Answer: 5.3
Step-by-step explanation: First, you have to use PEMDAS and then you will get 32 divided by 6, which is 5.3 repeating
Evaluate each general power function at the indicated values.
1.
f(x) = x^n, where n is even
f(1) = ?
f(-1) = ?
2.
g(x) = x^n, where n is odd
g(1) = ?
g(-1) = ?
Step-by-step explanation:
remember, an exponent n just means that the base is multiplied by itself n times.
so, e.g.
a³ = a×a×a = (a×a)×a
a⁶ = a×a×a×a×a×a = (a×a)×(a×a)×(a×a)
as you can see, any even exponent can be written as products of squares.
and any odd (uneven) exponent can be written as product of squares multiplied by one base.
a square of a real number is always positive. therefore, an even exponent of a real number is always positive.
and an odd exponent has the sign of the base (as the result of these multiplications is the product of the squares, that are always positive and one instant of the base, and +×+ = +, +×- = -).
and 1^n = 1
no matter how often I multiply 1 by 1, I get 1 as result.
also : -×- = +
1.
f(x) = x^n, n is even
f(1) = 1^n = (1×1)×(1×1)×...×(1×1) = 1×1×1×...×1 = 1
f(-1) = (-1)^n = (-1×-1)×(-1×-1)×...×(-1×-1) = 1×1×1×...×1 = 1
2.
g(x) = x^n, n is odd
g(1) = (1×1)×(1×1)×...(1×1)×1 = 1×1×1×...×1×1 = 1
g(-1) = (-1×-1)×...×(-1×-1)×-1 = 1×1×...×1×-1 = -1
A coat is marked down by 10% and the customer is given a second discount of 25% what is the sales price
The sales price of the coat is 67.5% of the original price
How to determine the sales price of the coat ?From the question, we have the following parameters that can be used in our computation:
Markdown rate = 10%
Second discount = 25%
The retail price of the coat can be calculated using the following equation
Retail price = original price * (1 - Markdown rate) * (1 - discount)
Substitute the known values in the above equation, so, we have the following representation
Retail price = original price * (1 - 10%) * (1 - 25%)
Evaluate the products
Retail price = original price * 0.675
Rewrite as
Retail price = 67.5% of the original price
Hence, the sales price is 67.5% of the original price
Read more about markup at
https://brainly.com/question/19104371
#SPJ1
how many ways are there to seat n couples around a circular table such that no couple sits next to each other?
2n(n−1)! ways n couples around a circular table such that no couple sits next to each other.
What is combination?
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant."Combining these two words indicates "Selection of things," where the order of the items is irrelevant.Depends on how you consider two ways as different ways.
If the seats are in fixed positions, then there are two possible seatings as the couple can swap with each other. In this case, choose a seat as reference. Swapping is available in each couple or between couples, on seat 0 and 2N sit one couple or different couples. So the answer is 2n+1n!If you consider seats as all same, pick a couple as reference. Still, husband can sit either on clockwise of his wife or counterclockwise. The remaining n−1 couples can choose their seats at will. In this case the answer is 2n(n−1)! when n>1. When n=1 there’s only 1 since the relative position becomes unimportant in this case.In case you still feel confused, take 2 for example. We have plan AaBb, AabB, aABb and aAbB
To know more about combinations check the below link:
https://brainly.com/question/11732255
#SPJ4
in the big bucks lottery, the chances of winning a $10.00 prize is 1%. what is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket to big bucks?
In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.
If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:
Total number of People = 1000
Chances of winning the lottery = 1%
How many people would win 10 dollar lottery = 1000 * 1%
= 1000 * 0.01
= 10 People.
So there are chances that 10 out of 1000 people will win the lottery.
To learn more about probability, visit the link below:
brainly.com/question/13810637
#SPJ4
Consider the function
f(x,y) = y\sqrt x - y^2 - 3 x + 11 y.
Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank.
f_x =
f_y = f_{xx} = f_{xy} = f_{yy} = The critical point with the smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
The critical point with the next smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
The critical point with the next smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
By using the concept of maxima, it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
What is maxima of a function?
