^2+4 = 5+3(x+2)^2
Combine like terms: 3(x+2)^2 = 5
Take the square root of both sides of the equation: (x+2)^2 = 5/3
Isolate x+2 on one side of the equation by taking the square root of both sides: x+2 = ±sqrt(5/3)
Solve for x by subtracting 2 from both sides of the equation: x = ±sqrt(5/3) - 2
So the solutions to the equation -3(x+2)^2-4 = 5 by factoring is x = ±sqrt(5/3) - 2.
It's important to note that the square root of a fraction is a positive and negative solution, so the solutions are x = sqrt(5/3) - 2 and x = -sqrt(5/3) - 2
Step-by-step explanation:
accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an impact on the rates of death and injury. in foggy, rainy, and sunny conditions, 1/6, 1/9, and 1/23 of the accidents result in death, respectively. sunny conditions occur 58% of the time, while rainy and foggy conditions each occur 21% of the time. given that an accident without deaths occurred, what is the conditional probability that it was foggy at the time? round your answer to three decimal places (e.g. 0.987). p
The probability that a death will result from an accident is 0.105, or 10.5%.
Given:
In foggy conditions, 25% of accidents result in fatalities.
Rain-related accidents result in fatalities in 12.5% of cases.
In sunny weather, 5% of accidents result in fatalities.
To find : The probability that a death will result from an accidents
The likelihood that a death will ensue from an accident
5% of 60%(sunny) (sunny)
25% of 20%(foggy) (foggy)
12.5% of 20%(rainy) (rainy)
Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22
Chance is 0.105
Chance is 10.5%.
There is a 10.5% chance that a fatal accident may occur.
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The local swimming pool is offering two programs. No membership fee and a $5 entrance fee per day OR a one time membership fee of $50 and an entrance fee of $3. 50. How many times will she need to go to make it worth paying the membership fee
She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.
To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:
Number of visits = membership fee / (cost without the membership - cost with membership)
Plugging in the values, we get:
Number of visits = $50 / ($5 - $3.50)
The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.
Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.
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Please help me w this!!!
Answer:
Step-by-step explanation:
X =90
1/2+1/3w=1/6
Please help it’s urgent
Answer:
See below
Step-by-step explanation:
1/2 + 1/3 w = 1/6 subtract 1/2 from both sides of the equation
1/3 w = - 2/6 multiply both sides by 3
w = -1
question 7 suppose all household incomes in california increase by 5%. how does that change the standard deviation of the household incomes?
The standard deviation of the household income will be increased by $5,000.
The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.
standard deviation is increased by 5x/100 = 0.05x
Change in standard deviation = $5000
There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.
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3. The graph of a polynomial function f is shown. Select all the true statements about
the polynomial.
-4 -3 +2
YA
12
9
6
3
1
2 B
-6
-9
-12
-15
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The leading coefficient is positive.
D. The leading coefficient is negative.
E. The constant term of the polynomial is positive.
F. The constant term of the polynomial is negative.
4
After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
What is polynomial function ?
A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.
Given ,
The graph is a polynomial function.
This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative
For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive
The leading coefficient is positive other wise the function would be flipped around the x axis
Inspect the graph. when x=0 y is 6 so the constant is +6 which is Positive
Hence , After inspecting the graph, when x=0 y is 6 so the constant is +6 which is Positive
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A 6-kg bowling ball sits on top of a building that is 120 meters tall.
Answer:
The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.
Step-by-step explanation:
Mason asked 280 7th and 8th graders in his school about the number of clubs they belong to. Here is some of the information he found.
150 of the respondents were 8th graders.
Twice as many 7th graders belonged to one club as no clubs.
10 fewer 7th graders belonged to more than one club than no clubs.
Twice as many 8th graders belonged to one club as more than one club.
56 respondents did not belong to any clubs.
Create a two-way frequency table to show the number of 7th and 8th graders that belong to zero, one, or more than one club.
The frequency table has been created in the attachment
The frequency tableGiven that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.
Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:
x = 2 * 56
Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:
y = 56 - 10
Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:
z = 2*w
Now we have the following system of equations:
x = 2 * 56
y = 56 - 10
z = 2*w
x+z = 150
y+w = 150
By solving the above system of equations we get:
x = 112
y = 46
z = 112
w = 56
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Pleasee Help !!!!
Given: ∆KLM, KL = LM m∠K = 17°, R = 1. 08 Find: KM
triangle is inside a circle with a midpoint O
From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.
