We will see that the odd functions were f(x) = x5 - 3*x3 + 2*x and f(x) = 1/x since only those were true under the specified circumstances.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. The most basic definition is that a function is a collection of ordered pairs of items, which in our instance will be numbers, but they may also be anything else, and which have the feature that their initial members are all distinct from one another. The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.
Here,
A function is odd,
f(-x) = -f(x) for every value of x in its domain.
1) f(x) = x^3 - x^2
f(-x) = (-x)^3 - (-x)^2
= -x^3 - x^2
f(-x) ≠ -f(x)
This function is not odd.
2) f(x) = x^5 - 3*x^3 + 2*x
f(-x) = (-x)^5 - 3*(-x)^3 + 2*(-x)
= -x^5 + 3*x^3 - 2*x = -f(x)
This function is odd.
3) f(x) = 4x + 9
f(-x) = 4*(-x) + 9
= -4*x + 9
-f(x) = -( 4*x + 9)
= -4*x - 9
f(-x) ≠ -f(x)
This function is not odd.
Because only these were true under the specified circumstances, we will find that the odd functions are f(x) = x^5 - 3*x^3 + 2*x and f(x) = 1/x.
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Here is a graph of a logarithmic function.
what is the base of the logarithm? explain how you know.
Answer:
base = 10
Step-by-step explanation:
alice and bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for alice. if they play 6 rounds, in how many ways can alice win or draw exactly three times? (answer: 300)
AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240
Permutation:
In probability, permutation refers the arrangement of objects in a definite order.
Given,
Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.
Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.
While we looking into the given question, we know that,
Total number of games = 6
Possible values = 3 ( win, loss, or draw)
Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,
=> 6! / (6 - 3)!
=> 6! / 3!
=> 120
Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,
=> 6!/ (6 - 3)!
=> 120
So, the number of ways can Alice win or draw exactly three times is
=> 120 + 120 = 240
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A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip.
The correct answer is (C) since the limitations to depict this real-world problem in inequality are 75 < x < 110 and 0 < y ≤ 50.
What is inequality?The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity.
This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
So, our senior trip will be a group excursion to a beach.
Only when the temperature is between 75 and 110 degrees does the resort permit swimming.
On your excursion, there is space for 50 people.
Let y represent the number of travelers and x represent the temperature.
The temperature ranges from 75 to 110 degrees:
75 < x < 110
On your excursion, there is space for 50 persons:
0 < y ≤ 50
Therefore, the correct answer is (C) since the limitations to depict this real-world problem in inequality are 75 < x < 110 and 0 < y ≤ 50.
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Complete question:
A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip.
a. 0 < x ≤ 50 and 75 < y < 110
b. x > 75 and y < 110
c. 75 < x < 110 and 0 < y ≤ 50
d. x < 110 and y > 75
Last year students planted 8 tomato plants and 16 pepper plants in a school garden
Answer:
whats the question
Answer:
What are you asking?
calculate the expected return for stocks a and b. (do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)b.calculate the standard deviation for stocks a and b.
a) The expected return for stocks a and b is 13.56% and 20.02% respectively.
b) The standard deviation for stocks a and b are 8.32% and 32.60%.
a) Expected return = Probability of recession × Return during recession + Probability of normal × Return during normal + Probability of boom × Return during boom
Expected return for stock A = 0.21 × 0.04 + 0.61 × 0.12 + 0.18 × 0.30
The expected return for stock A = 0.1356
The expected return for stock A = 13.56%
Expected return for stock B = 0.21 × (-0.41) + 0.61 × 0.31 + 0.18 × 0.54
The expected return for stock B = 0.2002
The expected return for stock B = 20.02%
b) Standard deviation of stock = √{Probability(Recession) × (Rate during recession - expected rate )² + Probability(Normal)(Rate during normal - expected return)² + Probability(Boom) × (Rate in boom - Expected return)²}
Standard deviation of stock A = √[(0.21 × (0.04-0.1356)² + 0.61 × (0.12 - 0.1356)² + 0.18 × (0.30-0.1356)²)]
The standard deviation of stock A = 0.0832
The standard deviation of stock A = 8.32
Standard deviation of stock B = √(0.21 × (-0.41-0.2002)² + 0.61(0.31 - 0.2002)² + 0.18 × (0.54-0.2002)²)]
The standard deviation of stock B = 0.3260
The standard deviation of stock B = 32.60%
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a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. two of the questions concerned eye and hair color. in the survey, the following codes were used:
a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools The U.S. Population Census is an example of a census
Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.
Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.
The primary objective of population census is to know the total size of the population of a country.
Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.
In conclusion, the U.S. population census is the only example of census.
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There are 4 tomato plants, 8 lettuce plants, and 2 cucumber plants in Jill's garden.
a. What is the ratio of tomato plants to lettuce plants?
b. What is the ratio of lettuce plants to cucumber plants?
a) The ratio of tomato plants to lettuce plants:
4 ÷ 8 ⇒ 1 ÷ 2b) The ratio of lettuce plants to cucumber plants:
8 ÷ 2 ⇒ 4 ÷ 1Carlos wants to buy some new video games. Each game he buys costs him $36. Is the relationship between the number of games Carlos buys and the total price proportional?
The relationship between the number of games Carlos buys and the total price is proportional.
What is a proportional relationship?
A proportional relationship exists between two or more variables if they move in the same direction. If one of the variables increases, the other variable increases.
As the number of games that are bought increases, the total price paid also increases. This means that the relationship is proportional.
The formula that is used to represent proportional relationship is:
T = kg
Where:
T = total price k = constant g = number of games boughtT = $36g
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Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.
Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know the formula for :
volume = x*y*z, as here it is a square base, so the volume will be
volume = x²*y, where x and y are the dimension of the base and height
So for the given reason,
=>x²*y = 500
=> y = 500/x²
Again, the surface area formula will be
S=x²+4xy, substituting the value of y in this question
=>S=x²+4x(500/x²)
=>S=x²+2000/x
Differentiating the above formula with respect to x, we get
=>2x-2000/x²=0
=>2x³= 2000
=>x³= 1000
=>x =10
so the substituting the x values of x in the equation y , we get
y = 500/x²
=>y = 5
so the dimensions are x= 10 and y=5
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aurelio is purchasing carpet tiles to cover an area of his living room floor that is 813 feet wide by 10 feet long. each carpet tile is a square 20 inches wide by 20 inches long. what is the minimum number of carpet tiles that aurelio must purchase to cover this area of his living room floor?
30 inches many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
Given that,
To cover an area of his living room floor that is 8 1/3 feet wide by 10 feet long, Aurelio is buying carpet tiles. The dimensions of each carpet tile are 20 inches broad by 20 inches long.
We have to find how many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
We know that,
1 feet=12 inches.
So,
8 1/3 feet = 25/3 feet =100 inches.
10 feet =120 inches.
=100+120 inches
=12000 inches.
So, now
20×20=400
We get
12000/400= 30
Therefore, 30 many carpet tiles will Aurelio need to buy at the very least to cover this portion of the floor in his living room.
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The two polygons are similar . Solve for x
Find an equation in point-slope form for the line having the slope m=2 and containing the point (8,2)
suppose our student center published data that the average starting salary for college graduates is 59k. you randomly sampled 49 college graduates and calculated the sample average salary is 44k. what test can you use to check whether the true average is 59k?
To check whether the true average is 59k or not, A sample mean T-Test needs to be conducted. The true value of 59k is 44k after the test.
What is an Average?In the field of statistics, average means that the ratio of the sum of the numbers of a given set, to the total number of characters in a given set. It is also called as the Arithmetic mean.
Equating :
It is given that the student center has published the data that the average salary of the college graduates is 59k. Accordingly, the sample of 49 college students were verified and the sample average salary came out to be 44k.
When we analyze the given question, we find that,
The total number of students were 49,The true average was found to be 59k,and the Sample average is found to be 44k.
Thus, in the present question we will use the One- sample T-test.