Maxima of a function gives the maximum value of a function in a given interval or within the whole domain.
f(x, y) = [tex]y\sqrt{x} -y^2 -3x + 11y[/tex]
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
Putting x = 0 in [tex]f_y(x, y) = 0[/tex],
-2y + 11 = 0
[tex]y = \frac{11}{2}[/tex]
[tex](0, \frac{11}{2})[/tex] is a critical point
Putting [tex]f_x(x, y) = 0[/tex] and [tex]f_y(x, y) = 0[/tex]
[tex]\frac{y}{2\sqrt{x}} - 3 = 0\\\frac{y}{2\sqrt{x}} = 3\\y = 6\sqrt{x}[/tex]
[tex]\sqrt{x} - 2y+11 = 0\\\sqrt{x} -2\times 6\sqrt{x}+11=0\\\sqrt{x}-12\sqrt{x} + 11 = 0\\11\sqrt{x} = 11\\\sqrt{x} = \frac{11}{11}\\\sqrt{x} = 1\\x = 1[/tex]
When x = 1, y = [tex]6 \times \sqrt{1} = 6[/tex]
(1, 6) is a critical point
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
The point (0, [tex]\frac{11}{2}[/tex]) is undefined in the second order partial derivative
For the critical point (1, 6)
[tex]f_{xx}(1, 6) = -\frac{1}{4}\\f_{yy}(1, 6) = -2\\f_{xy}(1, 6) = \frac{1}{2}[/tex]
[tex]f_{xx}f_{yy}-(f_{xy})^2[/tex]
[tex]-\frac{1}{4}\times -2-(\frac{1}{2})^2\\\frac{1}{2} - \frac{1}{4}\\\frac{1}{4} > 0[/tex]
[tex]f_{yy} = -2 < 0[/tex]
Hence (1, 6) is a point of local maxima
So it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
To learn more about maxima, refer to the link-
https://brainly.com/question/82347
#SPJ4
Which of the following is located 2/3 the distance from the vertex?
Circumcenter
Incenter
Centroid
Orthocenter
Answer:centroid
Step-by-step explanation:
Answer:Centroid I hope this helpful to you mark me brainlist if correct
Step-by-step explanation:
Hence, the correct statement is "The Centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side."The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangleCentroid theorem: the distance between the centroid and its corresponding vertex is twice the distance between the barycenter and the midpoint of the opposite side. That is, the distance from the centroid to each vertex is 2/3 the length of each median. This is true for every triangleThe centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side).
Simplify the rational expression. State any excluded values. x^2-64/16x-2x^2
Answer:
The answer is -x^2-4x
Step-by-step explanation:
Solve the equation or formula for the indicated Variable. explain answer please a=4b^5h, for h
Answer: The correct answer is h=a/4b^5
Step-by-step explanation:
Solve for h
a=4b^5h
Flip the equation
4b^5h=a
Divide both sides by 4b^5
4b^5h/4b^5 = a/4b^5
h=a/4b^5
Given: < 2. Choose the solution set. {x | x < 10/11} {x | x > 10/11} {x | x > 22/5} {x | x < 22/5}.
The solution set is {x | x < [tex]\frac{22}{5}[/tex]}.of the given evaluation.
What is a Solution Set?
The solution set of an equation is, however defined as the set of all solutions that satisfy the equation and since that set has no members the solution set is empty.
Given: [tex]\frac{5x}{11}[/tex][tex]< 2[/tex]
= [tex]5x < 22[/tex]
= [tex]x < \frac{22}{5}[/tex]
Hence, the correct solution set is {x | x < [tex]\frac{22}{5}[/tex]}.
To learn more about solution set :
brainly.com/question/9859818
#SPJ4
Carol,dan and eli each had ome coin
dan had twice a many a eli
carol had twice a many a dan
write down the ratio carol had to the number of coin eli had
give your anwer in it implet form
Carol had four times as many coins as Eli had, or a 4:1 ratio.
What is ratio?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 male and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every guy), meaning that there are 1 in 4 boys and 3 in 4 girls. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Here,
Dan has twice what Eli has ( D= 2 x E )
Carol had twice what Dan had ( C = 2 x D )
for example , let's suppose Eli had 2 coins
this means Dan had 4 coins,
and Carol had 8 coins .
carol 8 : 2 Eli
=4:1
The ratio in which carol had to the number of coin eli had will be 4:1.
To know more about ratio,
https://brainly.com/question/29467965
#SPJ4
this exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 5????/11 rad is 15 m2. find the radius of the circle. (round your answer to one decimal place.) 4.5 incorrect: your answer is incorrect. m
A 15 square metres sector will have a radius of 8.1 m and a central angle of 26.04 degrees.
What is sector?The region of a disk encompassed by two radii and an arc is called a circular sector, also known as a circle sector or disk sector. The smaller area is referred to as the minor sector, and the larger area as the major sector. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Here,
area of sector=θ/360°*πr²
θ=5/11*180/π
θ=26.04 degree
area=15 m²
15=26.04/360*3.14*r²
15=0.227r²
r²=66.08 m²
r=8.13 m
The radius of the sector whose area is 15 m² will be 8.1 m with the central angle of 26.04 degree.
To know more about sector,
https://brainly.com/question/15591260
#SPJ4
you have a box with a square base and no top. the surface area of the box is 220 ????????????????2. find the maximum volume.
The required maximum volume of the box would be 85184 cube units.
The surface area of a box is the total area of all of the box's faces. For a box with a square base and no top, the surface area is equal to the sum of the areas of the four sides and the bottom.
