The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
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Answer:
B.) f(x)=x5-3x3+2x is odd
D.) f (x) = 1/ x is odd
Step-by-step explanation:
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The amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t. Estimate the total trash that will be produced
over the next 8 years by interpreting the integral as an area under the curve.
tons
The total trash that will be produced over the next 8 years will be 107 trash
Functions and valuesGiven the function that represents the amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to
continue growing according to the formula P(t) = 75 + 4t
The total trash that will be produced over the next 8 years is expressed as:
p(8) = 75 + 4(8)
p(8) = 75 + 32
p(8) = 107
Hence the total trash that will be produced over the next 8 years will be 107 trash
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For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $50 .
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
The equation for the profit from selling the items is P = 40x-0.5x²-300. The values of x are 10 and 70.
How to solve for the expressionWe have the cost function in this question to be
Cx = 60x+300
Revenue = 100x−0.5x²
A. The revenue function is stated as the revenue - cost
= (100x−0.5x²)-60x+300
We have to open the equation
40x-0.5x²-300
B. when profit is 50 dollars
50 = 40x-0.5x²-300
We have to multiply both sides by 10
500 = 400x - 5x² - 3000
We have to collect like terms and form a quadratic equation
5x² - 400x - 3500 = 0
We have to solve the quadratic equation above using a quadratic calculator.
Hence
x = 10, 70
So the two values that would create a profit of 50 dollars is 10 and 70.
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1) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games? In your discussion, also state whether the expected value is positive or negative. 1 ) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino . What would you expect to be true for all expected values for these seven games ? In your discussion , also state whether the expected value is positive or negative.
As per the question seems, the expected value can be positive, negative or zero.
The given question is of probability, which cannot be negative so don't get confused between expected values and probability, expected value and be negative, positive or zero.
What is probability?
Probability can be defined as the ration of favorable outcomes to the total number of events.
If person playing different games in casino , the probability of that person winning could be varying from 0/7 to 7/7 which implies that person can win from zero games to all games. If that person wins all the 7 games that mean he the gain in values, but if the loses 1 games or more games there than he supposed have gain or have loosen expected values so it can be positive, negative or zero. however the person loosen every game their is certain negative expected values.
Thus, The expected value can be positive, negative or zero.
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x is increased by 50% and decreased by 30%. What is the result?
Answer:
its the same as increasing x by 5 percent
Answer:
1.05x is the answer
Step-by-step explanation:
11.
An IV of D5W 1000 mL was ordered to infuse over 8 hr at a rate of 42 gtt/min (42 macrogtt/min). Drop
factor: 20 gtt/mL. After 4 hr, you notice that only 400 mL has infused.
Recalculate the rate in gtt/min for the remaining solution
The rate is 50gtt per minutes.
How to calculate the growth rate?From the information, out of the total hours of 8 hours, four hours were used.
The volume will be:
= 1000 - 400
= 600ml
Time = 4 × 60 = 240 minutes
Drop factor = 20
Therefore, the growth rate will be:
= 600/240 × 20
= 50gtt/min
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Which ordered pairs make both inequalities true? Check all that apply.
We can actually deduce here that the ordered pairs that make both inequalities true are:
(1,1)(2, 2)What is inequality?An inequality is known to be an expression that shows that certain variables or values are not equal to each other. It is usually seen in an inequality expression as:
> (greater than)< (less than)≥ (greater than or equal to) ≤ (less than or equal to).We see the attached image that shows the graph of inequality and which completes the question.
The options that complete the question are:
A. –2, 2
B. (0, 0)
C. (1,1)
D. (1, 3)
E. (2, 2)
When we insert the values of each axes into the inequality expressions given, we will discover that the ordered pairs that the inequalities true is (1,1) and (2, 2).
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If you are driving at a rate of 55 miles per hour, about how many feet per second are you traveling?
290400 feet per second
0.015 feet per second
4840 feet per second
80.67 feet per second
Let R(x)=3x^3+2x^2+x and S(x)=4+1. Find R(x) * S(x)
Pls help!!!!
3x^3 x 4x^2 = 12x^5
3x^3 x 1 = 3x^3
2x^2 x 4x^2 = 8x^4
2x^2 x 1 = 2x^2
1x x 4x^2 = 4x^3
1x x 1 = 1x
12x^5 + 3x^3 + 8x^4 + 2x^2 + 4x^3 + 1x
Simplify
12x^5 + 7x^3 + 8x^4 + 2x^2 + 1x
Thus, answer is B
Hope this helps!
