The expression [tex]$\frac{3^{\frac{1}{3}}}{3^{\frac{1}{6}}}$[/tex] represents [tex]$\sqrt[6]{3}$[/tex]as rational exponents as a radical expression.
What is an expression?
"An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it."
The given expression is:
[tex]$$\begin{aligned}& \frac{3^{\frac{1}{1}}}{3^{\frac{1}{6}}} \\& =3^{\frac{1}{3}-\frac{1}{6}} \\& =3^{\frac{1}{6}} \\& =\sqrt[6]{3}\end{aligned}$$[/tex]
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A car is traveling at a rate of 48miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in 15 minutes?
Answer:
12 miles in 15 minutes
Step-by-step explanation:
To find the car's rate in miles per minute, we can divide the rate in miles per hour by the number of minutes per hour. There are 60 minutes in an hour, so the car's rate in miles per minute is 48 miles per hour / 60 minutes per hour = 0.8 miles per minute.
To find the number of miles the car will travel in 15 minutes, we can multiply the rate in miles per minute by the number of minutes. The car will travel 0.8 miles per minute * 15 minutes = 12 miles in 15 minutes.
Solve the system below by the method of your choice. Show all work.
−4x+4y=−8
4x−6y=16
Answer:
(- 2, - 4 )
Step-by-step explanation:
- 4x + 4y = - 8 → (1)
4x - 6y = 16 → (2)
adding (1) and (2) term by term will eliminate x
0 - 2y = 8
- 2y = 8 ( divide both sides by - 2 )
y = - 4
substitute y = - 4 into either of the 2 equations and solve for x
substituting into (2)
4x - 6(- 4) = 16
4x + 24 = 16 ( subtract 24 from both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
solution is (- 2, - 4 )
A student has a $50 bill, a $10 bill, a $5 bill, and a $1 bill.
a. If the student must select at least one bill, and the student may select up to all of the bills how many different sub somebody could the student make?
The student can select 1 bill or more than one bill. The student could make 15 different sum of money.
What is permutation?
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Given that a student has a $50 bill, a $10 bill, a $5 bill, and a $1 bill.
He must select at least one bill.
To find the number of ways where the order does not matter is nCr.
The number of bills is 4.
Case 1:
Assume that he select 1 bill.
The number of ways to select one bill is ₄C₁ = 4!/1!(4-1)! = 4
Case 2:
Assume that he select 2 bill.
The number of ways to select two bill is ₄C₂ = 4!/2!(4-2)! =6
Case 3:
Assume that he select 3 bill.
The number of ways to select two bill is ₄C₃ = 4!/3!(4-3)! =4
Case 4:
Assume that he select 4 bill.
The number of ways to select two bill is ₄C₄ = 4!/4!(4-4)! =1
The total number of ways is 4 + 6 + 4 + 1 = 15
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A taxi ride costs $3 plus $2.50 per mile, m. Write and graph an equation that represents the total cost, c, (in dollars) of a taxi ride.
Answer:
$5.50
Step-by-step explanation:
Add 3.00 plus 2.50.Which is 5.50.
An open cylindrical tank of radius14 m and height 3m is made of sheet metal.
(i) How much sheet of metal is required
(ii) How many litres of water can this tank hold?
(iii) What would be the cost of whitewashing this tank at the rate of ₹ 105. 5 per 2?
(i) 263.9 meters sheet of metal is required.
(ii) 1847.25 liters of water can this tank hold.
(iii) Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.
Given that,
A open cylindrical tank of radius 14 meters and height 3 meters is made of sheet metal.
We have to find
(i) The quantity of metal sheet needed.
(ii) How much water this tank is capable of holding.
(iii) How much would it cost to whitewash this tank at a rate of 105.5% per square foot?
We know that,
(i) To find the sheet required of metal is
Curved surface area of cylinder =2πrh
Here,
r is 14 and h is 3
=2π(14)(3)
=84π
=263.9
Therefore, 263.9 meters sheet of metal is required.
(ii)To find how much liters of water can tank hold.
Volume of the cylinder =πr²h
=π(14)²(3)
=588π
=1847.25
Therefore, 1847.25 liters of water can this tank hold.