We used this test, as the statistical hypothesis test is used to find if the unrecognized population mean is different from the specific value.
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Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.
Infinite solutions
No solution
y = −14
y = 0
NEED A ANSWER ASAP!!!!!!!
Answer:
None of the Above?
Step-by-step explanation:
1.) If we put this into words, we would get -5y+7/3y=-5-8/3y-4
2.) By moving all y terms to one side, we get -5y + 7/3y + 8/3y = -5 - 4
3.) By simplifying, you would get -4 2/3y = -9.
4.) If you divide both sides by -4 2/3, you would get that y = -9 * - 3/14 = 27/14
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.)
The integration by part is [tex]\frac{x^{3}In x }{3} -\frac{x^{3} }{9} +C[/tex] with indicated choices of u and dv.
What is integration by parts?
The method Integration by Parts is known to be a special method of integration that is often useful. In calculus, definite integrals are referred to as the integral with limits such as upper and lower limits. It is also possible to derive the formula of integration by parts with limits.
Given: ∫ [tex]x^{2} In x dx[/tex] ; [tex]u=In x[/tex] ; [tex]dv=x^{2} dx[/tex]
Consider [tex]u=In x[/tex] and [tex]dv=x^{2} dx[/tex]
⇒ [tex]u=In x[/tex] ⇒ [tex]dv=x^{2} dx[/tex]
⇒ [tex]du= \frac{1}{x} dx[/tex] ⇒ [tex]v=\frac{x^{3} }{3}[/tex]
Now, apply integration by parts to solve the integral
∫ u dv = uv - ∫ v du
the antiderivative of [tex]x^{n}[/tex][tex]=\frac{x^{n+1} }{n+1}[/tex] and the derivative of In x = [tex]\frac{1}{x}[/tex] .
⇒ ∫ [tex]x^{2} In x dx =[/tex][tex]\frac{x^{3} In x}{3} -\frac{x^{3} }{3} .\frac{1}{x} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{2} }{3} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
Hence, the final integration is [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
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The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20. 820. 820, point, 8 years; the standard deviation is 3. 13. 13, point, 1 years.
A z-score of 23.9 years must be located in the gorillas' lifespans in a specific zoo's typical normal distribution.
Define the term normal distribution?A data collection with a normal distribution is put up so that the majority of the values cluster as in midpoint of the range and the remaining values taper off symmetrically in either direction.The equation can be used to determine the z score.
z = (x - μ)/σ
In which,
X is age 23.9.The typical gorilla life span is M. (20.8 years).The standard deviation is s. (3.1 years).Then,
z = (23.9 - 20.8)/3.1
z = 1
According to the empirical rule, 68% of lifespans are within one standard deviation of the mean.
Half of it, 68/2 = 34% %, is on the right side of the mean's standard deviation.
Given that the likelihood of a gorilla lasting less than 23.9 years is 50%.
A gorilla's lifespan being less than the norm means is;
50% + 34% = 84% sits below z-score 1.
Thus, the probability of a gorilla living less than 23.9 years is 84%.
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The correct question is-
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the
standard deviation is 3.1 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a gorilla living less than 23.9 years.
find the open intervals on which the function f(x)axbxc, a0, is increasing and decreasing. describe the reasoning behind your answer.
The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a
Given that,
We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.
We know that,
Take the function equation,
f(x)=ax² + bx + c
The derivative of the function of x is
f'(x)=ax+b
So, f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
Then we can say
f'(x) > 0 , when b > 0 and a < 0
2ax + b < 0
2ax < - b
x<-b/2a
Now,
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
x>-b/2a
Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.
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suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). what is the margin of error of this confidence interval? responses
The margin of error for the confidence interval (6.5, 6.9) is 0.2 , the correct option is (c) .
In the question ,
it is given that ,
the 95% confidence interval for mean hours slept in the graduate students is (6.5, 6.9) ,
we have to find the margin of error ,
we know that the formula for the margin of error is
= (upper limit of confidence interval - lower limit )/2
From the given interval ,
we see that ,
upper limit of confidence interval = 6.9
lower limit of confidence interval = 6.5
Substituting the above value in margin of error formula ,
we get ,
margin of error = (6.9 - 6.5)/2
= 0.4/2
= 0.2
Therefore , the margin of error is 0.2 .
