Answers
The simplified form of the expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] after evaluating is equal to [tex]\sqrt[3]{2}[/tex]
What are Powers?
A power is created when a number is multiplied by itself. A power is typically represented by a base number and an exponent. The multiplier is revealed by the base number while the exponents, which are little numbers written above and to the right of base numbers, indicate how many times the base number has been multiplied.If a number is written as 6 to the power of 2, it is represented as, [tex]6^{2}[/tex]. Here, 6 is the base and 2 is the power.Steps to Combine and Simplify Exponents
The three basic rules of exponents used to combine the exponents and simplify the expression are as follows:
[tex]a^{m} \times a^{n} =a^{m+n}[/tex] -----(1)[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex] -----(2)[tex](a^{m})^{n} =a^{m \times n}[/tex] ------(3)Here, we have to simplify and evaluate the given expression using the rules of exponents.
We have the given expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] -------(4)
Using the exponents rules, [tex](a^{m})^{n} =a^{m \times n}[/tex] and [tex](a \times b)^{m}=a^{m} \times b^{m}[/tex] in the above expression, we get
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3} } \times 3^{\frac{2}{3} } \times 2^{3 \times \frac{1}{3} } }{2^{\frac{2}{3} } \times 2^{\frac{2}{3} } \times 3^{\frac{2}{3} }}[/tex]
Simplifying further using (1) and (2), we get (4) as,
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3}}}{2^{\frac{2}{3}+\frac{2}{3} }} \times \frac{3^{\frac{2}{3} } }{3^{\frac{2}{3} }} \times 2^{1} \\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =\frac{2^{\frac{2}{3}}}{2^{\frac{4}{3} }} \times 2^{\frac{2}{3}-\frac{2}{3} } \times 2\\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{\frac{2}{3}-\frac{4}{3} } \times 2^{0} \times 2[/tex]
We know that, [tex]a^{0} =1[/tex]
So, further simplifying we get
[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{-\frac{2}{3} } \times 1 \times 2\\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = 2^{-\frac{2}{3}+1 } \\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=2^{\frac{1}{3}}\\ \imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=\sqrt[3]{2}[/tex]
Therefore, the simplied form of the given expression is [tex]\sqrt[3]{2}[/tex]
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Related Questions
What would $1000 become in a saving account at 3% per year for 3 years when the interest is not compounded (simple interest: p*r*
$1000)?
What would the same amount become after 3 years with the same rate but compounded annually?
S
Do NOT type dollar signs or commas.
Round to the nearest hundredth
Blank 1:
Blank 2
Answers
The required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
Given that,
$1000 become in a saving account at 3% per year for 3 years when the interest is not compounded.
Simple interest is defined as the percentage of earning on the lending for a period of time
Here,
Simple interest earned = P × r × t /100
= 1000 × 3 × 3 /100 = 90
Amount = P + SI = 1000 + 90 = $90
Now, when interest is compounded annually,
Amount = 1000(1.03)³
Amount = $1092.72
Thus, the required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
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f(x) = 3x + 2, what is f(5)
Answers
f(5)=17
Step-by-step explanation:
f(5)=3(5)+3
=15+2=17....
At a local college, 198 of the male students are smokers and 792 are non-smokers. Of the female students, 330 are smokers and 770 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Answers
The probability that both male and female are non-smokers is 0.56.
Given that, at a local college, 198 of the male students are smokers and 792 are non-smokers.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
Number of male smokers=198
Number of male non-smokers=792
Total number of male smokers=198+792
= 990
Number of female smokers=330
Number of female non-smokers=770
Total number of female smokers=330+770
= 1100
Probability that both are non-smokers is given by
P(both are non-smokers ) = P(Male non-smoker) × P(female non-smoker)
= 792/990 × 770/1100
= 0.8 × 0.7
= 0.56
Therefore, the probability that both male and female are non-smokers is 0.56.
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Let A be the set of numbers that are multiples of 3 between 1 and 16 and B be the set of even natural numbers up to and including 20. Find A∪B.
Write your answer in proper set notation.
Make sure each element is only listed once.
Answers
========================================================
Work Shown:
A = set of multiples of 3 between 1 and 16
A = {3, 6, 9, 12, 15}
B = set of even natural numbers up to and including 20
B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {3, 6, 9, 12, 15, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}
---------------
Explanation:
The U stands for "set union". It's where we combine two or more sets together to form a larger set. The duplicates are tossed out. This is what your teacher meant when writing "Make sure each element is only listed once". Writing A u B indicates "the set of values in either set A, set B, or both".