(iii) To find the cost of whitewashing this tank at the rate of rupees 105.5 per 2.
=263.9×105.5
=27841.45
Therefore, Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.
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When you flip a biaed coin the probability of getting a tail i 0. 52. Find the probability of getting a head
The probability of getting a head given that probability of getting a tail is 0. 52 is 0.48.
Probability of getting at least one head is equal to the probability of all events (100 percent, or 1) less the likelihood of receiving all tails .
Therefore the probability of getting a head is ( 1 - 0.52)
= 0.48
A random event's occurrence is the subject of this area of mathematics. The range of the probability is 0 to 1.
The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Simplify (4 xy) (−2x)
Answer:
-x2 y
Step-by-step explanation:
15. Find the perimeter of the triangle.
2х + 1
3x
X
Answer:
6x + 1
Step-by-step explanation:
When you are finding the perimeter of any shape, you will combine the measurements of each side together. Note any variables when combining. They must have the same amount of the same variables to be combined:
[tex]P = (2x + 1) + (3x) + (x)\\P = (2x + 3x + x) + 1[/tex]
Combine like terms. Add 3x, 2x and x together:
[tex]P = (2x + 3x + x) + 1\\P = (6x) + 1\\[/tex]
The perimeter of the triangle is 6x + 1.
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pls help due now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 9x = 18
Step-by-step explanation:
4x - y + 5x + y = - 3 + 21
9x = 18
x = 2
Does 2x-4=x+1+x have exactly one solution
A triangle has vertices at (1, 4), (7, 4), and (7,-2). Select all the points which will lie on the median through the point (7,4).
All the points that will lie on the median through the point (7,4) are given as follows:
(4,1).(5,2).(2,-1).How to obtain the median of the triangle?The median that passes through the point (7,4) is a linear function that also passes through the midpoint of the vertices (1,4) and (7,-2).
The midpoint of two points is given by the mean of it's coordinates, hence the midpoint of the vertices (1,4) and (7,-2) is calculated as follows:
x = (1 + 7)/2 = 4.y = (4 - 2)/2 = 1.Then the two points on the line are given as follows:
(4,1) and (7,4).
Given two points, the slope is calculated as the division of the change in y by the change in x, hence:
m = (4 - 1)/(7 - 4)
m = 1.
Hence:
y = x + b
When x = 4, y = 1, hence the intercept b is obtained as follows:
1 = 4 + b
b = -3.
Then the function is given as follows:
y = x - 3.
And the points that lie on the median are all the points for which the x-coordinate is 3 less than the y-coordinate.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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A, B and C are Collinear and B lies between A & C. Determine all that are true:
AB=2, AC=2x + 4, and BC = x + 6.
Find x.
OBC=10
AC=12
Segment Addition Postulate
AC-14
x=4
OBC=11
O Angle Addition Postulate
Ox=5
The required statment that is true is AC = 12 and BC = 10. Option A is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A, B and C are Collinear and B lies between A & C.
AC = AB + BC
2x + 4 = 2 + x + 6
2x + 4 = x + 8
x = 4
Now,
AC = 8 + 4 = 12
BC = 4 + 6 = 10
Thus, the required statment that is true is AC = 12 and BC = 10. Option A is correct.
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Explain how a number line is used to determine the sum of -3 + 7
Explanation about number line is discussed below:
What is number line?Number lines are horizontal straight lines used in mathematics when integers are spaced at equal intervals. A number line may be used to visualise all the numbers in a succession. Both endpoints of this line continue forever.
Number lines aid in the development of a mental arithmetic approach for addition and subtraction. Research has proved the significance of number lines in fostering sound mental number sense and arithmetic techniques. No one disputes the significance of number lines.
Firstly, start from -3 on the number line.
Then, since we are adding 7, we would add 7 spaces to the right.
That should lead us to our answer; 4.
Another way is: 7 + (-3) or 7-3.
They all equal 4.
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This weekend, Jerome earned 252.50 in all. What was the dollar amount of the meals that Jerome served?
Jerome served $
worth of meals this weekend.
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
Given: The total amount Jerome earned this weekend is $252.50.