The given question is incomplete , the complete question is
Suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). What is the margin of error of this confidence interval? responses
(a) 6.7
(b) 0.4
(c) 0.2
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Solve for the variable. 2(k+8) = 44
Answer:
k = 14
Step-by-step explanation:
2(k+8) = 44
2*k + 2*8 = 44
2k + 16= 44
2k = 44 - 16
2k = 28
k = 28/2
k = 14
Check:
2(14+8) = 44
2*22 = 44
Enter the equivalent decimal.
9/9/25
Answer:
Step-by-step explanation:
.36
Find the value of the product (4a2 + 3b) (4a2+36) at a = 1, b = 2.
The final value of the product = 292
According to the given equation -
= (4a2+3b)x(4a2+36)
multiply the whole equation-
= 16a4+144+12a2b+108
as we can see that the values of a and b are given 1 and 2 respectively,
so putting the values of a and b in the equation we get -
= 16(1)4+144+12(1)2(2)+108
= 292
The product of the following equation will be = 292
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THIS IS URGENT!!!
A cube has 54 colored stickers across all six of its faces. Each face has the same number of stickers in the same format. On each face, each column and row has the same number of stickers.
The number of stickers in each row and column is
.
Answer:
3
Step-by-step explanation:
We know a cube has six sides.
Using this logic, we can divide 54 by 6.
54 ÷ 6 = 9
We can conclude that each side has 9 stickers.
If we think of a square, and the area of that square is 9,
3 × 3 = 9
The number of stickers in each row and column is 3
Answer:
3 stickers in each row and column
Step-by-step explanation:
so i divided 54 by 6 and that equals 9 and since you said there was the same number of stickers on each column and rows that would be 9 separated into a even amount of rows and columns would be 3
The functions f(x) and g(x) are graphed. On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). Which represents where f(x) = g(x)? Group of answer choices f(2) = g(0) and f(0) = g(4) f(2) = g(4) and f(1) = g(1) f(2) = g(2) and f(0) = g(0) f(2) = g(0) and f(4) = g(2)
f(2) = g(2) and f(0) = g(0) is representation of f(x) = g(x)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
the curved red line represents g(x) and the straight blue line represents f(x) .
The important thing here is that the equality of functions f(x)=g(x) is represented as a common function between their curves. So, we just need to find such a common point for both.
f(x) has points (0, 4) and (2, 0).
g(x) has points (0,4) and (2,0).
Notice that both functions have the same y-value for x=0 and x=2, that means f(0)=g(0) and f(2)=g(2)
Hence, f(2) = g(2) and f(0) = g(0) is representation of f(x) = g(x)
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Im so confused with this question 21≥3(a-7)+9
Answer:
I got you!
a ≤ 11
For more info, look at the steps in the attached image!
Step-by-step explanation:
Answer:
a ≥11
Step-by-step explanation:
[tex]21 \geqslant 3a - 21 + 9 \\ 21 \geqslant 3a - 12 \\ 21 + 12 \geqslant 3a - 12 + 12 \\ 33 \geqslant 3a \\ 3a \leqslant 33 \\ a \geqslant 11[/tex]
Write code using the range function to add up the series 15, 20, 25, 30,. 50 and print the resulting sum each step along the way.
The range function to add up the series is 15 ,35 ,60 ,90, 125,165,210 ,260
What is a python function?
A unit of code with a name is referred to as a function in Python. We utilize functions anytime we need to repeat a process repeatedly without writing the same code.
Given: Series 15, 20, 25, 30,.. 50
Program (Pascal ABC) and Result:
Program:
Var i, Summ : integer;
begin
i : = 15;
Summ : = 15;
While i <= 50 do
begin
WriteIn ( ' ' , Summ) ;
i : = i + 5 ;
Summ : = Summ + i ;
end ;
end.