To find the maximum volume of such a box, we can first find the length of one side of the square base. We can do this by dividing the given surface area by the number of sides of the box.
In this case, the box has 4 sides plus the bottom, so the length of one side is 220 / 5 = 44.
We can now use the length of one side to find the maximum volume of the box. The volume of a box with a square base and no top is equal to the length of one side cubed.
The length of one side is 44, so the maximum volume of the box is :
⇒ 44 × 44 × 44 = 85184.
Therefore, the maximum volume of the box is 85184 cube units.
Learn more about the volume of cuboids here:
brainly.com/question/23118276
#SPJ1
167. for the training adaptation of maximum strength, what is the recommended number of repetitions per set?
Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
To know more about percent,
https://brainly.com/question/16797504
#SPJ4
PLEASE HELP
For each table, determine whether it shows that x and y are proportional.
If x and y are proportional, fill in the blank with a number in simplest form.
1.not proportional
2.proportional:
Step-by-step explanation:
the first one has no constant rate meanwhile the second table goes up 14 for every 10 in y
Complete the equation so that it has the solution c=4
5(2c −
) =2(c+11)
Answer:
Step-by-step explanation:
c=45(2c−)=2(c+11)
We can't solve that type of equation or it may contain an error
is your problem in complete?
U have to estimate!!!!!!!!!! Please help now asap
what is the probability that someone who tests negative does not have the disease? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The probability that someone who tests negative does not have the disease is 0.8451
Given that,
The information shows the outcomes of a test for a specific illness. Assume a member of the group is chosen at random.
From given data table,
N = 144+ 22 + 14+ 120 = 300
n(not disease) = 22 + 120 = 142
n( negative And not disease) = 120
P( Not disease) = 142/300
P( Negative and not disease) = 120/300
Therefore,
P(Negative/ not ..disease) =[tex]\frac{P(Negative and not,.disease)}{P(Not ,.disease)}[/tex]
=[tex]\frac{120/300}{142/300}[/tex]
=[tex]\frac{120}{142}[/tex]
=0.8451
Hence, The probability approximately is 0.8451
Hence, the probability that someone who tests negative does not have the disease is 0.8451
To learn more about probability click here:
brainly.com/question/29538993
#SPJ4
50 POINTS! PLEASE HURRY!
f(x) = x2. What is g(x)?
Answer: g(x) = -x^2 -3
Step-by-step explanation:
We know that the y-intercept is -3, so we can eliminate the first 2 answers. For the last two answers, c is wrong because it is a negative slope and if we square root it, it will become a positive slope our graph slope is not positive, so the answer is d.
Is this how you do it?
A number cube is rolled. What is the probability that a number greater than 4 will be rolled?
Answer:
Below
Step-by-step explanation:
six possible rolls 1 2 3 4 5 6 only two are > 4 ( 5 and 6)
2 out of 6 = 1/3 chance
Answer: A one out of six chance for the number four to be rolled.
Step-by-step explanation:
Factor each polynomial
Answer: x^2 (x+1) (4x-9)
Step-by-step explanation:
We can test the equation above x^2 (x+1) (4x-9) to see if it is true or not by rewriting it
x^2 ( 4x^2 -9x +4x -9)
x^2 (4x^2 - 5x -9)
4x^4 - 5x^3 - 9x^2
So x^2 (x+1) (4x-9) is the correct answer for this equation!
If you can please give me a Brainliest, I only need one more to become an Expert, thank you
what are the major differences between a population that is experiencing logistic growth and one that is experiencing exponential growth?
If resources are unlimited, population will increase exponentially. A logistic growth happens as those resources are less readily available.
Explain the term logistic growth and exponential growth?Exponential Growth:
The term "exponential growth" describes a population's expansion through time at a pace that is directly proportionate to its size. The population's size is influenced by both the birth and death rates. When there are plenty of resources for everyone in the population, exponential expansion happens. When the number of objects is plotted against time, it yields a J-shaped curve.Logistic Growth:
A population growth known as logistic growth is a group of people whose rate of growth reduces as the number of individuals increases and becomes zero whenever the population reaches its maximum.People in the population compete for resources so when food supply and available space are limited.Thus, there are several key distinctions between populations growing logistically and those growing exponentially.
If resources are unlimited, population will increase exponentially. A logistic growth happens as those commodities become less widely available.To know more about the exponential growth, here
https://brainly.com/question/2102628
#SPJ4
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5.0 STAR RATING
Answer:
Step-by-step explanation: 347000 * 6.5% * 20%= 347000*0.065*0.2=4511
Answer is 4511
Answer:
$4,511
the agency makes 6.5% of 347000 which is 22,555 and the agent makes 20 percent of what the agency makes.
so 20% of 22,555 is 4511
△abc is similar to △lmn. also, angle b measures 35° and angle c measures 95°. what is the measure of angle l? enter your answer in the box. the measure of angle l = °
The measure of the angle I= is 50 degree
What is an example of geometry?A triangle has three sides and a total interior angle of 180 degrees. Four-sided shapes like a square, rectangle, or quadrilateral have a total interior angle of 360 degrees. Other polygons have different angles and different numbers of sides, such as the pentagon, hexagon, heptagon, and octagon.