He earned every weekend = $80.
He earned 15% of the cost of meals as tips by serving them.
To find: The cost of meals served by Jerome in this weekend.
The total amount, $252.50, is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.
Let x be the cost of meals that Jerome served this weekend.
The equation for the problem statement becomes
[tex]\$80 + \frac{15}{100} x = \$252.50\\\\[/tex]
Keeping only the x term on the left side of the equation and constant terms on the right side we get
[tex]\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\[/tex]
Multiply both the sides of the equation by 100
[tex]\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250[/tex]
Divide both sides of the equation by 15
[tex]\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150[/tex]
What is algebra?Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.
What is an equation?An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value on either side of the equal sign.
What is an algebraic expression?A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.
Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
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Point K i on line egment \overline{JL}
JL. Given JL=x10,JL=x10, KL=4x,KL=4x, and JK=2x,JK=2x, determine the numerical length of \overline{KL}. KL
If the value of x will be 2. Then the length of KL will be 8 units.
What does cooperation with an example mean?
Being ability to use your body properly while moving around and cooperating with other people or things is the concept of coordination.
A gymnast walking on a tightrope without falling is an illustration of coordination. Working together to arrange or coordinate a party is an example of coordination.
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x.
Then the value of x will be
JL = JK + KL
x + 10 = 2x + 4x
5x = 10
x = 2
Then the length of KL will be
KL = 4x
KL = 4 (2)
KL = 8 units
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The complete question is-
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x,
determine the numerical length of KL.
What is the 3n^2 first 4 terms and the 10th term?
Answer:
a1=3 ;a2=12 ;a3=27 ;a4=48 ;a10=300
Step-by-step explanation:
an=3n^2
a1=3(1)^2
a1=3
a2=3(2)^2
a2=12
a3=3(3)^2
a3=27
a4=3(4)^2
a4=48
a10=3(10)^2
a10=300
You have 10lbs of bananas after peeling the bananas you 3lbs. 6oz. Of banana peels. What is the yield percent
{(-2, 9), (0, -4), (3, 12), (1, 1))
A. Function
B. Not a Function
Answer:
B Not a Function. They are Coordinates
The 7th grade Science classes are raising money for charity. Their goal is $750.00
class has raised 50% of the total needed to meet the goal of $750.00.
class has raised one-third of the amount of their goal of $750.00
.How much more money is needed to reach their goal of $750.00?
round 163 to nearest 10
Answer:
160
Step-by-step explanation:
163
if the number was 5 and over, it'd be 170. But since the number is less than 5, the answer is 160.
A number truncated to 1 d.p. gives 5.3.
If that number originally had 2 decimal places, write down what that
number could have been.
5.??
Hence, the 2 decimal places a possible value of the number is 5.25, 5.26, 5.27, 5.28, 5.29, 5.31, 5.32, 5.33, 5.34
What are upper and lower bounds?
The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits. Error intervals can be utilised to write the upper and lower bounds.
Given, A number truncated to 1 d.p. gives 5.3
And, the number originally had 2 decimal places
Then, the number could have been
5.25, 5.26, 5.27, 5.28, 5.29, 5.31, 5.32, 5.33, 5.34
These are the possible value of the number.
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Simplify: 5m + 3b - 9m - 4w Responses 14m + 7b 14m + 7b 14m + 3b - 4w 14m + 3b - 4w -4m + 3b - 4w -4m + 3b - 4w 21
Answer:
3b-4w-4m
Step-by-step explanation:
3b-4w+5m-9m
3b-4w-4m
Answer:
-4m+3b-4w
Step-by-step explanation:
5m+3b-9m-4w
we combine like terms but in this case only the m are like terms
5m-9m+3b-4w
-4m+3b-4w
i cant really see the options but it looks like it is the second to last or c option
hopes this helps please mark brainliest
If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
Independent-samples t test statistical test is most appropriate for analyzing the results .
What is Independent-samples t test?
To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups.
An example of a parametric test is the Independent Samples t Test. The Independent t Test is another name for this test.
What is the difference between a dependent and independent samples t-test?
If the participants in one sample do not influence the participants in the other, then the two (or more) samples are said to be independent.