Solve for x. Enter the solutions from least to greatest.
Round to two decimal places.
(x + 8)^2 - 7 = 0
asap will give brainliest
The value of x according to the equation in the task content is; -5.35 or -10.65.
What is the value of x in the equation?The equation given in the task content is; (x + 8)² -7 = 0.
Hence, the equation can be solved as follows;
(x + 8)² - 7 = 0
x² + 16x +64 -7 = 0
x²+ 16x +57 = 0
By solving by means of the quadratic formula, we have;
x = -5.35
x = -10.65
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Which of the expressions below cannot be rewritten using the associative
property?
.
OA. 15 (410)
OB. (5+14) + 10
OC. 12 (17 ÷ 2)
OD. (12.9) •10
SUBMIT
Answer:
OA
Step-by-step explanation:
In what situation would you use an ANOVA statistical test over T-test?
Step-by-step explanation:
when means of more than two groups are to be compared, ANOVA is perferred
A rectangle with base b and height h has an area of 235 square-inches. Express the perimeter of the rectangle as a function of its base
The perimeter of the rectangle as a function of its base is P = 2(b + 235/b)
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape For all regular quadrilaterals, you add up the side lengths to determine the area
How to express the perimeter of the rectangle as a function of its base?The given parameters are
Area = 235 sqare inches
The area of a rectangle is calculated using
Area = Base * Height
Note that the area of a shape is the amount of space on the shape
Recall that the area of a rectangle is calculated using
Area = Base * Height
Rewrite the above equation as
A = bh
So, we have
bh = 235
Make h the subject of the formula
h = 235/b
The perimeter of the rectangle is
P = 2(b + h)
So, we have
P = 2(b + 235/b)
Hence, the perimeter of the rectangle as a function of its base is P = 2(b + 235/b)
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People were asked if they prefer Pepsi or Coke. The results are in the table below.
Pepsi Coke
Female 23 44
Male 28 39
a) If two people are chosen, what is the probability that they both prefer Pepsi?
b) If one person is chose, find the probability that they are Female or prefer Coke.
Using it's concept, it is found that the probabilities are given as follows:
a) 0.1431 = 14.31%.
b) 0.7910 = 79.10%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
The number of people is:
23 + 44 + 28 + 39 = 134.
The number of people that prefer Pepsi is:
23 + 28 = 51.
Hence, for the two people, the probability is:
p = 51/134 x 50/133 = 0.1431 = 14.31%.
Item b:
There are 23 + 44 = 67 females, and 39 males who prefer Coke, hence the probability is:
p = (39 + 67)/134 = 0.7910 = 79.10%.
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Help please quueens i need help
Answer:
x = 3
Step-by-step explanation:
We can use the following equation to solve for x:
[tex]315=9x-27+8x+24+5x-17+2x+23\\315=(9x+8x+5x+2x)+(-27+24-17+23)\\315=24x+3\\312=24x\\13=x[/tex]
solve which 2 digit number is one more than a square and one less than cube?
The 2-digit number is 26:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
How to find the number?
Here we want to find a 2-digit number N, such that:
N + 1 is a cube number.N - 1 is a square number.To do that, we can just create a list of cubic and square numbers of 2 digits, these are:
Square numbers:
4*4 = 16
5*5 = 25
6*6 = 36
etc...
Cube numbers:
3*3*3 = 27
4*4*4 = 64
etc...
Now, we can see that 25 is a square number and 27 is a cube number, then our 2-digit number can be 26.
Because:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
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please please out of certain people of all locality 50% speak Nepali language 55% speak English language and 5% speak not if 40 people speak both the language find total number of people,people who speak nepali language only english language only.Show the result in a venn diagram.
The given pics are your answers... Thank you
Suppose that an individual has a body fat percentage of 15.9% and weighs 159. How many pounds of her weight is made up of fat? Round to the nearest tenth
Answer:
25.3 lb
Step-by-step explanation:
We can multiply the whole by the percentage to find the part. Since 15.9% is equal to 0.159, the weight of fat is 159*0.159 = 25.281. Round this to the nearest tenth, and we get 25.3 pounds.
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer: x-7
Step-by-step explanation:
[tex]f(x)+g(x)=-3x-5+4x-2=\boxed{x-7}[/tex]
A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes. (a) find a formula for the number of bacteria at time (b) find the number of bacteria after one hour (c) after how many minutes will there be 50000 bacteria?