In this case, the duplicates are "6" and "12" since they are found in set A and B simultaneously. They are in the overlapped area of both sets. It might help to draw out a Venn Diagram.
Common convention is to sort the items in the set. Though technically a set like {1,2,3} is the same as {3,1,2}.
Don't forget about the curly braces to indicate to the reader that this is a set of values.
A veterinarian has dog patients numbered 1,2,3,4,5, cat patients numbered 1,2,3,4,5,6, and bird patients numbered 1,2. If a single animal is picked at random, what is the probability that the animal patient is NOT a bird?
Provide the final answer as a simiplified fraction.
Answers
The probability that the animal patient is NOT a bird as a simplified fraction is 11/13.
What is probability?
The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
As given in the question,
Number of dog patients is 5,
Number of cat patients is 6, and
Number of bird patients is 2.
So,
Total number of animal patients = 5 + 6 +2 = 13
Total number of ways of picking 1 animal patient = 13C1 = 13
Number of patients that are NOT birds = 11
So,
probability that the animal patient picked is not a BIRD = 11C1 / 13C1 = 11/13
Therefore, the probability that the animal patient is NOT a bird is 11/13.
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I don’t know the answer
Answers
After 15 years, Zephan will have a balance of $13181.07 in his savings account.
Given,
In the question:
Compound Interest is given by the formula.
A = P(1 + r)^t
Zephan invested $5500 in a savings .
Rate of interest is 6%
Time = 15 years
Now, According to the question:
We know that :
P = 5500
r = 6%
n = 1
t = 15
Compound Interest is given by the formula.
A = P(1 + r)^t
Substitute the values in above formula.
A = 5500. [tex](1+\frac{6}{100}/1 )^1^5[/tex]
Evaluate the equation/expression:
A = 13181.070062
Round 13181.070062 to the required place
= 13181.07
Hence, After 15 years, Zephan will have a balance of $13181.07 in his savings account.
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an arctic explorer reached the north pole and decided to erect the national flag . his eyes was 1.6 m from the ground and the angle of elevation to the top of the 3 m flagpole was 28. how far from the base of the flagpole did he stand?
Answers
The explorer stood 2.63m away from the flag pole.
What is Angle of Elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
If the pole is 3m high, and his eye is 1.6 meters from the ground.
Then distance from the top of the pole and his eyes would be 3 - 1.6 = 1.4m
The angle of elevation between the line of sight and the horizontal = 28°
so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.
Let the distance of the explorer from foot of pole be x,
so that,
tan 28 = 1.4/x
by cross multiplying,
x tan28 = 1.4
x = 1.4/tan28
x = 1.4/0.5317
x = 2.63m
In conclusion, the distance of the explorer to the base of the flagpole is 2.63m
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find the slope (4,2) (2,-1)???
pls helppp
Answers
Answer:
slope is 3/2
Step-by-step explanation:
m = y2 - y1 / x2 - x1
m = -1 - 2 / 2 - 4
m = -3/-2 ( can be simplified )
simplified ver. = 3/2
Answer:
Slope is 3/2
Step-by-step explanation:
To find slope, subtract the y's, put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction.
(4,2) and (2,-1)
Subtract y's:
2 - -1
=3
Put it on top of a fraction:
3/something
Subtract the x's:
4 - 2
= 2, put that on the bottom of the fraction.
3/2
Slope is 3/2.
Name the property used to justify the equation. (-2+5) +-7 = -2 + (5 +-7)
Answers
PLEASE BE FAST I HAVE 5 MIN LEFT!! <3
Answers
Step-by-step explanation:
Original prices of the office equipments
Computer = £650
Calculator = £27.75
Telephone = £69.50
45. The computer has a discount of 15%
[(100 - 15)/100]% × £650
85/100 % × £650
=£552.5
46. The calculator has a discount of 20%
[(100 - 20)/100]% × £27.75
80/100 % × £27.75
=£22.2
47. The telephone has a discount of 10%
[(100 - 10)/100] % × £69.50
90/100 % × £69.50
=£62.55
48. The saving for the computer is
= £(650 - 552.5)
= £97.5
49. The saving for the calculator is
= £(27.75 - 22.2)
= £5.55
50. The saving for the telephone is
= £(69.50 - 62.55)
=£6.95
Now, suppose this lottery expands to include a second number, ranging from 1-59. What would be your
chances of guessing both these numbers correctly? Round your answer to the nearest thousandth of a percent.