A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.
Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.
Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.
Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.
Now, ∠KOL is calculated as follows from the triangle KLO,
[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.
Now, ∠LOM is calculated as follows from the triangle MLO,
[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]
Then,
[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]
Using, the cosine law of the triangle KOM, we get,
[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]
Therefore, the required answer is 1.2079.
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through: (3,0), parallel to y=2/3x+1
The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:
y = (2/3)*x - 2
How to find the linear equation?A general linear equation can be written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.
Then a line parallel to:
y = (2/3)*x + 1
Is of the form:
y = (2/3)*x + b
And we want this line to pass through the point (3, 0), replacing these values we will get:
0 = (2/3)*3 + b
0 = 2 + b
-2 = b
Then the linear equation is:
y = (2/3)*x - 2
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5. Ken will flip a fair coin and then randomly choose one of three colored cards. The
possible outcomes are shown below.
Heads
Red
Blue
Green
Red
Blue
Green
What is the probability that tails will turn up and that he will choose a red card?
Tails
The probability that tails will turn up and that he will choose a red card is 1/6.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The probability of choosing a tail is 0.5.
The probability of choosing ref card is 1/3.
Therefore, the probability will be:
= 1/2 × 1/3
= 1/6
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Find the annual interest rate I= 20$ P=1000 t= 4 months
keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]
if the earth's spin axis were perpendicular to the earth's orbital plane (the ecliptic plane), then the seasons and seasonal variation would be
The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.
This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.
After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.
If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.
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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.
This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.
After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.
The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.
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Find the relationship used and solve for the variable
Answer:
55°
Step-by-step explanation:
For the line including the 110°, the angle of the supplementary angle is 70° which is the 'non-equivalent' length of the isosceles triangle. Then do:
(180°-70°)/2 = 55° to get x
Answer:
Supplementary angles, x = 55
Step-by-step explanation:
Supplementary angles: straight line means both angles add up to 180, this if the outside angle is 110 then the inside angle is 180° - 110° = 70°
Since it is an isosceles triangle, it means both angles are equal to x therefore
[tex]180 - 70 = 2x\\110 = 2x\\\frac{110}{2} = x\\x = 55[/tex]
(Simple)......Classify the transformation pls
The transformation represented by the figure is (c) translation
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have the following
A figure and its translated image
When a shape is translated to form another, then the transformation is a translation
Hence, the transformation is translation
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer: x=10
Step-by-step explanation:
x is an unknown number trying to figure out what number equals 20? You subtract 10 from 20 to figure out x.
On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). Its midpoint, M, is also
labeled and has coordinates of M (3, 2).
(a) Draw the perpendicular bisector of AB on the grid. Think about its slope compared to that of AB.
b) Write the equation of the line you drew in (a).
The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.
Perpendicular bisector:A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.
The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.
On both sides of the line segment being divided, it forms a 90° angle.
Here we have
On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).
Slope from A(-1,-1) and B(7,5)
=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4
When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)
The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)
=> [2 - 6]/[3 - 0] = - 4/3
Let the equation of the bisector is y = mx + c
=> y = (-4/3)x + c
=> 3y = - 4x + 3c [ ∵ Slope = -4/3 ]
As we know the bisector will pass through (3, 2)
=> 3(2) = -4(3) + 3c
=> 3c = 12 + 6
=> 3c = 18
Hence, the required equation of the line is 3y = - 4x + 18
Therefore,
The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.
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Whats the answer to my equations.
The equation for the linear function is y=3x -5.
Linear FunctionA linear function can be represented by a linear equation. The standard form for the linear equation is: y= mx+b , for example, y=10x+6.
The standard for the linear equation( y= mx+b), also it is known as the Slope-Intercept Form.
Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=10 and b=6.
The question gives some points of the linear function, see below.
x y
1 -2
2 1
3 4
4 7
From the given data you can find the slope by solving the system linear equation.
For example, you can write a system linear equation from the points: (1,-2) and (4,7).
-2=m+b (1)
7=4m+b (2)
Multiplying equation 1 by -1, you have
2= -m -b (1)
7= 4m+b (2)
Summing the previous equation, you can find the slope (m):
9=3m
m= 9/3
m= 3
If m=3, from equation 2, you can find the coefficient b.
7 = 4m + b
7 = 4*3 +b
7=12 + b
b= 7-12
b= -5
Thus, the standard form for the linear equation represented by the given table is y=3x -5.
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You use a juice mix to make orange juice.