The formula for the number of bacteria at time t is 1000 x (2^t).
The number of bacteria after one hour is 2828
The number of minutes for there to be 50,000 bacteria is 324 minutes.
What is the number of bacteria after 1 hour?The exponential function that can be used to determine the number of bacteria with the passage of time is:
initial population x (rate of increase)^t
1000 x (2^t).
Population after 1 hour : 1000 x 2^(60/40) = 2828
Time when there would be 50,000 bacteria : In(FV / PV) / r
Where:
FV = future bacteria population = 50,000PV = present bacteria population = 1000r = rate of increase = 100%In (50,000 / 1000)
In 50 / 1 = 3.91 hours x 60 = 324 minutes
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In how many ways can 3 cards be chosen from a standard deck of 52 cards?
[tex]\displaystyle\\\binom{52}{3}=\dfrac{52!}{3!49!}=\dfrac{50\cdot51\cdot52}{2\cdot3}=22100[/tex]
Median weekly earnings for women with some college for an associate degree.
1980.......$231
2013.............$657
Using today's dollars, the data in the bar graph can be described by the mathematical model
W = 13n + 231,
Where W represents median weekly earnings n years after 1980.
Does the formula underestimate or overestimate the median weekly earnings in 2013? By how much?
Using the given linear function, the formula underestimates the median weekly earnings in 2013 by $3.
What is the linear function for the estimate?The function that estimates the median weekly earnings n years after 1980 is given by:
W = 13n + 231.
2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by:
W = 13 x 33 + 231 = 660.
Since 657 < 660, the formula underestimates the median weekly earnings in 2013 by $3.
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PLS HURRRYYYyyyyyyyydhsbsbd
Answer:
116.5027
Step-by-step explanation:
degree/360 *pie * radius^2
Suppose that $4000 is placed in a savings account at an annual rate of 6.4%, compounded quarterly. Assuming that no withdrawals are made, how long will it
take for the account to grow to $4916?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
3.25 years (nearest hundredth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $4916P = $4000r = 6.4% = 0.064n = 4 (quarterly)Substitute the given values into the formula and solve for t:
[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]
[tex]\implies \sf t=3.247594892...[/tex]
Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.
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let A and B sets. when do we say set A is equal to set B
Step-by-step explanation:
It is said A=B I have drawn the Venn diagram of A=B
Find the surface of the cube with length of a side
Answer: 319.74 square mm
Step-by-step explanation:
[tex]6(7.3)^2=319.74[/tex]
Solve the inequality −38<5x+7≤17
66877383
Step-by-step explanation:
I made a single dad be single of ⅝
Please Answer! It is a emergancy! SUPER EASY
Answer:
x^-3
Step-by-step explanation:
1 / (x^3) = x^(-3)
2011?
7. Maria, a sales representative for a large consumer goods company, is paid 3% of the total profits earned by her company.
Her company averages 10% profit on sales. If Maria's total income for the year was $60,000, what total sales did her
company realize?
Step-by-step explanation:
60000÷ 10 = 600 and 600 ÷ 3 =20
The total sales realized by the company was $20,000,000.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let x be the total sales realized by the company.
Maria's pay is 3% of the total profits, which is 3% of 10% of total sales
0.03(0.1x) = 0.003x.
Her total income is given as $60,000, so we have:
0.003x = 60000
Solving for x:
x = 60000/0.003 = 20,000,000
Therefore, the total sales realized by the company was $20,000,000.
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Martin has written the first 50 terms of the sequence with nth term 150 -4n. Work out which term is the first negative term.
what is the answer to this help
The first negative term of the sequence is -2
How to find the terms of a sequence?The terms of the sequence which is the first negative term can be calculated as follows:
The sequence with nth term is 150 - 4n.
The first negative term will be the first term you will multiply by 4 that will be greater than 150.
Therefore,
nth term with first negative number = 150 - 4(38)
nth term with first negative number = 150 - 152
nth term with first negative number = -2
Therefore, the first negative term of the sequence is -2
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Evaluate the following.
Step-by-step explanation:
1) 3 + 4 = 7
2) 6 - 6 = 0
3) 1 + 3 = 4
4) 6 + 9 = 15
5) 10 - 14 + 2 = -2
6) 2 + 3 - 5 = 0