Answers
The probability of getting both these numbers correctly is of:
0.028%.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
In this problem, the probabilities are presented as follows:
First trial: one number from a set of 60 numbers.Second trial: one number from a set of 59 numbers, as the first number chosen cannot be chosen again, that is, numbers are not replaced.The probability of getting both these numbers correctly is given by the multiplication of the probabilities of getting the correct number on each trial, hence:
p = 1/60 x 1/59 = 0.00028 = 0.028%.
Missing InformationThe problem states that two numbers are selected from a set of 60, and it asks for the probability that both are guessed correctly.
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Use the graphs off and g to describe the transformation from the graph off to the graph g.
f(x) = -1/2x-5
g(x) = f(x-3)
Answers
The graph of f(x) is transformed 6 units horizontally to get the graph g(x). g(x) is a transformation form of the graph of f(x).
What is the reciprocal function?
The typical instance of reciprocal functions that we might run into is y = a/x, where a is a real number. Accordingly, reciprocal functions are those that have an algebraic expression in the denominator and a constant on the numerator.
Given functions are:
f(x) = -1/(2x-5)
g(x) = f(x-3)
The points on the graph f(x) = -1/(2x-5) are:
When x = 0, f(x) = 1/5
When x = 1, f(x) = 1/3
When x = -1, f(x) = 1/7
The graph of f(x) is added.
Putting x = x-3 in f(x) = -1/(2x-5) to find the function g(x):
g(x) = -1/(2x-6-5)
g(x) = -1/(2x-11)
The points on the graph g(x) = -1/(2x-11) are:
When x = 0, g(x) = 1/11
When x = 1, g(x) = 1/9
When x = -1, g(x) = 1/13
The graph of g(x) is added.
The graph g(x) is translated 6 units horizontally.
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Please help with number 6 and 7
Answers
work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Answers
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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Simplify.
8.4c-4.3c.
Answers
Answer:
4.1c
Step-by-step explanation:
8.4-4.3 is 4.1, and because you can combine like terms its 4.1c.
Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How many leaves did she collect by the end of the week?
Answers
Answer:
49 leaves
Step-by-step explanation:
7 days x 7 leaves per day = 49 leaves in total
What is the ordered pair for Point T?
(1,5)
(0,5)
(5,0)
(5,5)
Answers
Answer:
B
Step-by-step explanation:
point T is on the y-axis with x- coordinate 0 and y- coordinate 5, then
the ordered pair for point T is (0, 5 )
For a given right triangle, if
Sin(3x - 7) = Cos(x + 1)
Find x:
A:24
B:3
C:4
D:46.8
Responses
Answers
-x -x
2x -7 = 1
+7 +7
2x= 8
—. —
2. 2
X= 4
Is C:4
Alvin is 15 years younger than Elga. The sum of their of their ages is 43. What is Elga's age?
Answers
Answer:
Elga is 29Alvin is 14Step-by-step explanation:
You want Elga's age, given that Alvin is 15 years younger and the sum of their ages is 43.
SetupLet e represent Elga's age. Then (e-15) is Alvin's age, and the sum of their ages is ...
e +(e -15) = 43
Solution2e = 58 . . . . . . . add 15
e = 29 . . . . . . . divide by 2
Elga's age is 29.
e -15 = 29 -15 = 14 . . . . Alvin's age
Write the explicit formula for the arithmetic sequence below. 14, 9, 4, -1, ...
Answers
Step-by-step explanation:
To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5
Solve the following word problems. Show your work in the space below.
19. Demetrius bought 6 boxes of colored pencils. There were 15 pencils in each box.
How many colored pencils were there altogether?
Answers
6 Boxes of colored pencils
15 Pencils in each box
Total Number of colored pencils : 15 x 6 = 90 Pencils
x + 20 ≤ -10 please help progress leraning
Answers
The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
It is given that the expression is,
x + 20 ≤ -10
Rearrange the expression as
x≤ -10-20
x≤ -30
Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
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1) Graph the function by plotting the ordered pairs (0, 0) (10, 125) (20, 250) (30, 375) (40, 500) and
drawing a straight line through the points. Label the axes with appropriate
variable
quantities
and units. Label the points with the correct ordered pairs. Include a title for the graph.