Result : 15 ,35 ,60 ,90, 125,165,210 ,260
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PLEASE HELP ME ASAP !!!!!!!!!!!!!!!!!!!
The triangles in the diagram indicates that ΔABD is an isosceles triangle, therefore;∠2 ≅ ∠1
The two-column method can be used to prove that the angle m∠BAC > m∠C as follows;
Statement [tex]{}[/tex] Reasons
1. BC > BA [tex]{}[/tex] 1. Given
2. BA ≅ BD [tex]{}[/tex] 2. Given
3. ΔABD is an isosceles Δ[tex]{}[/tex] 3. Definition of isosceles triangle
4. ∠1 ≅ ∠2 [tex]{}[/tex] 4. Base ∠s of isosceles triangle ΔABD
5. ∠1 = ∠2 [tex]{}[/tex] 5. Definition of congruency
6. ∠1 = ∠3 + ∠C [tex]{}[/tex] 6. Exterior angle theorem
7. ∠2 = ∠3 + ∠C [tex]{}[/tex] 7. Substitution property
8. ∠2 - ∠3 = ∠C [tex]{}[/tex] 8. Subtraction property
9. ∠2 > ∠C [tex]{}[/tex] 9. Definition
What is an isosceles triangle?An isosceles triangle is a triangle that have a pair of congruent sides and one pair of congruent angles.
The reasons in the above two-columns used to prove m∠BAC > m∠C are as follows;
Isosceles triangle ΔABD
The triangle ΔABD that have side AB congruent to side BD is an isosceles triangle by definition of an isosceles triangle.
The base angles of an isosceles triangle that are angles opposite congruent sides in a triangle are also congruent.
Definition of congruency
A geometric figure is congruent to another figure if their measurements are the same.
Exterior angle theorem
The exterior angle of a triangle theorem states that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Substitution property
The substitution property of equality states that if a quantity a is equal to another quantity b then a can be substituted by b in expressions and equations without changing their value.
Subtraction property
The subtraction property of equality states that if the same quantity is subtracted from both sides of an equation, then the new amount obtained are also equal
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A baker uses 2 cups of vanilla to make 24 donut. how many ounces vanilla are there per donut?
Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?.
The probability that at least one customer will report a food allergy is; 0.6323
How to find the probability?The formula for Binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
Where;
P(X = x) is the probability of getting success.
x is number of trials
n is sample size
p is the probability of getting success in each event.
We are given;
n = 12
p = 0.08
Let x denotes the customer will report a food allergy.
Then, the probability that at least one customer will report a food allergy will be :
P(X ≥ 1) = 1 - P(X < 1)
P(X < 1) IS P(X = 0)
Thus;
P(X ≥ 1) = 1 - 0.3677
P(X ≥ 1) = 0.6323
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Complete question is;
When a customer places an order at Ying Ying's bakery, there is an 8 percent probability that the customer will report a food allergy. One day, 12 customers place orders at Ying Ying's bakery.
Assuming that each of the 12 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
Peter opened up a savings account by making an initial deposit. After the initial deposit, Peter has been adding
$50 to his savings account each month. If after 8 months Peter has a total of $600 in his savings account, what
was the amount of his initial deposit?
Answer:
$200
Step-by-step explanation:
so if peter has been depositing 50 each month for 8 months then you would just do 50x8 which equals 400 and 600-400=200
g please find out how many numbers must be selected from the set 1, 2, 3, 4, 5, 6, 7, 8 to guarantee that at least one pair of those numbers add up to 9 ?
To guarantee that at least on pair o the numbers adds up to 9, you must select at least 3 numbers from the set by combination
1. First, select any two numbers from the set.
2. Now, calculate their sum.
3. If the sum of the two numbers is not equal to 9, select a third number from the set.
4. Determine the three numbers' sum.
5. If the sum of the three numbers is still not equal to 9, select a fourth number from the set and calculate the sum.
6. Repeat this process until the sum of the selected numbers is equal to 9 by combination
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