Dependent samples are two (or more) samples where the members picked for one sample automatically determine the members chosen for the second sample.
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find the probibility that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating
The probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.
Explain the term binomial probability?A binomial experiment can have two possible outcomes: success or failure, and the term "binomial probability" refers to the likelihood of obtaining precisely x successes upon n repeated but independent trials. The probability of success on a single try is p, and the formula for the binomial probability is as follows:P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣLet X represent a random variable which represents the proportion all school graduates who secure employment in their profession of choice within a year of graduation:
With a binomial distribution,
X has a n = 5 and a p value of 0.57.
n = number of trial.
p = probability of success
x = number of success.
A binomial distribution's probability mass function is provided by:
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The likelihood that at least one gets employment in their field of choice within a year after graduation:
P(X ≥ 1) = 1 - P(X < 1)
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - ⁵C₀ . (0.57)⁰ . (0.43)⁹⁻⁰
P(X ≥ 1) = 1 - 0.603
P(X ≥ 1) = 0.9396
P(X ≥ 1) = 93.96%
Thus, the probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.
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The complete question is-
A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
1. predict whether you think this a fair game or not. explain your response. a. play the game 5 times. b. now do you think the game if fair or not? ju
A game that has an equal probability of winning or losing is said to be fair.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.
A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.
Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.
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IT takes Santa 5 minutes to fly 35 miles with the wind It takes him 7 min to go 35 miles against the wind Determine the speed of Santa 's sleigh in air (X) and the speed of the wind (Y)
Speed of Santa 's sleigh in air (X) is 6 units and the speed of the wind (Y) is 1 unit.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
Let 'y' stand for the speed of the wind and 'x' stand for the speed of Santa. We will use the general equation (distance)=(rate)(time) to write two equations from the given information:
With the wind:
35=(x+y)(5) -------(1)
Against the wind:
35=(x-y)(7) --------(2)
using equation 1 ,we have
x+y = 7
using equation 2 ,we have
x- y = 5
now solving both equations , we get
x = 6 and y = 1
Hence , speed of Santa 's sleigh in air (X) is 6 units and the speed of the wind (Y) is 1 unit.
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Translate the following statement into an algebraic expression:
Use x for your variable.
The sum of the square of a number and fifteen times the number.
Answer:
x^2+15x
Step-by-step explanation:
when doing word problems like these, keywords are "sum" and "square" and "times". They help discern the expression.
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Gavin observed 22 flowers on each block of his neighborhood. Each block has an equal number of flowers. Is this sample of the flowers in the neighborhood likely to be biased?
Yes, this sample of the flowers in the neighborhood is likely to be biased. This is because the number of flowers observed on each block is relatively small and may not be representative of the entire neighborhood.
What is neighborhood?A neighborhood is a local geographic area typically containing a cluster of families and individuals who live nearby and interact with each other. It is usually a residential area, although some neighborhoods may be mixed-use, containing both residential and commercial buildings. Neighborhoods are typically identified by geographical boundaries such as a street, a park, or a body of water. People living in a given neighborhood often share certain characteristics including socio-economic status, culture, ethnicity, and even language. Neighborhoods play an important role in the lives of individuals and families, providing a sense of belonging, safety, and identity.
Additionally, if there is any external factor that influences the number of flowers on certain blocks (such as the amount of sunlight or water) then the sample may be skewed.
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2x - 5y = 23 and -4x + 5y = -11 solve by elimination
Answer: x= -1 y= -5
Step-by-step explanation: Multiply by 2 to eliminate the x
4x - 10y = 46
-4x + 5y = -11
-5y = 35
y= -5
Put -5 back in the equation for the letter y, and you will get x = -1
The sum of two numbers is 45
and their difference is 5.
What are the two numbers?
Larger number
1
Smaller number
Answer: 20 and 25
Step-by-step explanation: we know that there are 2 numbers and the sum is 45. Let's put one number as x. The other number is x+5 because the difference is 5. So our equation is- x+x+5=45. After we solve the equation by subtracting 5 from each side and simplifying x, we get x=20. The other number should be 5 more so the second number is 25. The numbers are 20 and 25. Please rate this answer!