Answers
The graph of the given ordered pair is plotted and attached below.
Ordered pair:
Ordered pair refers the composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given,
Here we have the following ordered pair.
(0, 0) (10, 125) (20, 250) (30, 375) (40, 500)
Now, we have to plot the graph for this ordered pair.
In the given question, we have to perform the following steps.
The first process is to label the axis of the graph as x and y .Now, we have to point the given coordinates on the graphConnect the plotted point to make the straight line on itNow, we have to label the plotted pointsFinally, we have to put the title for the graph as function.After all these steps we get the graph like the following.
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(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
Answers
The probability that they two people are chosen and travel by different transport is 47/144
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
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Differentiate the following functions from first principles
(i) Y=10 x^4+3 x+50(4marks)
Answers
The solution of the differentiated equation is dy/dx = 40x³+ 3
How to differentiate the equation?From the question, we have the following equation that can be used in our computation:
Y=10 x^4+3 x+50
Rewrite properly
So, we have
y = 10x⁴ + 3x + 50
The rule of first principle of differentiation is represented as
If y = axⁿ, then dy/dx = naxⁿ⁻¹
Using the above as a guide, we have
dy/dx = 4 * 10x⁴⁻¹ + 1 * 3x¹⁻¹ + 0 * 50
Evaluate
dy/dx = 40x³+ 3
Hence, the equation result is dy/dx = 40x³+ 3
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What is a common denominator for 3/5 and 2/3
Answers
Answer:30
Step-by-step explanation:
Multiplies of 5: 5 10 15 20
Multiplies of 3: 3 6 9 12 15 18
3 x 5 = 15
5 x 3 = 15
Question 17 of 25 The side lengths of a triangle are 5, 12, and 13. Is this a right triangle? A. Yes, because 5² +12²= 13² OB. No, because 5 + 12 * 13. C. No, because 52+12²*13² D. Yes, because 5² + 12²
Answers
Answer:
A
Step-by-step explanation:
Right triangle hypotenuse can be calculated using
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
If a + b = 5 and ab = 6, find the value of a³ + b³
Answers
The value of a³ + b³ is 64.184
Here,
a + b = 5 .........(1)
and ab = 6
a = b/6
Substitute above value of 'a' in equation(1)
b/6 + b = 5
7b/6 = 5
7b = 30
b = 30/7
b = 4.28
So, a = 5 - 4.28
a = 0.72
We know that the formula of a³ + b³
a³ + b³
= (a + b)(a² + b² - ab)
= 5 * (0.72² + 4.28² - 6)
= 5 * 12.8368
= 64.184
Therefore, the value of a³ + b³ is 64.184
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A retail clothing store offers customers an opportunity to open up a credit card during checkout. One location of the retail clothing store states that the number of credit cards, A, that are opened t months since January can be modeled by the function A(t) = 10 + 2t. The number of credit cards opened at another location, B, is defined by the function B(t) = 25 − t. What is an expression that can be used to determine the total amount of credit cards opened at the two locations?
(A + B)(t) = 35 + t
(A + B)(t) = 35 + 3t
(A − B)(t) = −15 + t
(A − B)(t) = −15 + 3t
Answers
The expression that can used to determine the total number of credit cards opened at the two locations can be written as Option A.
( A + B ) ( t ) = 35 + t
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equation of function for number of credit cards at location A at t months is given by A( t ) = 10 + 2t
The equation of function for number of credit cards at location B at t months is given by B( t ) = 25 - t
Now , A function assigns the value of each element of one set to the other specific element of another set.
So ,
The total number of credit cards that are opened at both the location A and B is given by the equation =
Number of credit cards at location A at t months + Number of credit cards at location B at t months
The total number of credit cards that are opened at both the location A and B is given by the equation = A( t ) + B( t )
= ( A + B ) ( t )
= 10 + 2t + 25 - t
= 35 + t
Hence , the equation for the function of total number of credit cards opened at the two locations is given as ( A + B ) ( t ) = 35 + t
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What percent of 23 is 22? round your answer to the nearest percent.
Answers
Answer:
96% rounded to the nearest percent.
Step-by-step explanation:
Divide 100 by 23 which is approximately 4.35
Multiply 4.35 by 22 which is 95.7%.
If you round 95.7 to the nearest percent, it would be 96%.
Answer:
95.6521739%
explanation:
22 is 95.6522% of 23