You combine 12 ounces of the mix with 36 ounces of water.
What is a unit rate that describes your juice?
Answer: 12/48 = 25%
Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.
PLEASE HELP ME, WILL MARK BRAINLIEST
Tessa needs to find a courier to deliver a package. The first courier charges a fee of $15 plus $1 per pound. The second charges $13 plus $2 per pound. Tessa determines that, given her package's weight, the two courier services are equivalent in terms of cost. Write a system of equations and solve. How much does her package weigh and how much is delivery going to cost?
The system of equations are:
15 + x = y
13 + 2x = y
The weight of the package is 2 pounds.
The delivery cost for both services is 17$.
How to Solve a System of Equations?Here is a system of equations you can use to represent the cost of the two courier services:
First courier: 15 + x = y
Second courier: 13 + 2x = y
Where x is the weight of the package in pounds and y is the total cost of delivery.
We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:
15 + x = 13 + 2x
then we can subtract 15 from both sides
x = 13 + 2x -15
x = -2 + 2x
then we can subtract x from both sides
-x = -2
then we can divide both sides by -1
x = 2
The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.
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9 more than twice mai's score
The expression that shows John's score will be 2x + 9.
How to calculate the expression?It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, Mai has a score of x while John has 9 more than twice mai's score.
The expression for this relationship will be:
= (2 × x) + 9
= 2x + 9
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Complete question
Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.
if johnny has 23 candy and casey have only 3 candy how many times of 3 candy do we need to add more to 23 and try it
We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.
To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:
(23) / (3) = 7.666...
Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.
So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.
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Please answer im giving 25 points
The equation of the line in slope intercept form is y = -2.65x + 25.
The x-intercept means when the gift card has a balance of zero dollars.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).
Hence,
m = slope = 14.4 - 19.7 / 4 - 2
m = - 5.3 / 2
m = - 2.65
Therefore, let's find the y-intercept using (2, 19.7).
y = -2.65x + b
19.7 = -2.65(2) + b
b = 19.7 + 5.3
b = 25
Therefore, the equation of the line is y = -2.65x + 25.
The x-intercept is the value of x when y = 0.
Hence,
0 = -2.65x + 25
-25 = -2.65x
x = -25 / -2.65
x = 9.4
The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .
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5x+y =9
10x - 7y = -18
Find X and Y.
Answer:
x=1, y=4
Step-by-step explanation:
5x+y=9
10x-7y=-18
(Multiply top equation by -2)
-10x-2y=-18
10x-7y=-18
(Add)
-9y=-36
(Divide -36 by -9)
y=4
(Substitute y(4) into the top equation)
5x+4=9
(Subtract 4)
5x=5
(Divide 5)
x=1
Answer: x=1 , y=4
Step-by-step explanation:
5x+y =9 y=9-5x
10x - 7y = -18
10x-7(9-5x)=-18 y=9-5x
10x-63+35x=-18 y=9-5(1)
45x-63=-18 y=4
45x=-18+63
45x=45
x=1
Joy can choose to ride the bus,subway,or take a taxi on monday and tuesday which list show the possible outcomes of day one method of travel
A list that shows the possible outcomes of one day one method of travel:
Monday, bus,
Monday, subway,
Monday, taxi,
Tuesday, bus,
Tuesday, subway,
Tuesday, taxi
The correct answer is an option (B)
Let A represents the set of days.
A = {Monday, Tuesday}
And set B represents the method of transportaion/travel.
B = {bus, subway, taxi }
To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.
We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.
It is a set of all ordered pairs (a, b)
For above sets A and B,
A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}
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Find the complete question below.
how to determine if a function is even or odd algebraically
You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.
The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.
The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).
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In the figure, ABCD is a square. E is the midpoint of side AD, and F is the midpoint of side BC. The area of the shaded region is
what fraction of the area of square region ABCD ?
Correct option is D, the fraction of area of square region ABCD is 1/4.
A + B + C = D + E + F since diagonal QS divides the square into two equal portions.
We can see that the areas of regions A and F must be equal because they have the exact same measurements and form. Similar reasoning leads us to the conclusion that the areas of regions D and C are equal.
As a result, it follows that the size of regions E and B must likewise be equal. Due to the fact that URPT is a parallelogram, its area equals (base)(height)=(1)(2)=2.
Area of region E = Area of region B = 1 as a result.
The percentage of the square PQRS's area is represented by the darkened region 1/4 is a fraction.
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Complete question -