Is geometry easier than algebra?Compared to algebra, geometry requires less math, and the math that is needed is simpler. Geometry, on the other hand, necessitates the memorization of numerous rules and formulas, which for some students can be more challenging than fundamental algebra. Ask your teacher for assistance if you need it in a math class.
The ratio of the respective sides is proportional when two triangles are comparable to one another.
Additionally, the corresponding angles coincide.
Given in this case are B= 35° and C= 95°
the angle sum property now
A + B + C = 180°
A + 35 + 95 = 180
A + 130 = 180
130 is subtracted from both sides, giving us
A = 180 - 130
A = 50°.
Now
ABC and LMN
Consequently, in terms of similarity
A = L
But A = 50°.
Thus, L = 50°.
To know more about geometry click the following link:-
https://brainly.com/question/8277811
#SPJ4
How long will the air in the tank last at this rate
Answer:
60 minutes. (1 hour)
Step-by-step explanation:
An average recreational tank containing 200 bars or 12 L of air should last you for 60 minutes. However, several factors come into play while determining the lifespan of a scuba air cylinder. The amount of air that a diver needs depends on their air consumption rate, which in turn is based on their physical exertion level.
Answer: you have to say at what rate. we cant answer this question. there is part of this question that is missing.
Word problem for 2 divided by 1/4
Answer:
8
Step-by-step explanation:
2 : 1/4
2 x 4/1
2 x 4
8
a grandfather, two fathers and two sons bought passage for a voyage together and everyone paid for one berth each. how many berths did they buy in total?
Grandfather, two fathers and two sons purchased a total of three tickets.
What is a Mathmatical riddle?
Children must convert a few lines from a real-life incident into the appropriate set of mathematical equations in order to solve a math mystery. Mathematical riddles can be cracked by kids utilizing logic, inventive problem-solving, and common sense.
All three tickets:
Grandfather and His Son's Father
Father and his father's son.
Son.
Two fathers and two sons, then.
As a result, a total of 3 tickets were purchased by a grandfather, two fathers and two sons.
Learn more about mathematical riddle here;
https://brainly.com/question/29651890
#SPJ4
In investment of $1800 in the stock market are $278 in two years find the simple interest rate
The interest rate is -42.3%, where the negative sign indicates depreciation.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the investment of $1800 in the stock market is $278 in two years.
Therefore, the amount depreciated is:
278 - 1800
= -1522
Since 1522 is depreciated in 2 years, the amount depreciated in one year is:
1522/2
= 761
The rate at which the amount depreciated is:
(761/1800)×100%
= 42.3%
Hence, the interest rate is -42.3%, where the negative sign indicates depreciation.
Learn more about the interest rates:
https://brainly.com/question/13324776
#SPJ1
Find the volume of a right circular cone that ha a height of 16. 4 in and a bae with a radiu of 20 in
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
an instructor has given a short quiz consisting of two parts. for a randomly selected student, let and . suppose that the joint pmf of and is given in the accompanying table.
Random variable
a. E (X+ Y) = 14.10
E|(X – Y)| = 5.1
b. E[max(X ,Y )] = 9.60
E[min(x, y)] = 4.5
Conversely, once Y=y is observed, we would more likely be interested in the quantity E(X∣Y=y)=ρy which is a scalar.
Maybe this seems like needless complication, but regarding E(X∣Y) as a random variable in its own right is what makes things like the tower-law E(X)=E[E(X∣Y)] make sense - the thing on the inside of the braces is random, so we can ask what its expectation is, whereas there is nothing random about E(X∣Y=y).
a. E (X+ Y)
=∑∑( x +y)p(x ,y)
= (0+0)(0+2) + (0 + 5)(.06) + … + (10 + 15)(.01)
= 14.10
E|(X – Y)| = ∑∑ |x – y| p(x,y)
= |(0-0)|(0.02) + |(0-5)|(0.06) + ……+ |(10-15)|(0.01)
= 5.1
b.
E[max(X ,Y )] = ∑∑max(x+y).p (x ,y)
= (0)(.02) + (5)(.06) +…+(15)(.01)
= 9.60
E[min(x, y)] = ∑∑ min (x,y) p(x,y)
= 0(0.02) + 0(0.06) + ……+ 10(0.14) + 10(0.01)
= 4.5
To learn more about random variable:
https://brainly.com/question/17238189
#SPJ4